CFD Calibrated Thermal Network Modelling for Oil-cooled Power Transformers

CFD CALIBRATED THERMAL NETWORK MODELLING

FOR OIL-COOLED POWER TRANSFORMERS

A thesis submitted to The University of Manchester for the degree of

PhD

in the Faculty of Engineering and Physical Sciences

2011

WEI WU

School of Electrical and Electronic Engineering

CFD Calibrated Thermal Network Modelling for Oil-cooled Power Transformers

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Table of Contents

List of Figures .............................................................................................................. 6

List of Tables................................................................................................................ 8

Nomenclature ............................................................................................................... 9

Vocabulary ................................................................................................................. 11

Abstract ...................................................................................................................... 12

Declaration ................................................................................................................. 13

Copyright statement ................................................................................................... 14

Acknowledgements .................................................................................................... 15

Chapter 1 Introduction .......................................................................................... 17

1.1 Background ................................................................................................. 17

1.2 Statement of the problem ............................................................................ 19

1.3 Research objective and scope ...................................................................... 22

1.4 Original contribution and outline of the thesis ............................................ 25

Chapter 2 Literature review .................................................................................. 29

2.1 Transformer end-of-life ............................................................................... 30

2.1.1 Transformer life and transformer ageing ............................................. 30

2.1.2 Cellulose thermal ageing ...................................................................... 34

2.1.3 Thermal ageing mechanisms ................................................................ 36

2.2 Thermal performance .................................................................................. 37


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2.2.1 Transformer losses ............................................................................... 37

2.2.2 Transformer cooling ............................................................................. 42

2.2.3 Thermal diagram .................................................................................. 45

2.2.4 Heat run test .......................................................................................... 50

2.2.5 Direct measurement of the hot-spot temperature ................................. 52

2.2.6 Dynamic loading and overloading ....................................................... 57

2.3 Thermal modelling ....................................................................................... 64

2.3.1 CFD/FEM methods .............................................................................. 66

2.3.2 Experimental validation ....................................................................... 71

2.4 Network modeling ....................................................................................... 73

2.4.1 Introduction .......................................................................................... 73

2.4.2 Equations .............................................................................................. 74

2.4.3 Prediction on oil flow and temperature distributions ........................... 85

2.4.4 Review of the methodology ................................................................. 87

2.5 Summary ...................................................................................................... 88

Chapter 3 Network modelling and assumptions ................................................... 91

3.1 Paper 1 ......................................................................................................... 91

3.2 Paper 2 ......................................................................................................... 93

Chapter 4 CFD calibration for network modelling ............................................... 95

4.1 Paper 3 ......................................................................................................... 95

4.2 Paper 4 ......................................................................................................... 97


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Chapter 5 Comparison between network model and CFD predictions ................ 99

5.1 Paper 5 ......................................................................................................... 99

Chapter 6 Optimisation of transformer thermal design ...................................... 101

6.1 Paper 6 ....................................................................................................... 101

Chapter 7 Conclusions ........................................................................................ 103

References ................................................................................................................ 107

Appendix I Reference [19] .................................................................................... 115

Appendix II Reference [40] .................................................................................. 117

Appendix III List of publications .......................................................................... 119

The final word count, including footnotes and endnotes, is 47,590.


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List of Figures

Figure 1.1 A 410/120 kV, 400 MVA power transformer [5]. ................................... 17

Figure 1.2 Transformer thermal diagram in IEC loading guide [9]. ......................... 20

Figure 1.3 Predicted end-of-life from DP versus IEC thermal model [16]. .............. 21

Figure 1.4 The objectives of thermal network modelling work. ............................... 23

Figure 1.5 Overall research scope related to network modelling. ............................. 23

Figure 1.6 Calibration and application of network modelling. ................................. 24

Figure 2.1 Research theme framework covered by literature review. ....................... 29

Figure 2.2 Representative of paper insulation ageing to transformer ageing. ........... 31

Figure 2.3 Relative transformer insulation life – per unit life [49]. .......................... 33

Figure 2.4 Representation of DP and TS to cellulose chain scissions η for Kraft

paper [8,7]. ................................................................................................................. 35

Figure 2.5 Derivation of DP after a thermal ageing period. ...................................... 36

Figure 2.6 Transformer losses classification [56]. .................................................... 38

Figure 2.7 Three geometry models for winding eddy current loss simulation [57]. . 40

Figure 2.8 Magnetic leakage flux results from three geometry models in Figure 2.7

[56]. ............................................................................................................................ 41

Figure 2.9 Large eddy current loss at winding top and uniform DC loss distribution

[57]. ............................................................................................................................ 42

Figure 2.10 Transformer cooling oil circuit (non-directed mode). ........................... 43

Figure 2.11 Transformer cooling oil circuit (directed mode). ................................... 44


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Figure 2.12 Analytical derivation of hot-spot factor (2.12). ..................................... 48

Figure 2.13 Inverse accumulated distribution of hot-spot factors H [48]. ................ 49

Figure 2.14 Themes relevant to transformer heat run test. ....................................... 51

Figure 2.15 Arrangement of thermal sensors in [70]. ............................................... 55

Figure 2.16 Examples of fixation slots for optic-fibres inside windings [8]. ........... 56

Figure 2.17 Principle sketch of thermal circuit analogy [77].................................... 63

Figure 2.18 General procedure for CFD/FEM simulations. ..................................... 66

Figure 2.19 3D model and mesh for calculating [37]. .............................................. 67

Figure 2.20 Streamline results for the simulation case in [36]. ................................ 70

Figure 2.21 Hierarchy of network modelling equations. .......................................... 75

Figure 2.22 Hydraulic and thermal networks. ........................................................... 78

Figure 2.23 Flow chart for solving network models. ................................................ 82

Figure 2.24 Calculated disc temperatures with directed oil washers [26]. ............... 86

Figure 2.25 Calculated oil velocities of horizontal ducts with directed oil washers

[26]. ............................................................................................................................ 86


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List of Tables

Table 2-1 Normal insulation life of a well-dried, oxygen-free thermally upgraded

insulation system at the reference temperature of 110 oC. ......................................... 32

Table 2-2 Environmental factor and activation energy for oxidation and hydrolysis

of Kraft paper [8]. ....................................................................................................... 37

Table 2-3 Analogy to electric circuit principles [87]. ............................................... 62

Table 2-4 Categorised literatures list. ........................................................................ 65

Table 2-5 Categorised literatures related to CFD/FEM simulations. ........................ 68

Table 2-6 Categorised literatures related to experimental validation. ....................... 71

Table 2-7 Network modelling equations. .................................................................. 76

Table 2-8 Equations for Nusselt number at various conditions [30]. ........................ 83


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Nomenclature

θ Temperature

Θ Temperature in Kelvin (= θ + 273.15)

θh Hot-spot temperature

θa Ambient temperature

Δθhr Hot-spot-to-top-oil temperature rise at rated load

Δθh Hot-spot-to-top-oil temperature rise

Δθor Top-oil temperature rise at rated load

Δθo Top-oil temperature rise

Δθbr Bottom-oil temperature rise at rated load

Δθom,w Average oil temperature at winding

gr Winding-to-oil temperature gradient at rated load

g Winding-to-oil temperature gradient

H Hot-spot factor

K Load factor

R Ratio of load losses at rated load to no-load losses

R Molar gas constant, 8.314 J/(K∙mol)

x Oil exponent

y Winding exponent

k11 Thermal model constant



t Time

τo Oil time constant

τw Winding time constant

η Chain scissions of insulating paper

k Ageing rate of insulation

FAA Relative ageing acceleration rate

A Chemical environment pre-exponent

EA Activation energy

f Friction coefficient at fluid flow ducts

l Length of oil duct

Ac Cross-sectional area of oil duct

D Hydraulic diameter of oil duct (= 4Ac=wetted perimeter)

u Average flow velocity at oil duct

ΔP Pressure drop from upstream to downstream of oil duct


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ρ Density of oil

μ Dynamic viscosity of oil

μc The dynamic viscosity at oil duct centre

μw The dynamic viscosity at oil duct wall

C Specific heat capacity of oil

k Thermal conductivity of oil

Re Reynolds number

Nu Nusselt number

Pr Prandtl number

Gr Grashof number

Ra Raleigh number


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Vocabulary

LV Low voltage

HV High voltage

HSR Hot-spot temperature rise

MWR Mean winding temperature rise

TOR Top oil temperature rise

BOR Bottom oil temperature rise

MOR Mean oil temperature rise

ONAN Oil-Natural-Air-Natural cooling mode

ONAF Oil-Natural-Air-Forced cooling mode

OFAF Oil-Forced-Air-Forced cooling mode

ODAF Oil-Directed-Air-Forced cooling mode

DP Degree of Polymerisation of insulating paper

TS Tensile strength of insulating paper

LTC Load tap changer

1-D One Dimensional

2-D Two Dimensional

3-D Three Dimensional

CFD Computational Fluid Dynamics

N-S Navier-Stokes Equation

FEM Finite Element Method

FVM Finite Volume Method

JPL Junction pressure loss in network models

HWA Hot Wire Anemometry

TNM Thermal Network Modelling

TMDS Transformer Monitoring and Diagnosis System

GUI Graphic User Interface


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Abstract

Power transformers are key components of electric system networks; their

performance inevitably influences the reliability of electricity transmission and

distribution systems. To comprehend the thermal ageing of transformers, hot-spot

prediction becomes of significance. As the current method to estimate the hot-spot

temperature is based on empirical hot-spot factor and is over-simplified, thermal

network modelling has been developed due to its well balance between computation

speed and approximation details. The application of Computational Fluid Dynamics

(CFD) on transformer thermal analysis could investigate detailed and fundamental

phenomena of cooling oil flow, and the principle of this PhD thesis is then to develop

more accurate and reliable network modelling tools by utilising CFD.

In this PhD thesis the empirical equations employed in network model for Nusselt

number (Nu), friction coefficient and junction pressure losses (JPL) are calibrated for

a wide range of winding dimensions used by power transformer designs from 22 kV

to 500 kV, 20 MVA to 500 MVA, by conducting large sets of CFD simulations. The

newly calibrated Nu equation predicts a winding temperature increase as the

consequence of on average 15% lower Nu values along horizontal oil ducts. The new

friction coefficient equation predicts a slightly more uniform oil flow rate

distribution across the ducts, and also calculates a higher pressure drop over the

entire winding. The new constant values for the JPL equations shows much better

match to experimental results than the currently used „off-the-shelf‟ constants and

also reveals that more oil will tend to flow through the upper half of a pass if at a

high inlet oil flow rate.

Based on a test winding model in the laboratory, the CFD calibrated network model‟s

calculation results are compared to both CFD and experimental results. It is

concluded that the deviation between the oil pressure drop over the pass calculated

by the network model and the CFD and the measured values is acceptably low. It

proves that network modelling could deliver quick and reliable calculation results of

the oil pressure drop over windings and thereby assist to choose capable oil pumps at

the thermal design stage. However the flow distribution predicted by network model

deviates from the one by CFD; this is particularly obvious for the cases with high

flow rates probably due to the entry eddy circulation phenomena observed in CFD.

As no experiment validation has been conducted, further investigation is necessary.

The CFD calibrated network model is also applied to conduct a set of sensitivity

studies on various thermal design parameters as well as loads. Because the studies

are on a directed oil cooling winding case, an oil pump model is incorporated. From

the studies recommendations are given for optimising thermal design, e.g. narrowed

horizontal ducts will reduce average winding and hot-spot temperatures, and

narrowed vertical ducts will however increase the temperatures. Doubled oil block

washers are found to be able to significantly reduce the disc temperatures, although

there is a slight reduction of the total oil flow rate, due to the increase of winding

hydraulic impedance. The impact of different loadings, 50%~150% of rated load,

upon the forced oil flow rate is limited, relative change below 5%. The correlations

between the average winding and hot-spot temperatures versus the load factors

follow parabolic trends.


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Declaration

No portion of the work referred to in the thesis has been submitted in support of an

application for another degree or qualification of this or any other university or other

institute of learning.


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Copyright statement

i. The author of this thesis (including any appendices and/or schedules to this thesis)

owns certain copyright or related rights in it (the “Copyright”) and s/he has given

The University of Manchester certain rights to use such Copyright, including for

administrative purposes.

ii. Copies of this thesis, either in full or in extracts and whether in hard or electronic

copy, may be made only in accordance with the Copyright, Designs and Patents Act

1988 (as amended) and regulations issued under it or, where appropriate, in

accordance with licensing agreements which the University has from time to time.

This page must form part of any such copies made.

iii. The ownership of certain Copyright, patents, designs, trade marks and other

intellectual property (the “Intellectual Property”) and any reproductions of copyright

works in the thesis, for example graphs and tables (“Reproductions”), which may be

described in this thesis, may not be owned by the author and may be owned by third

parties. Such Intellectual Property and Reproductions cannot and must not be made

available for use without the prior written permission of the owner(s) of the relevant

Intellectual Property and/or Reproductions.

iv. Further information on the conditions under which disclosure, publication and

commercialisation of this thesis, the Copyright and any Intellectual Property and/or

Reproductions described in it may take place is available in the University IP Policy

(see http://documents.manchester.ac.uk/DocuInfo.aspx?DocID=487), in any relevant

Thesis restriction declarations deposited in the University Library, The University

Library‟s regulations (see http://www.manchester.ac.uk/library/aboutus/regulations)

and in The University‟s policy on Presentation of Theses.


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Acknowledgements

I would like to express my sincere gratitude to my supervisor Professor Zhongdong

Wang for her invaluable guidance and great support throughout the research project.

Her perpetual enthusiasm in research has motivated everyone including me, and

without her knowledgeable supervision and patient assistance, it would be impossible

for this thesis to be prepared.

I would like to thank National Grid and the Engineering and Physical Sciences

Research Council (EPSRC) – Dorothy Hodgkin Postgraduate Award (DHPA) for

providing the PhD scholarship at The University of Manchester. I would like to

express my gratitude to Paul Jarman of National Grid, John Lapworth of Doble

PowerTest, Edward Simonson of Southampton Dielectric Consultants Ltd and Dr

Alistair Revell and Professor Hector Iacovides from School of Mechanical,

Aerospace and Civil Engineering, University of Manchester for their precious

technical advices. Due appreciation should also be given to the colleagues of CIGRE

WG A2.38 for inspiring discussions.

To the colleagues of the Power Systems Research Centre, I would like to extend my

sincere gratitude. I would like to specially thank my colleagues and friends for their

support along the way, which makes my stay here such a tremendous experience.

Last and not least, I would like to thank my family for their support. I would like to

thank my parents for their encouragement and constant blessings. I would like to

thank my wife, Ting Dong, for her deep love and constant support to me and my

work, especially when I was facing difficulties.


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Chapter 1 Introduction

1.1 Background

Power transformers include the transformers connecting generation stations and

distribution networks as well as generator transformers, and their power ratings are

commonly larger than 500 kVA [1,2]. An onsite 400 MVA power transformer is

shown in Figure 1.1. Power transformers are key, and one of the most expensive

components of electric system networks. Their performance and reliability inevitably

influence the reliability of electricity transmission and distribution systems,

especially when a significant fraction of the transformer fleet has been in operation

for more than their designed life, 50 years [3,4]; for instance, in the UK network, by

2010 almost half of the in-service transformer population have approached or

exceeded their designed life.

Figure 1.1 A 410/120 kV, 400 MVA power transformer [5].

Although a transformer failure can originate from different components, such as tap-

changers, windings, bushings and tanks etc, and can be triggered from various events

from the network such as short circuits and lightning, thermal degradation of the

insulating paper is regarded as an important and ultimate factor for the deleterious

changes to the serviceability of transformers. The thermal degradation is a function


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of temperature [6,7,8], and as such the hot-spot temperature θh defined as the highest

temperature of transformer windings [9] becomes significant since the insulation at

the hot-spot will undergo the worst degradation. In consequence, it is of paramount

interest for transformer users, including electricity network operators, to predict and

constrain the magnitude of the hot-spot temperature, in order to limit the insulation

ageing rate and to manage the assets‟ lifetime.

The overall demand for energy in the UK is expected to increase by 1% per annum

over the period from 2007 to 2023 [10]. This increasing demand as well as the

increasing financial constraints placed on electricity utility companies by the Office

of Gas and Electricity Markets (OFGEM) force the companies to be more strategic

with the maintenance and replacement of their transformer assets.

The real load of a transformer varies with time due to the different usage of

electricity at different periods, so daily, weekly and yearly loading may vary with

time (being dynamic) and follow a certain pattern. The thermal overshoot phenomena

caused by dynamic loading may cause severe transformer life depletion. Thermal

overshoot means the hot-spot temperature rise over top-oil temperature Δθh may be

higher at a step increase of load than the fully established steady state value [11,12].

In the period of high electricity usage, the transformer may work with load exceeding

its rated load; in this scenario the transformer is overloaded. The impact of

overloading upon hot-spot and thermal ageing needs to be better understood before

overloading a transformer, especially the aged ones [13,14].

At the same time, manufacturers are also under increasing pressures from their

customers to produce transformers with better thermal performance, namely lower

mean winding temperature rise, hot-spot rise and top oil rise above ambient [8]. In

the factory heat run test, the mean winding and top oil temperature rises can be

measured, but hot-spot cannot be measured directly since its location is unknown.

Prediction of hot-spot location is challenging because the coolant oil distributions

flowing through the array of winding discs are complex and often inhomogeneous.

So far, there have been 3 CIGRE working groups (WG) assembled to carry out

studies which are relevant to transformer thermal performance, WG 12.09 “Thermal

aspects of transformers” in 1986, WG A2.24 “Thermal performance of transformers”


19

in 2003 and WG A2.38 “Transformer thermal modelling” in 2008. Particularly the

initiation of the on-going working group A2.38 emphasized the importance of

numerical thermal modelling tools to predict the hot-spot and to update the

manufacturers‟ thermal design tools.

1.2 Statement of the problem

The present ageing status of the in-service transformers in the electrical power

network prompts the examination of thermal design tools. Consequently the problem

studied in this PhD thesis is related to “how to accurately predict hot-spot

temperature and its location”.

When considering hot-spot [15], firstly manufacturers need to design oil cooling

systems to restrain the hot-spot temperature, including suitable oil driving methods,

i.e. naturally by buoyancy or forced by pumps, as well as sufficient oil duct

dimensions and block washer arrangement if necessary. Secondly winding-to-oil

temperature gradient gr and top-oil temperature rise Δθor of the manufactured

transformer is measured during heat run test and both values can then be used to

roughly estimate the hot-spot temperature with the standard thermal diagram.

The standard thermal diagram, Figure 1.2, in the IEC loading guide [9] is used to

predict the approximate hot-spot temperature. Hot-spot temperature θh is regarded to

be higher than top winding temperature and an empirical „hot-spot factor‟ H is

defined as the ratio of hot-spot-to-top-oil temperature gradient Δθhr to winding-to-oil

temperature gradient gr for estimating hot-spot θh.


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Top of the winding

Bottom of the

winding20 ºC

Ambient θa

Hot spot temperature

Com

ponen

t H

eight

Δθhr = Hgr = 26 K

Temperature

Win

din

g H

eight

6 K

gr = 20 K

TOR Δθor = 52 K

Top Winding Rise = 72 K

Hot spot temperature θhr = 98 ºC

T-B = 14 K

MOR = 45 K

MWR = 65 K

Figure 1.2 Transformer thermal diagram in IEC loading guide [9].

The methods currently used by transformer manufacturers to predict hot-spot

temperature rely on a general empirical hot-spot factor, which in truth, heavily

depends on individual designs and is also affected by the non-uniformity of winding

losses, local heat transfer coefficient over the winding height.

The approximate hot-spot factor values recommended from IEC 70076-7 are 1.1 for

distribution transformers, 1.3 for power transformers; the larger the transformer, the

greater the value should be used [9]. These recommended values may under-estimate

hot-spot temperatures; this impression is based on the mis-match between the

predicted transformer lifetimes from measured Degree of Polymerisation (DP) values

and from the IEC thermal model with the recommended hot-spot factors [16]. DP

values of paper at various locations are available from scrapping transformers, the

lowest DP of paper in a transformer can be used for estimating the worst insulation

ageing rate which can be converted into the transformer‟s lifetime. On the other hand

the worst ageing rate of paper in a transformer can be derived from the hot-spot

temperature, which is calculated with IEC thermal model, heat run test data,


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recommended hot-spot factors, load profile and ambient temperature. Figure 1.3 uses

the hot-spot factor of 1.3 and shows that for the 12 scrapped power transformers, IEC

thermal model predicted lifetimes are much longer than the lowest DP predicted ones

with only one exception. In the IEC thermal model predicted lifetimes, additional

factors such as the switch between natural and forced dual-cooling modes and the

different dominating ageing mechanisms in different applicable temperature ranges,

i.e. oxidation and hydrolysis, are all considered [16]; therefore the lifetime deviation

indicates that the general hot-spot factor 1.3 may be underestimated.

Figure 1.3 Predicted end-of-life from DP versus IEC thermal model [16].

Overall, to obtain the precise hot-spot factor requires accurate understanding of the

temperature distributions along the windings and costly detailed measurement

validations [17]. As a matter of fact, along with the development of computation

technologies, numerical modelling has been applied for predicting the temperature

distributions for over 40 years [18].

Due to the complexity of the transformer thermal phenomena, approximations of

different discretisation levels were made to deliver the calculation targets including

oil flow and temperature distributions and hot-spot temperature. So far the numerical

tools that have gained widespread usage can generally be categorised as either

1

10

100

1000

1 2 3 4 5 6 7 8 9 10 11 12

3788

Th

erm

al

end

-of-

life

(Y

ear)

Scrapped transformer number

Predicted end-of-life from DP vs IEC thermal model

Lowest DP predicted life IEC thermal model predicted life

up to


22

lumped parameter network modelling [19-33] or the methods which incorporate a

degree of Computational Fluid Dynamics (CFD) [13,34-44].

Generally as methods of the highest spatial resolution, CFD simulations can be

expected to provide more detailed results but also with a tremendous increase in the

required computational effort. In comparison to CFD, lumped parameter network

models cannot be expected to exhibit the detailed flow pattern at a junction point or

inside a duct region, but they are regarded as a quick and simple numerical

approximation and are convenient for industry use, as a large range of design

parameters can be trialed for a relatively low computational effort. Network models

are well balanced between its calculation speed and approximation details.

The primary principle of this thesis is therefore on network modeling and the main

objective of this PhD work is to develop more accurate and reliable network

modelling tools for industry. Network models incorporate significant assumptions

about the flow and subsequently empirical equations to describe physical properties

of the fluid, and these approximations and empirical equations are to be calibrated by

using CFD simulations within a well-defined range of transformer design parameters,

such as oil duct dimensions.

1.3 Research objective and scope

The ultimate purposes of the research are to develop accurate and reliable thermal

design tools and to aid transformers lifetime assessment by using these thermal

modelling tools to calculate the hot-spot temperature. This is briefly summarised in

Figure 1.4.

The overall research scope is shown in Figure 1.5. A complete thermal network

model comprises a network model for coping with multi-winding, an external

radiator model and a model for describing oil pumps, which will be present if the

transformer has a forced oil cooling mode. The latter two models can determine the

inlet oil flow rate and the temperature of oil supplied into the winding model. The

three parts are coupled together to model the complete coolant oil circulation from

the windings to the external radiators.


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Thermal network modelling

Thermal design tool

for manufacturers

Transformer end-of-

life assessment

Examine the hot-spot temperature

Figure 1.4 The objectives of thermal network modelling work.

Network modelling scope

Multi-winding network

model

External radiator

modelPump model

CFD calibration

Application on

transformer cases

Experimental

validationParametric studies

Figure 1.5 Overall research scope related to network modelling.

(The dash line parts are future work beyond this thesis scope.)

The winding network model was firstly calibrated by using CFD simulations for a

wide range of winding dimensions used by power transformer designs from 22 kV to

500 kV, 20 MVA to 500 MVA. The fully calibrated network model was then applied

to several winding cases, and parametric studies were also completed on oil duct

dimensions etc for suggesting optimal thermal design practice.

Both the external radiator model and experimental verification belong to the future

work beyond this thesis‟ scope. In particular, the CFD calibration minimized the

calculation error of network models by using CFD results as a baseline; however in


24

order to validate the models, experimental measurements are required. In the work of

[21-23,37,40,45-47] different test and measurement approaches, such as

thermocouples, hot wire anemometry (HWA) and Laser-Doppler velocimetry etc,

were used to valid the numerical model they had developed.

In detail, Figure 1.6 describes the items relevant to calibrating the network model

with CFD simulations. The CFD calibration work was conducted upon the three sets

of empirical equations on Nusselt number, friction coefficient at oil ducts and

junction pressure losses (JPL) respectively. The parametric studies using the

calibrated network model are classified into forced and natural oil cooling modes.

For the force oil cooling mode, the inlet oil flow rate is determined by oil pumps, and

as such the study incorporated pump models. For the natural oil cooling mode, the

inlet oil flow is driven by buoyancy, and a proper external radiator model is required.

Nusselt number

(Nu)

Junction pressure

losses (JPL)

Friction

coefficient

Forced oil cooling mode Natural oil cooling mode

Calibration

Computational Fluid Dynamics (CFD) simulations

Oil pump model External radiator model

Parametric study

Calibrated network modelling

Figure 1.6 Calibration and application of network modelling.

(The dash line parts are future work beyond this thesis scope.)


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1.4 Original contribution and outline of the thesis

In summary, this PhD thesis focuses on network modelling techniques and the

possible improvement when being calibrated by the CFD. This is achieved by

1. An analytical study conducted to prove that 2D channel flow approximation is

sufficient for modelling horizontal oil ducts in disc-type windings.

2. A mathematical model developed to predict the detailed temperature distribution

at a winding disc. The model was then used to verify the assumption in network

models that oil temperature is linearly increasing along disc surfaces and thus the

highest temperature is located at the downstream end of oil duct.

3. Large sets of CFD simulations produced for calibration of the empirical

expressions employed in network modelling, including Nusselt number, friction

coefficient and junction pressure loss (JPL) equations.

4. A network modelling prediction on both oil flow and winding temperature

distributions compared with the corresponding CFD predictions as well as the

available hydraulic-only experimental results.

5. A set of parametric studies, by using the CFD calibrated network model, upon

different design parameters including oil duct dimensions and block washer

arrangement etc. Recommendations on thermal design were concluded from the

study finally.

The remainder of this thesis is organized as follows:

Chapter 2: Literature review

This chapter presents a literature survey on the transformer thermal related issues,

including knowledge of insulation cellulose ageing, thermal end-of-life and

numerical thermal modelling. The latest meaningful work relative to the transformer

thermal modelling and applications are particularly mentioned.

Chapter 3: Network modelling and assumptions

This chapter comprises two papers, “Natural convection cooling ducts in transformer

network modelling”, published in Proceedings of the International Symposium on

High Voltage Engineering (ISH) 2009, and “Heat transfer in transformer winding

conductors and surrounding insulating paper”, published in Proceedings of the


26

International Conference on Electrical Engineering (ICEE) 2009. The first author of

the two papers is this thesis‟ author who did the work, and the other two authors are

this thesis‟ author‟s supervisor and advisor.

Chapter 4: CFD calibration for network modelling

This chapter comprises two papers, “CFD calibration for network modelling of

transformer cooling oil flows – Part I heat transfer in oil ducts”, accepted by IET

Electric Power Applications, and “CFD calibration for network modelling of

transformer cooling flows – Part II pressure loss at junction nodes”, accepted by IET

Electric Power Applications. The first author of the two papers is this thesis‟ author

who did the work. The second and the third authors are this thesis‟ author‟s

supervisor and advisor respectively. The fourth author of the first paper is a professor

in School of Mechanical, Aerospace and Civil Engineering (MACE), University of

Manchester, who contributed through technical discussions. The last author is the

transformer specialist of the sponsoring company, who gave technical advices

through discussions.

Chapter 5: Comparison between network modelling and CFD calculation results

This chapter comprises one paper, “Prediction of the oil flow distribution in oil-

immersed transformer windings by network modelling and CFD”, provisionally

accepted by IET Electric Power Applications. This paper was produced from the

collaboration work with Universität Stuttgart and the second author is this thesis‟

author who did 50% of the work. The first author is a PhD student in Institut für

Energieübertragung und Hochspannungstechnik (IEH), Universität Stuttgart, who did

the other half of the work, and the third author is his supervisor, the professor of IEH,

Universität Stuttgart. The last author is this thesis‟ author‟s supervisor.

Chapter 6: Optimisation of transformer thermal design

This chapter comprises one paper, “Optimisation of transformer directed oil cooling

design using network modelling”, submitted to IET Generation, Transmission &

Distribution. The first author of the paper is this thesis‟ author who did the work. The

second author is this thesis‟ author‟s supervisor and the third author is the

transformer specialist of the sponsoring company, who gave technical advices

through discussions.


27

Chapter 7: Conclusions

This chapter summarises conclusions of the PhD research and recommendations for

further study.

This thesis is structured in an alternative format due to the sufficient number of the

publications produced during the three years‟ PhD research. The publication list is in

Appendix III.


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Chapter 2 Literature review

In this chapter a literature survey is made on the background knowledge of insulation

cellulose ageing, thermal end-of-life and numerical modelling methods. The latest

worldwide worth-noting work relevant to transformer thermal performance, thermal

design optimization and thermal modelling are particularly mentioned.

A framework of the research themes covered by the literature review is shown in

Figure 2.1 to guide the readers.

Figure 2.1 Research theme framework covered by literature review.

Poor thermal performance, i.e. high operational temperatures, is the major underlying

reason for transformer life depletion. Thermal performance is assessed in three ways:

numerically by (1) thermal modelling and experimentally by (2) heat run test or (3)

optic-fibre temperature measurements where hot-spot temperature is always the most

desirable parameter to identify.

Thermal modelling techniques can be split into three major categories, two of which

are lumped parameter models, i.e. the thermo-circuit analogy and network models;

and the third one, CFD, which is based on highly discretised finite volume method

(FVM) or finite element method (FEM) methods. Thermal modelling is particularly

Heat run test Optic-fibre

Network models

CFD

IEC

model

IEEE

model

Other

variations

Life depletion

Insulation ageing

(Arrhenius equation)Lumped

parameter

models

FVM /

FEM

Short-circuit method

Open-circuit method

Measurement devices

Install

recommendations

Fluorescent

optic-fibreSimulation

of total

losses

Thermo-circuit

analogy

Thermal modellingThermal performance


30

useful when prediction of a hot-spot temperature becomes necessary during design

stage or for new operational loading scenarios. Heat run test is based on the principle

of total loss simulation, and according to the simulation approaches, is categorised

into short-circuit (simulated by copper loss, for large transformers) and open-circuit

(simulated by iron loss, for small transformers including distribution transformers)

methods. The shortcoming of heat run test is that it can only be used to assess the

global temperature parameters of a transformer such as top-oil temperature and

average winding temperature rise. This prompts the necessity to install the optic-

fibres for local temperature measurement.

2.1 Transformer end-of-life

2.1.1 Transformer life and transformer ageing

Lifetime evaluation of any equipment is related to its ageing process. Particularly for

transformers, the term „ageing‟ could refer to either the transformer or its insulating

material. The ageing terms can be described as in [48]

Ageing of transformers: irreversible deleterious changes to the serviceability of

the transformers.

Ageing of material: an irreversible negative change in a pertinent property of the

insulation‟s mechanical strength.

The difference between them is that transformers have functions to perform in a

sense that a material does not.

Assuming that the insulation ageing can represent the transformer ageing, the life

duration of transformer can be described almost exclusively by the insulation ageing,

or more specifically, the thermal degradation of the mechanical strength of the paper

insulation between the winding turns.

The ultimate life duration of a transformer is assumed to be the life duration of its

paper insulation, thus one-to-one correspondence exists between the transformer

remaining life and the value of a pertinent property under consideration. The

pertinent property can be either degree of polymerization (DP) or tensile strength

(TS). Then the correlation from transformer life to DP and TS is shown by the

framework in Figure 2.2.


31

Transformer lifetimeTransformer ageing

(functional)

Thermal degradation

of paper insulationPertinent properties

reflect

equivalent

DP TS

Figure 2.2 Representative of paper insulation ageing to transformer ageing.

The irreversible ageing or deterioration of paper insulation strongly depends on

temperature as well as moisture, acidity and oxygen etc. For sealed transformers, the

modern oil preservation systems minimise the moisture and oxygen contributions,

leaving temperature as the governing parameter accounting for the insulation ageing

[49]. For free breathing transformers, the ageing is equally affected by the moisture

and oxygen. The word „life‟ in the loading guides means calculated insulation life

rather than actual transformer life. As addressed in the IEC and IEEE loading guides

[9,49], many factors can influence the ageing process and it is difficult to use only

one straight-forward end-of-life criterion to contain all of these factors.

Arrhenius‟s Law of the thermal degradation at absolute temperature Θ, (2.1), is

commonly applied to express the insulating material ageing process. Due to the

temperature non-uniformity in a transformer winding, the part operating with hot-

spot temperature will undergo the worst degradation, and transformer end-of-life

would be estimated by (2.1) with the substitution of hot-spot temperature into the

temperature variable.

R/AE

eAk (2.1)

k = Ageing rate of insulation

A = Chemical environment pre-exponent

EA = Activation energy

R = Molar gas constant, 8.314 J/(K∙mol)

Θ = Temperature in Kelvin


32

2.1.1.1 IEC loading guide

As IEC loading guide [9] proposed, the ageing rate of non-thermally upgraded paper,

Kraft paper, would be doubled for each temperature increase of 6 oC [50,51], and this

rate suits for the temperature range from 90 oC to 110

oC [15]. A relative ageing rate

V can therefore be represented by (2.2), based on 98 oC reference temperature. For

thermally upgraded paper the ageing rate is relatively lower than that of Kraft paper

and (2.3) was suggested, in which 110 oC reference was used instead. Equation (2.3)

is referred from the “ageing acceleration factor” FAA equation in IEEE loading guide

[49].

6

98

2 98at rate ageing

at rate ageingh

CV

o

h

(2.2)

273

15000

273110

15000exp

110at rate ageing

at rate ageing

h

o

h

CV

(2.3)

For thermally upgraded paper, IEC Loading Guide also suggests four end-of-life

criteria at the reference temperature 110 oC, as in Table 2-1. Depending on the

different criteria, lifetime varies from 65,000 to 180,000 hours. The criterion of 200

retained DP value, equivalent to 20% retained TS, is commonly accepted and DP is

relatively easier to measure than TS in practice. With the reference lifetime and the

relative ageing rate V, lifetime at a given temperature can be estimated.

Table 2-1 Normal insulation life of a well-dried, oxygen-free thermally upgraded insulation

system at the reference temperature of 110 oC.

Basis Normal insulation life

Hours Years

50 % retained tensile strength of insulation 65 000 7,42

25 % retained tensile strength of insulation 135 000 15,41

200 retained degree of polymerization in insulation 150 000 17,12

Interpretation of distribution transformer functional life

test data

180 000 20,55


33

2.1.1.2 IEEE loading guide

IEEE loading guide [49] defines a relative “per unit life” and an “ageing acceleration

factor” FAA which has the same definition with the relative ageing rate V in IEC

loading guide. The per unit life is based on a reference temperature 110 oC and is

defined as

273

000,15exp1080.9lifeunit per 18

h (2.4)

where θh is the hot-spot temperature in oC.

Apparently per unit life is equal to 1 when θh = 110 oC, and it is more than 1 for

temperature θh below 110 oC whereas it is less than 1 for θh above 110

oC. The

correlation of per unit life to hot-spot temperature, in line with (2.4), is shown in

Figure 2.3.

Figure 2.3 Relative transformer insulation life – per unit life [49].

The FAA equation for thermally upgraded paper is the same as (2.3). FAA is more than

1 for hot-spot θh above the reference 110 oC, and otherwise it is less than 1. By

integral of FAA, the equivalent life consumed in a specific time duration can be

estimated.


34

All in all, the relative ageing rate and lifetime equations (2.2) to (2.4) indicate that

the insulation ageing and lifetime are sensitive to temperatures. The hot-spot

temperature θh then corresponds to the transformer‟s lifetime. This is the reason why

the prediction on hot-spot temperature is of primary interests for transformer thermal

design.

When concerning the lifetime management of an entire transformer fleet, statistical

tools such as normal or Weibull distribution models need to be applied using the

individual transformer ageing or lifetime as a sample [52]. Various operation

conditions, including loading profiles, ambient temperatures etc and various thermal

designs, should add variability to the population and therefore ageing and lifetime

prediction is a statistical matter for the entire fleet [53].

2.1.2 Cellulose thermal ageing

As previously discussed, transformer ageing can be reflected by a pertinent property

of the insulating paper. From a chemical viewpoint, the ageing of insulation materials

is a reflection of the molecular cellulose chains breaking, and thus the chain scissions

(η) can be used as an ageing factor. However because of the difficulty in directly

measuring η, equivalent quantities can be considered in practice to be a measurement.

Due to the cellulose chains breaking, the chain length and degree of polymerization

(DP) value of the cellulose reduce at the same time. Therefore DP can be chosen as a

measurable property to describe the chain scissions and for limited ageing, chain

scissions η is proportional with 1/DP [8].

DP of new Kraft paper is in the range of 1000 ~ 1200. After going through the

factory drying process, the paper in transformers will have a DP of ~1000 [7]. Along

with the material ageing the DP value reduces gradually. By experiments, a good

correlation between the reduction of mechanical strength and of DP has been shown

[54]. On the other hand, while DP values are above 200, chain scissions η is

proportional to tensile strength (TS) as well; TS can also be selected to reflect the

chain scissions. The relationships between cellulose chain scissions, DP and TS are

described in Figure 2.4.


35

´ = DP0=DPt ¡ 1

DP TS

Material chain

scissions η

´ = 0:06£ (110¡TS)

Figure 2.4 Representation of DP and TS to cellulose chain scissions η for Kraft paper [8,7].

It is found that 1/DP correlates linearly with thermal ageing time duration, t, i.e. (2.5),

and the thermal ageing rate, k, is also in Arrhenius equation, (2.1). (2.1) and (2.5) can

then be combined to obtain the DP equation in Figure 2.5.

ktt

0

DP

1

DP

1 (2.5)


36

1DPt

¡ 1DP0

= kt

k = A ¢ e¡EA=R£

DP(£; t) =DP0

1 + DP0 ¢At ¢ e¡EA=R£}Arrhenius equation

Linear reduction of DP with time

DP0: Initial value of DP

A: Chemical

environment parameterEA: Activation energy

Θ: Absolute

temperature

t: Time duration

R: Molar gas constant

Life span is the time duration for DP value decreasing from 1000 down to 200.

Figure 2.5 Derivation of DP after a thermal ageing period.

As a matter of fact, with the help of the equation, the DP reduction in a time duration

t, from DP0 to DPt, can be calculated if the hot-spot temperature θh in the duration is

known and substituted into Θ. In practice, θh varies with transformer loading; thereby

the operation time of a transformer can be discretised into a series of consecutive

time steps which are small enough that for each step, θh can be assumed as a constant.

In this way the equation in Figure 2.5 can be utilised to calculate the DP reduction of

each time step, and starting from the initial DP of 1000, the accumulation of all the

time steps for the DP value to continuously reduce to 200 is then the total lifespan of

the transformer insulation.

2.1.3 Thermal ageing mechanisms

Latest studies in [6,7,8] have identified the main ageing mechanisms of insulation

paper in an in-service transformer to be oxidation or hydrolysis. Oxidation dominates

at paper temperature within 60 °C and hydrolysis at higher range up to 150 °C. The

third mechanism, pyrolysis, requires much higher activation energy than oxidation

and hydrolysis and usually governs at temperatures higher than 150 oC, so it is not of

interest in this thesis.

While (2.1) is applied for calculating the insulation ageing rate k, A and EA are so-

called environmental parameter and activation energy respectively. Different ageing

mechanisms have different sets of A and EA values, and the values for Kraft paper are

listed in Table 2-2.


37

Table 2-2 Environmental factor and activation energy for oxidation and hydrolysis of Kraft

paper [8].

Oxidation (dry) Hydrolysis (1.5%

moisture content)

A (hour-1

)

EA (kJ/mol)

4.6×105

89

1.5×1011

128

Besides ageing mechanisms, the activation energy EA also depends on experimental

conditions. For example, in some experiments for oxidation in which copper dusts

were added to facilitate radical formation more easily, i.e. accelerating the ageing

rate [55], lower EA values around 50 kJ/mol was even found [8].

2.2 Thermal performance

Transformer thermal performance is reflected by the temperature rises of windings

and oil; the lower the temperature rises, the better the thermal performance is. The

temperature rises are the results from transformer losses, namely the heat source, and

the oil cooling circulation.

According to IEC standard, the thermal performance is assessed with factory heat run

test, in which the global temperatures such as the top oil and the average winding

temperature rises are measured. However the hot-spot temperature that reflects the

worst insulation ageing and the transformer‟s end-of-life is not directly measured in a

normal heat run test. While the hot-spot temperature estimation with the standard

thermal diagram and the recommended hot-spot factor is recognised to be over-

simplified, the direct temperature measurement on the localised hot-spot using optic-

fibres then becomes a necessity.

2.2.1 Transformer losses

The preparation step prior to performing thermal modelling on a winding comprises

the determination of the amplitude and the distribution profile of electromagnetic

losses. The losses behave as the heat source and they are commonly classified as in

Figure 2.6.


38

Total losses

No-load loss Load loss

DC loss Stray losses

Winding eddy loss Structural parts

Figure 2.6 Transformer losses classification [56].

Total losses comprise load loss and no-load loss. Load loss is measured from short

circuit tests, whereas no-load loss from open circuit tests. Load losses comprise DC

loss and stray losses. In no-load conditions, magnetic leakage flux is very small and

therefore stray losses on winding conductors and structural parts can be neglected

[56].

The DC loss, also called Joule loss or Ohmic loss, is due to the Joule heating of the

current in winding conductors and other current carrying parts. The stray losses, also

called eddy current losses, are induced by stray flux in winding conductors and other

metallic structural parts. The stray losses depend on the distribution of stray flux,

which is affected by the current distribution over all the windings [31].

Load loss determination is necessary for winding thermal modelling. While DC loss

can be calculated by the Joule‟s law and is uniformly distributed in a winding, eddy

current loss in winding conductors is non-uniformly distributed. [57] discovered that

with a uniform loss distribution, network modelling prediction on hot-spot matched

CFD predictions acceptably, but with a non-uniform distribution of loss, deviation

between these two approaches occurred, because in the top pass, where the hot-spot

located, hot streak is strengthened by the intensive eddy current loss at the winding

top and considerably affected the oil flow distribution. The phenomena of hot streaks

can only be captured by CFD; it will be further discussed in Section 2.3.1.


39

For the other metallic structural parts apart from windings, [58] used 3D finite

element method (FEM) simulations to model the eddy current loss at the clamp

plates and the un-shield transformer tank. [59] developed a new way to avoid

expensive electromagnetic computation by performing detailed simulations only on

the localized eddy current domain, such as bushing adapters and the tank part nearby

the bushing adapters. In the two simulation examples in [59], the time and effort for

eddy current calculation was reduced to 11% and 37% respectively.

This section concentrates on the methods to calculate the eddy current loss on copper

conductors.

2.2.1.1 Analytical equation

A winding comprises many conductors. The eddy current loss in one conductor can

be estimated by (2.6) [60], showing that eddy current loss is greater when the

frequency is higher; for high frequency transformers, it is therefore significant to

model eddy current loss accurately when investigating hot-spot [61,62].

(2.6)

= Eddy current loss produced in the conductor by the magnetic leakage

flux, in W

ω = Angular frequency, 2πf, in s-1

Bi = i component of the peak value of the magnetic leakage flux density, i

= x, y, in V∙s∙m-2

hi = The conductor dimension perpendicular to the direction of the leakage

flux density component Bi, in m

ρ = Electrical resistivity of the conductor, in Ω∙m

r = The distance from the conductor centre to the core axial, in m

Ac = The cross-sectional area of the conductor, in m2

2.2.1.2 Finite element simulations

Besides equation (2.6), finite element method (FEM) is commonly applied to

calculate eddy current loss. Due to the axisymmetric geometry of the winding, 2D

c

iic ArhB

P

2

24

2

eddy

cPeddy


40

axisymmetric modelling is often used for simplification. The 2D geometry can be

approximated into different models; for example, the LV winding in [57] could be

approximated into:

(a) 1x1 single section neglecting the structure of discs and conductors, shown in

Figure 2.7 (a).

(b) 78x1 sections to model the 78 individual discs, in Figure 2.7 (b).

(c) 78x18 sections to model all the individual conductors, in Figure 2.7 (c).

(a) 1x1 section for both LV and

HV windings.

(b) 78x1 sections for

LV winding.

(c) 78x18 sections for

LV winding.

Figure 2.7 Three geometry models for winding eddy current loss simulation [57].

Magnetic leakage flux can then be calculated based on the three geometry models by

using FEM simulations; the results are shown in Figure 2.8 respectively.


41

(a) 1x1 section for both

windings.

(b) 78x1 sections for LV

winding.

(c) 78x18 sections for LV

winding.

Figure 2.8 Magnetic leakage flux results from three geometry models in Figure 2.7 [56].

The geometry model (c) has the most detailed winding structure and can be used as a

baseline for evaluating the other two models. By comparing the loss calculation

results from the three models, [56] concluded:

The total DC loss result of the most simplified model (a) is only 0.8% lower

than that of the model (c). It means that the approximation of (a) is sufficient

for DC loss calculation.

The total eddy current loss result of the mode (a) is 6% lower than that of (c),

and (b) is 5% higher than (c). The errors mean that the most detailed (c) is

required to calculate eddy current loss with a good accuracy.

A FEM prediction on the loss distribution of this LV winding is shown in Figure 2.9.

The large increase at the winding top is due to the considerably large contribution of

eddy current loss resulted from the leakage flux radial component at the end of the

winding.


42

Figure 2.9 Large eddy current loss at winding top and uniform DC loss distribution [57].

The highest eddy current loss at the top disc predicted from the most simplified

model, Figure 2.7 (a), is 15% higher than that from the most detailed model (c) [57].

2.2.2 Transformer cooling

The cooling system of a transformer is designed to dissipate the heat generated due to

the losses. The primary purpose is to constrain the hot-spot temperature within a

requested threshold; in IEC loading guide [9] the hot-spot limit for oil-immersed

transformers under overloading conditions is 140 oC.

Based on coolant oil circulation, the oil absorbs heat from winding conductors across

insulating paper, cores and other active heating parts and then transports and

dissipates the heat out to ambient atmosphere by equipped external radiator facilities.

Figure 2.10, referring to [63], illustrates the oil circulation. The oil circuit comprises

the routes inside the transformer, through the tank, the core and the windings, and the

outside paths, including the pipework, pumps and external radiators. Arrows in the

figure show the oil flow directions along the routes and the colour shows oil

temperature; blue is cool and red warm.


43

Figure 2.10 Transformer cooling oil circuit (non-directed mode).

Figure 2.10 shows a typical disc-type winding. In the oil routine the part inside the

winding is the most complex one. In details, there are two vertical oil ducts at the left

and right sides of the winding and they are cross-linked with an array of horizontal

channels. All the ducts compose a network to maximize the oil-to-paper contacting

surface for optimizing heat absorption of the oil flow. In this way while oil flows it

becomes warmer and warmer and will merge at the winding top. Thereby, one might

expect that the maximum temperature is at the winding top but this is generally found

not to be true due to the effect of the non-uniform oil flow distribution across the

horizontal channels [64].

In order to drive the oil into the winding, additional oil pumps can be used, or if no

pump, the oil is driven only by buoyancy, so-called thermal driving force. Additional

cooling fans facilitated for external radiators can improve the radiator cooling

efficiency to enhance the thermal driving force. Pumps and fans are optional and

therefore drawn with dash lines in the figure. If there are oil pumps, the transformer

is in forced oil (OF) cooling mode, otherwise it is in natural oil (ON) mode.

Similarly, if there are cooling fans present, it is forced air (AF) mode, otherwise

natural air (AN) mode.


44

Another worthy point to discuss for the design of Figure 2.10 is that the oil flow is

free to distribute between the different routes inside the transformer, i.e. not directed.

This design is a non-directed cooling mode. Direction facilities such as oil guiding

and restriction washers can be arranged to direct more oil to major heating parts such

as windings and cores, in order to optimise the cooling oil distribution. The design

with direction facilities is then called directed oil (OD) cooling mode. As an example

of OD mode, Figure 2.11 shows the direction facilities. Compared to Figure 2.10, the

facilities have been arranged at the bottom oil inlet to direct more oil into the active

heating windings, and oil washers are also arranged inside the windings to force the

oil flow into horizontal channels.

Figure 2.11 Transformer cooling oil circuit (directed mode).

Overall, different cooling modes are designed for transformers in order to meet the

thermal criteria specified by the customers. The transformer cooling modes can be

summarised into the three categories:


45

1. Natural oil (ON) mode: oil is elevated through the windings due to the thermal

expansion and density reduction of oil. In another word, buoyancy is the only

driving force for oil flow.

2. Non-directed forced oil (OF) mode: pumps are applied to force the oil through

the windings and the radiators. The driving force is from the pumps which also

dominate the oil flow rate. OF mode often has a higher cooling performance than

ON mode but auxiliary power is also consumed by the pumps.

3. Directed forced oil (OD) mode: based on OF mode, additional direction facilities

are then equipped to optimize the oil flow distribution among the active heating

parts such as windings, and it becomes OD mode. In practice, oil block washers

are often used in OD mode to achieve more uniform flow distribution across

horizontal channels, and zig-zag like flow directions are then formed.

2.2.3 Thermal diagram

The standard thermal diagram is shown in Figure 1.2. Windings are heating parts and

the heat dissipation requires a temperature gradient to the surrounding coolant oil.

Therefore in the thermal diagram the winding temperature is higher than the oil

temperature by a winding-to-oil gradient gr; the subscript r indicates rated load.

Besides, the diagram applies the assumptions as follows

The increase of the winding and oil temperatures from the bottom to the top of

the winding is linear;

The winding-to-oil temperature gradient gr remains the same at all height levels

of the winding;

Hot-spot temperature is assumed to be at the winding top but higher than the top

winding temperature. The empirical hot-spot factor H is defined accordingly to

(2.7).

r

hr

gH

(2.7)

With hot-spot factor H, equation (2.8) is used to calculate the hot-spot temperature.

Theoretically the top oil temperature inside the winding should be used for the Δθor

instead of the top oil temperature in the tank [11]; the top oil in the tank is mixed


46

with the oil from all the bottom-to-top channels and its temperature may not be equal

to the top oil temperature inside the winding. Equation (2.9) is then believed to be

more reliable, since it uses the bottom oil temperature Δθbr as the reference

temperature instead of Δθor, and the bottom oil in the tank has the same temperature

with the bottom oil inside the winding [65,66].

rorahr Hg (2.8)

rbrwombrahr Hg )(2 , (2.9)

θhr = Hot-spot temperature at rated load

θa = Ambient temperature

Δθor = Top-oil temperature rise at rated load

Δθbr = Bottom-oil temperature rise at rated load

Δθom,w = Average oil temperature along the winding at rated load

H = Hot-spot factor

gr = Winding-to-oil temperature gradient at rated load

Here lies the necessity to determine the hot-spot factor H. Generally, if the hot-spot

temperature is exactly the top-winding temperature, referring to the thermal diagram

Figure 1.2, hot-spot factor is 1.0, but this value overlooks the intensified eddy current

loss at the winding top and the non-uniformity of oil flow distribution across

horizontal ducts, both of which cause that the temperature increase along the winding

height is not linear. Hot-spot factor represents the non-linearity. 1.0 is the lowest

limit of the hot-spot factor. IEC standard 60076-2 [67] recommended hot-spot factors

greater than 1.1, varying from transformer design to design, in general

H = 1.1 for distribution transformers;

H = 1.3 for medium size power transformers;

Regarding large power transformers, there are considerable variations on H

depending on different designs. The manufacturers should be consulted for a

proper value, unless real measurements are carried out [67].


47

In practice, these recommended H values are however controversial, and transformer

customers should consult the manufacturers for appropriate values of their

transformers [68].

2.2.3.1 Determination of hot-spot factor

A task force was set up in CIGRE working group (WG) 12.09 to attempt to

recommend simple formula for the hot-spot factor H calculation. The WG concluded

that the hot-spot factor ranges from 1.1 to 2.2 and suggested that 1.3 can be used for

power transformers below 100 MVA and that 1.5 for higher ratings.

Analytical determinations

All members of CIGRE WG 12.09 were asked to propose a formula for calculating

the hot-spot factor H, and the collected formulae include [48]

1) (2.10)

h = strand height in axial direction without insulation, in mm

= peak value of radial magnetic flux density, in T

J = rms (root-mean-square) value of current density, in A/mm2

k1 = constant depending on transformer design

k2 = constant depending on cooling mode

In this format no value was suggested for k1 or k2.

2) (2.11)

The variable denotation follows (2.10).

In this format no value was recommended for k1, but k2 = 0.6 was suggested for ON

or OF cooling modes and 1.0 for OD.

3) (2.12)

2

21

ˆ

J

BhkkH

B

22

1ˆ1

k

BhkH

HTFSF

2

.avg

.max1 kk

EL

ELH

k


48

max.EL = maximum per unit eddy current loss at the hot-spot

avg.EL = average per unit eddy current loss, corresponding to average winding

temperature rise

k2 = constant depending on cooling mode. 0.8 for ON and OF; 1.0 for OD

kSF = Surface factor =

2

surface cooling winding-average

spot-hotat suface coolingk

kHTF = Heat transfer factor =

This final equation has the most complex format and all the relative quantities are

explained in an intuitive way as in Figure 2.12. The hot-spot factor is calculated by

synthesizing the effect from the localised loss, the cooling surface area and the heat

transfer efficiency at the hot-spot.

Figure 2.12 Analytical derivation of hot-spot factor (2.12).

Equation (2.12) still relies on other empirical constants. The complexity of the

equation format implies the difficulty to propose a practically usable analytical hot-

spot factor expression. Finally CIGRE WG 12.09 did not recommend any one of the

three formats [48].

2

tcoefficienfer heat trans winding-average

spot-hotat t coefficienfer heat transk

H =³losses at hot-spotaverage losses

£ k0SF £ k0

HTF

´k2

Loss ratio Cooling surface ratio Heat transfer coefficient ratio

Cooling mode factor}0.8 for ON and OF

1.0 for OD


49

Experimental determinations

In order to examine hot-spot factor from experimental tests, CIGRE WG 12.09

collected hot-spot factor measurement samples from 7 countries: Australia, Austria,

Canada, Finland, France, Sweden and the USA, and the samples correspond to 60

different load tests upon 34 transformers [48]. The distribution of the H samples is

shown in Figure 2.13. The H dispersal leads to the recommendation that no

generalized formula or a constant can be used for the hot-spot factor, like what has

been recommended in IEC 354 [69].

Figure 2.13 Inverse accumulated distribution of hot-spot factors H [48].

Basic conclusions from Figure 2.13 are

1. The measure H values range from 0.51 to 2.06 and show no obvious trend toward

a concentration around a specific value. The values below 1.0 are not reliable and

may be caused by measurement at a wrong location other than hot-spot.

2. Statistical analysis of this data set showed that the H value is distributed almost

linearly from 1 to 1.5, with a 65% probability of occurrence and with a mean

probable value of 1.27.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Pro

ba

bil

ity

Hot-spot factor H

Inverse accumulated distribution of hot-spot factor


50

3. The dispersal proves that it is difficult to establish feasible correlations between

the hot-spot factor and the transformer design, size or rating etc.

4. There is no observable effect upon hot-spot factor from the different cooling

modes, ONAN, ON, OF or OD, though IEC 354 suggests 1.1 for ONAN and 1.3

for the others.

In consequence, a utility company that has no overload rules and wants to utilise the

load ability of its new transformers has two choices [48]:

1. Measure the hot-spot directly with sensors and, in the case of several similar

transformer designs, develop a thermal model for the hot-spot;

2. Use the manufacturer‟s calculated value deduced from previous knowledge of his

design.

2.2.4 Heat run test

Heat run test is performed in factory to measure the temperature rises, including

average winding and top and bottom oil temperature rises etc, of transformers under

rated load and overload. A typical heat run test procedure can follow IEC and IEEE

standards [9,69,49,68] and any other special requirements both customers and

manufacturers have agreed.

The purposes of heat run test is to check whether the thermal design meets the

requirement of the guaranteed temperature rise values, including bottom and top oil

temperature rises and mean winding temperature rise.

The principle of heat run test is the simulation of the total losses, i.e. the sum of no-

load and load losses. The loss simulation is achieved by short-circuit or open-circuit

test methods, as in Figure 2.14.


51

Figure 2.14 Themes relevant to transformer heat run test.

The typical sequence of the temperature rise test is

1. Measurement of winding resistance from the cold start condition, i.e. the winding

temperature is equal to ambient temperature;

2. Simulation of the total losses at required loadings by doing short-circuit or open-

circuit tests until the stabilization of the oil temperature rise. The stabilization

state means that the temperature rise does not vary more than 2.5% or 1 K,

whichever is greater, per hour over 3 consecutive hours [68]. In general a

temperature rise test lasts from 6 to 15 hours.

2.2.4.1 Short circuit test

Short-circuit test is often applied for large power transformers.

The principle of short-circuit test is that the total losses are simulated by copper loss.

Copper loss depends on temperature, at the commencement of the test, i.e. the cold

start, the current supply should be [15]

(2.13)

and at the end of the test the current should be

(2.14)

Heat run test

Temperature rises

Hot-spot temperature

Verify design

Principle:

simulation of

total losses.

}Short circuit test

Open circuit test

normal current£

sµiron loss + hot copper loss

cold copper loss

¶

normal current£

sµ

1 +iron loss

hot copper loss

¶


52

2.2.4.2 Open-circuit test

A transformer possessing a ratio of copper loss to iron loss lower than two would not

be suitable for short-circuit test, and open-circuit test will then be used instead.

Open-circuit test is mainly for small transformers, such as distribution transformers.

Assuming that the iron loss varies with the voltage square, the voltage supply

required for an open-circuit test is given by [15]

(2.15)

2.2.5 Direct measurement of the hot-spot temperature

As only global temperatures, such as top oil and average winding temperatures etc,

are measured in the heat run test, detailed temperature distribution along the winding

height cannot be obtained directly. Direct temperature measurement by optic-fibres

has been proposed as a more profound approach for verifying thermal design. Many

attempts have been made to develop reliable measuring devices, e.g. optic-fibres, and

also guidance for how to install the sensors, the sensor number and installation

positions.

In brief, the major incentives which promotes direct hot-spot measurement include

(in the order of importance)

1. To test the overloading capacity of a transformer;

2. To check and optimize the thermal design;

3. To have better load and overload monitoring and control in operational time.

The topics related to optic-fibre measurement are discussed in this section.

2.2.5.1 Measurement devices

The principle of the devices for direct temperature measurement is based on either

the wavelength change of visible or ultraviolet (UV) light in a crystal sensor or the

variation in phosphor fluorescent decay time with temperatures. The light is

transmitted via optical fibres and as such the devices are often called optic-fibres.

Experiences so far indicate no interference with electromagnetic fields for most

popular optic-fibre devices used nowadays.

normal voltage£

sµ

1 +1:2£ cold copper loss

normal iron loss

¶


53

The specification and performance of the optic-fibre devices include [48]

Accuracy: ±1°C is a normal value;

Permissible temperature: 90 oC for continuous measurements for long periods,

typically years, 140 oC for several days and 200

oC for hours. The operation time

can be longer if without mechanical load;

Long-time stability: when oil temperature ranges 95 – 130 oC, the optical

properties of the devices do not have any detectable degradation;

Calibration: calibrated in factory;

Mechanical durability: optical fibres are highly vulnerable to physical damage

and careful installation is required.

2.2.5.2 Sensor number and locations

For a transformer, 2 ~ 8 sensors are adequate for placing in the winding where a

localised high temperature is predicted. For prototype transformers, 20 ~ 30 sensors

should be sufficient [48]. The sensor positions should be very well supported by

sufficient thermal modelling work to guarantee the „real‟ hot-spot at windings is

being monitored [57].

It is recommended to place the sensors on the uppermost disc or turn, between the

conductors or embedded into spacers, also with circumferential position varied. On a

three-phase unit, the highest temperature is likely to occur near the top of the central

coil. In particular, when the transformer is equipped with a load tap changer (LTC), it

is recommended that the sensors are placed to minimize the interference between the

fibers and the LTC leads. It is also recommended the fibres to be located away from

the current transformer leads.

In brief, the two precautions when locating sensors are

1. The sensors should be located in one or more positions that previous experiences

or numerical thermal analysis have indicated to be the hot-spots of the

transformer;

2. Sensors and fibres should be arranged such that they are isolated from any

potential sources of physical damage.


54

A complete example from [70] would be helpful to illustrate on how to arrange

multiple sensors. In this case a 20.5/0.71 kV distribution transformer having

LV winding that consists of 18 Al-foil layers with an axial duct between layer 9

and 10.

HV winding that consists of 15 layers, each layer containing 66 conductors

except one containing only 21. Two axial ducts, one between layer 15 and 16 and

the other 10 and 11.

was facilitated with in total 28 sensors as follows [70]

Nine at the LV winding top, including 2 predicted hot-spot locations, shown in

Figure 2.15 (a). The sensors were inserted into adjacent foils with depth of 5 mm

to measure conductor temperatures.

Six at the HV winding top, including 1 predicted hot-spot location, shown in

Figure 2.15 (a).

Two in oil pockets at each side of the tank, ~30 mm from the tank wall, shown as

T2 in Figure 2.15 (b).

Two on the outside surface of the tank, B2 at the bottom and T3 at the top in

Figure 2.15 (b).

Two under the tank cover by 50 mm, T1 in Figure 2.15 (b).

Two in the mixed bottom oil, located on the center line and between two adjacent

phases, B1 in Figure 2.15 (b).

Four at both the oil duct inlet, B3, and the outlet, T4, of the HV winding and 1 at

the duct outlet, T4, of the LV at different phases, shown in Figure 2.15 (a) and

(b).

The basic conclusion from [70]‟s measurement results is that the top oil temperatures

measured from different locations vary too much. They follow the magnitude order:

T4 at the winding outlet > T1 under tank cover > T3 at tank surface > T2 at oil pocket.

For example, for the rated load, the temperatures at the 4 locations are 84.8 oC > 82.1

oC > 77.1

oC > 72.9

oC respectively. Thermal overshoot of hot-spot-to-top-oil

gradient was observed for the top oil measured under the cover T1, but not found for

the top oil at winding duct outlet T4. From a pure scientific viewpoint, the top oil at

the winding should be selected as the reference oil rather than the top oil at the tank,

but in a regular heat run test the top-oil at winding is not often present due to the

measurement difficulty [11].


55

(a) Position of sensors for phase C; top view.

(b) Position of sensors in tank, cross-sectional view; dimensions are in mm.

Figure 2.15 Arrangement of thermal sensors in [70].


56

The bottom oil temperatures also depend on locations, i.e. the temperature B1 at the

mixed bottom oil is greater than the B2 at tank surface by 25 K.

Another example in [17] is an ONAN transformer of 630 kVA, 10/6 kV, equipped

with 112 sensors (102 placed in the central positioned 10 kV winding). This paper

also noted that the top oil temperature measurement strongly depends on sensor

locations and therefore recommended to use bottom oil temperatures, as no thermal

overshoot was observed for bottom oil.

As more relevant publications, [71] built a 468 kVA, 22 kV transformer in laboratory

which is equipped with 16 optic-fibres for measuring winding temperatures and 24

thermocouples for measuring the temperatures at the core, the tank and the external

radiator. [72] also presented some examples of using optic-fibres to measure hot-spot

temperatures with different cooling designs.

2.2.5.3 Installation

Fibres are often placed in an S-shaped slot inside the spacers and inserted into

windings. The slot must be arranged to position the fibre sensor tip at the

measurement location, allow the spacer to enter the winding radially but should also

protect the fibre from being pulled out. Examples of the slots are in Figure 2.16.

Figure 2.16 Examples of fixation slots for optic-fibres inside windings [8].

As a recommended practice, a spacer which contains an optic-fibre will be installed

by replacing an existing spacer after the coil has been completed.


57

2.2.6 Dynamic loading and overloading

As mentioned in Section 1.1, it is of significance for electricity network operators to

comprehend the temperature responses to dynamic loading and overloading. Thermal

overshoot may be caused by dynamic loading and risks are associated with operating

transformers beyond their nameplate ratings, i.e. overloading transformers. Because

of economic reasons or the responsibility to ensure continuous power supply,

overloading a transformer may be required in practice. In order to reduce the

insulation ageing and to avoid severe damage associated with overloading cycles, it

is necessary to perform temperature rise tests at loads higher than the rated load

[68,73,74].

2.2.6.1 Steady state temperature rises

As for steady state calculations, the temperature rise equations recommended in IEC

standard 70076-7 [9] include

1. Top oil temperature rise

x

oroR

KR

1

1 2

(2.16)

x is oil exponent. When the load factor K > 1, (2.16) is for an overloading condition.

IEEE C57.119 [68] has recommended loads of approximately 70%, 100% and 125%

of the maximum nameplate rating should be used in tests to produce losses

approximately equal to total losses of 50%, 100% and 150% of that at rated load.

Additional values may also be chosen, yet the differences among these 3 losses is

sufficient to determine the oil and winding exponents x and y.

With the 3 measured temperature Δθo, the exponent x can be derived by curve fitting

the 3 data pairs of K and Δθo.

2. Hot-spot-to-top-oil temperature gradient

y

rhKHg (2.17)

y is winding exponent and may be determined from the line that best fits the 3 data

pairs of winding-to-oil gradient gr against K on log-log coordinates [68].


58

In the equations (2.16) and (2.17) the parameter R is the ratio of load loss at rated

load to no-load loss; it can be determined from transformer short-circuit and open-

circuit tests. gr is the winding-to-oil temperature gradient at rated load and can be

obtained from heat run test. H is hot-spot factor recommended in the loading guides.

If the hot-spot temperature has been measured by optic-fibres, H can be calculated by

(2.7) [70].

2.2.6.2 Temperature rises at dynamic loading

Two solutions are proposed in IEC standard 70076-7 [9] to describe the temperature

rises as functions of time, for varying load and overload conditions:

1. Exponential equations, suitable for a load variation according to a step function.

2. Difference equations, suitable for arbitrarily time-varying load factor K and time-

varying ambient temperature θa.

The two solutions are mathematically equivalent and as such this section will only

present the approach with exponential equations.

Exponential equations (2.18) to (2.21) are given to describe the unsteady temperature

responses to a step increase of load to a load factor K, including

1. Top oil temperature rise

)()()(1

tfKtoiooio (2.18)

)]/(exp[1)(111 o

kttf (2.19)

f1(t) describes the relative increase of the top-oil temperature rise according to the

unit of the steady-state value.

2. Hot-spot-to-top-oil temperature gradient

)()()(2

tfKthihhih (2.20)

)]//(exp[1)1()]/(exp[1)(222122212

ktkktktfow

(2.21)

f2(t) describes the relative increase of the hot-spot-to-top-oil gradient according to the

unit of the steady-state value. Thermal overshoot may occur for the hot-spot-to-top-

oil gradient according to the f2(t) [9]; thermal overshoot means that the temperature


59

difference in transient procedures jumps up to a higher value than the stabilised value

at the same load level [17].

Otherwise for a step decrease of load to the factor K:

)()()()(3

tfKKtooioo

(2.22)

)]/(exp[)(113 o

kttf (2.23)

f3(t) describes the relative decrease of the top-oil-to-ambient gradient according to

the unit of the total decrease.

Time constant

The winding and oil time constants of the temperature variations can be calculated by

using the method in IEC 70076-7 Annex A [9]. The winding time constant at the load

considered is

w

mww

P

gCm

60 (2.24)

mw The mass of the winding, in kg

Cm The specific heat of the conductor material, in J/(kg∙K) (390 for Cu and

890 for Al)

g The winding-to-oil gradient at the load considered, in K

Pw The winding loss at the load considered, in W

The oil time constant at the load considered is given by

P

Com

o

60

(2.25)

Δθom The average oil temperature rise above ambient temperature at the load

considered, in K

C The thermal capacity of oil cooling system, in J/K

P The supplied losses at the load considered, in W


60

The thermal capacity of the oil cooling system, C, depends on different cooling mode

and is determined by empirical equations. For example C for ON cooling mode can

be estimated by

OTAmmmC 400.00882.0132.0 (2.26)

mA The mass of core and coil assembly, in kg

mT The mass of tank and fittings (only the portions that are in contact with

heated oil shall be considered), in kg

mO The mass of oil, in kg

On the other hand, the time constants can also be measured during heat run test with

load step changes [68]. The oil time constant is equal to the time required for the oil

temperature to change by 63% of the ultimate temperature change.

The winding time constant may be calculated from the measured data of the average

winding temperature rise over the average oil temperature versus time. The time

constant is equal to the time required for the average winding temperature rise over

average oil temperature to decay to 37% of its initial value [68].

Load cycles

In addition, it is recommended to perform a temperature rise test with a specific

sequence of loads and overloads, so as to demonstrate the potential of the transformer

to be loaded with practical load profiles. Preferably, a typical load profile can be

suggested, with the minimum time interval being one hour, except for high

overloading durations a shorter interval can be used. For the intervals longer than one

hour, the root-mean-square (RMS) load is used for the period. Otherwise for the

intervals of one hour or less, loads can be the arithmetic average over time [68].

2.2.6.3 Model validation

In order to evaluate the thermal models on transformers‟ overloading capability,

Reference [11] compared measurement results with the IEC model calculated

responses, and found that the IEC model yields temperatures which are either

conservative or with a reasonable accuracy at a step increase of load. References [11]

and [65] compared measurement results with the calculation results from the model


61

in IEEE standard C57 [68] Annex G and then concluded that the IEEE model yielded

a good accuracy.

However, Reference [5] noted that the IEC and IEEE models give significantly low

hot-spot temperatures in the case of short-time emergency loadings. Short-time

emergency loading is a unusual heavy loading with less than 30 minutes, due to the

occurrence of one or more system events that severely disturb the normal loading [9].

In Reference [5] a short-time overload of 2.5 per unit load, following a preload of 0.3

per unit, lasted for 20 minutes and the hot-spot temperature reached 156 oC at the end

of the overload period, which is dramatically higher than the values predicted by the

IEC and IEEE models, 83 oC and 95

oC respectively.

Besides, transformers‟ overloading capability is also affected by ambient temperature

variations [75]. The thermal model in ANSI standard C57.92 [76] for overloading is

only valid for ambient temperature > 0 oC, so that Reference [66] presents a study,

which considers the high oil viscosity at temperatures below 0 oC, in order to extend

the thermal model down to ambient temperature of -40 oC. At such low temperatures,

the newly developed model calculated more reliable hot-spot temperatures than the

ANSI standard model. At a normal ambient temperature ranging from 0 oC to 40

oC,

results from both models are equivalent. The model in IEEE standard C57.91 [49]

suits for ambient temperature down to -30 oC.

2.2.6.4 Thermo-circuit analogy

Due to the significance of dynamic loading and overloading, the suitability of the

IEC and IEEE thermal models are increasingly questioned and based on fundamental

heat transfer principles, a new category of thermal models, named “thermal-circuit

analogy”, have been developed for calculating the temperature variation responding

to dynamic loading and overloading [17,70,77-86].

By comparing the governing equations, Fourier theory for heat transfer and Ohm‟s

law for electric circuit, the physical quantities and equations for both fields are

analogous; the quantities are summarized into Table 2-3. Hydraulic quantities are

also listed for analogy but without a storage element.


62

Table 2-3 Analogy to electric circuit principles [87].

Electric Thermal Hydraulic

Through variable Current

I

Amps

Heat transfer rate

q

Watts

Mass flow rate

Q

kg/s

Across variable Voltage

V

Volts

Temperature

θ

Degree C

Pressure

P

Pascal

Dissipation element Electrical resistance

Rel

Ohms

Thermal resistance

Rth

Degree C/Watt

Hydraulic impedance

Rp

Storage element Electrical capacitance

Cel

Farads

Thermal capacitance

Cth

Joules/Degree C

Based on the analogy between thermal and electric theories, Swift and Molinski et al

[77,78] presented the principle to use equivalent thermal circuits, Figure 2.17, to

describe the thermal energy transportation in oil-immersed transformers. The cooling

system is separated into different components: the active heating parts such as cores

and windings, and the coolant media such as oil and ambient air. The heat conduction

and convection are simulated by thermal resistances (Rhs for hot-spot and Roil for oil)

to the heat flows (qfe and qcu) from cores and windings to oil and from oil to ambient

air [80]. The analogy method models the two heat flows to the two circuits in Figure

2.17; Chs and Coil are the thermal capacity for hot-spot and oil respectively and the oil

temperature, θo, is the common quantity coupled between both circuits.

In practice, it is not necessary to be aware of the values of these R and C, because in

the differential equation derivation for θo and θh, R and C will be combined together

to be a time constant, for example, oil time constant τo = Roil∙Coil.


63

Figure 2.17 Principle sketch of thermal circuit analogy [77].

In the thermal circuit, the non-linearity of the convective heat transfer in cooling oil

or air is presented by a general non-linear model, (2.27).

n

th qR (2.27)

The exponent n in (2.27) depends on the cooling mode of the transformer [85]. For

natural cooling mode typically n = 0.8, and for forced cooling n = 1.0, because the

convection efficiency at a high flow speed becomes independent of temperature [77].

Because n is empirical, in order to determine its value [80] utilized a genetic

algorithm (GA) as a search approach to identify the non-linear thermal parameters.

The differential equation to calculate the top oil temperature θo was deduced from the

oil-to-air thermal circuit in Figure 2.17, with oil time constant τo = Roil∙Coil, as [77]

n

aoo

o

n

ordt

d

R

KR /1/12

1

1

(2.28)

In (2.28) the load loss at rated load to no-load loss ratio, R, the top oil temperature

rise at rated load, Δθor, and the oil time constant τo are all from heat run test, and the

top oil temperature θo at the given load factor K and ambient temperature θa can then

be solved. The equation is used to predict the oil temperature variation responding to

the load and ambient temperature conditions which were not included at the factory

heat run test.


64

Same is the derivation for the hot-spot temperature θh in the hot-spot-to-oil thermal

circuit in Figure 2.17. Note that θh is a localised temperature and as such it is actually

not related to the total loss qfe + qcu; however it is still valid to use the total loss in the

circuit by adjusting the Rhs and Chs values to compensate [77]. Unfortunately in [77]

it is not clearly stated how to derive the Rhs and Chs values nor how to adjust.

Because thermal-circuit models are lightweight calculation methods and consume

significantly less computational time than the detailed modelling approaches such as

network modelling and CFD, they are used to calculate the temperature response, as

a function of time, to dynamic conditions. For example, the thermal-circuit proposed

in [88] was applied to predict the real-time temperature response to the variations of

load and weather conditions, including ambient temperature, solar radiation and wind

velocity. It was concluded that the winding and oil temperatures were most affected

by the load, and that the tank temperature was more affected by the thermal radiation

from the sun. The wind velocity, 10 mph (14.7 m/s), could considerably reduce the

temperatures compared to the no wind condition, but the tripled wind velocity, 30

mph, only resulted in a small temperature reduction compared to the condition with

10 mph.

2.3 Thermal modelling

In Section 2.2.3, it was concluded that the standard thermal diagram is over-

simplified and it is difficult or impossible to determine a reasonable and general hot-

spot factor for transformers with different designs.

Since the appearance of computers, numerical analysis becomes possible and the

numerical tools on transformer thermal analysis were initiated at least 40 years ago

[21]. As mentioned in Chapter 1, the existing numerical solutions can be categorized

into two categories, network modelling and CFD/FEM simulations. Table 2-4

follows as a brief summary of the literatures on the three categories as well as their

experimental validations.


65

Table 2-4 Categorised literatures list.

Network modelling Oliver (1980) [19]

Simonson & Lapworth (1995) [20]

Allen & Szpiro et al (1981) [21]

Yamaguchi & Kumasaka et al (1981) [22]

Yamazaki & Takagi et al (1992) [23]

Declercq & Van der Veken (1998) [24]

Declercq & Van der Veken (1999) [25]

Vecchio & Feghali (1999) [26]

Vecchio & Poulin et al (2001) [27]

Zhang & Li (2004) [28,29]

Joshi & Deshmukh (2004) [30]

Buchgraber & Scala et al (2005) [31]

Radakovic & Sorgic (2010) [32]

CIGRE WG A2.38 (2011) [33]

CFD/FEM simulation Mufuta & Van den Bulck (2000) [35]

Shih (2001) [36]

Oh & Song et al (2003) [37]

Takami & Gholnejad et al (2007) [38]

Kranenborg & Olsson et al (2008) [39]

Weinläder & Tenbohlen (2009) [40]

Torriano & Chaaban et al (2010) [41]

Tenbohlen & Weinläder et al (2010) [42]

Lee et al (2010) [43]

CIGRE WG A2.38 (2011) [44]

Experimental validation Allen & Szpiro et al (1981) [21]

Yamaguchi & Kumasaka et al (1981) [22]

Yamazaki & Takagi et al (1992) [23]

Wang & Zhang et al (2000) [45]

Oh & Song et al (2003) [37]

Rahimpour & Barati et al (2007) [46]

Zhang & Li et al (2008) [47]

Weinläder & Tenbohlen (2009) [40]


66

These publications will be reviewed in detail in the following sub-sections, except

that the ones relevant to network modelling will be discussed in Section 2.4 more

profoundly, because the thesis concentrates on network models.

2.3.1 CFD/FEM methods

Generally speaking, a simulation with Computational Fluid Dynamics (CFD) or

Finite Element Method (FEM) comprises several steps, as listed in Figure 2.18.

Defining the geometry

Meshing the geometry

Solving

Post-processing and

visualising the results

Defining material properties

and boundary conditions

Choosing dominating

physical laws and equations

Figure 2.18 General procedure for CFD/FEM simulations.

Although the geometry modelling and meshing for a transformer could ideally be 3D

to model a complete structure, the geometry is often symmetrical and can be reduced

to some extent for saving computational resources. For example, [37] modelled a

single phase 400 kVA natural cooling transformer with layer type windings, and due

to the geometrical symmetry, only a quarter of the transformer was modelled in 3D.

The geometry model and the corresponding mesh are shown in Figure 2.19, and the

number of the mesh elements is around 600,000. A commercial CFD code was then

used to solve the model. In order to validate the CFD results, thermocouples were

installed into the windings, 4 sensors for each oil duct from the bottom to the top.

The calculated temperatures showed a good agreement with the measured values,

which means that the geometry approximation and the mesh elements were sufficient

for calculation accuracy.


67

Figure 2.19 3D model and mesh for calculating [37].

Upon the meshed domain required for solution, material properties such as density,

viscosity (only for fluid), thermal conductivity and specific heat should be defined;

the density and the viscosity of transformer oil are applied as temperature dependent.

On the other hand, boundary conditions such as inlet oil flow rate and temperature

and heat flux at winding disc surfaces etc need be prescribed at the boundaries of the

domain. No-slip boundary conditions are applied at all solid-fluid interfaces. Finally,

physical laws, such as conservation of mass, energy and momentum etc, expressed in

a set of mathematical equations, i.e. Navier-Stokes equations, can be solved with the

mesh.

The Navier-Stokes equations can be presented by using compact vector notation as

0 uDt

D

(2.29)

gpDt

uD

(2.30)

0

kuCDt

CD

(2.31)

In the equations, ρ, C and k are the density, specific heat and thermal conductivity of

the fluid respectively. t is the time, p is the pressure, τ is the viscous shear stress

tensor and g

is the gravity vector. u

and Θ are the fluid velocity and temperature


68

and both are unknown variables to be solved. The equations can be discretised via

finite volume method to produce a set of algebraic equations at each location, which

can subsequently be solved iteratively. From the solution the distributions of oil

velocity and temperature can be obtained. It is worth noting that numerical errors are

associated with the discretisation and in order to restrain the errors to be acceptable,

the control volumes need to be small enough which then means the geometry domain

should be meshed into a sufficiently large number of control volumes.

Various commercial and open-source software can be chosen for the CFD/FEM

modelling. Table 2-5 summarises the simulation software and the model cases from

literatures. For example, Shih used commercial CFD package, STAR-CD, and an

unstructured mesh. STAR-CD is the acronym of Simulation of Turbulent flow in

Arbitrary Regions – Computational Dynamics [36]. Kranenborg and Olsson et al

used Fluent, another commercial CFD code, to investigate the effects of buoyancy

and the phenomena of hot streaks [39]. Other software packages such as ANSYS-

CFX and COMSOL (FEMLAB) etc were used as well in the literatures

[38,40,41,42].

Table 2-5 Categorised literatures related to CFD/FEM simulations.

Software Transformer/model

details

Mufuta & Van den Bulck

(2000) [35]

2D Navier-

Stokes

equations

Shih (2001) [36] STAR-CD

Oh & Song et al (2003)

[37]

A commercial

CFD code

400 kVA

6600/220 V

Grid number: 600,000

Takami & Gholnejad et al

(2007) [38]

FEMLAB 250 MVA

OFAF/ONAN/OFAN

Kranenborg & Olsson et al

(2008) [39]

Fluent OF/ON/OD

No gravity and with

gravity


69

Weinläder & Tenbohlen

(2009) [40]

ANSYS-CFX Axial symmetric model

Torriano & Chaaban et al

(2010) [41]

ANSYS-CFX Axial symmetric model

Tenbohlen & Weinläder et

al (2010) [42]

ANSYS-CFX

UNIFLOW

Axial symmetric model

Lee et al (2010) [43] Fluent

CIGRE WG A2.38 (2011)

[44]

Fluent etc 66 MVA, 26.4/225 kV

ONAF

Shih [36] chose unstructured mesh for simulations, and the geometry model of the

study comprised half a core and two arrays of rectangular heating winding discs that

are separated with three vertical oil ducts, shown in Figure 2.20. From the simulation

results, it was found that there is more turbulence in the top oil domain than in the

bottom; the oil flow in the bottom is almost stagnant. This phenomenon is also

shown in the figure, where Ψ denotes stream function value. The contour of Ψ

presents streamlines, i.e. lines whose tangent is everywhere parallel to the local flow

velocity vector.

Takami and Gholnejad et al [38] considered the transformer winding structure to be

thermally anisotropic and used a 2D laminar flow model; the fluid was assumed to be

incompressible. The density and viscosity of oil were considered to be temperature

dependent and the loss at each conductor was calculated based on the temperature

dependent electric resistivity of copper. Steady state simulations were firstly done

with FEMLAB and MATLAB packages and showed that the maximum temperature

occurred in the neighbourhood of 80~90% of the axial and 50% of the radial

directions of the winding. The steady state model was then developed into an

unsteady one to predict the temperature response to a changing loss with time. With

the unsteady study, winding time constant was found to be around 4.5~5 min.


70

Figure 2.20 Streamline results for the simulation case in [36].

Mufuta and Van den Bulck [35] used finite volume method (FVM) on a geometry

that includes three vertical oil channels enclosing and between two arrays of winding

discs, similar to the structure of Figure 2.20. Assumptions include constant and

homogeneous heat flux at conductor surfaces, and uniform oil velocity at inlet.

Fluctuation of oil flow rate along the central vertical duct was found and the factor

affecting the fluctuation was then identified to be the interaction between inertia and

buoyancy forces. A quantity could be used to express the interaction; Gr is

Grashof number which approximates the ratio of the buoyancy to viscous force

acting on a fluid.

In a recent work, Kranenborg and Olsson et al [39] used 2D CFD model to recognize

the significant effects of buoyancy term and hot oil streak formations, the latter of

which could more or less worsen downstream oil temperatures. A hot oil streak is

formed from a streak of oil that flows along the disc surface, absorbs heat from the

disc, becomes hotter and hotter and can persist its temperature for a long distance,

due to the high Prandtl number of oil (~200), and subsequently rise the oil

Re=Gr12


71

temperature in the downstream. They noted that a very fine discretisation mesh is

required to capture this effect.

Torriano and Chaaban et al [41] presented a detailed CFD study on a single pass of

the 26.4 kV LV winding of a natural oil cooling 66 MVA transformer. It was

concluded that buoyancy is important to include and that the approximation of solid

domain, i.e. the winding discs, as homogenous copper blocks is sufficient for

calculation accuracy.

2.3.2 Experimental validation

The numerical thermal modelling requires experimental tests to validate. Table 2-6

summarises the literatures to classify their measurement parameters and the used

devices. Basically most works measured oil velocities or temperatures or both.

Table 2-6 Categorised literatures related to experimental validation.

Measured

parameters

Measurement method /

facilities

Allen & Szpiro et al

(1981) [21]

Oil velocity Hot wire anemometry

Yamaguchi & Kumasaka

et al (1981) [22]

Oil velocity Laser-Doppler

velocimeter

Wang & Zhang et al

(2000) [45]

Disc

temperature

Copper-constantan

thermocouples

Oh & Song et al (2008)

[37]

Oil

temperature

Small-sized

thermocouples

Rahimpour & Barati et al

(2007) [46]

Local

temperature

on discs

PT100 temperature

sensors

Zhang & Li et al (2008)

[47]

Oil and disc

temperatures

Flow meter, OMEGA

Model No. FL-6102A

Thermocouples with

error ±0.2 oC

Weinläder & Tenbohlen

(2009) [40]

Oil pressure

over winding

Oil pressure sensors


72

Various devices were used to measure oil flow velocity, basically including hot wire

anemometry (HWA) and laser-doppler velocimeter. A laser-doppler velocimeter was

used by Yamaguchi and Kumasaka et al [22] to measure the inlet oil velocity of a

self-cooled (ONAN) winding model. Their network model predictions agreed with

the experimental results within relative error of 15%, and they drew the conclusion

that the oil flow rate increases almost proportionally to the square root of the heat

amount produced in the winding. Doppler equipments are often expensive and

complex to adjust the coordinates of measurement locations. Cheaper devices like

HWA can be used instead.

Besides the cost reason, HWA was considered the best by Allen and Szpiro et al [21]

because they were measuring oil velocity inside windings in their laboratory. In a

metal tank the measuring points inside the windings are not accessible to a laser

beam but the probes of HWA are tiny enough to be inserted into thin oil ducts.

In principle, a HWA uses a fine wire, for which tungsten is popularly chosen, while

the wire is heated up to a temperature. Because the fluid flowing past the wire causes

a cooling effect, and the cooled down wire temperature can be related to its electric

resistivity, a correlation between the wire resistivity and the flow velocity can be

obtained beforehand which can then be utilized for determining flow velocities from

measuring electric resistivity. Therefore another advantage of the HWA is that it can

be used as a resistivity based thermometer at the same time for measuring local oil

temperature.

An alternative way to validate the numerical modelling from a hydraulic viewpoint is

to measure oil pressures instead of oil velocities. With CFD analysis [40] noted that

only the global oil pressure measurement over an entire winding pass is reliable for

modelling validation, and that the pressure measurement at other places rather than at

the oil inlet and outlet will contain unacceptable uncertainties.

With respect to temperature measurement, thermocouples were used in both [45] and

[37]. Electrical insulation should be taken care of when using thermocouples, since

the thermocouples are at earth potential. Thermocouple leads are often molded with

epoxy and then shielded with Kepton film to guarantee a good thermal conductivity

and insulation property at the same time [37].


73

By embedding thermocouples onto a natural oil cooled winding that is equipped with

oil block washers, [45] found that the block washers could considerably reduce the

winding temperature rise and that the reduction is proportional to the number of the

washers. However, the effect on the hot-spot temperature is not so straight-forward

because hot-spot is synthetically affected by a range of factors including the number

of block washers, pass sizes, horizontal duct dimensions and oil flow directions etc.

2.4 Network modeling

2.4.1 Introduction

Network modelling is initiated from the process of reducing the complex pattern of

cooling oil passages in a transformer down to a matrix of hydraulic oil flow duct

approximations, which are interconnected by junction points or „nodes‟. Because of

the axisymmetric winding geometry, 2D axisymmetric models can be used [40,41].

Moreover, since the circumferential width of an oil duct is significantly longer than

the duct‟s radial length, 2D flow duct models between infinite parallel plates can be

applied as a sufficient approximation of the oil ducts [19,28,38].

As one of the pioneering papers, Oliver [19] completely introduced the network

model developed at the Central Electricity Research Board (CEGB) in the 1980s. He

presented a network model which predicts hot-spot temperature and location. A

computer program, named TEFLOW version 1, was also developed to implement

iterative solutions for the equations. By taking a particular LV winding design as an

example, calculation results were presented and showed that the hot-spot occurs on

the middle disc of the topmost pass of the winding. Following from the work of

TEFLOW 1, TEFLOW 2 was developed for incorporating capacity of modelling

varying load cycles [20].

References [19,27] presented complete sets of the mathematical equations for

network modelling, and in the appendix of [19] a detailed solving procedure was

summarised. Both works focused on only single windings, and the empirical

equations employed were from general fluid dynamics and heat transfer handbooks

and had not been fully calibrated for transformer oil and oil ducts.

In order to model an entire transformer, [25,24] proposed a global model for multiple

windings and an internal network model for an individual winding respectively. In


74

the global model, the windings of a transformer are approximated as parallel

connected hydraulic impedances and thus oil flow rate distribution between them can

be calculated based on hydraulic piping principles. On the other hand the internal

model is a traditional network model for an individual winding, in which the inlet oil

flow rate is from the global model prediction. This internal model is to calculate the

oil temperature and velocity distributions inside each winding, and then contributed

to the global model by handing over the winding‟s new hydraulic impedance. In this

way the two models are coupled and with iterations they could achieve convergence

simultaneously. In [25] the algorithm was implemented into a software tool with user

friendly Graphic User Interface (GUI).

In the work of [30] a transformer was also modelled as a whole to develop a more

complete and accurate network model than the conventional single winding model;

even heat radiation of external coolers was included in this complete model.

2.4.2 Equations

The input parameters a single winding network model requires include

1. The structural design of the winding, including the disc number, disc and oil duct

dimensions and oil block washer arrangement.

2. Load current and the mass flow rate and temperature of the oil supplied from the

bottom inlet.

3. Oil and insulating paper properties, i.e. density, viscosity, thermal conductivity

and specific heat.

From these input data, network model employs a set of assumptions and equations to

calculate the oil flow rate and temperature distributions across the winding oil ducts

in order to identify the hot-spot.

The physical assumptions of network modelling are outlined as

1. Oil flow inside ducts is assumed to be entirely laminar due to the low Reynolds

number (Re = 25 ~ 100 [28]).

2. Oil ducts are approximated by a pair of infinite parallel flat plates; i.e. oil flow

inside ducts is approximated by 2D channel flow. As oil is viscous fluid, there is

frictional pressure loss along with the oil flow.


75

3. Oil temperature is assumed to rise linearly as the oil flows along a duct and picks

up heat from adjacent discs, i.e. the heat source. Moreover, because vertical ducts

are much shorter, only the heat flux into horizontal ducts is considered and it is

assumed that the oil temperature along vertical ducts remains constant.

4. Oil flow is completely mixed at nodes in terms of both hydraulic and thermal

aspects; i.e. the flow velocity and temperature profiles become uniform upon

departure from the junctions.

The equations of network modelling can be categorised into two coupled networks:

hydraulic and thermal networks. Both networks are based on a suite of mathematic

equations which are often analogously understood with the help of Kirchhoff‟s law.

The equation hierarchy is illustrated in Figure 2.21 and the equations are then listed

in Table 2-7. The details of these equations‟ application in network modelling will be

introduced in the following paragraphs.

Figure 2.21 Hierarchy of network modelling equations.

Network modelling

Hydraulic network

Mass conservation

Darcy equation (pressure drop

equation)

Thermal network

Thermal energy conservation

Heat transfer equations

Conduction equation

Convection equation


76

Table 2-7 Network modelling equations.

Illustrations Equations

ui¡1;i

ui;i+N+1

ui;i+1

i

Mass conservation X

j

½i;jAi;jui;j =¡ _m

Thermal energy conservation

X

j

·

C½i;jAi;jui;jµi;j +1

2As(i;j) _qi;j

¸

= ¡C _mµi

µ1; P1

µ2; P2

ul

D; A

_q As

Darcy-Weisbach equation (pressure drop

equation)

¢P =4fL

D

1

2½u2

Temperature increase equation

As _q =C½uA¢µ

2

m

1

(a) A combining junction.

1

m

2

(b) A dividing junction.

Junction pressure loss (JPL) equations for

combining and dividing junctions

2

22

2

i

imim

i

mimi

uKP

uKP

in which i = 1,2, K is JPL coefficient,

2

2

1

2

11

1

2

2

1

2

11

1

Re

276

Re

1000735.2337.3079.1

Re

72

Re

1000419.1729.1580.0

m

mm

m

m

mm

m

K

u

u

u

uK

K

u

u

u

uK

Convective heat transfer equation

_q =Nu ¢ k

D(µw ¡ µb)

Conductive heat transfer equation

_q =¡krµ


77

A small size network model example which only includes 3 winding discs is used to

illustrate how to apply the equations, as shown in Figure 2.22. In the example there

are 10 oil ducts and 8 duct junction nodes; the nodes are numbered in the figure and

the ducts are then denoted by a pair of numbers which are their start and end nodes.

The oil flow rates and oil temperatures of the 10 ducts are unknowns and they will be

solved from the hydraulic and thermal network respectively.

In the hydraulic network, as marked in Figure 2.22 (a), mass conservation is applied

at the 7 redly circled nodes to obtain 7 node equations and along the 3 closed loops,

indicated by the 3 blue arrows, the pressure drop summation is zero and thus 3 loop

equations can be written. In this way 10 independent equations in total can be given

for solving the 10 unknown duct flow rates.

In a generalised scenario, for N discs there are 2N + 2 nodes and 3N + 1 ducts. Node

equation, (2.32), can be applied at all the 2N + 2 nodes, i.e. i = 0,…,2N + 1, but only

2N + 1 of them are independent.

2N+1X

j=0

®i;j½i;jAi;jui;j = ¡ _m (2.32)

in which αi,j is the connection factor (αi,j = 1 if nodes i and j are connected by a duct

and i > j, αi,j = -1 if nodes i and j are connected and i < j and αi,j = 0 otherwise), ρ is

the fluid density, Ai,j is the cross-sectional area of duct (i, j), ui,j is the flow velocity

from node i to j. On the right hand side, _m is the imposed mass flow insertion at

node i; _m = Q, i.e. the total oil mass flow rate, if i = 0, (node i is the inlet), _m = -Q if

node i is the outlet and _m = 0 otherwise.


78

2

0

1

0

7

6

5

4

3

2

1

2,3

1,2

0,1

6,7

5,6

4,5

2,6

1,5

0,4

3,7

(a) Nodes and loops in hydraulic network.

2

0

1

0

7

6

5

4

3

2

1

2,3

1,2

0,1

6,7

5,6

4,5

2,6

1,5

0,4

3,7

(b) Nodes and temperature development paths in thermal network.

Figure 2.22 Hydraulic and thermal networks.

In the loop equations, Darcy-Weisbach equation, (2.33), is employed to describe the

frictional pressure losses along the oil ducts which compose the closed loops. Darcy-

Weisbach equation describes the correlation between the pressure drop, ΔP, and the

flow velocity, u, at a viscous channel flow.


79

2

2

14u

D

lfP

(2.33)

ΔP = Pressure drop from the upstream to the downstream of oil duct, in Pa

f = Friction coefficient at oil duct, dimensionless

l = Length of oil duct, in m

D = Hydraulic diameter of oil duct, in m

ρ = Density of oil, in kg/m3

u = Average flow velocity at oil duct, in m/s

Oil ducts can be sufficiently approximated by 2D channel flow between infinite

parallel plates. For 2D channel flow, friction coefficient f = 24/Re; Re is

dimensionless Reynolds number. In [26] friction coefficient f correlation from Olson

[89], (2.34), is used. The equation is however for ducts with rectangular cross-section

and with two sides and .

(2.34)

As shown in Figure 2.22 (a), the closed loops are composed, in general, by 4 ducts (i,

i + 1), (i + 1, i + N + 2), (i + N + 2, i + N + 1) and (i + N + 1, i), i = 0,…,N - 1. Denote

the set of these 4 ducts‟ subscripts as Ω, and the general format of a loop equation is

then

02

142,11,

),(

2

,,,

,

,,

vNiNiii

ji

jijiji

ji

jijilguK

D

lf (2.35)

The first term of (2.35) includes both the frictional and junction pressure losses; Ki,j

is the junction pressure loss (JPL) coefficient applied at duct (i, j) and its format is

listed in Table 2-7, depending on whether duct (i, j) bears the straight-through or the

branch direction of a combining or dividing junction. The second term considers the

gravity effect; lv is the length of the vertical ducts. The equation, (2.35), is nonlinear,

so when solving it iteratively, it needs to be linearised by the factorisation ui,j2 = |ui,j| ∙

a b (a < b)

f =K(a=b)

ReD

µ

ReD =½uD

¹

¶

K(a=b) = 56:91 + 40:31¡e¡3:5a=b ¡ 0:0302

¢


80

ui,j; in the first iterative step ui,j is the initialised value and in the following steps ui,j is

the result of the previous step.

All in all, in the hydraulic network, with the 2N + 1 node equations, (2.32), and the N

loop equations, (2.35), the 3N + 1 duct flow velocities can be solved.

On the other hand, in the thermal network, as marked in Figure 2.22 (b), thermal

energy conservation is applied at the 7 nodes for 7 independent node equations. In

addition, temperature development equations along the blue paths due to the heat

flux from the discs are then used. For example, ducts (0, 1) and (0, 4) both originates

from the same node 0 and their temperatures can be correlated; in particular, while

neglecting the heat flux into the vertical duct (0, 1), the temperature increase from

duct (0, 1) to (0, 4) is due to the heat flux into the horizontal duct (0, 4). Finally 10

equations in total can be given for solving the oil temperatures at the 10 ducts.

For the node 0 to 2N, the general format of the node equations in the thermal network

is

2N+1X

j=0

·

®i;jC½i;jAi;jui;jµi;j +1

2As(i;j) _qi;j

¸

= ¡C _mµi (2.36)

C is the fluid specific heat, θi,j is the average oil temperature at duct (i, j) and As(i,j) is

the total wall area of duct (i, j). θi is the temperature of the imposed flow insertion at

node i; θi is the bottom oil temperature if i = 0, (node i is the inlet), θi is the top oil

temperature if node i is the outlet and θi = 0 otherwise. _qi;j is the heat flux into duct

(i, j) and depends on the power loss at winding discs. In practice the power loss at a

disc comprises both DC and eddy current losses, as discussed in Section 2.2.1. Here

as a simplified case, the constant heat flux _qi;j boundary condition is prescribed at the

disc surfaces.

As shown in Figure 2.22 (b), the temperature increase along the ducts (i, i + N + 1), i

= 0,…,N - 1, is

µi;i+1 ¡ µi;i+N+1 +12As;(i;j) _qi;i+N+1

C½i;jAi;jui;i+N+1

= 0 (2.37)


81

Thus in the thermal network, with the 2N + 1 node equations, (2.36), and the N

temperature development equations, (2.37), the 3N + 1 duct oil temperatures, i.e. oil

bulk temperatures, can be solved.

After the oil bulk temperatures are obtained, not only the temperature dependent oil

properties such as oil density and viscosity can be updated for the next iterative step,

but also the oil temperature at duct surfaces, namely wall temperatures θw(i,j), can be

derived with (2.38). As the heat transfer in the ducts is convective, Nusselt number is

employed to correlate the heat flux _qi;j to the temperature drop from the duct wall to

the bulk. Secondly, the heat conduction from the copper conductors to the duct walls

is described by Fourier‟s law, and the temperature of the conductor adjacent to duct

(i, j) θc(i,j) is then calculated with (2.39).

µw(i;j) = µi;j +_qi;j ¢Di;j

Nu ¢ k (2.38)

in which Di,j is the equivalent hydraulic diameter of duct (i, j).

µc(i;j) = µw(i;j) +_qi;j ¢ dp

12As(i;j) ¢ k

(2.39)

in which dp is the thickness of insulating paper.

The complete set of network model equations can also be found in [19] and Chapter

5. The equations require iterative approaches to solve, because both of the hydraulic

and thermal networks are coupled via the temperature dependent oil properties such

as viscosity and density. The solving procedure of network modelling is summarised

in Figure 2.23. Starting with the initialisation of oil velocities and temperatures, the

algorithm updates the oil properties and calculates the new oil velocities with the

hydraulic network. Based on the newly obtained oil velocities, the oil temperatures at

ducts are calculated with the thermal network. The new temperatures together with

the new velocities are used to update the oil properties anew for the next iteration

step. Until the relative changes on oil velocities and temperatures between two

consecutive iteration steps fall in a tolerance range, the convergence is regarded to be

reached. Finally the wall temperatures and winding disc temperatures can be derived

according to the oil bulk temperatures and the heat transfer equations.


82

Initialise oil velocities and bulk

temperatures at ducts

Calculate oil velocities at ducts

Calculate disc temperatures

Calculate bulk temperatures at ducts

Calculate wall temperatures

at ducts

error < toleranceerror < toleranceChecking step errors on oil

velocities and bulk temperatures

Update temperatures dependent oil

properties at ducts

error >= toleranceerror >= tolerance

Quit

Hydraulic networkHydraulic network

Thermal networkThermal network

Figure 2.23 Flow chart for solving network models.

With respect to the fluid properties, transformer oil viscosity is measured to be highly

temperature dependent and, for example, the expression format (2.40) can be used

for an estimation, in which B and C are constants that are different for different types

of fluid [90]; [12] used B = 1.3573 × 10-6

, C = 2797.3 respectively. Otherwise [26]

borrowed the equation (2.41) for oil viscosity from Kreith and Black (1980) [91].

)273/( TCeB (2.40)

3)50(

6900

T (2.41)

Oil density also depends on temperature, although the variation with temperature is

slight, i.e. the thermal expansion coefficient is 6.5×10-4

K-1

. Thermal conductivity

and specific heat can be constant values 0.13 W/m/K and 2060.0 J/kg/K respectively

[19].


83

The empirical equations for Nusselt number and junction pressure losses (JPL) will

be discussed in detail in Chapter 4.

2.4.2.1 Equation calibrations

Empirical expressions are also applied in network models and they are

Convective heat transfer related expressions for Nusselt number and the

temperature correction of friction coefficient at oil ducts.

Junction pressure loss (JPL) related expressions used to estimate pressure

losses due to oil flow mixing at duct junctions.

In [14,19,27,30,92-94] different formats and parameters for Nusselt number, friction

coefficient and JPL expressions have been proposed from general fluid dynamics and

heat transfer handbooks but, to the author‟s best knowledge, their suitability for

transformer oil and oil duct dimensions has never been fully explored. It is then

necessary to evaluate them in order to improve the accuracy of network modelling.

Chapter 4 will show the principle work of this PhD thesis on empirical equation

evaluation, and this section briefly reviews the equations.

Nusselt number

Joshi and Deshmukh [30] borrowed five equations, (2.42) to (2.46), from [95] to

calculate the Nusselt number for various conditions, listed in Table 2-8.

Table 2-8 Equations for Nusselt number at various conditions [30].

Equation Applicable condition

(2.42) For heat transfer at vertical isothermal surfaces,

e.g. tank walls and radiator fin surfaces. (2.43)

(2.44) For heat transfer at colder fluid over horizontal plate or hotter

fluid below horizontal plate. (2.44) was used for the top cooling

surface of winding discs.

(2.45) For heat transfer at colder fluid below horizontal plate or hotter

fluid over horizontal plate. (2.45) was used for the bottom

cooling surface of winding discs.

(2.46) If there is a fan and the air flow over radiator fins is laminar flow

at the beginning but followed by turbulence, for

the rest of the entire fin, (2.46) can be applied.

Ra < 109

Ra > 109

(Re < 5£ 105)


84

(2.42)

(2.43)

(2.44)

(2.45)

(2.46)

Besides, [94] proposed Nusselt number expressions (2.47) to (2.49) for the heat

transfer at horizontal oil duct bottom and top surfaces and vertical ducts respectively.

3

1

4

34.2

165.0

5 Pr012.0PrRe1056.1Nu

Gr

l

h (2.47)

3

1

4

34.2

165.0

5 Pr004.0PrRe1056.1Nu

Gr

l

h (2.48)

3

1

6.0

52.0

Pr35.0PrRe9.1Nu

Gr

l

h

w

c

(2.49)

h = Height of oil duct, in m

l = Length of oil duct, in m

Re = Reynolds number at oil duct, dimensionless

Pr = Prandtl number at oil duct, dimensionless

Gr = Grashoff number at oil duct, dimensionless

Nu = 0:68 +0:67Ra0:25

0

@1 +

Ã0:492

Pr

!0:56251

A

4=9

Nu =

0

BBBBBBB@

0:825 +0:387Ra1=6

0

@1 +

Ã0:492

Pr

!0:56251

A

8=27

1

CCCCCCCA

2

Nu = 0:54Ra0:25

Nu = 0:15Ra0:25

Nu =¡0:036Re0:8 ¡ 836

¢Pr1=3


85

μc = The dynamic viscosity at oil duct centre, in Pa∙s

μw = The dynamic viscosity at oil duct wall, in Pa∙s

Junction pressure losses

Junction pressure losses (JPL) are often associated with the flow turning at bends or

mixing at branches, and the losses are due to the energy loss with sudden or gradual

changes in flow directions. [28] noted that, although JPL is conventionally regarded

as minor losses, they can actually play a predominant influence on oil flow

distributions. Joshi and Deshmukh [30] used (2.50) and (2.51) to determine pressure

drops at right angle bends and „Tee‟ junctions respectively.

(2.50)

(2.51)

The equations for Nusselt number, friction coefficient and JPL will be calibrated by

using large sets of CFD simulations in Chapter 4.

2.4.3 Prediction on oil flow and temperature distributions

By using network modelling, [19] predicted that oil flow and disc temperature

distributions follow patterns with a series of peaks and valleys; the number of the

peaks (or valleys) corresponds to the number of the passes in the winding. This is the

same pattern with the profiles in Figure 2.24 and Figure 2.25 [26]. In the figures, it is

interesting to see that there are additional special patterns at the disc number 40 and

100, because the discs arranged there were thinner and the oil ducts were therefore

widened. Although [26] did not present more details about the winding design, the

special patterns illustrate that localised high temperatures could be due to specific

designs.

¢Pbend =7000

Re

½u2

2

¢Ptee =4200

Re

½u2

2


86

Figure 2.24 Calculated disc temperatures with directed oil washers [26].

Figure 2.25 Calculated oil velocities of horizontal ducts with directed oil washers [26].

It is necessary to mention that the results of [26] did not include junction pressure

losses which has been addressed to be significant for predicting oil flow distributions

in [28].


87

2.4.4 Review of the methodology

In order to validate the network modeling, [57] conducted both network and CFD

modelling on the LV winding of a transmission transformer, 66 MVA, 225/26.4 kV,

ON cooling mode, and concluded that for uniform loss distribution, the network

model predictions on hot-spot temperature and location matched the CFD predictions

very well, even if network model could not capture details such as hot streaks, which

were previously noted in [39].

However, for non-uniform loss distributions, the deviation between network model

and CFD became greater [57].

Reference [30] used network modelling and concluded that:

1. If there are a large number of discs in one pass, say 20 or more, possibly oil flows

in horizontal ducts do not follow the same directions.

2. If the ratio of disc width to duct height exceeded 35, in case of ONAN, and 50, in

case of ONAF and OFAF, insufficient oil could reach up to the middle of the disc

width so that the measured winding temperature rise would be higher than the

modelling predicted value. It was then recommended that numerical approaches

can be particularly improved to include this effect.

Reference [29] conducted sensitivity studies using a network model, in which effects

of various winding design parameters such as oil duct dimensions and pass sizes etc

were investigated and summarised. In the studies both the oil flow rate and

temperature at the bottom inlet are set as constants, but in reality the modification of

winding design may modify the hydraulic impedance of the winding and as such, if

the original external radiator and pump is kept, (pump is only for forced oil cooling

mode), the inlet oil flow rate and temperature may also vary.

Reference [31] developed a network model and applied it into a Transformer

Monitoring and Diagnosis System (TMDS). The model is intended to provide

information about heat generation and oil flow distribution in the transformers being

monitored. Because of the integration with the TMDS, the thermal model can gather

input parameters directly from the available measurement sensors and the


88

transformer database. This application of network modeling can be a compensation

for the on-line monitoring systems of transformer thermal fault [96,97].

2.5 Summary

In this chapter, a literature review on transformer insulation ageing, end-of-life,

thermal performance, thermal modelling and its experimental validation has been

made. The basic conclusions from the literatures include

1. A transformer‟s lifetime is evaluated by its insulation ageing rate and the ageing

rate is strongly related to temperature. The insulation at the hot-spot undergoes

the worst ageing scenario and its lifetime therefore represents the transformer‟s

end-of-life.

2. Better thermal performance means lower top oil, average winding and hot-spot

temperatures. The traditional assessment of a transformer‟s thermal performance

relies on the factory heat run test; however only the global temperatures can be

measured in a heat run test and the hot-spot temperature is roughly estimated by

the empirical hot-spot factor. This prompts the necessity to directly measure the

hot-spot by using optic-fibres. In order to guide the optic-fibre installation,

numerical modelling approaches are used to predict the hot-spot location.

3. Among the thermal modelling approaches, network modelling offers a good

balance between calculation speed and approximation detail. Compared with

network modelling, the thermal-circuit analogy methods are faster but

approximate the oil cooling system into only several integral components and

cannot predict the details of oil flow and temperature distributions. CFD

simulations require significantly more computational efforts than network

modelling but with better representations of details and sometimes CFD can

reveal some fundamental fluid dynamics phenomena, which network modelling

cannot represent.

4. The assumptions and empirical equations employed in network modelling for

describing Nusselt number, friction coefficient and junction pressure losses (JPL)

were from general fluid dynamics and heat transfer handbooks. Their suitability

for transformer oil and oil duct dimensions may require a full calibration.

5. Numerical modelling requires experimental validation to check its calculation

accuracy and network modelling is no exception. Various measurement devices


89

such as optic-fibres, hot wire anemometry (HWA), Laser-Doppler velocimetry

and oil pressure sensors etc can be applied for the experimental validation.


90


91

Chapter 3 Network modelling and assumptions

3.1 Paper 1

Natural convection cooling ducts in transformer network modelling

W. Wu, Z.D. Wang and A. Revell

2009

The 16th International Symposium on High Voltage Engineering (ISH)

NATURAL CONVECTION COOLING DUCTS IN TRANSFORMERNETWORK MODELLING

W. Wu1, Z.D. Wang1∗ and A. Revell21School of Electrical and Electronic Engineering,

2School of Mechanical, Aerospace and Civil Engineering,The University of Manchester, Manchester, M60 1QD, UK

∗E-mail: [email protected]

Abstract: In the context of transformer thermal performance and end-of-life criteria, theaccurate prediction of the magnitude and location of the maximum temperature or ‘Hot-spot’ inside a transformer is of great importance. In the attempt to accurately represent thecharacteristics of this hot-spot, various thermal modelling approaches have been developed,one of which can be generally classified as ‘network models’ such as TEFLOW developed inthe UK in the late 1980’s. Of the two flow cooling modes employed in a transformer: forcedoil flow cooling (OF) and natural oil flow cooling (ON), the latter is ordinarily acceptedto be the more challenging of the two to model. As such it comes as little surprise thatnetwork models like TEFLOW are believed and observed to be able to better cope withOF conditions. This paper begins by reviewing the physical background and theory used todescribe coolant oil flow with natural convection inside the cooling ducts of power transform-ers. Furthermore, it highlights aspects of ongoing research which are anticipated to enableenhancements in the TEFLOW code, specifically for the modelling of flow in the naturalconvection cooling mode. In particular, the pressure drop network model is redevised toconsider the effect of a non-uniform cross-sectional area.

LIST OF SYMBOLS

H = height of the fluid ductL = length of the fluid ductW1 = inner width of the fluid ductW2 = outer width of the fluid ductW = average width of the fluid ductP1 = pressure at inner side of the fluid ductP2 = pressure at outer side of the fluid duct∆P = pressure drop between inner and outer

sides of the fluid ductU1 = inner velocity of the fluid ductU2 = outer velocity of the fluid ductU = average velocity of the fluid ductρ = average density of fluidµ = average dynamic viscosity of fluidµw = dynamic viscosity of fluid at the wall tem-

peratureµb = dynamic viscosity of fluid at the bulk tem-

peraturef = average dimensionless friction coefficient

of the fluid ductRe = Reynolds number ρUH/µ

1. INTRODUCTION

Power transformers are core components of electricsystem networks, and inevitably the reliability ofelectricity transmission and distribution systems isultimately influenced by the performance of trans-formers. Prediction of the magnitude and locationof the maximum temperature or ‘Hot-spot’ inside atransformer winding is of importance for power sys-tem asset management. In large power transformers,

windings are generally cooled by oil flowing from thebottom to the top of the winding through an exten-sive network of crossover ducts and passages. How-ever, the hot spot is generally found not to be locatedat the top winding disc as one might expect, due tothe effect of a non-uniform oil flow [1].

Numerical modelling has been used for thermal anal-ysis of power transfomers for at least 40 years,see Allen & Finn (1969) [2], and Network Mod-elling is one of the numerical tools that has gainedwidespread usage. Network Modelling is a processof reducing the complex pattern of passages downto a matrix of simple hydraulic duct approxima-tions, which are interconnected by junction points or‘nodes’. In the transformer cooling system, oil flowsthrough numerous horizontal ducts between “heatgenerating” winding discs, thereby extract the heataway from the source. Horizontal ducts join up toa single vertical duct which carries the oil up andacross to next section of the winding. The cross-point linking a horizontal duct and a vertical duct isregarded as a node in the network model.

Figure 1 shows the process by which the geometryfor a 2D network model is approximated from a disc-type transformer winding. Due to axial symmetry,a 3D segment between two adjacent spacers is firsttaken, and a 2D slice of this segment is then repro-duced to represent the network of oil flow ducts. Inthis 2D model, we define a single pass as the sectionbetween two adjacent block washers (as labelled inFigure 1).

The Network modelling methodology can be best de-

ISBN 978-0-620-44584-9Proceedings of the 16th International Symposium on High Voltage Engineering

Copyright c© 2009 SAIEE, Innes House, Johannesburg

Pg. 1 Paper F-32

pass

disc

ducts

nodes

Figure 1: Derivation of geometry for a 2D network model from a disc-type transformer winding.

scribed as a ‘lumped-parameter’ model, which im-plies that it is based upon the assumption thatcoolant oil is well mixed at each node of the flowjunctions so that physical characters, such as tem-perature and velocity, can be reasonably representedby a single mean value. It is not therefore possibleto examine the detailed flow pattern at a node lo-cation or inside a duct when using network models,although this would be possible by employing othernumerical methods of higher spatial resolution suchas Computational Fluid Dynamics (CFD) [3].

In Network Modelling, the mechanics are separatedinto two aspects: the hydraulic network and the ther-mal network. The hydraulic network is a mass trans-fer system, in which the conservation of mass can beapplied to the pressure drop equation. On the otherhand, the thermal network is an energy transfer sys-tem, in which energy is conserved and heat transferequations are employed.

Oliver (1980) [1] derived a set of detailed mathe-matical equations, developed an algorithm for iter-ative calculations, and also implemented them intothe network modelling software called TEFLOW ver-sion 1. Following on from this work, TEFLOW 2introduced by Simonson & Lapworth (1996) [4], wasdeveloped to incorporate a modelling capability oftransient loading, so that the program can be usedto predict the temporal variation of load on a trans-former. In a later review paper of Network Modellingby Zhang & Li (2004) [5], the inability to account fora non-uniform cross-sectional area of horizontal cool-ing ducts was identified as over-simplistic, and it wasstated that a more detailed geometric analysis shouldbe incorporated into the model, although they didnot undertake this development. As such, this paperbegins by presenting the hydraulic network model in

its original form, and then provides examination andanalysis of the geometry of the non-uniform horizon-tal cooling ducts.

2. COOLING DUCTS EQUATION

The horizontal cooling ducts represent the primarypath of heat transfer from winding discs to coolantoil and as such are of great significance. Figure 2shows both a cross-sectional view and a top view ofa horizontal cooling duct between two winding discs.The equation used to describe balance of forces forthe oil flow in the cooling duct is

∆P = P1 − P2 = fL

H

ρU2

2(1)

Equation (1) is so-called Darcy-Weisbach Equation,which is widely used in hydraulics and describes re-lationship between pressure loss ∆P and the averagevelocity U . Here, duct length L and height H areboth known, but the friction coefficient f must bedetermined.

For ducts with rectangular cross-section of sides aand b, and with a < b, the friction coefficient may beapproximated following the equation given in Vec-chio and Poulin et al (2001) [6]:

f =56.91 + 40.31

(e−3.5a/b − 0.0302

)4Re

(2)

In Oliver (1980) [1] and Declercq (1999) [7], Equation(3) is adopted to calculate f for transformer coolingducts.

f =24Re

(3)



Pg. 2 Paper F-32

Figure 2: Winding cooling duct (topview and cross-sectional view).

p1 p2

¡¹dudr

l

rH = 2R

Flow direction

Figure 3: Control volume inside the fluid flow region betweentwo infinite parallel plates.

From Figure 2 it is clear that the inner and outersides of the duct are not of equal width, although theabove equations intrinsically assume an infinite span.Zhang & Li (2004) [5] notes that non-uniform cross-sectional area in the radial direction of the flow has asignificant influence on flow distribution within cool-ing ducts and should not be neglected. It is thereforethe task of the following section to derive an equationwith consideration of this non-uniform cross-section,so as to improve approximation of the flow frictioncoefficient f .

To represent heat transfer effects and the temper-ature distribution across the duct, a simple modi-fication is made to Equation (3) to account for thevariation of molecular viscosity between the near wallflow, µw, and the bulk flow, µb (Oliver, 1980 [1]).

f =24Re

(µwµb

)0.58

In the following section of analysis, this thermalmodification is omitted for clarity.

3. ANALYTIC DERIVATION

Due to the low Reynolds number of the flow in cool-ing ducts [1, 5], the oil motion may confidently betreated as laminar flow, such that the shear stresscaused by viscosity is the primary source of fric-tional force acting to resist the driving pressure force.Since the width of the cooling duct is generally muchgreater than its height; W � H.

The following analysis starts by considering fluid flowbetween two parallel plates of infinite width, or 2-dimensional flow before deriving a modification toaccount for the width expansion effect.

3.1. INFINITE WIDTH DUCT FLOW

For convenience, we define half of the height betweenthe two infinite parallel plates as R = D/2, and se-lect an infinitessimal control volume from the flow

(sufficiently far from the walls) for analysis, whichis shown in Figure 3. For this control volume, usinglowercase letters, height is defined as 2r, length l andpressure drop ∆p = p1 − p2.

Considering only the pressure drop and shear stressdue to viscosity, the balance of forces should be

−2lµdu

dr= 2r∆p,

to which the no-slip boundary condition u(R) = 0 isapplied and the resulting differential equation solvedto obtain

u(r) =∆p2µl

(R2 − r2) .

The mean velocity across the duct is obtained byintegration of velocity u, as follows:

U =

∫ R0u dr

R=

13

∆pµlR2. (4)

This is then used to provide an expression for thepressure drop as:

∆p =12µlUH2

= ∆P =24Re

L

HρU2

2, (5)

where finally, it has been assumed that the duct issufficiently long to ensure that the flow is fully devel-oped along the entire length of the duct; i.e. ∆p andl may be replaced by ∆P and L respectively. Wethus arrive at the friction coefficient approximationcurrently employed in TEFLOW (given in Equation(3)).

3.2. RADIAL EXPANSION OF THE DUCT

The infinite span duct flow approximation assumesa constant averaged velocity U throughout the fluidflow, although in the case considered here therewould clearly be a velocity drop in the direction of



Pg. 3 Paper F-32

x

dx

W1 W2

L

U1 ¹U U2

Figure 4: Schematic of the cooling duct: top view.

the width expansion due to the conservation of massflow rate, as shown in Figure 4. Therefore we haveto consider the velocity variation with width of ductsegment, which can be expressed by

U(x) = U1W1

w=

U1W1

W1 + xL (W2 −W1)

(6)

where w is the duct width at location x. From nowon U is a function of location x. The average ve-locity along the duct is given by U = 0.5 (U1 + U2).Substitution of Equation (6) into Equation (5) gives

dP =12µH2

U1W1

W1 + xL (W2 −W1)

dx

Then with integration of pressure along the duct, amodified pressure drop, ∆P ′ is obtained

∆P ′ =∫ L

0

dP =12µH2

U1W1L

W2 −W1lnW2

W1(7)

It is convenient to define a ‘width expansion coef-ficient’, α = W2/W1, so that Equation (7) may beexpressed as

∆P ′ =12α+ 1α− 1

lnα12µLUH2

(8)

Furthermore, by comparing Equation (8) with Equa-tion (5), a ‘pressure loss factor’, β is defined:

β =12α+ 1α− 1

lnα (9)

such that

∆P ′ = β12µLUH2

= β∆P and f ′ = β24Re

= βf

(10)

The pressure loss factor, β, has thus been introducedto account for the variation of fluid velocity in theflow direction due to the width expansion. As W2 →W1, i.e. as the cross-sectional area of the fluid ductbecomes uniform, α→ 1. It can easily be shown that

in the limit α→ 1 the equation returns β = 1 and socollapses to the original model f ′ = f , ∆P ′ = ∆P :

β(1) = limα→1

12α+ 1α− 1

lnα = 1

4. ANALYSIS AND FUTURE WORK

Figure 5 displays the variation of β against differentα values. It is interesting to note from that β ≥ 1and so f ′ ≥ f and ∆P ′ ≥ ∆P .

For transformers, the ratio α is commonly found tolie in the range 0.5 → 2; as given by Zhang & Li(2004) [5]. From the above analysis it may then beshown that the estimated difference between f ′ andf , (f ′ − f) /f = β − 1, is no more than 5%.

Using typical geometric parameters for transformerducts presented in Zhang & Li (2004) [5] and thenewly derived form of the pressure network model(Equation (10)) within TEFLOW code, calculationswere made to investigate the predicted impact of dif-ferent values of α, α = 1.00, 1.18, 1.43, 1.82 (corre-sponding toRI−O = 1.00, 0.85, 0.70, 0.55 in Zhang &Li (2004) [5]), as shown in Figure 6. At the extremecondition, α = 1.82, the mass flow rate is increased(or decreased) by 12.6%, i.e. less than the 33.7%change predicted by Zhang & Li (2004) [5].

The ongoing work on cooling ducts will incorporatenatural convection heat transfer effects. A two di-mensional CFD investigation of this flow is also un-derway as an alternative method to Network Mod-elling; as illustrated in Figure 7, the mesh usedfor CFD simulation is much finer than the domaindiscretisation used in Network Modelling. WhileCFD offers a drastically increased resolution of flowphysics, this is accompanied by a significant increasein cost, both in terms of the required computa-tional processing power and computation time. Assuch, this approach is not expected to become awidespread practical alternative to Network Mod-elling in the near future. The initial aim of the CFDstudy will be to provide verification of the NetworkModelling code, beyond which it is anticipated thatpredicted CFD results would be analysed with a viewto enhancing approximations in the existing modelsused in Network Modelling codes such as TEFLOW.

5. ACKNOWLEDGEMENTS

Financial support is gracefully received from the En-gineering and Physical Sciences Research Council(EPSRC) and National Grid Company. The authorsappreciate the technical support given by Paul Jar-man from National Grid, John Lapworth from DoblePowerTest and Edward Simonson from Southamp-ton Dielectric Consultants Ltd. Mr. Wei Wu wouldalso like to thank EPSRC-National Grid DorothyHodgkin Postgraduate Award (DHPA) for partially



Pg. 4 Paper F-32

0.5 1 1.5 21

1.01

1.02

1.03

1.04

α

β

Figure 5: Relationship between factors β and α. Figure 6: Comparison between different mass flowrate distributions on varied α values.

Figure 7: Comparison of the domain discretisation used in Network Modelling and CFD (where mesh densityis much higher).

providing the PhD scholarship at The University ofManchester.

REFERENCES

[1] A. J. Oliver. Estimation of transformer windingtemperatures and coolant flows using a generalnetwork method. IEE PROC., vol. 127, no. 6,pp. 395–405, 1980.

[2] P. H. G. Allen and A. H. Finn. Transformerwinding thermal design by computer. IEE Conf.Publ., vol. 51, pp. 589–599, 1969.

[3] E. J. Kranenborg, C. O. Olsson, B. R. Samuels-son, L.-A. Lundin, and R. M. Missing. NUMERI-CAL STUDY ON MIXED CONVECTION ANDTHERMAL STREAKING IN POWER TRANS-FORMER WINDINGS. 5th European Thermal-Sciences Conference, The Netherlands, 2008.

[4] E. Simonson and J. Lapworth. Thermal ca-

pability assessment for transformers. Reliabil-ity of Transmission and Distribution Equipment,1995., Second International Conference on the,pp. 103–108, Mar 1995.

[5] J. Zhang and X. Li. Coolant flow distributionand pressure loss in ONAN transformer windings.Part I: Theory and model development. PowerDelivery, IEEE Transactions on, vol. 19, no. 1,pp. 186–193, Jan. 2004.

[6] R. M. D. Vecchio, B. Poulin, P. T. Feghali, D. M.Shah, and R. Ahuja. TRANSFORMER DESIGNPRINCIPLES : With Applications to Core-FormPower Transformers. The Netherlands: Gordonand Breach Science Publishers, 2001.

[7] J. Declercq and W. van der Veken. Accurate hotspot modeling in a power transformer leading toimproved design and performance. Transmissionand Distribution Conference, 1999 IEEE , vol. 2,pp. 920–924 vol.2, Apr 1999.



Pg. 5 Paper F-32


93

3.2 Paper 2

Heat Transfer in Transformer Winding Conductors and Surrounding

Insulating Paper

W. Wu, A. Revell and Z.D. Wang

2009

The International Conference on Electrical Engineering (ICEE)

1

Abstract--The accurate prediction of magnitude and location of

the maximum temperature or ‘hot-spot’ of transformer windings

is of great importance for evaluating transformer thermal

performance. In the attempt to accurately represent

characteristics of this hot-spot, various thermal modelling

methodologies have been developed, including methods which

employed forms of Computational Fluid Dynamics (CFD). In the

simplified scenario where eddy loss is ignored, the ohmic power

generated by winding conductors is the only heat source to be

extracted by the coolant oil flow, and a winding disc of multiple

cable elements is modelled as a uniformly distributed volumetric

heat source at the duct surface boundary. In CFD such an

assumption reduces the complexity of modelling process; however

it limits the predictive accuracy. This paper considers the heat

transfer phenomena inside winding discs comprising copper

conductors and surrounding insulating paper, and proposes a

non-uniform temperature distribution among conductors. It is

envisaged that this would help improve boundary conditions used

for the CFD modelling of transformer coolant oil circulation.

Index Terms--Power Transformer, Thermal Modelling, Heat

Transfer, Hydraulic, CFD

I. NOMENCLATURE

= thickness of insulating paper layer

= width of copper conductors

= height of copper conductors

= temperature of node

= temperature of node

= temperature of boundary node

= distance between nodes and

= height of the contacting surface area between

nodes and

= length of the winding conductors

= thermal conductivity of insulating paper

= thermal conductivity of copper conductors

= heat generated at a source node of heat

= heat flux from nodes to

This work is funded by the Engineering and Physical Sciences Research

Council (EPSRC), National Grid, Dorothy Hodgkin Postgraduate Award

(DHPA) in the UK.

W. Wu is a PhD student in the School of Electrical and Electronic

Engineering at University of Manchester.

A. Revell is a Lecturer in the School of Mechanical, Aerospace and Civil

Engineering at University of Manchester.

Z.D. Wang is a Senior Lecturer in the School of Electrical and Electronic

Engineering at University of Manchester (e-mail:

[email protected]).

= heat flux from node to boundary node

= total number of nodes

= total number of boundary nodes

= connection matrix for the nodes network:

1 if and nodes and are connected

0 if or nodes and are not connected

= connection matrix between the nodes network

and the boundary nodes:

1 if node and boundary node are connected

0 if node and boundary node are not

connected

= coefficients defined for the matrix solution

Subscripts

Refers to node

Refers to node

Refers to boundary node

Refers to connection linking nodes and

Refers to connection linking node and

boundary node

II. INTRODUCTION

OWER transformers are core components of electric

system networks, and as such thermal performance of

transformers directly influences reliability of electricity

transmission and distribution. In order to evaluate transformer

thermal ageing, the accurate prediction of magnitude and

location of maximum temperature or ‘hot-spot’ inside a

transformer winding is of great importance. In the attempt to

accurately represent characteristics of hot-spot, various

thermal modelling methodologies have been developed over

the past tens of years, see network model by Allen & Finn [1]

and the model by Kranenborg, Olsson, Samuelsson, Lundin &

Missing which incorporates some forms of Computational

Fluid Dynamics (CFD) [2].

The process by which a 2D CFD model is obtained for a

disc-type winding is described as follows (where ○1 ○2 ○3 ○4 ○5

refer to labels in Fig. 1):

(a) Starting from part of a disc-type transformer winding

○1 , due to axial symmetry, a 3D segment between two

adjacent spacers may be extracted, shown as ○2 ;

(b) A 2D slice of the segment ○2 is then reproduced to

represent the geometry of oil flow ducts, shown as ○3 .

In ○3 , note that the hot winding discs are heat sources,

Heat Transfer in Transformer Winding

Conductors and Surrounding Insulating Paper W. Wu, A. Revell and Z.D. Wang, Member, IEEE

P

The International Conference on Electrical Engineering 2009

2

while the oil ducts could be classified as either

horizontal ducts which are the primary cooling paths,

or vertical ducts which carries the oil up and across to

the next section of the transformer winding;

(c) In particular, the geometry of oil ducts ○3 is meshed for

CFD modelling, shown as ○4 (a sub-region was

specified for example). However, heat flux from

winding discs must be provided as boundary conditions

for the CFD model ○4 . The inner structure of a winding

disc ○5 is composed of multiple copper conductors

covered by insulating paper.

Fig. 1. Derivation of 2D CFD model of a disc-type transformer winding.

Neglecting eddy loss, the ohmic power generated by current

passing through transformer winding conductors is the sole

source of heat which must be extracted away from the source

by cooling oil circulation. Each winding disc is treated as a

single homogenous heat source so that a uniform heat

boundary condition may be applied for the CFD simulation;

i.e. effects due to different heat transfer rates through different

materials are ignored. This is a working assumption to reduce

the complexity of modelling; however it limits the predictive

accuracy.

In reality, conductors will accumulate and dissipate heat at

differing rates based on their locations; depending on

geometry and layout of the conductor and its insulating paper

of the disc. For instance, a centrally located conductor has

smaller heat-dissipating surface area than the one located at the

sides of the disc. In order to more accurately represent the heat

flux boundary conditions for CFD modelling, it becomes

necessary to consider both of the paper and the individual

conductors, and also to account for the downstream

accumulation of heat due to the raised temperature of the oil

fluid as it moves down the duct.

This paper reports the initial results from an in-house code,

TEDISC when it is applied to the heat transfer cross a single

winding disc composed of copper conductors and surrounding

insulating paper.

III. THE NUMERICAL MODEL

A. Assumptions and Discretisation

The inner structure of the winding disc is shown as part ○5

of Fig. 1, and this is where the heat transfer between

conductors and insulating paper occurs. It is possible to use a

collection of interconnected copper conductor and insulating

paper elements to discretise the thermal field inside this

region, as shown in Fig. 2. For each element, an average

temperature value is assumed to represent the temperature

property of the whole element region, while a ‘node’ is defined

to be at the centre of this element.

Following these definitions, the following implicit

assumptions are stated:

1) The thermal conductivity of copper ( ~380 Wm-1

K-1

[3]) is much higher than that of insulating paper,

( ~0.2 Wm-1

K-1

[3]); so the temperature gradient

inside the conductor is assumed to be negligible;

2) The thickness of the insulating paper is relatively thin

(less than a few mm), i.e. ; so temperature

variation across the paper thickness may be ignored.

Temperatures at the outer boundaries of the insulating

paper (this paper layer surface boundary can also be described

as oil duct surface boundary or winding disc surface boundary,

depending on the context in the paper) have been applied from

previous calculations.

3

Fig. 2. Nodes representation of the winding disc.

Fig. 2 illustrates a network of these nodes, including

unknown temperature nodes inside the winding disc as well as

the known temperature nodes at the boundaries. Each

component block of one conductor and its surrounding

insulating paper has been represented by nine nodes in total.

Therefore, for a winding disc containing conductors, the

total number of unknown nodes will be , and the total

number of boundary nodes will be .

B. Equations Employed

The physical model is composed of the following:

1) Heat transfer equation applied between adjacent nodes

or applied between a node and a neighboring boundary

node;

2) Thermal energy conservation applied to each node.

The first of these can be summarized as two contacting

nodes and , as shown in Fig. 3, or between one node and a

boundary node next to it. Condition (A) in Fig. 3 represents

the heat transfer across a homogenous material, while

condition (B) is used for heat transfer across two different

materials. In the real scenario, condition (A) may be used for

heat transfer between two adjacent insulating paper nodes, as

well as between a paper node and a neighboring boundary

node (use instead of in Fig. 3 for this situation); on the

other hand, condition (B) will be adopted to cope with heat

flux between a copper conductor node and a paper node

adjoining to it.

According to Fourier’s law, the thermal heat flux through a

surface is proportional to the negative temperature gradient

across the surface , and the ratio between them is defined

as the thermal conductivity . Fourier’s law can be expressed

by

Using discretised form of Fourier’s law, for condition (A)

in Fig. 3, heat flux from nodes to is

Fig. 3. Heat flux geometry between two adjacent nodes and .

(1)

where and are the height and width of the contacting

surface area respectively, and is the distance between

nodes and , as labeled in Fig. 3.

For condition (B), heat flux from nodes to is

(2)

where . are used to express ‘sub-

distance’ and thermal conductivity in the segments belonging

to nodes and respectively. An equivalent thermal

conductivity can be defined to incorporate (2) into (1), as

given by (3). Thereby, it is possible to only use (1) for

expression of heat flux from now on.

(3)

Conservation of thermal energy for each node gives

(4)

The first sum term is the total thermal energy diffused from

node to any existing neighboring nodes. The second sum

term is the total thermal energy flowing to existing adjacent

boundary nodes. Both of heat flux term and in (4) can

be calculated according to (1). Further substitution of (1) into

(4) gives the primary matrix equation, which must then be

solved.

C. Solution Procedure

Substitute (1) into (4) and obtain

(5)

4

Denote

Then (5) can be rewritten into

(6)

Equation (6) is a set of linear simultaneous equations. In the

equations, and can be determined by the geometric

parameters of the disc, and and depending on the

layout of the inner structure. With respect to , it could be

determined as the following:

1) If node is located at insulating paper layer,

;

2) If node belongs to a copper conductor, is the

ohmic loss generated per unit length of that winding

conductor.

In conclusion, there are linear equations corresponding

to unknown node temperatures, in (6), and it is sufficient

to solve for using the Gaussian elimination method.

MATLAB was chosen as the development platform of

TEDISC since it has a good matrix manipulation library.

IV. AN ILLUSTRATIVE TEST CASE

Using the transformer winding disc geometry presented in

Oliver (1980) [3] and the newly developed TEDISC code,

calculations were made to investigate temperature distribution

inside a winding disc. In this winding disc, there are 22

conductors; i.e. the size of the matrix to be solved will be 198

by 198.

A. Case I: uniform temperature

Initially, a uniform temperature values is applied at all

boundaries, as shown in Table I.

TABLE I

UNIFORMLY DISTRIBUTED BOUNDARY CONDITIONS

Boundary Temperature values (oC)

Top side 72.6

Left side 72.6

Bottom side 72.6

Right side 72.6

Dimensions are defined as shown in Fig. 4 for clarity. Fig. 4

defines , and as such the line describes

the top paper layer location, gives the bottom paper

layer location, while shows where the conductor nodes

are.

Fig. 4. Dimensions definition for the calculation results presentation.

The calculation results for temperatures at y = 0 and y = d

are shown in Fig. 5. Due to symmetry of the boundary

conditions set as Table I, the temperatures at is

distributed as the same way with y = d . Plateau-like

temperature distribution patterns can be seen from Fig. 5, and

the saw-teeth shape temperature distribution for paper layer is

probably due to the limited number of discretised elements and

different lengthes represented by nodes.

Fig. 5. Results with uniform temperature boundary conditions.

B. Case II: linearly increasing temperature

In the real case scenario, it is unlikely that surrounding

cooling oil temperature is uniformly distributed. Since there is

heat flux from the winding disc heat source to the oil flowing

along the ducts, the oil temperature will increase gradually.

Therefore an increasing series of temperature values for

bottom and top boundaries is now applied so as to take this

effect into consideration. With respect to the vertical oil ducts,

the temperature is considered staying uniform; being a

reasonable approximation given that the disc height is

comparably small.

Oliver (1980) [3] assumed the oil temperature variation

along the horizontal cooling ducts to be linear. The boundary

temperature values applied in this case are shown in Table II.

5

TABLE II

LINEARLY INCREASING BOUNDARY CONDITIONS

Boundary Temperature values (oC)

Top side 67.0 to 78.2

Left side 67

Bottom side 67.0 to 78.2

Right side 78.2

With the linear boundary conditions, the calculation

reproduced different results, as shown in Fig. 6. There is an

obvious peak value, rather than the plateau shape in Fig. 5. It

is interesting to note that the peak value is located close to the

downstream end of the winding disc (the 19th conductor),

instead of the end conductor itself. This is reasonable since the

end conductor has a much lower temperature due to its lack of

a neighbor and consequent extra free surface area to dissipate.

Fig. 6. Results with linearly increasing boundary conditions.

C. Discussion

In Fig. 6 the solid curve is a prediction of conductor

temperatures using an expression derived in Oliver (1980) [3],

given below as (7); to obtain average and maximum values of

the conductors’ temperatures in a winding disc. The necessary

parameters include wall temperatures of bottom and top

horizontal cooling ducts.

(7)

Fig. 6 displays a comparison of results from (7) with results

predicted by TEDISC code. Away from either end of the disc,

in the mid-section, the gradient of both results are clearly seen

to be in good agreement. However, it is important to note that

Oliver’s method assumes the hot-spot to be located at the

downstream end of the winding disc whereas TEDISC’s result

shows that the hot-spot is close to, but not exactly at the

downstream end. Table III provides a quantitative summary of

these results.

TABLE III

COMPARISON OF STATISTICAL RESULTS BETWEEN OLIVER’S METHOD AND

TEDISC

Conductors’

temperature Oliver’s Equation TEDISC

Average (oC) 93.8 94.1

Maximum (oC) 99.4 99.6

The hottest

conductor

number

22nd

(at the

downstream end)

19th

From Table III it can be seen that the difference between

average and maximum temperatures from both methods is less

than 1%, which implies the assumption made by Oliver’s

equation is sufficient to predict the magnitude of the hot-spot

although it is unable to predict hot-spot’s precise downstream

location.

V. SUMMARY AND FUTURE WORK

It is anticipated that CFD modelling will be able to provide

an improved prediction of the temperature distribution in

transformer cooling oil circulation and it is the long term aim

to undertake a comprehensive CFD analysis of this study case.

However for this aim to be realized, it is important to provide

an accurate representation of the winding discs’ surface

temperatures to be used as CFD boundary conditions. As such,

the work was set out to define a mathematical model and lead

to the development and validation of TEDISC code. In this

way, TEDISC is able to provide a detailed heat flux

distribution at the paper layer surfaces.

Based on the temperature values obtained for the insulating

paper layers, heat flux distribution as shown in Fig. 7 can be

obtained, which would replace the basic assumption which

regards the winding disc as a uniformly distributed heat

source.

Fig. 7. Heat flux distribution at the top surface with both the uniform and the

linearly increasing boundary conditions, as shown in Table I and Table II.

6

The ongoing work on winding discs will incorporate

coupling between thermal calculations for both winding discs

and surrounding cooling oil. The current boundary conditions

used for TEDISC are obtained from previous cooling oil

models, in which the heat flux from discs to oil is regarded to

be uniformly distributed as well as the temperature

development along the cooling ducts is assumed to be linear.

However, Fig. 7 clearly displays a non-uniform distribution of

heat flux at the surface of winding discs; it is therefore

considered to be valuable to update the heat flux assumption

used in former cooling oil models in order to recalculate oil

temperatures. Using an iterative numerical process, a

converging result matching both of the winding discs and the

cooling oil models simultaneously can be expected.

VI. ACKNOWLEDGMENTS

Financial support is gracefully received from the

Engineering and Physical Sciences Research Council

(EPSRC), National Grid and Dorothy Hodgkin Postgraduate

Award (DHPA). The authors appreciate the technical support

given by Paul Jarman from National Grid, John Lapworth from

Doble PowerTest and Edward Simonson from Southampton

Dielectric Consultants Ltd. Mr. Wei Wu would also like to

thank EPSRC-National Grid Dorothy Hodgkin Postgraduate

Award for providing the PhD scholarship at The University of

Manchester.

VII. REFERENCES

[1] P. H. G. Allen and A. H. Finn, "Transformer winding thermal design by

computer," IEE Conf. Publ., vol. 51, pp. 589-599, 1969.

[2] E. J. Kranenborg, C. O. Olsson, B. R. Samuelsson, L.-A. Lundin, and R.

M. Missing, "Numerical study on mixed convection and thermal

streaking in power transformer windings," 5th European Thermal-

Sciences Conference, The Netherlands, 2008.

[3] A. J. Oliver, "Estimation of transformer winding temperatures and

coolant flows using a general network method," IEE PROC., vol. 127,

no. 6, pp. 395-405, 1980.

Wei Wu was born in Shaanxi Province, China in

1983. He received his BEng. and MEng. degrees in

Electrical Engineering from Tsinghua University,

Beijing in 2004 and 2006, respectively. Wei is a

PhD student at the Electrical Energy and Power

Systems Group of the School of Electrical and

Electronic Engineering at University of Manchester.

His research interests lie in transformer thermal

modelling and simulation.

Alistair Revell was born in Buckinghamshire,

England in 1980. He graduated from UMIST in

2002 with a degree in Aerospace Engineering with

French. He received his PhD in Turbulence

Modelling and Computational Fluid Dynamics at

The University of Manchester in 2006, including

placements at ENSMA, EDF and IMFT in France

and Stanford in the USA. Recent research topics

relate to applications in Aerospace and Nuclear

engineering and in particular, the development,

validation and dissemination of the open-source CFD software Code_Saturne.

Zhongdong Wang was born in Hebei Province,

China in 1969. She received her BEng. and MEng.

degrees in high voltage engineering from Tsinghua

University of Beijing in 1991 and 1993,

respectively, and her PhD degree in electrical

engineering and electronics from UMIST in 1999.

Dr. Wang is a Senior Lecturer at the Electrical

Energy and Power Systems Group of the School of

Electrical and Electronic Engineering at University

of Manchester. Her research interests include

transformer condition monitoring and assessment techniques, transformer

modeling, ageing mechanism, transformer asset management and alternative

oils. She is a member of IEEE since 2000 and a member of IET since 2007.


94


95

Chapter 4 CFD calibration for network modelling

4.1 Paper 3

CFD calibration for network modelling of transformer cooling oil flows – Part I

heat transfer in oil ducts

W. Wu, Z.D. Wang, A. Revell, H. Iacovides and P. Jarman

2011

IET Electric Power Applications

Accepted

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1

IET Electr. Power Appl., © The Institution of Engineering and Technology 2011

ISSN 1751-8660

CFD Calibration for Network Modelling of Transformer Cooling Oil

Flows – Part I Heat Transfer in Oil Ducts

W. Wu1, Z.D. Wang1, A. Revell2, H. Iacovides2 and P. Jarman3 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK.

2 School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK.

3 Asset Strategy, National Grid, Warwick, CV34 6DA, UK.

E-mail: [email protected]

Abstract — In the context of thermal performance and thermal lifetime, it is of great importance to predict the magnitude and

location of the ‘hot-spot’ temperature inside a transformer. Various calculation approaches have been developed in the attempt

to gain an accurate prediction of hot-spot, including so-called ‘network models’ such as TEFLOW. In terms of the methodology

used in network modelling, the complex pattern of oil ducts and passes inside a winding is reduced to a matrix of simple

hydraulic channel approximations, where empirical analytical expressions are employed to hydraulically and thermally describe

oil flow and heat transfer. The heat transfer equations contain empirical parameters, often obtained and verified by a limited

number of experimental cases of relatively simple flows. Applicability of these equations should therefore be carefully

evaluated and if necessary corrected, when being used in the wide range of conditions of transformer oil flow; this is the

primary objective of this paper. A detailed parametric study has been performed using the ‘COMSOL’ multiphysics software

package for Computational Fluid Dynamics (CFD), which offers a higher order of accuracy relative to network modelling. The

resulting data sets are processed, based on which a new set of parametric heat transfer equations are proposed specifically for

transformer cooling oil flow. Comparison is finally made between the newly proposed equations and the currently used ‘off-the-

shelf’ expressions.

1 NOMENCLATURE

a, b = Constant parameters for Nusselt number

expressions

As = Area of fluid duct (duct height H × duct length

L)

c, d = Constant parameters for friction coefficient

expressions

Cp = Specific heat capacity of fluid

D = Equivalent hydraulic diameter of fluid duct

f = Average dimensionless friction coefficient of

fluid duct

fc.p. = Average dimensionless friction coefficient of

fluid duct with constant property fluid

H = Height of fluid duct

hc = Convective heat transfer coefficient of fluid

duct

k = Thermal conductivity of transformer oil

L = Length of fluid duct

m, n = Constant parameters for the viscosity terms in

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Nu and f expressions

Nu = Nusselt number

Nuc.p. = Nusselt number of constant property fluid

Pr = Prandtl number

q = Heat flux from winding to fluid duct

R2 = The square of the correlation between the

response values and the predicted response

values

Re = Reynolds number

tb = Bulk temperature of fluid duct

tw = Wall temperature of fluid duct

u = Local flow velocity at the differential element

∂A

U = Average flow velocity of fluid duct

α, β,

γ

= Extra constant parameters for friction

coefficient expressions

μb = Dynamic viscosity of fluid at bulk temperature

μw = Dynamic viscosity of fluid at wall temperature

ρ = Density of fluid

∂A = Area of a differential element

ΔP = Pressure drop between the inlet and outlet of

fluid duct

Subscripts

b Value at bulk temperature

c.p. Value at constant property fluid

w Value at wall temperature

Acroynms/Shorthand


JPL Junction pressure loss

LV Low voltage

2 INTRODUCTION

Power transformers are key, and one of the most expensive,

components of electric system networks. Transformer lifetime

and insulation ageing are strongly dependent upon the

temperature distribution and fluctuation. An improved

understanding of the thermal ageing of insulation can assist

the policy making of transformer asset management [1].

In power transformers, windings are commonly cooled by

oil flowing up, from the bottom to the top, through an

extensive network of crossover ducts and passages. As the oil

flows upwards, it gains in temperature by absorbing heat

transferred to it from the windings, yet the maximum

temperature, called ‘hot-spot’, is generally not found on the

top-most winding disc as one might expect. This is due to, in

part, the effect of a non-uniform oil flow rate [2]. In this

scenario the magnitude and the location of the hot-spot inside

the windings is important since it identifies the location of the

worst insulation ageing.

Numerical modelling has been used to predict the hot-spot

for over 40 years [3]. These numerical approaches can

generally be categorised as either ‘network models’ [2, 4-5] or

methods which incorporate a degree of Computational Fluid

Dynamics (CFD) [1, 6-7]. Generally CFD simulations can be

expected to provide more detailed results but with a large

increase in the required computational effort. In comparison to

CFD, network models are regarded as a quick and simple

numerical approximation which is often convenient for

industry to use, as a large range of design parameters can be

trialled for a relatively low computational effort. However,

network models incorporate significant assumptions about the

flow and subsequently empirical equations to describe

physical properties of the fluid, and the principle objective of

this series of paper is therefore to assess the accuracy of these

empirical equations and underlying assumptions within a well

defined range of transformer cooling oil flow parameters, with

a view to providing more consistent expressions.

3 APPROXIMATIONS IN NETWORK MODELLING

In brief, network modelling is the process of reducing a

complex pattern of multiple passages down to a matrix of

simple hydraulic duct approximations, interconnected by

junction points or ‘nodes’. A node is defined as a cross-point

linking a horizontal duct with a vertical duct [8]. As an

example, Figure 1 shows the process by which the domain

dimensions for a 2D network model are approximated from a

3D disc-type transformer winding; retaining geometric

elements such as discs, ducts, nodes and passes. As the

winding is axial symmetric and the circumferential width of a

oil duct is significantly longer than the duct’s radial length,

2D channel flow models between infinite parallel plates are

suitable approximations and will be applied for all the oil

ducts following the experiences in [2, 6, 9]. This 2D geometry

also neglects the spacers and assumes that there is no

circumferentially directed oil flow. The oil flow through

horizontal ducts, between rows of ‘heat generating’ winding

discs, acts to transfer the heat away. Horizontal ducts join up

with a single vertical duct which carries the oil upwards and

through a gap to next pass. Bulk averaged parameters are

assumed to represent the variation of physical quantities

across each duct and at each node, and a set of ‘lumped

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parameter’ expressions are applied, thereby constructing both

thermal and hydraulic networks across the transformer.

ducts

nodes

discs

a pass

oil

Winding raduis

Figure 1 Geometric derivation of a 2D network model for a

disc-type transformer winding.

To derive a practical and tractable set of equations to

describe the network model, the following physical

assumptions are further made in addition to the geometric

assumptions previously outlined:

a. Oil flow inside ducts is assumed to be entirely laminar

due to the low Reynolds number (Re = 25 ~ 100 [9]).

b. Oil ducts are approximated by a pair of infinite parallel

flat plates.

c. Oil temperature is assumed to increase linearly as it

flows along the duct and gains heat from adjacent discs,

i.e. the heat source [2].

d. Oil flow is completely mixed at nodes in terms of both

hydraulic and thermal aspects; i.e. the flow velocity

and temperature distribution becomes uniform upon

departure from the junctions.

The real scenario could deviate from these conditions, so

the suitability of these assumptions must be verified.

Assumption (b) was shown by [8] as deemed reasonable with

a predictive error of less than 5%, whereas [10] found that

although assumption (c) precludes an accurate prediction of

the hot spot location, the prediction error in hot-spot

temperature is less than 1%.

The set of network model equations based on the

assumptions outlined above can be found in [2]. These

equations require an iterative approach to solve, because the

hydraulic and thermal variations are coupled via the

temperature dependent properties of oil, such as oil viscosity

and density.

Crucially, it should be noted that the following empirical

expressions are incorporated into the network model equations:

i. Convective heat transfer: expressions for both Nusselt

number, Nu, and temperature corrected friction

coefficient, f.

ii. Junction pressure loss (JPL): expressions used to

estimate mixing losses occurring at junctions.

In [2] and [5], forms and parameters for Nu, f and JPL

expressions have been identified from heat transfer literature

but, to the authors’ best knowledge, their suitability for

transformer oil flow has never been fully explored. Therefore,

the current work will focus on evaluating existing expressions

for Nu and f, and proposed modifications will be given.

Additional work to evaluate expressions for the JPL shall be

addressed in an accompanying paper.

4 ANALYSIS ON OIL FLOW IN COOLING DUCTS

The majority of heat transfer occurs along the horizontal oil

ducts between adjacent discs rather than vertical ducts, as

vertical ducts are much shorter and have only a single contact

surface with the heat source. In view of this [2] made the

assumption that the heat transfer to oil in vertical ducts may

be neglected altogether; the present paper follows the same

assumption and thus in the following paragraphs, cooling

ducts refer to the horizontal ducts only. Table 1 gives typical

cooling duct dimensions, duct inlet temperature and velocity

ranges, covering a wide spread design parameters for

transformers from 22 kV to 500 kV, 20 MVA to 500 MVA. It

is granted that duct dimensions vary with rated voltages and

power ratings of transformers and the inlet temperature and

velocity depend on the operating cooling mode and loading

condition, as well as the position of the duct in a winding,

however the expert experiences on the vast amount of existing

designs show that they are expected to lie within the

parameter ranges listed in the table.

Table 1 Typical parameters of power transformer cooling

ducts.

Parameter name Variation range

Duct height, H

(m) 0.003 → 0.010

Duct length, L

(m) 0.05 → 0.15

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Inlet temperature

(oC)

10 → 70

Inlet velocity, U

(m/s) 0.01 → 0.16

Nusselt number, Nu, is the ratio of convective heat transfer

coefficient to conductive heat transfer coefficient and is used

to evaluate the efficiency of convective heat transfer in fluid

flow. One may compute Nusselt number as follows:

k

DhNu c (1)

where hc is convective heat transfer coefficient, D is

equivalent hydraulic diameter and k is the thermal

conductivity of fluid. A common value of the thermal

conductivity of transformer oil, k, is 0.13W/(m∙K) [2]. For

infinite parallel plate models, the hydraulic diameter is

generally taken to be twice the duct height, i.e. D = 2H. Thus

if the Nusselt number is known, the convective heat transfer

coefficient can be obtained directly.

A number of expressions have been developed to

approximate Nu for engineering applications, and the proper

form of the expression depends upon which of the three

laminar flow regimes is in operation [11],

LF1: Fully developed (both hydraulically and thermally),

LF2: Thermally developing (hydraulically fully

developed),

LF3: Simultaneously developing (hydraulically and

thermally developing).

In order to identify a regime, the ‘entrance length’ must be

known, which is defined as the distance downstream of a duct

entrance that the fluid travels before centreline values of

friction coefficient (hydraulic system) or Nusselt number

(thermal) attain values within 1% away from the fully

established centreline value. In each case, hydraulic and/or

thermal flow is considered to be fully developed only for duct

lengths beyond this entrance length.

4.1 Hydraulic entrance length

For hydraulically fully developed flow between infinite

parallel plates, the friction coefficient can be shown to scale as

fc.p. = 24/Re. As a flow develops the friction coefficient will

progress towards this fully developed value. The subscript c.p.

refers to values derived for a ‘constant property fluid’, in

which the fluid properties are independent of fluid

temperature.

Based on the data provided by [12], Figure 2 illustrates the

development of local friction coefficient floc for laminar flow

between parallel plates. The local friction coefficient is

defined at a distance x, from the inlet of the duct, and f is the

average value of the local friction coefficient floc along the

duct.

Figure 2 Local friction coefficient floc development for the

laminar flow between parallel plates.

According to the correlation between floc and x shown in

Figure 2, the flow becomes fully developed at around x =

0.015Re∙D. Using typical values for transformer cooling

ducts, i.e. Re = 100 [9] and D = 0.01m [2], the hydraulic

entrance length is estimated to be 0.015m, which accounts for

15% of the typical cooling duct length, 0.1m. This implies that

the oil flow will generally be at a fully developed state

through around 85% of the duct length.

4.2 Thermal entrance length

The thermal entrance length can be estimated as the product

of the hydraulic entrance length and the Prandtl number, Pr

(typically ~ 200 for oil [2]), and using the same values as

above, the thermal entrance length is therefore of the order of

3m, which is much longer than the typical cooling duct length,

0.1m [2].

Consequently, the typical oil flow in transformer cooling

ducts belongs to the second flow category, LF2. Since the

flow is thermally developing, it implies that the Nusselt

number is continuously developing along the flow direction

and does not reach a stable value.

4.3 Average Nusselt number along duct

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In the context of lumped parameter modelling, the local

Nusselt number is generally represented as a single value,

averaged over the entire duct length. In [5], empirical equation

(2) was used to estimate the average Nusselt number for the

oil flow in cooling ducts, where constants a and b are

empirical parameters. These constants are taken to be a = 1.86

and b = -1/3 [5], which are derived for flow through circular

pipes [13-15]. The implication of (2) is that Nu depends on the

dimensionless group {L/D, Re, Pr}.

b

pc

DLa

PrRe

/Nu

.. (2)

Similarly, [2] adopted the same value for b but proposed a

~30% higher value of a = 2.44 for duct models of flow

between infinite parallel plates; obtained by fitting data

provided by [12].

It should be noted that neither of the Nu expressions

described above accounts for the variation of the fluid

properties with temperature. There is, however, a significant

functional dependence of viscosity upon temperature which

may be included in a network modelling framework, and this

is discussed in the following section.

4.4 The variation of oil viscosity with temperature

Neglecting thermal effects, [8] proposed a frictional

pressure drop equation for a cooling duct and demonstrated

that the velocity profile across the duct height takes the form

of a parabolic curve, as shown by curve (a) in Figure 3. Yet, in

practice, the oil viscosity is known to decrease significantly

with temperature [2, 12], and the associated velocity variation

that results from the change in oil viscosity, from the wall

surfaces towards the centre of the duct, is shown as curve (b)

in Figure 3. As the flow temperature increases further, the

observed distortion will increase.

ab

Flow direction

Figure 3 Velocity in a heated duct (a) constant viscosity; (b)

temperature dependent viscosity.

For engineering applications, [12] proposed a simple

correction to account for the temperature dependency of

viscosity upon both bulk Nusselt number and friction

coefficient, shown as (3) and (4). [2] proposed constant values

of n = -0.14 and m = 0.58. Since the viscosity ratio μw/μb < 1, a

negative value for n implies that the heat transfer efficiency is

augmented by the velocity distortion while, conversely, a

positive m factor weakens the friction force due to viscosity,

in line with intuition.

n

b

w

pc

..Nu

Nu (3)

m

b

w

pcf

f

..

(4)

Equations (5) and (6) summarise the thermal and hydraulic

expressions for oil flow in 2D cooling ducts. However, both

expressions are empirical and [2] specifically emphasised that

m = 0.58 was obtained for flow through a circular pipe; a clear

indication that these values may not be directly applicable to a

transformer cooling duct which is better represented by an

infinite parallel plate model, so further verification is required.

14.03/1

PrRe

/44.2Nu

b

wDL

(5)

58.0

..

b

w

pcf

f

(6)

5 CFD MODELLING

5.1 Nusselt number

As the Nu equation is assumed to take the general form as

n

b

w

bDL

a

PrRe

/Nu (7)

our subsequent work is then to verify the suitability of this

form for Nu in cooling ducts and to identify the constants a, b

and n.

CFD as a numerical approach with much higher

discretisation, is used to calculate a large number of flows in

2D cooling duct models, and heat transfer data can be

extracted. Nusselt number would then be computed from its

definition equation as

k

D

tt

q

k

hDNu

bw

(8)

where heat flux q , thermal conductivity k and hydraulic

diameter D are all known a priori, and the bulk and wall

temperatures, tb and tw can also be extracted. The bulk

temperature tb, expressed by (9), is the energy-average

temperature over the fluid flow domain, and the wall

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temperature tw is the average temperature along the length of

the duct walls [16]. In (9), ρ, Cp, u and t denote the density,

specific heat, fluid velocity and temperature respectively at

the differential element ∂A of the entire duct area As.

s

s

Ap

Ap

b

AuC

AutCt

(9)

5.2 Friction coefficient

From these CFD calculations, the pressure drop between

the two ends of the duct is extracted, and the friction

coefficient f is computed from (10); thus the quantity f/fc.p.

may then be obtained to verify (6).

L

D

U

Pf

22

(10)

5.3 CFD simulations

COMSOL Multiphysics software package was used for the

CFD simulations reported here. As an example, duct geometry

of height 0.005m and length 0.1m from the 22 kV low voltage

(LV) winding of a 250 MVA transformer was constructed.

The winding current is 6561 A and the loss power generated

by per unit length of conductor is 55 W [2]. For this duct

example the ratio of the length against its circumferential

width is only 3% and therefore 2D channel flow model

between infinite parallel plates is suitably applicable for the

geometry.

Boundary conditions were defined as shown in Figure 4 (a).

Constant values of fluid velocity and temperature were

defined at the inlet of the duct, while the pressure at the outlet

was set to 0, i.e. the reference value. A no-slip condition was

applied at the walls (i.e. u = 0) where a heat flux of

6111W/m2, due to the losses, was also prescribed.

A grid independence study was undertaken for mid range

values and a computational grid of 10318 cells was deemed

sufficiently fine to ensure calculation accuracy to an

acceptable degree. Figure 4 (b) illustrates the oil velocity

development along the duct centreline from an individual

CFD calculation (typical geometry, inlet temperature of 40 oC

and inlet velocity of 0.08m/s); the distance from the inlet to

the peak velocity location is the hydraulic entrance length, and

the subsequent decrease is due to the temperature dependent

oil viscosity. As shown in the figure, the COMSOL result was

verified by CFD results calculated using the open source CFD

software, Code_Saturne [17], which indicated an agreement

within 1% error bounds. For laminar flow modelling, CFD has

been proved by practical cases to be highly reliable.

Inlet

(velocity,

temperature)

Outlet

(pressure = 0)

Wall (heat flux)

Wall (heat flux)

Flow direction

(a) Boundary conditions set for CFD simulations.

(b) Development of fluid velocity along duct centreline.

Figure 4 CFD simulation boundary conditions and velocity

results using typical parameter values.

A sensitivity study for key parameters of duct height,

length, inlet temperature and velocity, across an informed

range around typical baseline values [2] as listed in Table 1,

was performed. A number of steps were chosen within the

parameter ranges to form combinations of the parameter

values. For each combination, a data sample was extracted

from the fully converged 2D CFD calculation. The resulting

dataset of 2520 samples was then used to approximate the

parameters in (7) and (4).

6 DERIVATION OF CORRELATION

6.1 Study on Nusselt number

The 2520 CFD samples are used to plot the relationship

between Nusselt number and (L/D)/(Re∙Pr), as depicted in

Figure 5 (a). The four different parameters, duct height,

length, inlet temperature and velocity, govern curve trends

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along different directions as indicated in the figure. For

example, with inlet oil velocity higher than 0.01m/s and duct

height above 0.004m, most samples gather on the left hand

side where (L/D)/(Re∙Pr) is below 0.015. At the highest oil

velocity, 0.16m/s, and the greatest duct height, 0.01m, Nu

reaches to the maximum.

Duct height

Inlet velocity

Inlet temperature

Duct length

Highest inlet velocity

& biggest duct height

Longest duct length

(a) CFD simulated Nu samples.

12

5

(b) Comparison between the samples, fitted equation (11) and

originally proposed equation (5).

Figure 5 Curve fitting results on Nusselt number of flow

between infinite parallel plates.

A range of different equation forms were tested upon the

Nu correlation and the fitness scores are compared in Table 2.

A form which does not include a term of the viscosity ratio

μw/μb can yield a high correlation fitness score, R2 = 0.9871;

although this implies that the impact of viscosity variation

upon Nu is not dramatic, the dispersity of the samples

observed from the figure indicates possibilities to have better

fittings. Table 2 reveals that the introduction of a viscosity

ratio term can improve the correlation fit, while the inclusion

of a constant acts to restrain the error range. The best fit is

then (11), with an error below 1%.

08.3PrRe

/29.1Nu

16.038.0

b

wDL

(11)

On average (11) gives Nu values that are 15% lower than

(5), which is listed at the last row of the table as a comparison

baseline; a detailed comparison between (11) and (5) in Figure

5 (b) illustrates that (11) yields Nu values which match the

samples better than (5). Lower Nu will predict higher winding

temperatures.

6.2 Study on friction coefficient

As for expression (4), the term (μw/μb)m was incorporated

into the formulation approximating friction coefficient f, in

order to account for the temperature dependency of fluid

viscosity. From the same set of CFD results described above,

data samples of f/fc.p. and their corresponding values of μw/μb

were obtained for each of the parametric conditions proposed

in Table 1, so that a similar curve fitting analysis could be

performed; in order to identify a suitable value for the

exponent m.

The CFD predictions of f/fc.p. versus μw/μb are illustrated in

Figure 6. These samples are observed to cluster in a

discontinuous pattern and indeed distinct groups are formed.

When the duct becomes shorter and/or wider, the friction

coefficient values will deviate more from the constant

property fluid scenario. The original expression given by (6) is

also plotted in Figure 6, though clearly a simple form of this

nature is unable to adequately fit the sample distribution.

Consequently, additional dimensionless groups must be

introduced to account for this discontinuity of the samples. As

in common practice, the dimensionless groups Re, Pr and L/D

are added to incorporate the hydraulic, thermal and

dimensional factors into the expression respectively, and thus

a form is proposed as

dD

Lc

f

fm

b

w

pc

PrRe..

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Table 2 Comparison between different Nu expressions.

(Relative error: the relative difference from expression value to sample value.)

Expressions R2

Relative error (%)

Mean error Error range

33.0

PrRe

/45.2Nu

DL 0.9863 3.8 0 – 22.5

06.3PrRe

/60.1Nu

37.0

DL

0.9871 3.4 0 – 13.1

14.034.0

PrRe

/03.2Nu

b

wDL

0.9984 1.3 0 – 25.1

08.3PrRe

/29.1Nu

16.038.0

b

wDL

0.9992 0.7 0 – 11.7

14.03/1

PrRe

/44.2Nu

b

wDL

0.9984 17.8 0.4 – 21.9

Duct height

Inlet temperature

Inlet velocity

Duct length

12

6

Figure 6 Curve fitting results on f/fc.p. of flow between infinite

parallel plates.

Curve fitting was conducted onto this form and (12)

returned an acceptable correlation (R2 = 0.9739). Since the

form is newly proposed, extracted dimensionless group ranges

are listed in Table 3 to give the underlying governing

hydraulic-thermal and dimensional regime.

61.0PrRe17.0

90.055.0

15.037.0

..

b

w

pcD

L

f

f

(12)

Table 3 Ranges of the dimensionless groups.

Dimensionless

groups

Mean

value

Min

value

Max

value

Re 89 1 594

Pr 331 49 1135

L/D 8.9 2.5 25.0

Table 4 compares the performances of the expressions, (12)

and (6). The average error of (12) is around 3%, which is ~10

times lower than that of (6). In Figure 6, the comparison with

the samples reveals that (6) consistently underestimates the

impact of the viscosity variation on the friction coefficient f.

On average, the new equation (12) predicts higher f values

than (6) by 48%. Higher f values imply that it is more difficult

for oil to flow along the ducts.

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Table 4 Comparison between the two f/fc.p. expressions.

Expressions R2

Relative error (%)

Mean error Error range

61.0PrRe17.0

90.055.0

15.037.0

..

b

w

pcD

L

f

f

0.9739 3.1 0.0 – 29.8

58.0

..

b

w

pcf

f

0.4602 30.6 8.6 – 65.7

Moreover, Figure 6 shows that there is a region where μw/μb

< 0.3 and (12) has errors in this region higher than the overall

average error of 3%. An example falling into this region is

when cool oil slowly flows along long ducts (inlet temperature

≤ 20 oC, velocity ≤ 20 mm/s and duct length > 100 mm). Still,

the average error of (12) in this region would be above 15%;

far better than 30% yielded by (6). It implies that one should

be careful when using (12) to design long oil ducts for natural

cooling transformers.

7 EVALUATION OF EMPIRICAL EQUATIONS IN

NETWORK MODEL

The LV winding example from [2] was used to evaluate the

influence of the proposed modifications of the Nu equation in

network modelling. In this test case there are 100 horizontal

ducts in the winding, divided into 5 passes by block washers.

The heat source input was assumed to be entirely constituted

from constant DC loss (Ohmic loss), i.e. not affected by local

temperature of the conductors. Furthermore, minor pressure

losses occurring at junction nodes were neglected in order to

focus upon the influence of the models from parameters Nu

and f.

Calculations of this case were performed with the

TEFLOW, a network model implementation developed in the

UK in the late 1980’s, and the influence of different Nu and f

equations upon the resulting oil flow and temperature

distributions is assessed, as shown in Figure 7. Results from

the original models are regarded as a baseline. While the new

Nusselt number equation does not alter the oil flow rate

distribution among horizontal ducts, the magnitude of winding

temperatures is predicted to take values which are

approximately 3 degrees higher than those of the original

model. This follows logically as a smaller value of Nu will

result in a lower heat transfer efficiency. Otherwise, the

qualitative variation of the winding temperature distribution is

seen to remain largely unaffected.

(a) Comparison between oil mass flow distributions from

using different expressions.

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(b) Comparison between maximum disc temperature

distribution from using different expressions.

Figure 7 Comparison between resulting distributions from

using different expressions.

Figure 7 (a) indicates that a more uniform oil flow

distribution is predicted by the newly derived equation for f;

this is because the new equation calculates more friction on

faster oil flows than slow ones, and thus the flows in the

vicinity of block washers are constrained and the flow

distribution then becomes slightly evener. However, the effect

is not dramatic; Figure 7 (b) reveals that the reduction of the

hot-spot temperature resulting from the newly derived

equation for f is around 0.1 oC compared to the original one.

The low impact of friction coefficient in this particular case is

because μw/μb values lie within the range 0.5 ~ 0.6, and the

average f is 18% higher than the original model, still relatively

small as compared to the mean difference of 48% in the full

sensitivity study range. In another word, the frictional pressure

loss at cooling ducts of this case is 18% higher. On the other

hand, if we consider the relative pressure drop over the entire

winding, which can be computed by integrating a complete oil

duct routine from the inlet to the outlet minus the static

pressure due to oil gravity, the new Nu equation does not

affect, but the new f equation (12) predicts a relative pressure

drop 6% higher than the original equation (6), resulting into a

value of 722 Pa for this particular design.

For forced oil cooling mode, an accurate prediction on the

winding pressure drop is of importance for determining a

pump to supply the required inlet oil flow, and logically, a

higher pressure drop requires a bigger pump to guarantee the

same oil flow. For natural oil mode, a higher winding pressure

drop means that it is more difficult for the cooling oil flow

upwards through the winding structure.

8 CONCLUSIONS

Accurate transformer thermal modelling is of significance

for investigating convective heat transfer phenomena in

winding cooling ducts and predicting hot-spot temperature

and its location. The Nusselt number and friction coefficient

expressions employed in network models are often empirical

and their validities need to be verified.

By employing a detailed parameter study using a large set

of 2D CFD calculations, functional dependence of the result

data was analysed and curve fitting then applied to obtain new

equations for both Nusselt number and friction coefficient.

These equations are presented and compared with the

corresponding equations from [2]. Using the LV winding from

[2] as an example, the evaluation reveals that, compared to the

original model, the newly proposed equations predict an

increase in winding temperature as a consequence of lower

Nusselt number values along horizontal oil ducts. In

particular, the new f equation, (12), predicts a slightly more

uniform oil flow rate distribution across the ducts, and also

calculates a higher pressure drop over the entire winding.

Experiments using non-intrusive flow measurement facilities

such as Particle Image Velocimetry (PIV) are planned to be

carried out for validating the oil duct CFD models. With the help

of PIV measurement, flow velocity distributions across the oil

channels can be obtained with details and accuracy, and it would

then be possible to assess the CFD results in a more profound

way.

An accompanying paper will address an improved

modelling of the pressure loss at the junction nodes (JPL), and

evaluate their impacts on network modelling.

ACKNOWLEDGMENT


Engineering and Physical Sciences Research Council

(EPSRC) Dorothy Hodgkin Postgraduate Award (DHPA) and

National Grid. Due appreciation should be given to our MSc

project student Mr Joseph Awodola who carried out the initial

investigation of the idea in this paper under the supervision of

the authors.

REFERENCES

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11


[1] Tanguy, A., Patelli, J. P., Devaux, F., Taisne, J. P., and

Ngnegueu, T.: ‘Thermal performance of power

transformers: thermal calculation tools focused on new

operating requirements’. Session 2004, CIGRE, rue

d'Artois, Paris, 2004

[2] Oliver, A. J.: ‘Estimation of transformer winding

temperatures and coolant flows using a general network

method’. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp.

395-405

[3] Allen, P. H. G., and Finn, A. H.: ‘Transformer winding

thermal design by computer’. IEE Conf. Publ., 1969, vol.

51, pp. 589–599

[4] Simonson, E.A., and Lapworth, J.A.: ‘Thermal

capability assessment for transformers’. Second Int.

Conf. on the Reliability of Transmission and Distribution

Equipment, 1995, pp. 103-108

[5] Del Vecchio, R.M., Poulin, B., Feghali, P. T., Shah, D.

M., and Ahuja, R.: ‘Transformer Design Principles: With

Applications to Core-Form Power Transformers’

(Gordon and Breach Science Publishers, 2001)

[6] Takami, K. M., Gholnejad, H., and Mahmoudi, J.:

‘Thermal and hot spot evaluations on oil immersed

power Transformers by FEMLAB and MATLAB

software's’. Proc. Int. Conf. on Thermal, Mechanical and

Multi-Physics Simulation Experiments in

Microelectronics and Micro-Systems, EuroSime 2007,

2007, pp. 1-6

[7] Kranenborg, E. J., Olsson, C. O., Samuelsson, B. R.,

Lundin, L-A., and Missing, R. M.: ‘Numerical study on

mixed convection and thermal streaking in power

transformer windings’. 5th European Thermal-Sciences

Conference, The Netherlands, 2008

[8] Wu, W., Wang, Z.D., and Revell, A.: ‘Natural

convection cooling ducts in transformer network

modelling’. Proceedings of the 16th International

Symposium on High Voltage Engineering, South Africa,

2009

[9] Zhang, J., and Li, X.: ‘Coolant flow distribution and

pressure loss in ONAN transformer windings. Part I:

Theory and model development’. IEEE Transactions on

Power Delivery, 2004, vol. 19, pp. 186-193

[10] Wu, W., Revell, A., and Wang, Z.D.: ‘Heat Transfer in

Transformer Winding Conductors and Surrounding

Insulating Paper’, Proceedings of The International

Conference on Electrical Engineering 2009, Shenyang,

China, 2009

[11] Rosenhow, W.M., Cho, Y.I., and Hartnett, J.P.:

‘Handbook of heat transfer’ (New York: MCGraw-Hill,

1998, 3rd edn.)

[12] Rosenhow, W.M., and Hartnett, J.P.: ‘Handbook of heat

transfer’ (New York: MCGraw-Hill, 1973)

[13] Knudsen, J.G., and Katz, D.L.: ‘Fluid dynamics and heat

transfer’ (New York: McGraw-Hill, 1958)

[14] Muneer, T., Jorge, K., and Thomas, G.: ‘Heat transfer : a

problem solving approach’ (London: Taylor & Francis,

2003)

[15] Kreith, F., and Bohn, M. S.: ‘Principles of heat transfer’

(New York: Harper & Row, 1986, 4th edn.)

[16] Incropera, F.P., and Dewitt, D.P.: ‘Fundamentals of heat

and mass transfer’ (New York: John Wiley & Sons, 2002,

5th edn.)

[17] Archambeau, F., Mehitoua, N., and Sakiz, M.:

‘Code_Saturne: a finite volume code for the computation

of turbulent incompressible flows – industrial

applications’. International Journal on Finite Volumes,

2004


97

4.2 Paper 4

CFD Calibration for Network Modelling of Transformer Cooling Flows – Part

II Pressure Loss at Junction Nodes

W. Wu, Z.D. Wang, A. Revell and P. Jarman

2011


Accepted

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ISSN 1751-8660

CFD Calibration for Network Modelling of Transformer Cooling

Flows – Part II Pressure Loss at Junction Nodes

W. Wu1, Z.D. Wang1, A. Revell2 and P. Jarman3 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK.

2 School of Mechanical, Aerospace and Civil Engineering, University of Manchester, Manchester, M13 9PL, UK.



Abstract — Two important factors affecting the characteristics of ‘hot-spot’ inside an oil cooled transformer winding are the

total amount of oil being supplied into the winding and its flow distribution across the discs arrangement. The latter is

unavoidably related to the hydraulic network of winding ducts where oil flow is combining or dividing at duct junctions. The

expressions describing junction pressure loss (JPL) often contain a significant number of empirical parameters obtained by

limited experimental tests. Applicability of these parameters should therefore be carefully verified for the use in network

modelling; this is the objective of this paper. Computational Fluid Dynamics (CFD) simulations have been performed upon a

large set of 2D junction models, based on which new values of the empirical parameters were then obtained specifically for

winding oil ducts. A validation test showed that the newly proposed parameter values give better performance than the currently

used ‘off-the-shelf’ values.

1 NOMENCLATURE



fluid duct

H = Height of fluid duct

K = Junction pressure loss coefficient


Nu = Nusselt number

Q = Volume flow rate of fluid duct

R2 = The square of the correlation between the

response values and the predicted response

values



ν = Kinematic viscosity of fluid


ΔP = Pressure drop between the inlet and the outlet

of the duct

ΔPw = Pressure drop between the inlet and the outlet

of the winding

Subscripts

1 Value at the duct of the straight-through

direction

2 Value at the duct of the branch direction

m Value at the common duct

1→m Value for combining junction, from duct 1 to

m


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m

m→1 Value for dividing junction, from duct m to 1


Acroynms/Shorthand

2D 2 dimensional

3D 3 dimensional

BOT Bottom oil temperature

CFD Computational fluid dynamics

HSF Hot-spot factor

HST Hot-spot temperature


LV Low voltage

MWT Mean winding temperature

TOT Top oil temperature

2 INTRODUCTION

Temperatures represent the most limiting factors for power

transformers’ loading operations, and the maximum

temperature of winding conductors, so-called ‘hot-spot’, has

to be under certain limits for it affects insulation ageing and

transformer lifetime. In the attempt to accurately predict the

hot-spot inside a transformer, a range of numerical modelling

approaches have been developed, which can generally be

categorised as either ‘network models’ [1-4], or methods

which incorporate a degree of Computational Fluid Dynamics

(CFD) [5-7]. In comparison to CFD methods which require

unreasonably long computation time from the thermal design

viewpoint, network models can provide quick and convenient

numerical approximations which are often easier for industries

to use as design tools.

However, the suitability of the assumptions and the

empirical expressions applied in network modelling has to be

ascertained [8-10] to guarantee the calculation accuracy. Part I

of this series of paper attempted to evaluate the expressions

for Nusselt number (Nu) and temperature affected friction

coefficient (f), and to propose calibrated equations by CFD

simulations [10]. In this accompanying paper, the currently

employed empirical junction pressure loss (JPL) equations

will also be evaluated through CFD simulations, with a view

to proposing more consistent expressions for constructing

accurate and reliable network models.

Figure 1 (a) pictorially shows the junction nodes in network

model geometry. According to the flow behaviour at the

junctions, the junction nodes are commonly classified into two

types: combining and dividing nodes; denotation for both is

prescribed in Figure 1 (b) and (c) respectively. Literally, in a

combining scenario the straight-through direction flow, flow 1,

is combined with the branch direction flow, flow 2, and a

common flow forms after the junction. On the other hand, a

dividing junction is defined when a common flow divides at

the junction into two separated flows, i.e. flow 1 and 2 along

the straight-through direction and the branch direction

respectively. In both types the fluid mixing which takes place

at the junction results in a pressure loss, namely junction

pressure loss. According to [4], the pressure loss at a junction

in a transformer winding becomes of equal or even greater

magnitude than the frictional pressure loss occurring at an oil

duct, especially for the short vertical ducts. As junction

pressure loss plays an important role in governing the oil flow

distribution, the expressions for describing JPL in network

models must be carefully identified.

Junction

nodes

oil

2

m

1

(b) A combining node.

1

m

2

(a) Junction nodes in a network

model.

(c) A dividing node.

Figure 1 Junction nodes in a network model and denotations

for the flows (combining and dividing scenarios).

3 ANALYSIS ON PRESSURE LOSSES IN NETWORK

MODELS

When viscous fluid flows through a straight duct, a viscous

force acts at the duct wall to resist the fluid moving, which

incurs a frictional pressure loss along the duct. This frictional

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pressure loss depends on the Reynolds number of the flow, Re

= UL/ν, however for sufficiently low Re, it implies a laminar

flow and can be expressed by Darcy-Weisbach Equation as

2

4 2U

D

fLP

(1)

where f = 24/Re is often called friction coefficient.

Besides frictional pressure losses occurring at horizontal

ducts, there are additional pressure losses in transformer

windings due to the change of oil flow directions when these

flows combine or divide at junctions, which are referred as

junction pressure loss in this paper. At a junction, energy is

lost due to the mixing or re-circulating or both flow regimes;

junction pressure loss is actually a reflection of this energy

loss. As an example, when a slower flow is combined into a

faster one, the resulting flow velocity shall reduce and a

pressure loss has occurred. In contrast, when a faster flow is

combined into a slower one, the resulting flow velocity shall

increase which means it has gained energy and

mathematically, a negative pressure loss has occurred [11].

Figure 2 gives symbolic representations of the frictional

and junction pressure losses around junctions, which

correspond to Figure 1 (b) and (c) respectively. ∆P1, ∆P2 and

∆Pm are referred to the frictional pressure losses expressed by

(1). ∆P1→m, ∆P2→m, ∆Pm→1 and ∆Pm→2 are junction pressure

losses occurring at the flow turning paths 1 to m, 2 to m, m to

1 and m to 2 respectively, and they are added accordingly onto

the two branch paths before or after the junction. It is a

common practice [12] to represent the JPL with the product of

a coefficient and the velocity head (ρU2/2) as in (2). Thus

K1→m, K2→m, Km→1 and Km→2 in (2) are named as JPL

coefficients for different junction pressure loss types.

2

m

1

∆Pm

∆P1→m

∆P2

∆P1

∆P2→m

(a) Combining junctions.

2

1

m

∆Pm

∆Pm→1

∆P2

∆P1

∆Pm→2

(b) Dividing junctions.

Figure 2 Frictional and junction pressure losses in the vicinity

of junction nodes (combining and dividing scenarios).

2

2

2

2

2

2

22

2

1

11

2

2

22

2

1

11

UKP

UKP

UKP

UKP

mm

mm

mm

mm

(2)

The JPL coefficients K can be derived analytically by

considering the conservation of momentum as introduced in

[12]. After obtaining the analytical expressions, [12] used

experimental results to obtain correlations between the four

JPL coefficients K and Reynolds number (Re1 and Re2) as

well as the velocity dispatch ratio at the junction (U1/Um). In

the experiments, SAE No. 10 cylinder oil flowing through 3/4

inch standard black iron pipes and galvanised screwed tees

was used to observe junction pressure loss, and the pipes were

sufficiently long, 590 diameters, to be consistent with the

assumption that the flow can re-gain hydraulically fully-

developed status after the junction disturbance. Based on the

experimental data samples published in [12], equation (3) was

then derived in [1] for quantifying the JPL coefficients.

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2

2

1

2

11

1

2

2

1

2

11

1

Re

7000

Re

10002.1176.1965.10

Re

7300

Re

10002.1176.1965.10

m

mm

m

m

mm

m

K

U

U

U

UK

K

U

U

U

UK

(3)

Equation (3) basically relies on the assumptions which are

made by analysing the experimental results presented in [12],

which include

For combining scenarios, K1→m is related to the

velocity ratio U1/Um [1, 12]. Oppositely, K2→m is

largely unaffected by the flow combination, because at

a low Reynolds number below 1000, the branch flow is

directed by the straight-through direction flow and

gradually and smoothly turns around the bend with a

minimum of interruption, and as such the loss is

stabilised [12].

So is for dividing scenarios, i.e. Km→1 is velocity ratio

dependent and Km→2 is only related to Re2 [12].

These assumptions and the expression formats of (3) are

followed in this paper.

Other literature which discussed the issue of junction

pressure loss are [4] and [13]. It was reckoned in [4] that K1→m

should be independent of U1/Um and therefore (4) should be

used instead. The work of [13] included an expression for

coefficient Km→2, (5), in which the volume flow ratio Q2/Qm is

used instead and Km→2 is irrelevant to Reynolds number.

Unfortunately, [13] did not give corresponding expressions for

the other three coefficients, K1→m, K2→m and Km→1, and the

only equation of (5) cannot be tested independently in

network models.

1

1Re

2100

mK (4)

2

22

2944.1117.00.1

mm

mQ

Q

Q

QK (5)

4 CFD MODELLING

Rather than extracting the empirical JPL coefficients from a

set of experimental data as in [12], this paper uses sets of

numerical CFD simulations to obtain the dataset of pressure

losses across a range of different parameters, corresponding to

variation in geometry and flow conditions of transformer

windings. Before proceeding to use the numerical datasets to

optimise the JPL coefficients, CFD simulations were first

undertaken on the case exactly as described in [12] to validate

the CFD modelling methodology, and since the experiments

used circular pipe junctions, 3D rather than 2D simulations are

necessary for the validation.

4.1 Validations of CFD methodology

A numerical mesh was created corresponding to the

geometry described in [12]. The modelling process can be

clarified into the following steps:

a. Construct a 3D geometry model of circular pipes,

illustrated by Figure 3.

b. Mesh the geometry with a sufficiently fine grid; the

proper order of fineness was obtained by sensitivity

studies so as to guarantee the accuracy of simulation

results.

c. Configure the boundary conditions and the CFD solver.

As an example, Figure 3 shows the boundary

configuration for a combining junction. Fully

developed velocity profiles with average values U1 and

U2 were prescribed at the inlets respectively, and a

pressure reference value, 0, was assigned to the outlet

boundary; the rest are all configured as wall boundaries.

d. Run CFD solver to obtain the converged solution of

the problem.

e. Extract the pressure drop results between the inlets and

the outlet. In Figure 3, the pressure drops from duct

end 1 to m and 2 to m are extracted from the CFD

results. JPL are then calculated by subtracting the

frictional losses along the ducts from these obtained

pressure drops.

COMSOL multiphysics software was used to perform CFD

calculations. By modelling the combining junction of Figure 3,

fixing the ratio U2/U1 = 1/3, and varying U2 from 0.04 m/s to

0.19 m/s (the corresponding Re2 = 35 ~ 170, i.e. the flow

remains laminar) [12], a set of simulations was undertaken.

The correlation of K2→m against Re2 was extracted and shown

in Figure 4, together with the experimental results presented in

[12] and the K2→m expression in (3) for comparison. On

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average, the relative difference between the CFD simulation

samples to the results calculated from (3) is 4%. Equation (6)

is deduced from these CFD samples by curve fitting, and the

difference between the constants in (6) and (3) is only 1%,

which confirms that CFD methodology is as good as

experimental approach.

Inlet (U1)

Outlet

(pressure = 0)

Wall

Flow directionWall

Inlet

(U2)

Lm

L1

L2

H1

H2

Figure 3 Denotations and boundary conditions for a

combining junction model.

2

2Re

7377

mK (6)

Figure 4 Correlations of K2→m versus Re2 on a circular

pipeline model.

4.2 CFD simulations

Literature [1, 4] used the experimental test results published

in [12] for deriving the JPL coefficient expressions which are

currently used in network modelling, yet the tests were based

on circular pipeline models. In contrast, oil ducts in disc-type

windings are axial symmetric, which are formed by the space

between stacked parallel discs (horizontal ducts) or between

the discs and inner or outer pressboard cylinders (vertical

ducts); because the circumferential width of the oil ducts is

significantly longer than their radial length, 2D duct flow

models between infinite parallel plates are sufficient

approximations. Following the experiences in [1, 4, 6], 2D

models are applied in this paper. Notwithstanding the model

outlined by Figure 3, the ducts 1, 2 and m were modelled

specifically as 2D channels instead of 3D circular pipelines;

the boundary definitions stay the same as described in Section

4.1.

In the 2D model, the duct heights H1 = 0.015m and H2 =

0.005m, which are the heights of the vertical and the

horizontal ducts of the low voltage (LV) winding example in

[1]. Although H1 : H2 = 3:1, the JPL expressions derived from

the model can also be applied for other dimensions, as long as

the ratio H1 : H2 ≥ 1 [11].

For a combining junction, the duct lengths L1 = 0.0056m,

L2 = 0.05m [1] and Lm = 0.12m; Lm must be adequately long

because the merged flow should re-gain fully developed state

before reaching the zero pressure outlet. As for a dividing

model, Lm = 0.0056m, instead L1 should be long enough to

allow the flow to fully develop after the junction separation.

This geometry was meshed afterwards with a density of ~16

cells per mm2; as this mesh order could guarantee the required

calculation accuracy.

Table 1 lists the variation ranges of velocity U2 and

velocity ratio U1 : Um; the ranges are basically from Part I of

this series of papers [10]. The principle work of this paper is a

parametric study using a large set of CFD simulations across

the parameter ranges. For each combination in Table 1, a fully

converged 2D CFD calculation was performed and the data

sample was produced. Consequently, two resulting datasets,

each comprising 63 samples, were summarised to approximate

the JPL coefficients for both combining and dividing junctions

respectively.

Table 1 Typical parameters for junction nodes of transformer

oil ducts.

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Parameter name Variation

range

Variation

steps

U1 : Um 0.2 → 0.8 7 steps

U2

(m/s) 0.01 → 0.16 9 steps

4.3 Derivation of correlation

The obtained dataset for both combining and dividing

scenarios are shown in Figure 5. Curve fitting was undertaken

upon these CFD samples, and the correlations of the JPL

coefficients, K, were then studied. By following the forms of

(3), four expressions have been derived as listed in (7).

(a) K1→m versus Re1 at combining scenario.

(b) K2→m versus Re2 at combining scenario.

(c) Km→1 versus Re1 at dividing scenario.

(d) Km→2 versus Re2 at dividing scenario.

Figure 5 Correlations between JPL coefficients K and

Reynolds number at both combining and dividing scenarios.

2

2

1

2

11

1

2

2

1

2

11

1

Re

276

Re

1000735.2337.3079.1

Re

72

Re

1000419.1729.1580.0

m

mm

m

m

mm

m

K

U

U

U

UK

K

U

U

U

UK

(7)

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Equation (7) has lower constant coefficient values than (3)

by almost one order of magnitude; this means for oil ducts the

junction pressure losses yielded by (3) which is based on

circular pipes would unrealistically govern the oil flow

distribution than frictional pressure losses. In view of this,

next section will focus on evaluating the representation of

junction pressure loss to show that (7) better represents the

reality than (3).

In (3), the expressions for K1→m and Km→1 are identical and

K2→m and Km→2 use similar constants, which means that the

junction pressure losses at a combining junction and a

dividing one are almost equivalent. It implies that the JPLs at

both of the inner and outer vertical oil ducts of a winding are

symmetrical. However, equation (7) reveals that it is relatively

easier for oil flows to combine than to split. Asymmetrical oil

flow distribution might be predicted from this asymmetrical

equation.

Moreover, in (7) K1→m and Km→1 are from curve fitting

which include the impact of the velocity ratio, U1/Um; both

fittings yielded high correlation scores, R2 > 0.97. K2→m and

Km→2 expressions however represent the average orders of the

JPL across the laminar zone [12]. As a matter of fact, sample

variations from the average curves are observed in Figure 5 (b)

and (d); the upper bound of the variation range is at the

velocity ratio U2 : Um = 0.2 and the lower bound U2 : Um = 0.8.

It is actually possible to obtain velocity ratio dependent JPL

equations for both K2→m and Km→2 with better fitting scores.

However, those fitted equations would practically prevent

network models from converging and yielding any calculation

results; this could be the reason why [1, 4] used the velocity

independent formats for K2→m and Km→2. Tests were therefore

undertaken to evaluate the impact of the variation bands upon

network modelling results. By using the typical LV winding

example in [1], the upper bound at U2 : Um = 0.2 and the lower

bound at U2 : Um = 0.8 were curve fitted and applied for K2→m

and Km→2 coefficients, and it was found that the upper bound

value slightly decreases the average winding and hot-spot

temperatures, whereas the lower bound increases them.

However the resulting difference was so minor that only less

than 1% for the average winding temperature and less than 2%

for the hot-spot temperature were found. This test indicates

the high reliability to use (7) for calculating K2→m and Km→2 to

be used in network models.

5 EVALUATION OF EMPIRICAL EQUATION IN

NETWORK MODEL

The disc-type winding model of one-pass and its

experimental and CFD simulation results from [14] were used

to validate (7). There are 8 discs in the winding pass example;

the pass starts from the block washer equipped just below the

bottom disc and thus there are 8 horizontal ducts in total. The

dimensions are briefly described in Table 2. In order to be

consistent with [14], this paper neglects the heat source input

at discs in order to focus on the hydraulic aspect. The model

was calculated with the network model implementation,

TEFLOW, and different sets of JPL coefficient expressions,

(3), (4) and (7), were tested.

Table 2 Dimensions of the winding pass example in [14].

Parameter Value

Height of vertical oil ducts

(mm) 5.0

Height of horizontal oil ducts

(mm) 4.22

Height of discs

(mm) 9.4

Radial length of discs

(mm) 90.1

Figure 6 shows the relationship between the pressure drop

over the pass and the rate of oil flow supplied at the inlet. This

is often defined as the hydraulic characteristic curve of a

winding design. First of all, the model without including

junction pressure losses predicts lower pressures than the

experiment results, which implies the necessity to incorporate

JPL expressions; the results yielded by the existing two JPL

models, both (3) and (3) & (4), show similarly unrealistically

higher pressures, and finally (7) produced a much better match

with the experimental results as well as the CFD predictions.

It is of significance to derive an accurate hydraulic

characteristic curve for the winding structure at the thermal

design stage, since this curve will then affect the choice of oil

cooling pump.

Figure 7 shows the different oil flow rates distributed

across the eight horizontal oil ducts in the pass, corresponding

to the four JPL models and the CFD simulation results

presented in [14]. Figure 7 (a) illustrates almost symmetrical

flow distribution profiles that are irrelevant to the inlet oil

flow velocity ranging from 2 to 25 L/min, which are

corresponding to around 50 to 625 mm/s. It shows that the two

original JPL models do not affect the flow distributions. On

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8


the other hand, the newly proposed JPL model, equation (7),

predicts non-uniform flow distributions which are sensitive to

different inlet oil flow velocities and this is similar to the

results calculated by CFD simulations [14] shown as the dash

curves in Figure 7 (b).

0

100

200

300

400

500

600

0 5 10 15 20 25

Rel

ati

ve

pre

ssu

re d

rop

ov

er t

he

pa

ss,

Pa

Oil flow, L/min

No JPL Experimental result [14]

CFD result [14] Eqn. (7)

Eqn. (3) [1] Eqn. (3) & (4) [4]

Figure 6 Pressure drop over the entire pass.

(a) Relative flow rate without JPL included and with JPL

equations [1, 4] applied.

(b) Relative flow rate by CFD simulations in [14] and

with equation (7).

Figure 7 Oil flow rate distribution across the horizontal ducts.

In Figure 7 (a), the profiles predicted by (3) are

symmetrical because the K1→m and Km→1 expressions in this

JPL model are exactly the same, and thus the JPLs added onto

the inner and outer vertical ducts are then the same. Although

as previously addressed, equation (3) causes higher pressure

loss upon the pass than the measured one, this junction

pressure loss equation does not affect the flow distribution

profile and are even overlapped with the calculation results

without the consideration of JPL. The application of (4) for

K1→m does bring asymmetry but only to a tiny extent. In brief,

equation (3) and (4) do not show any trend sensitivity of flow

distribution for low to high inlet oil flow rates.

In Figure 7 (b), at higher oil flow rates, e.g. 25 L/min, more

oil will tend to flow through the upper half of the pass,

whereas at low flow rates, more oil tends to go through the

lower half. This is logical since fast oil flow will easily reach

the upper half, being blocked by the washer and then turning

its direction to the upmost horizontal duct. In contrast, the

CFD results in Figure 7 (b) are severely less uniform. CFD

predicts that much more oil flow is distributed to the top ducts,

irrespective of the flow rate. At the high flow rate of 25 L/min,

inversely directed flow even occurs at the 2 bottom ducts as it

is seen that the oil velocity is negative. This could be an

implication of internal recirculation phenomena happening at

extremely high oil velocities, and such recirculation

phenomena have also been observed by other CFD study

cases.

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Obviously there are deviations exiting when comparing

flow distributions from network and CFD modelling in detail,

nevertheless the improved JPL equations (7) could capture the

apparent trend sensitivity of flow distribution for low to high

inlet oil flow rates, while the old equations (3) and (4) showed

nothing related to this. From this aspect an incremental

forward progress has been made. Moreover, neither of the

exact patterns predicted by (7) or CFD simulations has been

validated by experiments due to the difficulties in measuring

flow distributions [14], therefore non-intrusive flow

measurement facilities such as Particle Image Velocimetry

(PIV) are planned to be carried out in order to verify either

model’s closeness to the reality. It is hoped that with the help

of PIV measurement, flow velocity distributions across the oil

channel regions can be obtained with details and accuracy, it

would then be possible to assess the results in Figure 7

although the acceptable agreement on the global pressure

drops in Figure 6 has shown the progress achieved in this

paper.

6 CONCLUSIONS

An accurate model to assess the pressure losses at oil duct

junctions is of great importance for determining the hydraulic

characteristics of windings and predicting flow distributions

across horizontal ducts. Following the work of Part I, which

has proposed modifications on Nusselt number and friction

coefficient expressions [10], this paper studied the JPL

expressions in network models.

By performing CFD simulations on a large set of 2D oil

duct junction models instead of conducting experimental tests,

a detailed parametric study was undertaken for identifying

JPL coefficient correlations. With the help of curve fitting on

the CFD results, new constant values for JPL coefficient

expressions were finally obtained and then compared with the

currently used ones from [1, 4].

The expressions have been evaluated with the network

model implementation TEFLOW on a winding pass example

from [14]. The results indicate that the presence of JPL will

rise the hydraulic pressure needed to supply an oil flow rate

into the pass; however the ‘off-the-shelf’ JPL models, i.e.

equation (3-4) from [1, 4], yield unrealistically high pressure

losses due to the fact that they are derived from circular

pipeline junctions rather than transformer winding duct

junctions. On the other hand, the prediction given by the

newly obtained equation (7) could provide a better match to

the experimental results. Unlike JPL models (3-4) which

predict symmetrical oil flow distribution patterns across the

pass that are identical irrespective of inlet oil flow rates,

equation (7) reveals that more oil will tend to flow through the

upper half of a pass if at a high inlet oil flow rate.

Because of the exaggerated junction pressure loss the

network model with (3) or (3-4) will prescribe an oil pump

bigger than that really required, and the extra oil flow supplied

can reduce the winding temperature. However, the

overestimated Nusselt number in [1] would underestimate the

winding temperature. In consequence, both effects from JPL

and Nu are adverse and probably cancel each other to some

extent, so the network model presented in [1] might give

reasonable results.

A possible limitation of (7) might come from the fact that

short vertical oil ducts are designed for windings. Vertical

duct lengths are so short that the upward oil flow just

departing from a junction will shortly arrive at the next

junction, which implies that it may be difficult for the vertical

oil flow to re-achieve fully developed state in the real scenario.

Future CFD study on the interaction between neighbouring

junctions should therefore be conducted.

ACKNOWLEDGMENT


Engineering and Physical Sciences Research Council (EPSRC)

Dorothy Hodgkin Postgraduate Award (DHPA) and National

Grid. The authors appreciate the technical support given by

Professor Hector Iacovides from School of Mechanical,

Aerospace and Civil Engineering, University of Manchester.

Due appreciation should also be given to our MSc project

student Mr Qi Li who carried out the initial investigation of

the idea in this paper under the supervision of the authors.

REFERENCES




395-405




Equipment, 1995, pp. 103-108


M., and Ahuja, R.: ‘Transformer Design Principles: With

Applications to Core-Form Power Transformers’


www.ietdl.org

10




Theory and model development’. IEEE Transactions on



Ngnegueu, T.: ‘Thermal performance of power


operating requirements’. Session 2004, CIGRE, rue



‘Thermal and hot spot evaluations on oil immersed


software's’. Proc. Int. Conf. on Thermal, Mechanical and



2007, pp. 1-6


Lundin, L-A., and Missing, R. M.: ‘Numerical study on


transformer windings’. 5th European Thermal-Sciences


[8] Wu, W., Wang, Z.D., and Revell, A.: ‘Natural


modelling’. Proceedings of the 16th International


2009

[9] Wu, W., Revell, A., and Wang, Z.D.: ‘Heat Transfer in


Insulating Paper’, Proceedings of The International


China, 2009

[10] Wu, W., Wang, Z.D., Revell, A., Iacovides, H., and

Jarman, P.: ‘CFD calibration for network modelling of

transformer cooling oil flows – Part I Heat transfer in oil

ducts’, IET Electric Power Applications, 2011, to be

published

[11] Blevins, R. D.: ‘Applied Fluid Dynamics Handbook’

(New York: Van Nostrand, 1984)

[12] Jamison, D. K., and Villemonte, J. R.: ‘Junction losses in

laminar and transitional flows’. J. Am. Soc. Civ. Eng.

1971, 97, (HY7), pp. 1045-1061

[13] Yamaguchi, M., Kumasaka, T., Inui, Y., and Ono, S.:

‘The flow rate in a self-cooled transformer’. IEEE

Transactions on Power Apparatus and Systems, 1981,

vol. PAS-100, pp. 956-963

[14] Weinläder, A., and Tenbohlen, S.: ‘Thermal-hydraulic

investigation of transformer windings by CFD-

Modelling and measurements’. Proceedings of the 16th

International Symposium on High Voltage Engineering,

South Africa, 2009


98


99

Chapter 5 Comparison between network model and

CFD predictions

5.1 Paper 5

Prediction of the Oil Flow Distribution in Oil-immersed Transformer Windings

by Network Modelling and CFD

A. Weinläder, W. Wu, S. Tenbohlen and Z.D. Wang

2011


Provisionally accepted

www.ietdl.org

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ISSN 1751-8660

Prediction of the Oil Flow Distribution in Oil-immersed Transformer

Windings by Network Modelling and CFD

Andreas Weinläder1, Wei Wu2, Stefan Tenbohlen1 and Zhongdong Wang2 1 Institute for Power Transmission and High Voltage Technology, University of Stuttgart, Stuttgart, Germany (e-mail:

[email protected]) and (e-mail: [email protected]).

2 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK (e-mail:

[email protected]) and (e-mail: [email protected]).

Abstract — In the context of thermal performance and thermal design, it is of significance to predict the magnitude and the

location of the ‗hot-spot‘ temperature inside a power transformer. In the attempt to accurately predict this hot-spot in an oil-

immersed transformer, various numerical modelling approaches have been developed for calculating the cooling oil flow

distribution, which are generally categorised as either ‗network models‘ or the methods which incorporate forms of

Computational Fluid Dynamics (CFD). In network modelling, the complex pattern of oil ducts and passes in a winding is

approximated with a matrix of simple hydraulic channels, where analytical expressions are then applied to describe oil flow and

heat transfer phenomena. On the other hand, CFD models often adopt discretisations of much higher fineness, which can be

expected to offer a higher order of accuracy but also comes with a large increase in the required computational resources. In

order to compare both modelling approaches, the network model implementation TEFLOW and a commercial CFD package,

ANSYS-CFX, were applied on a typical ―zigzag‖ oil channel arrangement of a disc type winding to predict oil flow distribution

and disc temperatures; experiments on hydraulic models have also been performed to validate the models. The principle work of

this paper is then comparing the results and concluding recommendations to industrial practices.

1 NOMENCLATURE


dp = Thickness of insulating paper


fluid duct

k = Thermal conductivity of transformer oil


Nu = Nusselt number

Pr = Prandtl number

q = Heat flux from winding to fluid duct


tb = Bulk temperature of fluid duct

tc = Temperature of winding conductor

tw = Wall temperature of fluid duct

T = Absolute temperature


ΔP = Pressure drop between the inlet and outlet of

the duct

μ = Dynamic viscosity of fluid


Subscripts

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cond Value of heat conduction

conv Value of heat convection

b Value at bulk temperature

c Value at winding conductor

w Value at wall temperature

1 Value at the duct of the straight-through

direction of a junction

2 Value at the duct of the branch direction of a

junction

m Value at the common duct of a junction


m


m



Acroynms/Shorthand


HTC Heat transfer coefficient


LV Low voltage

NM Network modelling

2 INTRODUCTION

Power transformers are key and expensive components in

electric system networks. To avoid failure and ensure

continual power supply, the thermal management of a power

transformer is critical in controlling its ageing due to high hot-

spot temperatures that degrade insulation materials, finally

causing electrical failure. Thereby, accurate thermal

assessment is of significance for both design procedure in

manufacturers and asset management policy making in

utilities [1]. In particular, large power transformers are

generally cooled by natural or forced oil flow, and as such for

these oil-immersed transformers, improved understanding of

the oil flow distribution across the oil ducts inside transformer

windings is meaningful to avoid localised oil starvation and

hot-spot temperatures. Commonly, the cooling oil flows up

from the bottom to the top of a winding; however the hot-spot

is not always found on the top-most winding disc, due to, in

part, the effect of a non-uniform oil flow distribution [2].

Numerical modelling has been used to predict the oil flow

and hot-spot for over 40 years [3]. During the period, two

categories of numerical approaches were developed, which are

‗network modelling‘ such as TEFLOW (developed in the UK

in the late 1980‘s) [2, 4-7], and methods which incorporate

Computational Fluid Dynamics (CFD) [1, 8-11]. Generally,

with the help of much higher fineness of the discretisation,

CFD simulations can be expected to provide more detailed

results but meanwhile, with a large increase in the required

computational resources. In comparison to CFD, network

modelling however provides a fast solution which is often

more convenient for industry to use. In addition, a large range

of parameters can be tested with this tool for relatively low

computational effort, when only critical temperatures such as

hot-spot are required and a high level of local

flow/temperature information is not really necessary.

The objective of this paper is using a same winding pass

design as an example to compare the two different numerical

approaches with the experimental results; a pass is defined as

the section of a winding between two adjacent oil block

washers. The differences between the results from them would

provide recommendations for those who are choosing thermal

analysis tools for oil-immersed transformers.

3 DIMENSIONS OF THE INVESTIGATED GEOMETRY,

MATERIAL PROPERTIES AND EXCITATION

CONDITIONS

The pass example is from a disc-type winding and the

studied section is between two neighbouring spacers, as

shown in Figure 1 (a), followed by the other 3 sub-pictures

depicting the front, side and top views of the model structure

respectively. There are 8 discs in the pass; they are cooled

with oil which flows in from the bottom inlet, through

horizontal channels between the rows of ‗heat generating‘

discs, and joins up with a single vertical channel at the

opposite side that carries the oil upwards and through a gap to

next pass. The next pass starts from the oil block washer

equipped just below the 9th disc; all washers are assumed as

fully tight. A winding can then be periodically composed by a

series of this type of passes, resulting in a zig-zag like oil flow,

and due to the periodicity, only a single pass is investigated in

this paper. In an ideal cooling design, firstly sufficient oil

should be supplied into the pass by buoyancy or oil pumps,

and secondly the oil can be distributed uniformly across the

horizontal ducts for avoiding any localised oil starvation.

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Disc

Spacers

Front

view

Side

view

(a) The studied section in winding.

Horizontal

duct

Washer

One

pass Disc

Lexan glasses

Top view

(b) Front view.

Washer Stick

Spacer

(c) Side view.

Lexan

glass

Lexan

glass

Spacers

Sticks

(d) Top view.

Figure 1 Structure of the disc-type winding pass used for

study.

In order to perform numerical modelling on the pass

example, the geometric parameters, the physical properties of

the material and the investigated parameter ranges are

summarised into Table 1-3 respectively. The dimensions were

used to construct the geometry of the numerical models, and

the inlet oil flow rate and temperature, listed in Table 3, were

applied as boundary conditions.

Table 1 Geometric parameters of the winding pass example.

Parameter name Value

Width of vertical channels

(mm) 5.0

Width of horizontal channels

(mm) 4.22

Height of discs

(mm) 9.4

Clear distance between the spacers

(circumferentially uncoiled)

(mm)

129.7

Radial length of the discs

(mm) 90.1

Bevel corner radius the disc

(mm) 0.92

Thickness of insulating paper

(mm) 0.5

Table 2 Physical properties of oil and solid materials.


a. Oil properties of Shell Diala DX at absolute

temperature T K

Dynamic viscosity

(mPa∙s) 0.0757 × exp[605.8 / (T – 178.3)]

Density

(kg/m3) 874 – 0.65 × (T – 293.15)

Heat conductivity

(W/(K∙m)) 0.124 – 6.25× 10-5 × (T – 293.15)

Heat capacity

(J/(K∙kg)) 2020 + 4,375 × (T – 293.15)

b. Oil properties of Shell Diala DX at absolute

temperature 60 °C

Dynamic viscosity

(mPa∙s) 3.8

Density

(kg/m3) 848

Heat conductivity

(W/(K∙m)) 2195

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Heat capacity

(J/(K∙kg)) 0.1215

c. Properties of the solid materials

Thermal conductivity of conductors

(W/(K∙m)) 410

Thermal conductivity of insulating paper

(W/(K∙m)) 0.15

Thermal conductivity of spacers

(W/(K∙m)) 0.15

Table 3 Investigation parameter ranges.


Flow rate at the pass inlet

(L/min) 2, 5, 10, 15, 20

Oil temperature at the pass inlet (°C)

(only for the hydraulic-thermal models) 60

Loss power per disc (W) (only for the

hydraulic-thermal models) 15, 30

4 EXPERIMENTAL MEASUREMENTS

Hydraulic measurements were especially done to validate

the simulations. The procedure of the hydraulic measurements

was taking a physical model of the winding pass example,

illustrated in Figure 1, and inputting the specified oil flow rate

from the pass inlet. The supplied flow rate causes a pressure-

drop along the flow path, and this pressure-drop can be

measured at some locations that are reachable without

disturbing the flow considerably. Only the pressure-drop was

measured because it is often difficult to measure the in-duct

pressure profiles accurately; on the other hand numerical

simulation can yield detailed results in the entire domain with

much less practical effort [8].

The model that was applied in this experiment represents a

section of a real transformer winding. Since a typical disc-type

winding repeats periodically in both axial and circumferential

directions, it is sufficient to investigate only such a section

which also saves effort compared to the operation at a

complete winding. Such a section is usually small and it is

possible to keep its dimensions according to a real transformer;

therefore there was no need to apply laws of similarity to the

measured data afterwards. Since for the first step only

hydraulic data were of interest, the discs were made of

transformer board according to the outer form of real discs.

The scheme of equipments for acquiring the pressure drop

is outlined in Figure 2.

Computer

Winding Model

Pressure

Sensor (1)

Shortt Circuit

Valve

Pressure

Sensor (6)

Shortt Circuit

Valve

Point A Point B Reference Point

Figure 2 Scheme of equipments for pressure acquisition.

From the picture, it can be seen that each pressure

transducer is switched between two channels. The measured

data are constantly recorded by a computer until a steady state

is reached. Once finished, a new flow rate can be imposed and

studied. To have realistic properties of the fluid according to

them of transformer oil at a typical operating temperature, a

special hydrocarbon was used instead of regular transformer

oil. This hydrocarbon is similar to kerosene but has a higher

flame point, an eligible viscosity and density at room

temperature, listed in Table 4. Due to this in the measurements

there is no heating required and the oil temperature remains

constant.

Table 4 Properties of the hydrocarbon used for hydraulic

measurements at ambient temperature.


Dynamic viscosity

(mPa∙s) 2.4

Density

(kg/m3) 803

5 NETWORK MODELLING

In brief, network modelling first reduces the complex

pattern of the oil flow inside a transformer winding down to a

matrix of simple hydraulic channel approximations,

interconnected by junction points or ‗nodes‘ [12]. Figure 3

shows the geometry approximated from the experimental

setup in Figure 1 for 2D network model; lumped elements

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such as discs, ducts and nodes are indicated. Bulk averaged

parameters are assumed to represent the variation of physical

quantities at each duct and node, based on which a set of

‗lumped parameter‘ equations are applied to construct both so-

called thermal and hydraulic networks across the entire

winding.

ducts

nodes

oil

disc

Figure 3 Geometry for 2D network modelling of the

experimental setup.

Additionally, the following physical assumptions are made

in network modelling: oil is modelled as laminar flow

between a pair of infinite parallel flat plates [12-13]; oil

temperature is assumed to rise linearly along horizontal

channels due to the uniform heat flux at disc surfaces [14]; oil

mixing at nodes is complete hydraulically and thermally. A

group of mathematic expressions, i.e. (a-e) as follows, are

then employed to constitute the hydraulic and thermal

networks respectively. Due to the temperature dependence of

the physical properties of oil, such as viscosity and density,

the hydraulic and thermal networks are coupled and as such an

iterative approach is required for a solution.

a. Mass conservation at nodes;

b. Pressure drop equation, namely Darcy-Weisbach

Equation, (1), applied onto ducts [12];

2

4 2U

D

fLP

(1)

c. Thermal energy conservation at nodes;

d. Conductive heat transfer equation, (2), to express the

heat conduction across insulating paper;

)(cond wc

p

ttd

kq (2)

e. Convective heat transfer equation, (3), along horizontal

ducts to express the heat convection from the duct

walls to the flow bulk.

)(Nu

conv bwtt

D

kq

(3)

Moreover, empirical equations are incorporated for

estimating the Nusselt number, Nu, friction coefficient, f, at

oil ducts and junction pressure losses (JPL). These equations

were previously from general fluid dynamics and heat transfer

handbooks, but have recently been calibrated by large sets of

CFD simulations for a wide range of transformer designs, with

overall minimised deviation from CFD predictions [15-16].

The calibrated equations (4-6) were applied in this paper.

08.3PrRe

/29.1Nu

16.038.0

b

wDL

(4)

61.0PrRe17.0Re

2490.055.0

15.037.0

b

w

D

Lf

(5)

2

2

1

2

11

1

2

2

1

2

11

1

Re

276

Re

1000735.2337.3079.1

Re

72

Re

1000419.1729.1580.0

m

mm

m

m

mm

m

K

U

U

U

UK

K

U

U

U

UK

(6)

6 CFD MODELLING AND VISUAL LOCALISED

RESULTS

The CFD computation was done with commercial CFD

software ANSYS-CFX, which is a finite-volume based CFD-

solver, while the mesh generation with ICEM-CFD. Because

modelling in 2D saves an enormous amount of computational

effort, but CFX does not have the explicit capability to treat

2D problems, (due to the underlying finite-volume algorithm),

the approach was modelling the geometry in an ordinary 2D

way and then extruding only one cell into the circumferential

direction for constructing 3D elements. For the simulation,

this model was assumed as infinitely extruded along this

direction. It implies that the small wall effect of the spacers,

which bounds the horizontal ducts in the circumferential

www.ietdl.org

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direction, was neglected. This is justified because of the large

ratio between channel width and channel height [12]. On the

other hand, the radial boundaries, where in reality pressboard

cylinders are bounding the winding, were applied as

isothermal wall boundaries since the heat flux through those

surfaces is commonly regarded as negligible. Finally for the

hydraulic-thermal modelling, constant loss density was

impressed into the conductor volumes.

At the inlet oil flow with homogenous velocity and

temperature was impressed respectively, while the outlet was

closed by a zero static-pressure condition, as shown in Figure

4. As a matter of fact, there are 3 passes involved in this

model and only the middle pass was intended to deliver the

results, because the upper and lower passes were facilitated to

deliver proper boundary conditions for the middle pass. When

modelling the material, Newtonian fluid model was applied,

where viscosity only depends on temperature in an

exponential manner. The density, the specific heat capacity

and the heat conductivity are all assumed to be temperature

dependent in a linear manner. Since the Reynolds number was

reliably low, no turbulence model was employed in the

simulation.

The discretisation was done with around 900,000 elements,

shown in Figure 4. For the shape functions the 2nd order

upwind scheme was used and the single-precision solver was

tested to be sufficient for this problem. The convergence

criterion was set as a RMS-residual of 10-5, and a global

balance of each conservation quantity of 10-3 has been

required and reached.

Figure 4 Principal model and details with mesh.

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In Figure 5 the streamlines resulting from hydraulic-only

models were plotted for both flow rates of 2 and 20 l/min. It

gets obvious that separation eddies are blocking a portion of

the entrance for horizontal channels, especially at the lower

region, because the oil washer equipped at the top prevents oil

flowing up, effectively forcing them turn to the horizontal

channels, and thus the eddies at these channels are largely

suppressed. The entrance separation eddies actually account

for the junction pressure losses described by equation (6) in

network modelling. By the comparison between Figure 5 (a)

and (b), the eddies are strengthened with high inlet flow rates,

and because of this the flow distribution becomes more

unequal; for example, in (b) of 20 l/min, the 3 upmost

channels obtains almost the whole amount of flow rate which

has been supplied into the pass. Due to this reason the 5 lower

channels get small proportion of oil and they would get

relatively higher oil temperature if constant heating power

were imposed.

(a) 2 l/min. (b) 20 l/min.

Figure 5 Streamlines for two oil flow rates.

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(a) 2 l/min and 15 W per disc. (b) 20 l/min and 30 W per disc.

Figure 6 Contours of fluid temperature.

With a hydro-thermal model, Figure 6 displays the

temperature distribution within the fluid domain for the case

with loss power of 15 W per disc and flow rate of 2 l/min and

the case with 30 W per disc and 20 l/min. For the case with 2

l/min, the oil flowing through the middle region is less and

local temperature at these ducts therefore becomes higher; in

Figure 6 (a) the highest temperature is observed to occur at the

thermal boundaries of the middle ducts and the cooling for the

bottom and top ducts is better. In particular, due to high

Prandtl number (typically ~200 for oil [2]), it can be seen that

a strong cold streak from the former pass is entering the

bottom duct and moves from there lasts until the outer vertical

duct; however, the cold streak does not reduce the thermal

boundary temperature because it flows almost along the

centreline rather than contacting a channel wall. On the other

hand, at the outer side vertical duct, there are hot-streaks

formed and lasting till the pass outlet and they could affect the

cooling efficiency at the entrance of next pass [9].

For the case with 20 l/min, most extra supplied oil flows

through the upper half of the pass and the duct wall

temperatures at the lower half remain higher. In Figure 6 (b)

the worst temperature is observed at the lower right corner; at

the dead corner oil is almost stagnated. Secondly, due to the

high flow rate at some horizontal ducts, there are second eddy

circulations generated at the entrance regimes; fortunately it

was not found that these second eddies would reduce the flow

rate at the ducts. Furthermore, at the outer vertical duct there

are also hot-streaks discovered, but these hot-streaks have

lower temperatures than those in the sub-figure (a), (due to

high flow velocities), and therefore, their influence upon the

next pass is smaller than that in the case of 2 l/min.

To emphasize the effect from the flow rate on the

convective heat transfer, the heat transfer coefficient (HTC)

distribution around the bottom disc of the studied pass was

plotted in Figure 7 for both the case of 2 l/min and 15 W per

disc and the case of 20 l/min and 30 W per disc. These HTC

values were evaluated from the heat flux and the wall

temperature difference, on the oil side of the insulating paper,

from a reference temperature; the heat flux and wall

temperature could be extracted from the CFD results, and the

inlet temperature of the pass, 60°C, was taken as the reference

temperature. As network modelling assumed, the heat flux is

uniform and the wall temperature difference rises linearly

from the upstream to the downstream of a channel, so the

HTC profile follows a linear reduction. With the help of CFD,

the assumption can be examined in a more detailed way.

Figure 7 shows the local HTC values for the cases with

2l/min and 15W per disc and 20l/min and 30W per disc.

Figure 7 (a) shows the values along the bottom side of the disc,

which actually bounds on the last horizontal duct of the

previous pass. Since the portion of flow in this horizontal duct

is the highest of all passes, the HTC values are also high. The

kink distribution patterns at the upstream end, i.e. the left-

hand end, are due to the entry eddy circulations, then the HTC

value gradually reduce, typically following hyperbolic trends,

and are finally involved into the downstream flow

combination. The difference between the two cases can be

explained by the difference in the oil flow rates; high flow rate

brings high HTC values.

Figure 7 (b) displays the HTC values at the upside of the

disc. Beginning with the entry eddy caused kink patterns at

the upstream end, i.e. the right-hand end, the HTC values

decrease hyperbolically along the duct; this is known from

literatures for heated infinite parallel channels. At the

downstream combination profiles are then observed. The HTC

values after 40 mm from the entry is almost overlapped

because the flow velocities within the duct are in a quite

similar range; for the high flow rate case, this first duct is

actually blocked by the separation eddy at its entry.

7 RESULTS COMPARISON

As the first step, the pressure drop along the complete pass

has been compared. The pressure drop over a winding

describes the hydraulic impedance the supplied oil flow

should resist to flow upwards through the winding; at a design

stage, structures and dimensions of windings are supposed to

be carefully optimised to minimise this pressure drop. It is

especially significant for forced oil cooling mode, because

capable oil pumps have to be chosen and equipped to

guarantee oil flow.

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(a) Bottom side. (b) Top side.

Figure 7 Heat transfer coefficient around first disc.

Since only pressure drop of unheated cases was available

from measurements, hydro-only calculations with the material

data, Table 4, were performed for comparison. The obtained

results are shown in Figure 8 (a); the calculation results

closely match the measurement values with the maximum

deviation less than 15 Pa, which equates to 1.8 mm hydraulic

head. In Figure 8 (b), the pressure drop for the case of 30 W

per disc losses is shown and the deviation between the

network model and the CFD results is still small, less than 30

Pa. The difference of the pressure drop between the cases with

15 W and 30 W per disc losses was below 2%, so that the

results for 15 W are relinquished to display here. By the

comparison the network modelling was proved to give well fit

pressure drop correlations.

In the following Figure 9 the flow distribution among the

horizontal channels is shown; the percentage refers to the

whole oil flow, which enters the inlet of the pass and

distributes among the individual horizontal channels. As it can

be seen in Figure 9 (a) and (c), the flow distribution calculated

by the network model is quasi-parabolic and nearly

symmetrical to the axial middle of the pass, though slightly

more oil tends to flow through the upper half of the pass for

the cases with higher flow rates. In contrary to this, the flow

distribution calculated by CFD is distinctly and visibly

asymmetrical even for low flow rates. It gets increasingly

imbalanced for higher flow rates; for example, in the case of

10 l/min most of the flow passes through the top two ducts.

This is what was indicated by the streamline plots in Figure 5,

in which it got visible that separation eddies are blocking the

lower ducts of the pass in the case with such a high flow rate.

The difference in the flow distribution between the cases

with losses of 15 W per disc and 30 W per disc is obviously

small, which implies that buoyancy forces are not very

dominant, especially for high flow rates. In particular the

network model did not show any difference between 15 W

and 30 W and tiny difference is only shown within the CFD

cases of 2 l/min, visible in Figure 9 (b) and (d). At such a low

flow rate, the buoyancy forces are able to drive the oil flow

from the hotter outlet vertical channel to the colder inlet

vertical channel, and this tends to reverse the flow in the upper

horizontal ducts into the opposite direction and the flow in the

lower horizontal ducts into its original direction. Finally the

flow distribution with higher losses becomes more

symmetrical.

- 2l/min and 15W per disc




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0

25

50

75

100

125

150

175

200

0 2 4 6 8 10 12 14 16 18 20

Oil flow, l/min

Rela

tiv

e p

ress

ure d

ro

p, P

a

Pressure drop from NM

Pressure drop from CFD

Pressure drop from measurements

0

25

50

75

100

125

150

175

200

0 2 4 6 8 10 12 14 16 18 20

Oil flow, l/min

Rela

tiv

e p

ress

ure d

ro

p, P

a

Pressure drop from NM

Pressure drop from CFD

(a) Case without losses. (b) Case with 30 W per disc.

Figure 8 Pressure drop over the pass.

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8

Duct number (from bottom to top)

Oil

ma

ss f

low

ra

te p

ercen

tag

e

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8


Oil

ma

ss f

low

ra

te p

ercen

tag

e

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

(a) From network model for 15 W per disc. (b) From CFD for 15 W per disc.

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8


Oil

ma

ss f

low

ra

te p

ercen

tag

e

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

0%

10%

20%

30%

40%

50%

1 2 3 4 5 6 7 8


Oil

ma

ss f

low

ra

te p

ercen

tag

e

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

(c) From network model for 30 W per disc. (d) From CFD for 30 W per disc.

Figure 9 Flow distributions on the horizontal oil ducts.

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In Figure 10 the maximum temperature of the individual

discs is displayed. In network modelling assumptions this

maximum temperature locates at the downstream end of each

disc; however in CFD results the whole volume of each

conductor bears almost the same temperature due to the high

thermal conductivity of copper, and this temperature is taken

as the maximum temperature. The temperature profiles in

Figure 10 correspond to the flow distributions in Figure 9. As

observed the temperatures calculated by the network model

are scaled by the factor of loss density. For the CFD results

the situation is similar, but the only exception is in the case of

20 l/min, where a slight temperature peak is recognisable at

the second disc from the bottom, probably due to the channel

entry eddy circulations. Another difference between the two

modelling approaches is that, for the low flow rates,

particularly 2 l/min, the network model predicted higher

temperatures than the CFD for both losses. This is because the

network model predicted less uniform flow profiles than the

CFD at the low flow rates. For high flow rates, especially 20

l/min, the network model temperature prediction is relatively

lower than the CFD, since CFD showed that the bottom oil

ducts are blocked by entry eddy circulations and thereby

localised temperature peaks are formed.

63

64

65

66

67

68

69

70

71

1 2 3 4 5 6 7 8

Disc number (from bottom to top)

Av

era

ge c

on

du

cto

r t

em

pera

ture i

n °

C

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

63

64

65

66

67

68

69

70

71

1 2 3 4 5 6 7 8

Av

era

ge c

on

du

cto

r t

em

pera

ture in

°C


2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

(a) From network model for 15 W per disc. (b) From CFD for 15 W per disc.

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

1 2 3 4 5 6 7 8


Av

era

ge c

on

du

cto

r t

em

pera

ture i

n °

C

2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

67

68

69

70

71

72

73

74

75

76

77

78

79

80

81

1 2 3 4 5 6 7 8

Av

era

ge c

on

du

cto

r t

em

pera

ture in

°C


2 l/min

5 l/min

10 l/min

15 l/min

20 l/min

(c) From network model for 30 W per disc. (d) From CFD for 30 W per disc.

Figure 10 Temperature distributions on the winding conductors.

8 CONCLUSIONS As transformer thermal modelling tools, network models

and CFD both require the same input parameters such as

model geometry, oil properties and boundary conditions

www.ietdl.org

12


including loading and bottom oil flow rate and temperature.

Fundamentally, network models employ the mathematic

equations for the average quantities, such as oil velocity and

temperature etc, on each lumped element, i.e. oil duct or

junction node, and some of the equations are empirical. On the

other hand CFD uses much higher spatial discretisation and

gets rid of empirical equations especially when the flow is

laminar. In this paper, both modelling approaches were

compared based on the same winding pass model in order to

assess the influence of the different discretisation of both

approaches upon the modelling results.

From the comparison conducted, it was concluded that the

deviation between the pressure drop calculated by CFD and

the measured values is quite low and that, once adapted, the

network modelling method delivered reliable results for the

pressure drop as well. It is a proof to show that network

modelling would be able to provide a quick solution for

predicting winding pressure drops and thereby assist to choose

capable oil pumps for forced oil cooling at thermal design

stage. It is to remark that only the model and material

parameters were inputted into the CFD and network model

programs and no any calibration or adaption from the

measurement results was applied.

Secondly, with high total oil flow rates such as 20 l/min,

the flow distribution across the horizontal ducts delivered by

the network modelling bore deviation from the one by CFD.

The main difference was particularly due to the entry eddy

circulations at the bottom ducts; the phenomena were

observed from the CFD results. Moreover, the resulted disc

temperatures from network model are lower than those from

CFD for high oil flow rates; however the comparative relation

acts oppositely for low flow rates.

ACKNOWLEDGMENT

Stefan Tenbohlen and Andreas Weinläder would like to

thank the Deutsche Forschungsgemeinschaft (DFG) for

sponsoring this research project. Zhongdong Wang and Wei

Wu would like to thank the Engineering and Physical

Sciences Research Council (EPSRC) – National Grid Dorothy

Hodgkin Postgraduate Award (DHPA) and National Grid for

their financial sponsorship. Due appreciation should be given

to the colleagues of CIGRE WG A2.38 for inspiritive

discussions. Financial support is also gracefully received from

the Academic Research Collaboration (ARC) Programme

between the British Council and Deutscher Akademischer

Austausch Dienst (DAAD) for facilitating this collaborated

paper.

REFERENCES


Ngnegueu, T.: ‗Thermal performance of power


operating requirements‘. Session 2004, CIGRE, rue


[2] Oliver, A. J.: ‗Estimation of transformer winding


method‘. Proc. Inst. Elect. Eng. C, 1980, vol. 127, pp.

395-405

[3] Allen, P. H. G., and Finn, A. H.: ‗Transformer winding

thermal design by computer‘. IEE Conf. Publ., 1969, vol.

51, pp. 589–599

[4] Simonson, E.A., and Lapworth, J.A.: ‗Thermal

capability assessment for transformers‘. Second Int.


Equipment, 1995, pp. 103-108


M., and Ahuja, R.: ‗Transformer Design Principles: With

Applications to Core-Form Power Transformers‘


[6] Zhang, J., and Li, X.: ‗Coolant flow distribution and


Theory and model development‘. IEEE Transactions on


[7] Radakovic, Z., and Sorgic, M.: ‗Basics of detailed

thermal-hydraulic model for thermal design of oil power

transformers‘. IEEE Transactions on Power Delivery,

2010, vol. 25, pp. 790 -802


‗Thermal and hot spot evaluations on oil immersed


software's‘. Proc. Int. Conf. on Thermal, Mechanical and



2007, pp. 1-6


Lundin, L-A., and Missing, R. M.: ‗Numerical study on


transformer windings‘. 5th European Thermal-Sciences


[10] Weinläder, A., and Tenbohlen, S.: ‗Thermal-hydraulic

investigation of transformer windings by CFD-modelling

www.ietdl.org

13


and measurements‘. Proceedings of the 16th


South Africa, 2009

[11] Torriano, F., Chaaban, M., and Picher, P.: ‗Numerical

study of parameters affecting the temperature

distribution in a disc-type transformer winding‘. Applied

Thermal Engineering, 2010, vol. 30, pp. 2034-2044

[12] Wu, W., Wang, Z.D., and Revell, A.: ‗Natural


modelling‘. Proceedings of the 16th International


2009

[13] Zhang, J., and Li, X.: ‗Coolant flow distribution and


Theory and model development‘. IEEE Transactions on


[14] Wu, W., Revell, A., and Wang, Z.D.: ‗Heat Transfer in


Insulating Paper‘, Proceedings of The International


China, 2009


Jarman, P.: ‗CFD Calibration for Network Modelling of

Transformer Cooling Oil Flows – Part I Heat Transfer in

Oil Ducts‘, IET Electric Power Applications, 2011, to be

published

[16] Wu, W., Wang, Z.D., Revell, A., and Jarman, P.: ‗CFD

Calibration for Network Modelling of Transformer

Cooling Oil Flows – Part II Pressure Loss at Junction

Nodes‘, IET Electric Power Applications, 2011, to be

published


101

Chapter 6 Optimisation of transformer thermal

design

6.1 Paper 6

Optimisation of Transformer Directed Oil Cooling Design Using Network

Modelling

W. Wu, Z.D. Wang and P. Jarman

2011

IET Generation, Transmission and Distribution

Submitted

www.ietdl.org

1

IET Gener. Transm. Distrib., © The Institution of Engineering and Technology 2011

ISSN 1751-8687

Optimisation of Transformer Directed Oil Cooling Design Using

Network Modelling

W. Wu1, Z.D. Wang1 and P. Jarman2 1 School of Electrical and Electronic Engineering, University of Manchester, Manchester, M13 9PL, UK.



Abstract — The requirement on thermal design of a transformer is to guarantee that the transformer is able to pass factory heat

run test and to restrain hot-spot temperature. The ‘network model’ implementation has been developed to gain accurate

prediction of the hot-spot inside oil-immersed transformers. In this paper, based on a CFD calibrated network model, the

impacts of oil duct dimensions and block washer number on oil flow and temperature distributions are investigated for design

optimisation using a directed oil (OD) cooled low voltage (LV) winding as an example. During the parametric study oil pump

performance curves are incorporated to determine the inlet oil flow rate. Narrower horizontal ducts, wider vertical ducts and

less disc numbers per pass are recommended for optimising oil flow distribution and reducing average winding and hot-spot

temperatures.

1 NOMENCLATURE

H = Hydraulic head of winding, in meters

Q = Oil flow rate supplied to a winding, in liters

per minute

Acroynms/Shorthand

CFD Computational fluid dynamics

HCC Hydraulic characteristic curve

HST Hot-spot temperature


LV Low voltage

MWT Mean winding temperature

OD Directed oil cooling mode

OF Forced oil cooling mode

PPC Pump performance curve

WP Working point

2 INTRODUCTION

Power transformers are key, and one of the most expensive

components of electric system networks. Their performance

and reliability inevitably influence the reliability of electricity

transmission and distribution systems, especially when a

significant fraction of the UK transformer fleet has been in

operation for more than their designed lifetime [1-2]; for

instance, by 2010 almost 50% of the in-service transformer

population were 50 years old. Ageing is strongly associated to

the degradation of insulating paper which is a function of

temperature, and as such hot-spot temperature becomes

significant since the insulation at hot-spot undergoes the worst

thermal ageing.

The overall demand for energy in the UK is expected to

increase by 1% per annum over the period of 2007 to 2023,

which is an rise from 351 to 373TWh [3]. The increasing

demand as well as the financial constraints placed on electric

network companies by the Office of Gas and Electricity

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Markets (OFGEM) force the companies to be more strategic

with the maintenance and replacement of their transformer

assets. The electric network companies are interested in

purchasing the transformers with lower hot-spot temperatures,

especially when overloading transformers beyond the rated

capacities is considered [4]. Transformer manufacturers are

consequently under the pressure from their customers to

design transformers with lower hot-spot temperatures.

Numerical thermal modelling such as network modelling is

applied as a tool to assess the oil flow distribution and hot-

spot temperature of power transformers and to assist the

design of oil cooling systems [5-6]. The recent advance on

network modelling techniques includes using highly

discretised CFD simulations to calibrate and to improve the

calculation accuracy [7-8]. One of the merits of network

models is that they can be used to carry out a large amount of

sensitivity studies on design parameters due to its low

requirement on computational effort.

To the authors’ best knowledge, the only recent work

which evaluated the impact of structural dimensions of

transformer windings is [9]. It was found that the oil duct

dimensions as well as the disc number per pass strongly affect

both oil flow distributions and pressure losses across the

winding.

[9] focused on the hydraulic model and thus did not

consider winding power losses or oil viscosity and density

variation upon temperatures. However the optimisation in

terms of restraining hot-spot temperature can only be

performed in conjunction with temperature calculations.

Moreover, it did not consider the oil flow rate altered by

design parameter modifications, i.e. a constant flow rate was

used alone within the whole parametric investigation. This

deviates from the reality; taking forced oil cooling (OF/OD)

modes as an example, the hydraulic impedance of the entire

winding changes while oil duct dimensions are altered, and as

such the oil flow rate would vary according to the oil pump

capabilities.

In this paper, by applying the CFD calibrated network

model and incorporating the pump specifications, winding

design parameters are optimised to achieve the best winding

temperature and oil flow distribution.

3 DIRECTED OIL COOLING DESIGN PRINCIPLE

The goal of thermal design is to pass the heat run test, in

which average winding temperature rise of 65 oC and top oil

temperature rise of 60 oC are the criteria [10]. In order to

guarantee the temperature rises, a sufficient oil flow rate is

required [5]. For a directed oil cooling transformer, a capable

pump should be equipped for driving this oil flow.

Pumps are generally specified in terms of the hydraulic

head, or ‘head’ for short, in meters versus the flow rate in

litres per second. Head reflects the total hydraulic resistance

that a pump must overcome in the flow system. In oil-cooled

transformers the hydraulic resistance comes from not only the

frictional pressure losses along the oil channels inside cores

and windings, pipe fittings and external radiator fins, but also

the local pressure losses due to pipe bends and junction

connections. As the oil circulation is a closed system, the

static head which represents the gravity effect does not need to

be resisted by the oil pump.

Pump manufacturers release performance curves for all

their models of pump. Pump performance curve (PPC)

describes the head a pump can generate at different flow rates,

as shown in Figure 1. Although the curve starts from zero

flow rate, the head at zero flow does not represent a static

head but the reference maximum pressure, and a pump should

not be allowed to run at zero flow due to the issue of

overheating.

System hydraulic

characteristic curve

Pump performance curve

Flow, L/s

Hea

d,

m

0

Working

point

Guarenteed

flow rate

Figure 1 Intersection of pump performance curve and system

hydraulic characteristic curve is pump working point.

On the other hand, at the design stage, the pump pressure

head required for the complete oil circulation at different oil

flow rates are calculated and a system hydraulic characteristic

curve (HCC) can be derived, as shown in Figure 1. The

intersection of the system characteristic curve and the pump

performance curve is the pump working point. A proper pump

model should meet with the system characteristic curve at a

working point whose flow rate does not deviate from the

designed value much, in order to meet the temperature criteria.

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Some pumps have a performance curve which starts with a

plateau pattern but after a knee point, the head rapidly reduces

along with a small increment of flow rate. For this type of

pump, the working point should be designed at the vicinity of

the knee point to utilise the maximum stable pump head,

otherwise any small disturbance of flow rate would greatly

affect the head.

4 HYDRAULIC HEAD OF WINDINGS

Although the thermal design for an entire transformer is not

as simplistic as for a single winding, the principle is the same

and the paper takes the low voltage (LV) winding example

from [5] to perform the parametric analysis for identifying

optimised design parameters. This 3-phase delta connection

disc type winding, from a 250 MVA transformer, was

operating at 22 kV and winding current of 6561 A. There are

95 discs cooled with 100 horizontal oil ducts arranged into 5

equal size passes by 4 oil washers. The widths of the

horizontal, the inner and outer vertical ducts are 5 mm, 15 mm

and 15 mm respectively. These duct dimensions and the

washer number are to be further optimised in this study.

While cooling oil with different flow rates are forced into

the winding, the oil flow should require different pump heads

to resist the pressure losses inside the winding, including the

frictional losses occurring along oil ducts and the local losses

caused by duct bends and junctions, i.e. junction pressure loss

(JPL). The head varies with the inlet oil flow rate and the

correlation between them is referred as the hydraulic

characteristic curve of the winding.

With a winding structure designed, its characteristic curve

can be calculated by network modelling, in which junction

pressure loss equations play important roles [8]. For instance,

Figure 2 presents the three characteristic curves of the LV

winding example [5] when JPL are calculated by three

different sets of mathematic expressions. If JPL are neglected

when calculating the hydraulic characteristic curve, the low

curve values would result in a smaller oil pump than the one

really required. Consequently the expected oil flow rate

cannot be guaranteed and the winding will suffer from higher

temperatures than designed values. Furthermore the JPL

existence also makes the disc temperature distribution across

the whole winding less uniform which often causes severer

hot-spot temperature. Modelling excluding JPL is thereby

unreliable. Inversely, if people use the unrealistically high

characteristic curve predicted from the equations in [5], the

chosen pump will be unnecessarily more powerful than

required. It may seem good since this pump will supply more

oil flow than desired. However, a dramatically high oil flow

rate will affect the oil flow distribution across horizontal ducts

and result in hot-spot shifting downwards to the pass bottom

[11]. For optic-fibre measurement, sensors which have been

installed at a previously predicted hot-spot location will

incorrectly underestimate the hot-spot temperature. Besides, a

bigger pump costs more and consumes unnecessarily more

power. In contrast, the characteristic curve deduced from the

CFD calibrated equations provide a better match with

experimental results and will be used in this paper [8].

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60

Hea

d, m

Oil flow rate, L/s

No JPL Eqn. in [5] CFD calibrated eqn. [7-8]

Figure 2 Hydraulic characteristic curves of the LV winding

example [5].

In order to guarantee the temperature criteria, a sufficient

oil flow rate, 21.3 L/s, is aimed at for the LV winding

example [5]. Note that this designed flow rate is only for a

single winding; the necessary oil flow rate for the entire

transformer will however be several times greater. A pump is

chosen to deliver cooling oil into this single winding and its

performance curve is illustrated in Figure 3, in which the

winding characteristic curve is also overlapped to identify the

feasible working point. The intersection of both curves yields

the working point (24.5 L/s, 2 m); the corresponding flow rate

is 24.5 L/s, 15% higher than the design value, 21.3 L/s.

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0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0 5 10 15 20 25 30 35 40 45 50

Hea

d, m

Flow, L/s

PPC Winding HCC WP Designed WP

Figure 3 Intersection of pump performance curve (PPC) and

winding hydraulic characteristic curve (HCC) is working

point (WP).

5 PARAMETRIC ANALYSIS AND DISCUSSION

As discussed in Section 4 the working point is at Q =

21.3L/s, H = 2m for that particular design. Fixing the pump

model, when the winding design is further modified, the

winding hydraulic characteristic curve will possibly be shifted

downwards or upwards, the working point then moves along

the pump performance curve and the oil flow rate may also

change accordingly. In most scenarios, it is not necessary to

replace the pump model anew if the altered oil flow rate can

still guarantee the temperature rise criteria.

In this paper, design changes are made by varying major

dimension parameters, including oil duct widths and the

number of block washers equipped. Their impact is discussed

in consistence with the pre-condition not to change the pump.

5.1 Effect of Oil Duct Widths

In the sensitivity study, the oil duct widths were varied

around their designed values within ±20% ranges; for example,

for the horizontal duct which is designed to be 5 mm wide, the

widths of 4 mm, 5 mm and 6 mm were tested respectively,

and similarly for inner and outer vertical ducts. There are 4

cases conducted; in the first 3 cases only one type of duct was

changed and in the 4th case all the three types were modified

simultaneously. The modified winding hydraulic characteristic

curves of the 4 cases are shown in Figure 4 respectively, in

which the pump performance curve (PPC) is overlapped to

identify the new working points and oil flow rates.

In Figure 4, it is observed that narrower ducts require

higher hydraulic head to retain a same oil flow rate and thus

the winding characteristic curve is shifted upwards. While the

pump performance curve is fixed, the narrowed ducts move

the working point to lower flow rates; the widened ducts result

in higher flow rates. The results show that the degree of

impact follows the order, outer side vertical duct ≈ inner side

vertical duct > horizontal duct. The flow rate variations are

summarised in Table 1; the magnitude of the variations is

limited and thus verifies the pre-assumption that it is

unnecessary to change the pump.

The corresponding results of mean winding temperature

(MWT) and hot-spot temperature (HST) are obtained into

Table 1 and the oil flow distributions in the top pass are

illustrated in Figure 5 for comparison; only the top pass is

presented because hot-spot locates in this pass. In Table 1, the

combinations are grouped in correspondence to the 4 cases

and the investigated duct width in each case is highlighted for

clarity.

Conclusions drawn from Table 1 include: the narrowed

horizontal duct reduces the average winding and hot-spot

temperatures; the narrowed vertical duct increases the

temperatures; with all ducts narrowed altogether, their effects

cancel each other but the temperatures still reduce slightly,

because the degree of impact follows the order, horizontal

duct > outer side vertical duct ≈ inner side vertical duct. The

impacts of oil duct widths upon winding temperatures relies

on the fact that both narrowed horizontal ducts and widened

vertical ducts improve the uniformity of flow distribution, as

observed in Figure 5. The distribution becomes more uniform

because either narrowed horizontal ducts or widened vertical

ducts or both can force more proportion of oil to flow upwards

from the inlet to the centre of the pass and compensate the oil

flow starvation there. Inversely, with narrowed vertical ducts

or widened horizontal ducts more oil will turn direction upon

departure from the inlet and flow through the bottom

horizontal ducts, and the pass centre then has less cooling oil.

www.ietdl.org

5


(a) Of different horizontal duct widths. (b) Of different inner side vertical duct widths.

(c) Of different outer side vertical duct widths. (d) All types of duct widths are altered together.

Figure 4 Impact of oil duct widths upon winding characteristic curves.

Table 1 Impacts of oil duct widths upon oil flow and winding temperatures.

(MWT = mean winding temperature, HST = hot-spot temperature)

Duct dimensions, mm Calculation results

Horizontal

duct width

Inner vertical

duct width

Outer vertical

duct width

Oil flow

variation MWT,

oC HST,

oC

4 15 15 -2.45% 70.3 78.5

5 15 15 0 73.6 83.7

6 15 15 +1.22% 76.9 89.9

www.ietdl.org

6


5 12 15 -4.49% 74.8 86.7

5 15 15 0 73.6 83.7

5 18 15 2.86% 73.0 82.2

5 15 12 -5.31% 74.8 86.5

5 15 15 0 73.6 83.7

5 15 18 3.27% 73.0 82.4

4 12 12 -11.84% 72.1 82.2

5 15 15 0 73.6 83.7

6 18 18 6.94% 75.4 85.9

(a) Of different horizontal duct widths. (b) Of different inner side vertical duct widths.

(c) Of different outer side vertical duct widths. (d) All types of duct widths are altered together.

Figure 5 Impact of oil duct widths upon oil flow distributions in top pass.

www.ietdl.org

7


Moreover, hot-spot location is almost not affected by the

variation of horizontal duct width; however narrowed vertical

ducts would shift the hot-spot upwards (by inner side vertical

duct) or downwards (by outer duct). This is because, for

example, with a narrowed inner duct, more oil tends to flow

through the bottom horizontal ducts to the wider outer duct

that has relatively lower hydraulic impedance, rather than to

flow upwards, and as such the upper half of the pass will be

hotter. The reason for narrowed outer duct is similar.

Finally, as shown in Figure 5 (d), adjusting all the duct

widths synchronously does not modify the flow distribution

largely, which implies that the width proportion between ducts

determines the flow distribution pattern.

5.2 Effect of Block Washers

With network modelling, the significance of block washer

number was examined. The winding characteristic curves of

the original block washer arrangement (19 discs per pass) and

the doubled block washer number arrangement (interleaved 9

and 10 discs per pass) were both calculated and are exhibited

for comparison in Figure 6 (a). Doubled washers increase the

hydraulic impedance of the winding, which then results in an

flow rate reduction of 7.76%. On the other hand, Figure 6 (b)

shows the maximum disc temperature distribution across the

topmost pass, 19 discs. The figure reveals that, although with

the flow rate reduced, the disc temperatures are significantly

restrained. In particular, the hot-spot temperature reduces by

7.4 K and shifts upwards to the 5th disc counted from the

winding top; previously it was at the 8th disc.

(a) Impact of block washer arrangements upon winding

characteristic curves.

(b) Impact of block washer arrangements upon

maximum disc temperature distributions in top pass.

Figure 6 Impacts of doubled block washer arrangement.

It seems that pass size of ~10 discs is more optimal for this

LV winding design than the original size, 19 discs per pass, in

terms of lower and more uniform temperature distribution

with a slightly reduced oil flow rate.

5.3 Performance at Different Loads

Apart from the design parameters, the impact of loading

variations was also studied with network modelling. Loadings

can be varied depending on the different demands of different

areas and periods. It is thereby meaningful to examine the

thermal performance of a transformer under different loadings

even though it has passed factory heat run test under rated

load.

In a similar way, the impact of different load factors upon

winding hydraulic characteristic curves was calculated and

shown in Figure 7 (a). While the load factor rose from 0.5 per

unit up to 1.5 per unit, the characteristic curve shifted slightly

and the altered working point only caused flow rate variation

within ±5%. Higher loadings resulted in higher flow rates; this

follows logically as oil becomes less viscous at higher

temperatures.

www.ietdl.org

8


(a) Impact of load factors upon winding characteristic

curves.

(b) Impact of load factors upon oil flow distributions in

top pass.

(c) Correlation of mean winding and hot-spot

temperatures versus load factors.

(MWT = mean winding temperature, HST = hot-spot

temperature)

Figure 7 Impacts of load variation.

Figure 7 (b) shows the oil flow distribution in the top pass,

affected by load factors 0.5, 1.0 and 1.5 respectively. It can be

observed that the impact of load upon the flow distribution is

almost negligible except the distinctiveness at the bottom and

the top of the pass. The distinctiveness is due to the single side

heated bottom and top ducts in this particular design; the other

side of the ducts is non-heating oil washer. In single side

heated ducts oil is relatively cooler and more viscous and thus

flow rate is lower. High loadings would deepen the effect as

observed in Figure 7 (b).

Figure 7 (c) indicates that with directed oil cooling mode,

the correlations of average winding and hot-spot temperatures

versus loading factors follow parabolic trends. This is logical

because the DC loss, namely Joule loss, of conductors is

proportional to load current square and the impact of the flow

variation within ±5% upon temperatures remains limited.

6 CONCLUSIONS

Numerical approaches especially network modelling are

helpful for optimisation of the design parameters for new

transformers, such as oil duct dimensions and block washer

arrangement etc. A recent CFD calibrated network modelling

implementation was thereby applied to conduct a parametric

study for analysing the impacts of design parameters upon oil

flow rate, flow distribution and average winding and hot-spot

temperatures. The study focused on directed oil cooling mode

and in particular pump performance curves were incorporated

to determine the inlet flow rate.

The results obtained indicated that narrowed oil ducts shift

the winding hydraulic characteristic curve upwards and oil

flow rate then reduces to some extent. Although the flow rate

is reduced, narrowed horizontal ducts optimise the uniformity

of flow distribution and consequently lower down average

winding and hot-spot temperatures. Narrowed vertical ducts

result in less uniform flow distributions and higher average

winding and hot-spot temperatures. Doubled number of oil

block washers reduces the inlet flow rate slightly, due to the

increment of winding hydraulic impedance, but significantly

optimises the uniformity of flow distribution and thus

effectively restrains the average winding and hot-spot

temperatures.

www.ietdl.org

9


In general, narrowing horizontal ducts, widening vertical

ducts and reducing disc numbers per pass are recommended

for optimisation of directed oil cooling transformers.

ACKNOWLEDGMENT


Engineering and Physical Sciences Research Council (EPSRC)

Dorothy Hodgkin Postgraduate Award (DHPA) and National

Grid. The authors appreciate the technical support given by

John Lapworth from Doble PowerTest and Edward Simonson

from Southampton Dielectric Consultants Ltd. Due

appreciation should also be given to our MSc project student

Mr Lee Smith who carried out the initial investigation of the

idea in this paper under the supervision of the authors.

REFERENCES

[1] Bossi, A., Dind, J.E., Frisson, J.M., Khoudiakov, U.,

Light, H.F., Narke, D.V., Tournier, Y., and Verdon, J.:

‘An international survey on failures in large power

transformer in service’, Electra, 1983, no. 88, pp. 21-47

[2] White, A.: ‘Replacement versus refurbishment end of

life options for power transformers’, IEE colloquium on

transformer life management, London, UK, 1998, pp.

10/1-10/3

[3] UK Department for Business, Innovation and Skills

(2007) 2008 Energy Market Outlook - Electricity

Demand Forecast Narrative. [Online] Available from:

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[4] Taghikhani, M.A., and Gholami, A.: ‘Heat transfer in

power transformer windings with oil-forced cooling’,

IET Electr. Power Appl., 2009, vol. 3, No. 1, pp. 59-66




395-405




Equipment, 1995, pp. 103-108


Jarman, P.: ‘CFD calibration for network modelling of

transformer cooling oil flows – Part I Heat transfer in oil

ducts’, IET Electric Power Applications, 2011, to be

published

[8] Wu, W., Wang, Z.D., and Jarman, P.: ‘CFD calibration

for network modelling of transformer cooling oil flows –

Part II Pressure loss at junction nodes’, IET Electric

Power Applications, 2011, to be published


pressure loss in ONAN transformer windings. Part II:

Optimization of Design Parameters’. IEEE Transactions

on Power Delivery, 2004, vol. 19, pp. 194-199

[10] IEC standard 60076-2: ‘Power transformers – part 2:

Temperature rise’, 1997

[11] Weinläder, A., and Tenbohlen, S.: ‘Thermal-hydraulic

investigation of transformer windings by CFD-

Modelling and measurements’. Proceedings of the 16th


South Africa, 2009

http://www.berr.gov.uk/files/file49433.pdf


103

Chapter 7 Conclusions

Accurate transformer thermal modelling is of great importance for predicting the hot-

spot temperature and its location. Because the thermal models proposed in IEC and

IEEE loading guides [9,49] is over-simplified and strongly relies on the empirical

hot-spot factor, thermal network modelling has been relied upon whenever a

fundamental understanding of oil flow and temperature distributions in a transformer

structure is required. Network modelling is developed and has gained spread usage

also because it is well balanced between its calculation speed and approximation

details and requires relatively low computational effort. With network modelling

sensitivity studies can be more easily performed upon a large range of thermal design

parameters and loads.

In comparison to network modelling, CFD are general numerical methods with much

higher spatial discretisation, and can be expected to exhibit more details about the

flow and temperature patterns inside oil ducts or junction node regions, although this

requires a tremendous increase of computational effort.

The principle of this PhD work concentrated on developing a more accurate and

reliable network model. Firstly a mathematic analysis was conducted to prove that

the 2D channel flow between infinite parallel plates is a sufficient approximation to

model the flow in winding oil ducts; the relative error due to the radial expansion of

the oil ducts is less than 5% for typical transformer designs.

Secondly based on thermal conduction principles, a mathematic model, TEDISC,

was developed to predict the conductor temperature distribution of winding discs.

From the study using TEDISC, it was identified that the network model‟s assumption,

i.e. the conductor temperature linearly increases towards the oil flow downstream

end of discs, could predict the hot-spot temperature with relative error below 1%.

The major research of this PhD is then focusing on conducting large sets of highly

discretised 2D CFD simulations to calibrate the empirical equations employed in

network modelling. The empirical equations for Nusselt number (Nu), friction

coefficient and junction pressure losses (JPL) were fully calibrated for transformer


104

oil and oil duct dimensions. The newly calibrated Nu equation predicted a winding

temperature increase as the consequence of on average 15% lower Nu values along

horizontal oil ducts. The new friction coefficient equation predicted a slightly more

uniform oil flow rate distribution across the ducts, and also calculates a higher

pressure drop over the entire winding. The calculation results based on the new JPL

equation constants were compared with the results with the current „off-the-shelf‟

constants from [19,28] and also the experimental results from [40]. The new

constants showed significantly better match to the experimental results and revealed

that more oil will tend to flow through the upper half of a pass if at a high inlet oil

flow rate.

The oil flow distribution was calculated on the same winding pass model by both the

calibrated network modelling and CFD. The calculation results were also compared

with the experimental results, and it was concluded that the deviation between the oil

pressure drop over the pass calculated by the network model and the CFD and the

measured values is acceptably low. It verified that network modelling could deliver

quick and reliable calculation results of the oil pressure drop over windings and

thereby assist to choose capable oil pumps at the thermal design stage. However the

oil flow distribution predicted by the network model deviates from the one by CFD,

especially at high flow rates.

Sensitivity studies on various thermal design parameters and loads were conducted

by using the CFD calibrated network model in conjunction with a pump model. The

studies were using a directed oil cooling low voltage winding case [19]. The

conclusions basically include:

1) Narrowed oil ducts increase winding hydraulic impedance and as such reduce the

inlet oil flow rate, but their effect on temperatures depends: narrowed horizontal

ducts optimise the uniformity of the oil flow distribution and reduce the average

winding and hot-spot temperatures; narrowed vertical ducts increase the average

winding and hot-spot temperatures.

2) Arranging doubled number of oil block washers would significantly decrease the

disc temperatures with the inlet oil flow rate slightly reduced, 7.8%, due to the

increment of winding hydraulic impedance.


105

3) The impact of different loadings, 50%~150% of rated load, upon the inlet flow

rate is limited, relative change below 5%. The correlations between the average

winding and hot-spot temperatures versus load factors follow parabolic trends.

The future work can be classified into several points:

1. For deriving the junction pressure loss (JPL) equations, a possible limitation

might come from the fact that short vertical oil ducts exist in windings. Vertical

duct lengths are so short that the upward oil flow upon departure from a junction

will shortly arrive at the next junction, which implies that it may be difficult for

the vertical oil flow to re-achieve fully developed status after the junction

interruption. Further studies on the interaction between adjacent junctions along

the vertical duct will be a necessity.

2. The flow distribution predicted by the network modelling deviates from the one

by CFD. This is particularly obvious for the cases with high flow rates probably

due to the entry eddy circulation phenomena that were observed in CFD. Neither

of the predictions on flow distribution has been validated by experiments;

experimental validation is therefore a necessity for future work.

3. Sensitivity study on natural oil cooling transformers requires external radiator

models. Suitable external radiator models need to be researched for the thermal

design optimization of natural oil cooling transformers.


106


107

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115

Appendix I Reference [19]

Estimation of transformer winding temperatures and coolant flows using a

general network method

A.J. Oliver

1980

IEE PROC, Vol. 127, Pt. C, No. 6

Estimation of transformer winding temperaturesand coolant flows using a general network method

A.J. Oliver, M.A., Ph.D.

Indexing term: Transformers

Abstract: The windings of large modern transformers are generally cooled by pumping oil through a networkof ducts in the winding. The resulting value of the hottest conductor temperature and the position it occursin the winding are important parameters in the design and operation of a transformer. There is a standardmethod for estimating the value of this hot spot but there is very little information on the position at whichit occurs. Also, devices have been developed which when inserted in a winding will measure the localtemperature. These instruments could be used to measure the hot-spot temperature of a winding in a trans-former on load. However, it would obviously be advantageous if the position of the hot spot could beestimated so that the device could be installed in the optimum position. The work reported here attemptstwo things: first, to improve on the standard method for estimating the winding temperature distribution andhot-spot temperature and secondly to estimate the position of the hot spot. The computer programdeveloped to do this can be used to estimate the flows, fluid temperatures and boundary temperatures forany network of flow paths. However, only its application to a transformer is considered here. The methodused to obtain the required predictions is described, and estimates are presented of the winding temperaturedistribution for a particular design of transformer operating with a steady load.

R

Re

S

t

tl

to

List of symbols Q

aijibi,Cij,di — coefficients defined in the AppendixA = duct cross-sectional areaAc = conductor cross-sectional area .As = duct surface area ^c

b = radial thickness of conductor and insulation,see Fig. 3b

bc = radial thickness of conductor, see Fig. 3bCp = specific heat of fluidD = duct equivalent diameter (4/4 4- wetted

perimeter)dc = axial conductor depth, see Fig. 3bdp = insulation thicknessds = thickness of spacer in transformer—depth of

cooling duct, see Fig. 3bdv = width of vertical ducts in transformer see

Fig. 3bf — friction factor (fanning)g = gravitational accelerationh = vertical heighthf = convective heat transfer coefficient/ = currentK, K', K" = pressure-loss coefficientsk = thermal conductivity of fluidkc = thermal conductivity of conductorkp = thermal conductivity of paperL = duct length — for the disc type transformer

winding problem this is equivalent to theradial width of the winding, see Fig. 3b

M = total number of nodes in the networkm = number of parallel paths joining two nodesm = mass flowrate at a source of mass flow

(m > 0 denotes an input of mass, m < 0denotes an output)

Nu = Nusselt numberP = pressure (in the transformer predictions

it denotes total pressure)Pr = Prandtl number

Paper 997C, first received 31st October 1979 and in revised form30th July 1980 SubscriptsDr. Oliver is with the Central Electricity Research Laboratories,Kelvin Avenue, Leatherhead, Surrey H

IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980

c,w

power input at a source of heat (Q > 0denotes an input of heat, Q < 0 denotesan output)wall heat fluxheat generated in unit time by unit lengthof conductorelectrical resistance for unit length ofconductorReynolds number based on equivalentdiameterchange in pressure caused by a pressuresourcetemperaturebulk temperature of fluidconductor temperaturetemperature of any fluid injected at a nodereference temperature for electrical resistanceat which R= Ro

average wall temperaturefluid velocitydistance along a duct in the direction of flowthermal admittance between the conductorand the oil for unit length of conductorthermal admittance of insulation for unitlength of conductordistance along the conductortemperature coefficient of electrical resis-tanceconnection matrix for the flow network,its value is:+ 1 if nodes / and / are connected and / > /— 1 if nodes / and / are connected and / < /

0 if nodes / and / are not connecteddynamic viscosity of fluid at its bulktemperaturedynamic viscosity of fluid at the walltemperaturekinematic viscosity of fluid at its bulktemperaturea dependent variable

Refers to disc H

395

0143-7046/80/06395 + 11 $01-50/0

Authorized licensed use limited to: The University of Manchester. Downloaded on May 10, 2009 at 17:22 from IEEE Xplore. Restrictions apply.

to

/ Refers to node ij Refers to node /. Similarly for k and mJ Refers to disc Jloc Local value0 Reference value corresponding

temperature t0

i, j Refers to duct connecting nodes i and /p, q Refers to duct connecting nodes p and qi, j , I Refers to /th duct connecting nodes i and j

when there is more than one duct between/ and j

Superscripts

001

Refers to nth iteration

Introduction

The windings of large modern transformers are generallycooled by pumping oil through a network of ducts in thewinding. Usually the oil enters at the bottom of the-winding and exhausts at the top. This results in an overallincrease in temperatures up the winding. However, thehottest conductor temperature does not occur at the topof the winding. This usually considered to be due tothe combined effect of maldistribution of oil flow andlosses.

Knowledge of the temperature and position of this hotspot is important for the design and operation of thetransformer. For example, the rate of deterioration of thewinding insulation increases as the conductor temperatureincreases. Therefore, it is necessary to know the hottestconductor temperature in order to ensure a reasonablelife for the insulation. At present, design methods for atransformer give values for the rise of average windingtemperature above the average bulk oil temperature. Thisvalue is then added to the oil temperature at the top ofthe winding to give the conductor temperature at thetop. Then an arbitrary 10% of the average windingtemperature rise is added to the top conductor temperatureto get an estimate of the hot-spot temperature. This isthe standard method for estimating this temperature.1

The position of the hot spot is not known with any accuracy.Several devices have been developed to measure the

local conductor temperature, for example, the'Vapourtherm' device described by Hampton andBrowning.2 However, if any of these devices are to be usedit would be advantageous to know the approximate positionof the hot spot so that they can be positioned there.

The purpose of the work reported here is to improve onthe standard method for estimating the hot-spottemperature and to provide an estimate of the positionof the hot spot. The mathematical model which has beendeveloped to do this also provides estimates of thetemperature, oil flow and oil pressure throughout thewinding. The model has been developed into a computerprogram called TEFLOW.

TEFLOW can be used to estimate the flows, fluidtemperatures and boundary temperatures for any networkof flow paths. However, only its application to a transformeris considered here.

2 The mathematical model

2.1 Approach used

A collection of interconnecting flow paths or ducts can berepresented on the network diagram of the type shown in

396

Fig. 1. Each element of the network represents a singlepath with the nodes usually being placed at the junctions.In the model, values of the pressure and bulk temperatureare determined for each node. Values of fluid velocity andaverage wall temperature are determined for each path. Ifthe temperature varies significantly along a path, then thatpath could be split into several elements in order tocalculate this variation.

The required values of pressure, bulk temperature,fluid velocity and wall temperature are obtained by solvingthe set of equations which can be obtained from thefollowing:

(a) conservation of mass applied to each node(b) conservation of thermal energy applied to each node(c) pressure-drop equation applied to each path(d) heat-transfer equation applied to each path.

The actual equations and the method of solution arediscussed in the next section.

2.2 Solution Procedure

The following assumptions were made in deriving theequations:

(i) conduction along the duct wall is negligible(ii) there is complete mixing at a junction so that

the fluid entering each of the exits from a junctionis at the same bulk temperature.

The set of equations which are obtained from (a) to (d)in Section 2.1 are given below.

Application of the conservation of mass to a node i, seeFig. 1, gives

M

1°"-' (1)i=

where 2 a,-;- represents all the paths which connect nodesj

j to node /.2 allows for more than one path between a node / and a

node /. The case of / > 1 can be handled by the solutionprocedure, but to simplify the equations it will be assumedfor the rest of this Section that two nodes / and / aredirectly connected by only one path (i.e. / = 1). In thiscase eqn. 1 reduces to

M

I ai,jPiJuUAU = ~mi (2)

The pressure drop equation for a path (/, /) joining nodes

• •

(j.k.2)

i ( i . j )

Fig. 1 Simple network diagram

• node— duct



i and / can be expressed as

Pi-Pi = -

II

.Q «P,Q - Pu 8 (hf -

IV

(3)

V

where term I represents the losses which are related to thevelocity head, for example friction; terms II and III are thelosses which are proportional to the velocity head inanother pipe, these could occur at junctions; term IVrepresents the gravitational head; term V allows for anypressure sources (pumps) or sinks.

Conservation of thermal energy applied to each nodegives

''"' KJ

(4)

The first term in curly brackets is + 1 if the flow is fromnode / to node / and is zero otherwise. The second termin curly brackets is + 1 if the flow is from node / to node/ and is zero otherwise. The last two terms of eqn. 4 allowfor the injection or extration of mass at node /.

The equation for the transfer of heat from the wallto the fluid for the path (i, j) can be written as

(5)

where the term in square brackets is the mean bulktemperature of the fluid in the path (/, /).

Eqns. 2 to 5 are the required equations. These representthe flow and heat transfer in the network considered. Theequations have been written so that the correct flowdirections in the network will be predicted even if theseare not known a priori.

Before these equations can be solved information mustbe supplied which enables the coefficients of the equationsto be derived. This information consists of: the physicalproperties of the fluid; the geometry of the network;pressure loss coefficients; friction factors; Nusselt numbersor heat transfer coefficients; source/sinks of pressure, heatand mass. Clearly, the values of these coefficients aredependent on the particular problem being considered.Also the relevant boundary values for the problem needto be specified. This is discussed further in Section 3 for aparticular case.

These equations form a complete set for the networkconsidered. Their solution provides values of pressure,Pi, and bulk temperature (fb),- at each node and values ofvelocity, ut}-, and mean wall temperature (tw)itj for eachduct. In order to solve the equations, they are rearrangedto give:

(a) a set of simultaneous linear equations for pressurewith variable coefficients depending on velocity (andtemperature if the properties are temperature dependent)

(b) a set of simultaneous linear equations for bulktemperature with variable coefficients

(c) nonlinear equations for velocity and walltemperature.These equations are solved by an iterative technique.Further details of the solution procedure are given in theAppendix.

The method described so far is of general applicability.The remainder of this paper describes its application to theprediction of temperatures and cooling oil flow rates forthe winding of a large transformer.

3 Representation of the cooling in a large transformer

3.1 The cooling of a transformer winding

The case considered is a disc type of winding which iscooled by the direct forced flow of oil. The basic design ofa single phase of a transformer is shown in Fig. 2. It consistsof an iron core around which is wound a low-voltage anda high-voltage winding. The mathematical model describedin this section applies to either of these windings. Thewinding consists of an insulated conductor which is wound

l.v.winding

h.v. winding

Fig. 2 Schematic diagram of windings for single phase of atransformer

IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 397


spirally into discs. Each disc is separated from its neighboursso that there are gaps, referred to as ducts, between theadjacent conductor discs through which cooling oil canflow, see Fig. 3.

Oil is pumped into the bottom of the transformer.From there it flows into the regions occupied by thewindings and then the design is such that is should flowup the windings in the manner shown in Fig. 3.3 Theblockwashers completely block the oil duct on one side ofthe winding. Thus, at that level all the oil flows past thewinding on one side. The blockwashers, which are approxi-mately equispaced up the winding, alternate from one sideof the winding to the other. The group of cooling ductsbetween adjacent blockwashers is known as a pass. Thusthe winding is made up of several similar passes in series.On reaching the top of the winding the oil passes intoa header and then onto the coolers.

3.2 The network model

The group of cooling ducts which constitute a pass can berepresented by a network such as that shown in Fig. 4for a pass with seven cooling ducts. The conductor discsand blockwashers are shown for clarity.

The model of the complete winding is constructed byjoining together several networks like that of Fig. 4 so thatthere is one for every pass in the winding. If necessaryadditional resistances can be added to the model to allowfor entrance and exit effects on the oil flow at the top andbottom of the winding.

3 '

- • -o i l retaining wall

-conductor disc

. blockwasher

pass

Fig. 3A Flow paths in winding - vertical section

insulation b;

conductor t>, \V

• conductor disc

Fig. 3B Details of conductor disc — vertical section

398

Eqns. 2 and 4 may then be applied to each node of the.network and eqns. 3 and 5 to each duct of the network. Theresulting set of equations can then be solved using thesolution procedure of Appendix 9.1 to give the flow andthe wall temperature for each duct of the network togetherwith the pressure and temperature for each node.

The following subsections describe the quantities thatneed to be defined in eqns. 2 and 5 and they also suggestways of obtaining these quantities. The method ofobtaining conductor temperatures is also described.

It is necessary to define the winding geometry, thecooling fluid properties, the heat generation, the boundaryvalues and the following coefficients for the ducts: frictionfactors, pressure-loss coefficients and Nusselt numbers.The source term, Sitj, in the pressure equation is zerofor the network considered. For the application consideredthe oil flow into the bottom of the winding and its inlettemperature also need to be specified.

3.3 Coefficient values

The Reynolds numbers for the flows in the cooling ductsof a winding will generally be considerably less than 2000,so the flow is assumed to be laminar.

For the friction factors, the solution procedure assumes

/ \ d

= a Rec[ —

where a, c and d are constants. The values used for a and cwere those given by Rosenhow and Hartnett4 for a parallelplate duct, i.e. a rectangular duct with a very high aspectratio, namely a = 24 and c = — 1. The value of d used,0-58, was that given by Rosehnow for a liquid flowing ina tube — no other more relevant information could be found.

For Nusselt number, the assumed form is

Nu = (6)

For transformer oil, Pr ~ 200, thus thermal entrance effects

1 pass <

[conductor disc

block washer

Fig. 4 Network representation of pass with seven cooling ducts



could be important. Rosenhow and Hartnett4 give analyticalvalues for the local Nusselt number in the thermal entranceregion of a parallel-plate duct with a constant heat flux ateach wall and a constant property fluid. These can berepresented by

Nuloc =

Nuloc = 8-2

-1/3

x/D

RePr

x/D

RePr> 0008

< 0008 (7)

(8)

(Junctionloss) , .„

(Junction loss)2

The pressure-loss coefficients which require specificationfor this problem represent the pressure losses which areattributable to the junctions. Following Stephenson6 thejunction loss between the main combined flow and abranch of a junction is incorporated into the loss coefficientfor the branch.

The only information found on the pressure losses atjunctions with laminar flow is the measurements of Jamisonand Villemonte7 for tee-joints with pipes of equal size andshort radiused corners. Using the notation shown on Fig. 5,their measurements can be approximated by

= [lO-65-1976 g

x £

\pu?

7-3 x 103

Re,

combining

(Junction loss)™^! = 110-65 - 19-76 | ^ -

(Junction loss)7 0 x

Re-,

However, the value Nu required by the solution procedureis an average value over the length L of the duct, therefore

Nu =\0Nulocdx

(9)

Also, it is necessary to take account of the effect of viscosityvariations with temperature. According to Knudsen andKatzs this can be approximately represented by a factor(idw/UbT0'14 • ThiS' combined with eqns. 7 to 9 gives thefollowing expression for Nu:

-1/3 -0.14

o . LID\ / / OKRePrl \P

L/D

RePr< 0-026

-0.14

Nu = 8-2 —LID

RePr0-026

Comparison of eqns. 6 and 10 gives

-1/3

r, = 2-44 I

0 = y = 1/3, 5 = - 0 1 4

LIDRePr

< 0026

I 2x 2 PU2

dividing

It is assumed that these formulae apply to the cooling-ductjunctions in a transformer.

3.4 Boundary values

For any flow network problem, a pressure must be specifiedat one node at least. Furthermore for a node i with a masssource it is necessary to either

(i) specify w,- and (tb)jor

(ii) specify Pt and (fb),-and for a node / with a mass sink then either

(iii) specify m}

or(iv) specify Pj

For the transformer network conditions (ii) and (iii) wereused.

The heat source at a node which is represented by Q waszero for all nodes. The only other boundary value to bespecified was the wall heat flux for each duct qtj. Thiscan be derived from the heat generated within the conductor.

3.5 Representation of heat generation

As mentioned in Section 2.2, the solution procedureignores heat conduction in any boundary. This means thatheat conduction along the conductor is assumed to benegligible. Justification of this assumption is given inAppendix 9.2.

77 = 8-2, 0 = 7 = 0,

6 = - 0 1 4 . . . LID > 0 026RePr


Fig. 5 Notation used for junction losses

399


The heat removed by the cooling oil consists primarilyof the ohmic losses of the winding conductor plus losseswhich are caused by the induced eddy currents in thewinding. Most transformer windings are designed so thatthe eddy losses are comparatively small. In the caseinvestigated in this paper, they have been ignored forsimplicity. Thus, the losses for a disc / , see Fig. 4, can beexpressed as

(QC)J = (11)

where qc is the heat generated in unit length of theconductor.

However, the quantity required by the network modelis the heat flux through unit surface area of the duct.For duct (i, /), this is denoted by qt j . Using the notationof Fig. 4, (qc)j can also be expressed as

(QC)J = Yew [(tc)j-(tw)itj] + YCiW[{tc)j-{tw)ktl)

where the thermal admittance, Yc w

(12)

is defined for unitlength of conductor. In this case, the heat flow out of thevertical ends of each disc is ignored as it is generally smallin comparison. However it can be allowed for if necessaryin eqn. 12 and in the following analysis. The heat flow intothe duct (/, /) comes from the discs J and H. Together, unitlengths of conductor in discs </ and H contribute 2 x 6to surface area of the duct (/, / ) . Therefore for unit surfacearea

Qij = ^ {Yc,u,[(tc)j-(.tw)u] +Yc>w[(tc)H-(tw)u]}

(13)

By equating eqns. 11 and 12 the following eqns. for {tc)jcan be obtained

The conductor temperature tc can be obtained from theconverged temperature predictions by using eqn. 14.

3.6 Estimation of temperature variation through a disc

Using a network as illustrated in Fig. 4 results intemperature predictions which are values averaged overa given disc. As the oil flows through a given cooling duct,its temperature will rise as it picks up heat and theconvective heat-transfer coefficient may change due tothermal-entrance effects. Assuming the heat-transfercoefficient varies conventionally and decreases with down-stream distance, then the conductor and insulationtemperatures towards the downstream end of the disc willbe higher than those towards the upstream end. In order toestimate the maximum conductor temperature for eachdisc, the following method was used.

The oil temperature at the downstream end of the discwhere the temperatures will be, approximately, maximumis given by

ML = (tb)i + 2[(tb)m-(tb)i]

where (tb)m is the average value obtained from TEFLOW.Thus the maximum oil/insulation interface temperature canbe obtained from

2[(tb)m-(tb)i)}(Muloc)L/D

where (Nuloc)L is defined by eqn. 7 or eqn. 8 with* = L,the properties being evaluated at the known averagetemperature. Then the estimated maximum conductortemperature for a disc J, can be obtained from eqn. 14 withtw replaced by (tw)L.

(tw)kJ] + I2R0 (1 -at0)T; T T (14)

Similarly an eqn. for (tc)H can be obtained from equationswhich are equivalent to eqns. 11 and 12 but for conductordisc H.

Substitution of eqn. 14 and the corresponding equationfor (tc)H into eqn. 13 gives the required equation for wallheat flux:

Y 2Ic'w

2b(aI2R0-2YCtW){[(tw)u-(tw)8th]

- l

2b\I2R0 2YC>105)

The thermal admittance between the conductor and theinsulation/oil interface for unit length, Yc w, was taken as

-*c,w

3.7 An illustrative example

In order to illustrate the method, the following examplewas chosen. The l.v. winding of a 250 MVA transformeroperating at 22 kV has been considered. This gives awinding current of 6561 A for a 3-phase delta connection.This current is assumed to be carried by all the 22 turnsin one disc of the winding connected in parallel.

The winding geometry used was that given by Lampe,Persson and Carlsson8 for a winding model to which theyrefer. The geometrical details are given in Table 1, usingthe notation explained in Fig. 3. A winding with fivepasses and 20 ducts per pass was considered..

Property values for transformer oil based on thosespecified in the British Standard for transformer oil9 aregiven in Table 2. These values were taken as constantexcept for the density and viscosity. The density wascalculated from the expansion coefficient and the viscosityof the oil was calculated using the following formulasuggested by Spiers10 for oils:

l o g l 0 ( u x l 0 6 ) =

The coefficient A was taken as — 2-34 and B as 5-88.This gives values which for t > 10°C are within 5% of theviscosity values specified in the British Standard.

400 IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980


Table 1: Geometrical detailst

Oil duct length (L)Oil duct depth ids)Vertical oil duct width (dv)Width of conductor + insulation (b)Thickness of paper insulation [dp)Width of conductor {bc)Depth of conductor (dc)

100 mm5 mm

15 mm4-5 mm0-6 mm3-3 mm

10 mm

Table 2: Properties of transformer oil

Density (at 20°C)Expansion coefficientSpecific heatThermal conductivity

0-895 X 103 kg/m3

000065/K20600 J/(kgK)

0-13W/(mK)

4. Results

Predictions of the oil-flow distribution in the first twopasses are shown in Fig. 6. The results for the remainingthree passes are the same to within 1%.

Predictions of mean and maximum conductor disctemperatures are shown in Fig. 7. Also shown are thepredictions of oil temperature at the inlet and outletof each pass. The variation in heat flux up the transformerwinding owing to the thermal effects represented in eqn. 15is not insignificant for the conditions investigated. Theseeffects are due to the change in electrical resistance withtemperature and the dependence of heat distribution froma disc on the conductor to oil temperature difference oneach side of the disc. The variation was of the order of10% through a pass owing to a combination of theseeffects. However, the variation up the winding for a givenduct in each pass was only 4%; this explains why thereis no noticeable deviation from a linear profile for the oiltemperature predictions in Fig. 7. The peaks in conductortemperatures towards the centre of each pass are a directconsequence of the low flows existing there.

0 14

0 13

0 12

on

010

009

008

D

C»

c"oo

0 07

* ° 0 6

2 005

= 004o

003

002

001

Predictions were also obtained for constant oil propertiesto illustrate the importance of allowing for propertyvariations. This resulted in the velocities of Fig. 6 beingchanged by a maximum of 5% and the conductortemperatures of Fig. 7 were increased. The maximumincreases in temperature occurred towards the centre ofeach pass where the mean values were increased by approxi-mately 3°C and the maximum values by 5°C.

Also shown in Fig. 7 are estimates of the conductorhot-spot temperature calculated by the standard methoddescribed in Section. The average conductor temperatureand the oil temperatures required for these calculationswere obtained from the predictions.

100

90

80

)

• 70i

[so

' 50

30

*. x x •** ° *** " "* **

pass number

Fig. 7 Conductor temperatures in each disc• mean value for each discX maximum value for each disco mean winding temperatureQ hot-spot temperature (standard method)A oil temperature

1 2 6 8 10 12 14 16 18 20 1 2 3 4 8 10 12 14 16 18 20-

number 1 pass

Fig. 6 Distribution of flow between cooling ducts

t See Figs. 3 and 5


number 2 pass

• cooling ductsnumbered frombottom of pass

401


5 Discussion

Clearly the computer program TEFLOW that has beendeveloped can be used to predict the conductor temperaturesand the oil flow and pressure in a directed flow, forced oilcooled transformer.

Qualitative experimental confirmation of the predictedoil flow distribution (Fig. 6) is provided by themeasurements of Allen, Szpiro and Campero.11 They havemeasured oil flows in a Perspex model of a pass of a disctype winding. Their experimental results confirm the shapeof the profile in Fig. 6 with minimum flows being measuredin the ducts towards the centre of the pass and maximumflows in the ducts at the top and bottom of the pass.

The predictions indicate that the hot spot for therepresentation used occurs in the middle-conductor discof the top pass of the winding. It is thus possible to getan indication of where to position a device which seeks tomeasure the hot-spot temperature, such as the Vapourtherminstrument mentioned in Section 1. The program could alsobe used to study the effects of modifications to existingcooling-circuit designs or to investigate new designs.

It is worth noting from the predictions that the peakconductor temperature in each of the top few passes doesnot differ by more than a few degrees from the windinghot-spot temperature.

The conventional hot-spot computation, which gives noinformation on position, agrees with the maximum valueof the predicted mean conductor temperature averaged overa disc, but it underestimates the absolute maximumconductor temperature, this is for a situation where theconductor temperature rise across a disc is significant.Also the conventional hot-spot computation may not do aswell as the described procedure when there arenonuniformities in a winding which may produce high localtemperatures without significantly affecting the meanwinding temperature.

Clearly, all the predictions presented are dependent onthe relationships used for the loss coefficients, frictionfactors and heat-transfer coefficients of the network. Thecoefficients used for the winding example can only beregarded as estimates. In order to get accurate predictionsfor a transformer it will be necessary to either checkthese coefficients experimentally or to use alternativevalidated values if they are available. However thetechnique, even with the unvalidated coefficient valuesreported, provides far more useful information than thestandard method for predicting the winding hot-spottemperature.

6 Conclusions

A numerical procedure has been developed that predictsthe flow and pressure of a fluid flowing in a network ofinterconnecting ducts. If heat is transferred to or from thefluid then the fluid and duct-wall temperatures can alsobe predicted. The variation of viscosity and density withtemperature is allowable.

The procedure, which has been incorporated into acomputer program, has been applied to the oil flow in atypical directed flow, forced-oil-cooled transformer.Predictions of oil flow and temperature and conductortemperature have been obtianed. This enables the windinghot-spot temperature and its position to be determined. Forthe particular representation of a transformer considered,the results indicate that the hot spot occurs in the top passof the winding on the middle-conductor disc.402

The computer program could also be used to investigatenew designs and the effect of modifications of existingcooling-circuit designs.

7 Acknowledgements

This work was carried out at the Central ElectricityResearch Laboratories and it is published by permission ofthe Central Electricity Generating Board.

8 References

1 ALLEN, P.H.G.: 'Transformer rating by hottest spot tem-perature', Electr. Times, March 1971, pp. 33-38

2 HAMPTON, B.F., and BROWNING, D.N.: 'Rating of powertransformers', CEGB Tech. Disclosure Bull, 1967, 79

3 CEGB Modern Power Station Practice, Vol. 4 (Pergamon Press,1971)

4 ROSENHOW, W.M., and HARTNETT, J.P.: 'Handbook of heattransfer' (MCGraw-Hill, 1973)

5 KNUDSEN, J.G., and KATZ, D.L.: 'Fluid Dynamics and HeatTransfer' (McGraw-Hill, 1958)

6 STEPHENSON, P.L.: 'MORIA: a program to calculate the flow-and pressure drop in a pipe network'. Central Electricity ResearchLaboratories Report. RD/L/P7/76, 1976

7 JAMISON, D.K., and VILLEMONTE, J.R.: 'Junction lossesin laminar and transitional flows, /. Am. Soc. Civ. Eng. 1971,97, (HY7),pp. 1045-1061

8 LAMPE, W., PERSSON, B.G., and CARLSSON, T.: 'Hot spotand top-oil temperatures proposal for a modified heat speci-fication for oil immersed power transformers'. Proceedings ofthe International conference on large high tension electricsystems, 1972, Paper 12-02

9 British Standard: Insulating oil for transformers and switchgear,1972, No. 148

10 SPIERS, H.M.: 'Technical data on fuel.' British NationalCommittee, World Power Conference, 1966

11 ALLEN, P.H.G., SZPIRO, O., and CAMPERO, E.: 'The powertransformer winding as a thermal problem'. Proceedings of theCNR symposium on power and measurement transformers,positano, September 1979, pp. 75-81

12 WOOD, D.J., and CHARLES, C.O.A.: 'Hydraulic networkanalysis using linear theory', Proc. Am. Soc. Gv. Eng., 1972,98,(HY7),p. 1157

9 Appendix

9.1 Details of the solution procedure

As described in Section 2,2, the first step was to derivea set of simultaneous linear equations for pressure. Themethod used was derived from that used by Stephenson6

and Wood and Charles.12 From eqn. 3:

[-.,.,,.,,4,,Table 3: Further property and coefficient values

Thermal conductivity of insulation (kp)Temperature coefficient of electrical

resistance (a)Thermal conductivity of conductor (kc)Heat generated per unit length of

conductor at f0 = 75°C (/2 Ro)Convective heat-transfer coefficient (/»/•)

from predictionsApproximate half-length of winding in

a disc (/)Typical temperatures for a disc, f,

obtained from predictions f2fa

0-2W(mK)43 X10" " /K

3-8 X 102 W/(mk)55W/m

325W/(m2K)

3 5 m

82° C95° C39° C



L 'ui,j* ' i,J'

Substituting in eqn 3 and applying it to each node / = 1

M

X OijPj = bt i = 1 -> Mj

(17)

(16)

where

Mau = I a u PuAu

fl

ij

aU = ~a

bt = -rhi

j - 1aupuAu au - Q u2

PfQ

fL

M

Eqn. 17 represents the required simultaneous linearequations for pressure. For a node / = / where the pressureis specified as /*, = Pj, then the coefficients are

aj,j = 1; ajj = 0.../ * J

bj = Pj

Eqn. 4 applied to each node can be expressed asM

(18)

\;lJ

where

AM,-

Eqn. 18with/= 1 -> M represents the required simultaneouslinear equations for bulk temeprature. For a node wherethe bulk temperature is specified the treatment is the sameas that for the pressure equation.

The wall-temperature equation can be obtained byrearranging eqn. 5 to give

Ml l i UjCn \UU\

AM;

= -\ctu\\The set of equations represented by eqns. 16 to 19 weresolved by an iterative procedure. For the «th iteration thesteps in the solution were

IEEPROC, Vol. 127, Pt. C, No. 6, NOVEMBER 1980 403


Step 1: the linear simultaneous equationsM

i = \ M

were solved for Pi<-n) using Gaussian elimination with

partial pivoting. The superscript {n — 1) indicates that thevalues of the dependent variables occurring in the coefficientare to be obtained from the (n—l)th iteration.

2: the linear simultaneous equationsM

i = I -*- M

were solved for (?b),(n).

Step 3. the equation for wall temperature was expressed inthe form

(t V (n)

\kNuu ^'—"ft(n-l)

^i,j\

(n-1)

and was solved for (tw)i/n) for each path (/, /).

t: the equation for velocity was expressed as

1-1/2) vj—Pj)( n - l )

\/l

0-001-0003

where the value chosen depends on the particular problem.

9.2 Importance of heat conduction in the winding ofa transformer

Consider a given disc conductor in a winding. The oil flowsacross the disc surface in a direction normal to theconductor. A simple heat balance shows that the risein oil temperature as it flows across the disc is small forthe magnitude of heat fluxes that occur. For a simplifiedanalysis, the situation can be represented by a fluid at aconstant temperature flowing across a conductor of length/, where / is the length of the conductor in the disc. Theconductor is surrounded by paper insulation and heat isgenerated in the conductor. A heat-balance equation forunit length of the conductor allowing for heat conductionin the conductor is

(20)

where the first term represents conduction, the second termrepresents the heat flow to the oil and the third term is theheat generation. The admittance Yc a represents the thermaladmittance between the conductor and the oil for unitlength of conductor. In deriving this quantity it is assumedthat the heat flow through the insulation passes onlythrough regions of width bc at the top and bottom of theconductor, see Fig. 3; in the conductor disc most of theremaining insulation faces onto adjacent conductors so theheat loss through this insulation is small. Thus

Solving eqn. 20 for tc gives

i ~ hj) - au Su

( n - D

( n - 1 )

with

This denotes an iteration equation with underrelaxation.The value of the relaxation coefficient is 0-4. Theseequations were solved for w,jy

<") for each path (/, /).

Step 5: go to step 1 and repeat steps 1 -> 5 for the (« + 1 )thiteration.

The iterative loop represented by steps 1 -»• 5 wasrepeated until the following convergence criterion wassatisfied for each dependent variable:

404

tc = A exp (mz) + B exp (— mz) +

I2Ro(l-octo)+YCtatc

Yc>a-otI2Ro

where

m -J Yca-ocI2Ro

(21)

The constants A and B can be evaluated from the following



boundary conditions:

atz = 0, tc = tx

atz = /, tc = t2

where z = 0 denotes a position on the conductor in thedisc where the temperature is known to be tx and z = /represents a position where it is known to be t2 •This gives

— tx exp (—ml) —

A =

I2R0(l-at0)+Yc>atc

caaI2R0

[1 —exp (—ml)]

exp — t2 —

exp (ml) — exp (—

I2R0(l-at0)+ Yc.ata

(22)

Yc,a-aI2R0

[exp (m/) — 1 ]

B =exp (ml) — exp (— ml)

(23)

The importance of conduction is indicated by the value ofthe following ratio

r =kc

Yc

Ac

d2tc

dz2

tc-ta)

Substituting for tc using eqn. 21 gives

r =(Yc,a - oJ2Ro)[A exp (mz) + B exp ( - mz)\

Yc a I A exp (mz) + B exp (— mz) +I2R0(l-at0)+

YCta-otI2Ro— t,

(24)

Typical values of the quantities required in the evaluationof eqn. 24 are given in Table 3. With these values

z = 1 metre -> F ^ 1 x 10"3

z = (I-I) metre -+ T ^ 1 x 10"3

where / is approximately half the length of conductor in adisc. For z = 1 -> (/— 1) metre, F is smaller. This provesthat for the conditions investigated heat conduction iscertainly not important at more than one metre from theends of the conductor. Therefore the neglect of conductionis justified.

A similar calculation has been made for the magnitudeof the conduction from conductor to conductor throughthe paper. This also has been found to be negligible.

IEEPROC, Vol. 127, Pt. C,No. 6, NOVEMBER 1980 405



117

Appendix II Reference [40]

Thermal-hydraulic investigation of transformer windings by CFD-modelling

and measurements

A. Weinläder and S. Tenbohlen

2009

The 16th International Symposium on High Voltage Engineering (ISH)

THERMAL-HYDRAULIC INVESTIGATION OF TRANSFORMER WINDINGS BY CFD-MODELLING AND MEASUREMENTS

A. Weinläder1*, S. Tenbohlen1 1 Universität Stuttgart, Institute of Energy Transmission and High Voltage Technology,

Pfaffenwaldring 47, 70569 Stuttgart, Germany *Email: [email protected]

Abstract: In modern development of transformers there is a strong requirement for adherence of the temperature limits of the used insulation materials on the one hand and - on the other hand - not to use more material and further resources than necessary. These aims can only be achieved by a precise calculation of the temperature distribution in the windings. The conventional way of calculating the temperature distribution is to calculate the bulk temperature of the oil in the winding channels by the known losses, the flow rate and the thermal capacity of the oil. The temperature in the solid insulation is further calculated by an assumed heat-transfer coefficient which is in reality known only very roughly. The topic of this article is a more precise alternative way of calculating the temperature distribution. The flow field is calculated by CFD (Computational Fluid Dynamics) models and thus a much more accurate value for the local heat-transfer coefficient between oil and solid insulation is achievable. The paper also describes how the CFD models were validated by measurements of the oil flow in winding models.

1. INTRODUCTION

A reliable calculation of the temperature distribution within oil cooled windings is a basic precondition for a fail-safe and material saving design of power transformers.

The importance of an accurate determination of the temperature distribution becomes obvious when a basic law of ageing of insulation material is taken into account. This law says that the ageing rate increases exponentially whit the temperature of the insulation material. Particularly for the case of paper insulation –as mainly used in power transformers- this means a doubling of the ageing rate each 6-8°C.

Within this paper only oil cooled power transformers are regarded. In such a transformer, oil flows upwards through the winding channels while it warms up. Then it flows downwards through the cooler back again into the vessel (ON/OF mode) or directly back into the windings (OD mode). The oil flow is thereby forced by a pump (OD/OF mode) or occurs autonomous from the thermal caused change in density (ON mode).

To estimate the temperature distribution within the windings, first the volume flow of the oil (oil volume/time) through the regarded winding needs to be known. When this size is known then it is possible to estimate the averaged oil temperature at a particular point of the flow path in the winding by evaluating the balance between the known losses of the winding and the thermal energy removed by the oil. To calculate this oil volume flow, it is mainly essential to know the hydraulic resistance of the winding.

When the averaged temperature of the oil is known, the next step is to calculate the temperature of the

conductor. This is nearly identical to the maximum temperature of the submerging solid insulation.

To calculate the difference between the now known averaged oil temperature and the conductor temperature, it is now necessary to know the heat transfer coefficient at the boundary surface between oil and solid insulation. This coefficient is a function of a number of local variables, especially of the velocity in the respective channel, the channel length and the temperature. This means that -beneath the hydraulic resistance- especially the velocity within the particular channels is of fundamental meaning to the calculation of temperatures in the solid insulation.

2. DESCRIPTION OF THE INVESTIGATED GEOMETRY

Representatively for often used winding types, a so called “zigzag” arrangement of a disc-type winding was investigated (Fig.1). In such a case, winding discs are layered above each other, while so called spacers keep the axial distance between the discs and determine the height of the horizontal ducts for the oil. The sticks ensure the proper fixation of the spacers and keep the radial distance between the discs and the outer cover. The vertical ducts are formed by the space between discs and outer cover.

The oil is leaded from the bottom into the vertical ducts and flows from there upwards, while it distributes into the particular horizontal ducts. To ensure a proper distribution of the oil to the horizontal ducts, which should be as equal as possible, the vertical duct is intermitted -alternating between the inner and the outer duct- after a specified number of discs by so called washers. This leads to an oil flow in a “zigzag”



Pg. 1 Paper D-22

manner. Two washers with the discs in between form a so called pass (see also Fig.2).

By putting a washer between each pair of discs, it would be possible to supply each disc with the same oil flow. On the other side, the thermal resistance between the conductors and the oil would be increased by these washers and the hydraulic resistance of the pass would also be increased enormously. Therefore the ideal number of discs between two washers is an optimization problem, which can be treated well with the approaches described below.

Outer Vertical Channel Inner Vertical Channel

Stick

Outer Vertical Channel Inner Vertical Channel

Horizontal Channel

A - A

B - B

Spacer

Stick

Disc

A A

B B

Figure 1: Investigated winding geometry.

3. HYDRAULIC MEASUREMENTS

The hydraulic measurements were especially done to verify the results of the CFD-simulations since it is much easier to achieve results by simulation. A further advantage of the simulation is that there all data from everywhere in the flow field are available for postprocessing, whereas in measurements it is a large effort to get data only at a few points of interest.

The procedure of the hydraulic measurements is to take a model of a section of a transformer winding, into which a specified flow rate is impressed. This flow rate causes a pressure-drop along the flow path, which is measured at some points which are reachable without disturbing the flow significantly.

The model, which is used, represents a section of a real transformer winding according to Fig.2-4. Since a typical winding of a transformer repeats periodically in circumferential and axial direction, it is sufficient to investigate only such a section which also safes a lot of effort compared to the operation at a complete

winding. Since such a section is usually small, it was possible to keep its dimensions according to an example of a real transformer and therefore there was no need to apply laws of similarity to the measured data. Since for the first step only hydraulic data were of interest, the discs were made of transformer board according to the outer form of real discs.

Horizontal Channel

Washer

One PassDisc

Lexan Glass

Oil

Oil

Figure 2: Side view of the model

Washer Stick

Spacer

Figure 3: Front view of the model

Lexan Glass Spacer

Stick

Figure 4: Top view of the model

The pressures were measured at boundary points at the front side of the model as the difference between a reference port (Bin) at the beginning of the pass and the particular points of interest. These points are shown in Fig.5 which shows again the side view according to Fig.2.



Pg. 2 Paper D-22

As sensors, inductive differential pressure transducers of the type DP103 from Validyne were used. The typical accuracy of the pressure measurements was around +-3%.

Figure 5: Scanning points for the pressure

The pressure is acquired according to the scheme of Fig.6 where it can be seen that each pressure transducer is switched between two channels. The data are permanently logged by the computer until steady state is reached. After that a new (known) flow rate is impressed.

Computer

Winding Model

Pressure Sensor (1)

Shortt Circuit Valve

Pressure Sensor (6)

Shortt Circuit Valve

Point A Point B Reference Point

Figure 6: Measurement arrangement

4. CFD SIMULATIONS

4.1. Description

Numerical computer simulations were done with commercial CFD software. The computation was done with Ansys-CFX, which is a finite-volume based CFD-solver, while the mesh generation was done with ICEM-CFD.

For the numerical simulation, the model was assumed as infinitely extended in circumferential direction. This

means that the small wall effect of the spacers which bound the horizontal ducts in circumferential direction is neglected. This seems to be justified because of the large ratio between channel width and channel height. Moreover, modelling in 2D safes an enormous amount of computational effort and time. Since CFX does not have the explicit capability to treat problems in 2D, the approach for that is simply to model in 3D and to pull only one layer of 3D-elements into the circumferential direction. The boundaries in this direction get just a symmetry boundary condition instead of a wall boundary condition.

As the material, a Newtonian fluid was chosen, where viscosity and density depend only on temperature. The flow field was declared as isothermal. Since the Reynolds-number was reliably low, no turbulence model was employed.

The discretization was done with about 1.2 Mio. elements (Fig.7). For the inlet it was assumed that there is a fully developed channel flow with parabolic velocity profile, the outlet was closed by a zero static-pressure condition.

Figure 7: Discretized section of the geometry

4.2. Validation of the simulations by measurements on winding models

Since the distribution of the flow over the horizontal ducts of a path is one of the main quantities of interest, one would like to measure them in such a model. On the other hand it would take a large effort to measure these velocities directly with a high accuracy and reliability. Therefore it was chosen to measure the pressure distribution along the boundary of the vertical ducts, as described in the upper section. From these pressures only the pressure drop over the whole pass is of direct interest since it indicates the hydraulic resistance of the pass. The pressure values from the points in between serve just as a kind of fingerprint for verification i.e. when the pressure distribution at the boundary is equal to that of the CFD-simulation it

Bin

B1

B2

B3

B4

B6

F1

F2

F3

F4

F6

Fout

Oil

Oil



Pg. 3 Paper D-22

seems to be justified to assume the CFD-model as verified. From that point on, only the CFD-model is needed to deliver all quantities of interest within the whole modelled domain. In Fig.8 the pressure drop over the whole pass is plotted in dependence of the impressed flowrate.

0 5 10 15 20Flowrate �l�min� �

50

100

150

200

250

300

Pressure

difference

�Pa

��

Figure 8: Pressure drop over the whole pass (From Bin to Fout)

Fig.8 shows quite small deviations between the measurements and the simulations. Although the model was erected quiet thoroughly, it was not avoidable that inaccuracies of +-1mm within larger dimensions could occur i.e. especially the positions of the pressure taps in vertical direction were unsure within that range. For this reason we extracted from the results of the CFD-simulation different curves for each of these points: One curve (red) where the measurement point is shifted 1mm downwards while the reference point (Bin in Fig.5) is shifted 1mm upwards, a further curve (blue) where the measurement point is shifted 1mm upwards while the reference point is shifted 1mm downwards. Between these two “worst cases” the measured curve will lie if the CFD-model is correct and the inaccuracy of the model for measurements is not larger as the mentioned +-1mm. It can be seen from Fig.8 that the results for the pressure drop over the whole pass are less sensitive for this shift.

For the scanning points in between the situation looks different as Fig.9 shows. The measured values lie fully within the possible range but this rage is quite huge. This means that –especially for high flowrates- it gets really difficult to deliver the proof that the lab model is equal to the numerical model due to the manufacturing inaccuracies of the winding model. It is to mention that the supposed unphysical progress of the lower curves in Fig.9 is to explain with a large separation eddy in the range of the respective scanning point.

0 5 10 15 20 25Flowrate �l�min� �

0

10

20

30

40

Pressure

difference

�Pa

��

Figure 9: Pressure drop from Bin to B6

4.3. Example of a pure hydraulic simulation

In this simulation typical mineral transformer oil at a temperature of 77°C was assumed. The flowrates mentioned in the following are referring to the volume flow of only one section between two spacers with typical dimensions. As a main result, the distribution of the velocity in the horizontal ducts is displayed in Fig.10. The values M_i are the massflows through the particular horicontal ducts while M_mean is the value of M_i, averaged over all eight horizontal ducts. The lines between the points are just for better orientation. For this example case it is obvious, that the distribution of velocity is getting worse for increasing flowrate i.e. increasing Reynolds Number. Mainly the flow in the ducts at lower position is getting very small and can even return into backflow, how the distribution for 25l/min shows.

In Fig.11 for the same example, the streamlines at a flowrate at 25l/min –as typical in OD mode- are displayed. Especially at the upper ducts there are large separation eddies which are reducing their effective width. It is therefore obvious that simple decomposition of the pass into primitives as straight channels, branches and confluences, as it is proposed in [3] and [4], is only applicable for low Reynolds Numbers.

For higher Reynolds Numbers, the boundary condition of a fully developed pipe flow at the interfaces of each primitive element of the pass, which is assumed for the most data available for primitive pipe elements in literature, is no more given. Therefore especially for such high Re-Numbers, as occurring in OD mode, the pass has to be regarded as a whole. This means no great effort in the case of using CFD-simulation.

CFD with points shifted from each other

CFD with points shifted to each other

Measured

CFD with points shifted from each other

Measured

CFD with points shifted to each other



Pg. 4 Paper D-22

-0,5

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

5

1 2 3 4 5 6 7 8

Horizontal Ducts Numbered from Bottom of Pass

Flow

Rat

e D

istri

butio

n M

_i/M

_mea

n

2l/min 10l/min 25l/min

Figure 10: Velocity distribution in the horizontal channels

Figure 11: Streamlines for a flowrate of 25l/min

4.4. Example of a coupled thermal-hydraulic simulation

It is further possible to incorporate also the effects of heat conduction into the CFD simulation. This was done in the now presented case. The flow modelling and the discretization is similar to the former case. The now focused heat transfer requires also modelling of the thermal conductivity of the oil and the solid materials and the thermal capacity of the oil. Beneath that, the solid domains need to be discretized and the known loss distribution within the conductor volume has to be impressed. In the simulation the Navier-Stokes-Equations, which describe the flow, are solved simultaneously with the equations for heat transfer.

In this example a loss density of 142 kW/m3 (according to a current density of 2.6 A/mm2) was impressed into the whole conductor volume. The assumed flowrate at the inlet was 1.7 l/min and the oil temperature at the inlet was 70°C. Fig.12 shows the scheme of the model while the resulting temperature distribution within the

marked range is shown in Fig.13. The marked range was chosen for postprocessing since the upper and the lower vertical boundaries of the model were assumed as adiabatic like all outer boundaries. This was necessary since the little heat fluxes from the bounding upper and lower parts of the winding are unknown. The errors caused by these unwanted thermal boundary effects are minimal in the middle of the model.

Figure 12: Scheme of the thermal-hydraulic model

Figure 13: Temperature distribution

The computation of this both-side coupled thermal-hydraulic system leads to a strongly increased effort, especially because of much slower convergence due to the increased number of variables. Therefore it seems to be more promising to get the values of the heat transfer coefficient from the calculated velocities over empirical correlations and to verify this approach by a low number of simulations that include heat transfer. This is especially a practicable way for OD/OF-cases, where the buoyancy effects are often negligible compared to the pump driven oil flow and therefore the mutual coupling between thermal and hydraulic system can be simplified to a one-way coupling.

Washer Conductor



Pg. 5 Paper D-22

5. CONCLUSIONS

It has been demonstrated that thermal-hydraulic modelling and simulation of transformer windings with CFD is a useful way to get essential data for further calculation of the thermal behaviour of the transformer. Measured and simulated oil flow over a whole pass of a winding segment agree fairly well. Based on that it is possible to determine the values of local heat transfer coefficients much more reliable than usual in the conventional way. As in the last example shown, even the whole temperature distribution is available. The drawback of this comfortable and accurate solution is a strongly increased computational effort. Since additionally the hydraulic resistance of the winding is determined, it is possible to model the whole thermal hydraulic system of a transformer in a network-based simulation with only the need of previously modelling small repetitive sections of the transformer with CFD.

6. REFERENCES

[1] Radakovic, Z., Cardillo, E., Feser, K.: Temperature distribution in windings of transformers with natural oil circulation. 15th International Conference on Electrical Machines (ICEM) 2002,Brugge, Belgium, 25.-28. August 2002, paper no. 415.

[2] A. Weinläder, S. Tenbohlen, “Thermohydraulische Untersuchung von Transformatorwicklungen durch Messung und Simulation“. ETG-Fachtagung: Grenzflächen in elektrischen Isoliersystemen, Würzburg 2008

[3] Jiahui Zhang and Xianguo Li, Coolant flow distribution and pressure loss in ONAN transformer windings — part I: theory and model development, Power Delivery, IEEE Transactions on Power Delivery, Volume: 19, Issue: 1, Jan. 2004, pp. 186-193.

[4] Jiahui Zhang and Xianguo Li, Coolant flow distribution and pressure loss in ONAN transformer windings — part II: optimization of design parameters, Power Delivery, IEEE Transactions on Power Delivery, Volume: 19, Issue: 1, Jan. 2004, pp. 194-199.



Pg. 6 Paper D-22


118


119

Appendix III List of publications

1. W. Wu, Z.D. Wang and P. Jarman. “Optimisation of transformer directed oil

cooling design using network modelling”, IET Generation, Transmission and

Distribution. Submitted, 2011

2. A. Skillen, A. Revell, H. Iacovides, W. Wu and Z.D. Wang. “Numerical

prediction of local hot-spot phenomena in transformer windings”, Applied

Thermal Engineering. Submitted, 2011

3. D.Y. Feng, W. Wu, Z.D. Wang and P. Jarman. “Transmission Transformer End-

of-life Modelling: Incorporating Insulating Paper‟s Thermal Lifetime Analysis

with Ordinary Statistical Analysis”, The 17th International Symposium on High

Voltage Engineering (ISH). Hannover, Germany, 2011

4. A. Weinläder, W. Wu, S. Tenbohlen and Z.D. Wang. “Prediction of the Oil Flow

Distribution in Oil-immersed Transformer Windings by Network Modelling and

CFD”, IET Electric Power Applications. Provisionally accepted, 2011

5. W. Wu, Z.D. Wang, A. Revell and P. Jarman. “CFD Calibration for Network

Modelling of Transformer Cooling Flows – Part II Pressure Loss at Junction

Nodes”, IET Electric Power Applications. Accepted, 2011

6. W. Wu, Z.D. Wang, A. Revell, H. Iacovides and P. Jarman. “CFD Calibration for

Network Modelling of Transformer Cooling Flows – Part I Heat Transfer in Oil

Ducts”, IET Electric Power Applications. Accepted, 2011

7. W. Wu, Z.D. Wang and A. Revell. “Natural Convection Cooling Ducts in

Transformer Network Modelling”, The 16th International Symposium on High

Voltage Engineering (ISH). Cape Town, South Africa, 2009

8. W. Wu, A. Revell and Z.D. Wang. “Heat Transfer in Transformer Winding

Conductors and Surrounding Insulating Paper”, The International Conference on

Electrical Engineering (ICEE) 2009. Shenyang, China, 2009

Documents

CFD Calibrated Thermal Network Modelling for Oil-cooled Power Transformers