Temp Variation of Bearing in Hydro Power

8/11/2019 Temp Variation of Bearing in Hydro Power

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Modelling and Simulation of Temperature Variations ofBearings in a Hydropower Generation Unit

A dissertation submitted to theDepartment of Energy Technology, Royal Institute of Technology,

Sweden for the partial fulfilment of the requirement for theDegree of Master of Science in Engineering

By

CGS Gunasekara

Department of Energy TechnologyRoyal Institute of Technology,

Stockholm, Sweden


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Modelling and Simulation of Temperature Variations of Bear-

ings in a Hydropower Generation Unit

by

CGS Gunasekara

Supervised byDr. Primal Fernando,Dr. Joachim Claesson


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Declaration

The work submitted in this thesis is the result of my own investigation, except where otherwisestated.

It has not already been accepted for any other degree and is also not being concurrently submittedfor any other degree.

CGS Gunasekara

Date

We/I endorse declaration by the candidate.

Dr. Primal Fernando


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Modelling and Simulation of Temperature Variationsof Bearings in a Hydropower Generation Unit

Abstract

Hydropower contributes around 20% to the world electricity supply and is considered as the mostimportant, clean, emissions free and economical renewable energy source. Total installed capacityof Hydropower generation is approximately 777GW in the world (2998TWh/ year). Furthermore,estimated technically feasible hydropower potential in the world is 14000TWh/ year. The hydro-power is the major renewable energy source in many countries and running at a higher plant-factor.Bearing overheating is one of the major problems for continues operations of hydropower plants.Objective of this work is to model and simulate dynamic variation of temperatures of bearings(generator guide bearing, turbine guide bearing, thrust bearing) of a hydropower generating unit.The temperature of a bearing is depends on multiple variables such as temperatures of ambient air,cooling water and cooling water flow-rate, initial bearing temperatures, duration of operation andelectrical load. Aim of this study is to minimize the failures of hydropower plants due bearing tem-perature variations and to improve the plant-factor. The bearing heat exchange system of a hydro-power plant is multi-input (MI) and multi-output (MO) system with complex nonlinear characteris-tics. The heat transfer pattern is compel in nature and involves with large number of variables.Therefore, it is difficult to use conventional modelling methods to model a system of this nature. Sothat Neural Network (NN) method has been selected as the best where past input and output datais available, and the input characteristics can be mapped in order to develop a model. In this reporta neural network model is developed to model the hydropower plant, using Matlab neural networktool box and matlab as the implementation language.


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Acknowledgments

Thanks are first due to my supervisors, Dr Primal Fernando and Dr Joachim Claesson for theirgreat insights guidance and sense of humour. My sincere thanks should go to the Post GraduateOffice, Royal Institute of Technology, Stockholm, Sweden for helping in various ways to clarify thethings related to my academic works in time, with excellent cooperation and guidance. Next, Iwould like thank, staff of the Post Graduate Section of ICBT, Sri Lanka who facilitated to carry outmy studies throughout the course.

Lastly, I should thank many individual friends and colleagues who have not been mentioned herepersonally in making this educational process success. May be I could not have make it without

your support.


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List of Abbreviations

aAdxwhHHEKLLGBMMIMOnNNNQRsSTTGBTHBUUGBwx

OutputSurface areaWall thickness of heat exchangerEnthalpyNormalized enthalpyHeat exchangerThermal conductivityLoadLower guide bearingNumber of trialsMultiple-input, multiple-outputOutput of neuronNumber of layersNeural networkHeatNumber of input nodesEntropyNormalized entropyTemperatureTurbine guide bearingThrust bearingHeat transfer coefficientUpper guide bearingWeightsSteam quality

Subscripts

Am AmbientCa Circulating airc Cooling water

cwi Cooling water inletcwout Cooling water outletdotc Cooling water flow ratedotoil Cooling oil flow rate

ElectricalEL Electrical LoadLGB Lower guide bearingLGBoin LGB oil inLGBoout LGB oil out

MassO OilTG Turbine guide bearinTGB TGB metalTGBoi TGB oil inTGBoout TGB oil outTHB Thrust bearingUGB Upper guide bearingUGB UGB metalUGB UGB oilUGBoin UGB oil inUGBoout UGB oil out


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Greek symbols

Individual heat transfer coefficient Weight adjusting scala Efficiency of heat exchanger


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Modelling and Simulation of Temperature Variationsof Bearings in a Hydropower Generation Unit

1 Introduction.........................................................................................................................101.2 The hydropower generating unit................................................................................. ...111.3 Bearing arrangement of Hydropower unit........................................................,...........121.4 Purpose and contribution of the thesis..........................................................................12

1.5

Organization of dissertation............................................................................................13

2 Overview of the Modelling..................................................................................................142.1 The research problem.......................................................................................................14

2.1.1 Aimand scope..........................................................................................................142.1.2 Theresearch question.................................................................................................14

2.2 Approach............................................................................................................................14

3 Neural Networks.................................................................................................................243.1 Introduction................................................................................................................. .....243.2 Formal definition...............................................................................................................243.3 Biological Neuron..............................................................................................................243.4 Mathematical Model of a neuron....................................................................................25

3.4.1

Neuron with multi-inputs..........................................................................................273.4.2 Layer of Neurons......................................................................................................28

3.4.3 Muli-layer neurons....................................................................................................293.4.4 General Structureof NN.................................................................................,........293.4.5 Traininga neural network.........................................................................................303.4.6 Trainingprocess........................................................................................................30

3.5 Demonstration of developing a NN by example.........................................................313.5.1 Problem.....................................................................................................................313.5.2 Systemas a NN model.............................................................................................323.5.3 Data used.................................................................................................................333.5.4 Training...................................................................................................................333.5.5 Simulation................................................................................................................363.5.6 Results......................................................................................................................36

4 Developing the model.........................................................................................................404.1 Selection of input variables..............................................................................................404.2 Selection of data.................................................................................................................414.3 Approach of developing a dynamic model....................................................................41

4.3.1 Developing a static NN model............................................................................414.3.2 Trainingthenetwork andtrainingresults..................................................................434.3.3 Staticmodel simulation results...................................................................................454.3.4 Developingthe dynamicmodel...................................................................................45

5 Results.................................................................................................................................475.1 Static model simulation results........................................................................................47

5.1.1 Staticmodel simulation results for bearingmetal temperature......................................47

5.1.2

Co-relation coefficient of thestaticsimulation results...................................................48

5.1.3 Staticmodel simulation results for bearingoil temperature..........................................495.1.4 Correlation coefficients of simulation on bearingoil temperature..................................505.1.5 Summary results of staticmodel.................................................................................51

5.2 Dynamic simulation results..............................................................................................525.2.1 Dynamicsimulation results for bearingmetal temperature..........................................525.2.2 Dynamicsimulation results for bearingoil temperature...............................................53

5.3 Dynamic simulation results for reduced flow rate.......................................................535.3.1 Bearingmetal temperaturevariation...........................................................................535.3.2 Bearingoil temperaturevariation...............................................................................54


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6 Discussion.....................................................................................................................56

7 Conclusions.................................................................................................................. 57

8 References.................................................................................................................... 58

Appendix A : NN initial weight and bias values (NN example).................................... 59

Appendix B: Training record ( NN example)................................................................. 62

Appendix C: Sample data used for training the model................................................... 76

Appendix D: training Matlab script for model.................................................................80

Appendix E: Initial values of trained model.................................................................... 84


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1Introduction

1.1 General overview

Hydro power contributes around 20% of the world electricity generation [1]. As a renewable energysource it has become more important economical resource compared to other renewable sources.Hydro power produces no direct waste and contribution to CO2,green house gasescompared to fos-sil fuel plants. Global installed capacity of Hydropower generation (electrical) is approximately777GW (2998TWh/ year) [1]. It is around 88% of the renewable energy sources [2].

In Sri Lanka about 40% of electricity is generated by hydropower. At present, all most all hydro po-tentials available in the country have been utilized for electricity generation and few remaining areunder construction.

Total Pow er Generation GWh

Hired power

1%

Wind

0%

Private Pow er

37%

Thermal

Complex

22%

Other Hydro

8%

Laxapana

Hydro Complex

15%

Mahaweli Hydro

Complex

17%

Fig.1.1 Hydro electricity contribution in 2009(Source: Ceylon Electricity Board, statistics 2009)

The electricity generation by different sources in the year 2009 is shown in Fig. 1.1. Electricity gener-ated in three major hydropower complexes (Mahaweli Hydro complex, Laxapana Hydro Complexand Other Hydro Complexes) in Sri Lanka [3], contributes 40% to the national energy supply whilethe rest is coming from thermal power, mainly diesel. Hence, obtaining the maximum possible sharefrom hydropower would be great saving to the national economy.

Around 95% of existing hydro power plants in Sri Lanka have passed the 25 year limit of their lifespan. Sri Lanka is not in a situation to replace old-hydro power plants, within a short period and alsoits energy production is mainly depends on hydropower. Age analysis of the hydropower plants in SriLanka is shown in Table 1.


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Table 1: Age analysis of hydropower stations in Sri Lanka(Source: Ceylon Electricity Board, Generation data)

Name of the Station Installed

Capacity/MW

Commissioned

year

Age

(years)InginiyagalaNortonUdawalaweOld LaxapanaPolpitiyaUkuwelaBowatennaNew LaxapanaCanyonKotmale

VictoriaSamanalawela

RandenigalaNilambeRantambeKukule

11.255065075404010060201210120

1223.25070

195019501955195519601976198119841984198519851985

1986198819902002

656560605034292626252525

24222008

Therefore, it is essential to obtain the maximum capacity from the existing plants by minimizing thedowntime through proper operations. In that context, predicting the availability of hydroelectric gen-erating units for fault free operation is one of the crucial factors.

Bearing oil temperature plays a vital role in continues operation of hydropower plants.Stable bearingtemperatures in the turbine and generator are essential for their successful continues operations. Allhydraulic and lubricating fluids have operating temperature limits. A machine could lose its stability

and experiences conditional failures whenever the systems fluid temperature exceeds these limits.Increase in temperatures in a machine may happen due to lack of heat losses, higher ambienttemperatures and long operations at higher mechanical loads. The power plant staff should closelymonitor the bearing oil and metal temperatures in order to ensure a safe operation [4]. Typicalacceptable bearing temperatures of a vertical shaft hydropower turbine are shown in Table 2.

Table 2: Bearing temperature limits (refer Fig. 1.3)Bearing Type Temperature / deg C (Alarm)

Metal OilUpper Guide Bearing (UGB)Lower Guide Bearing (LGB)Thrust Bearing (THB)Turbine Guide Bearing (TGB)

8858575

7707070

In this project, from the measured temperature variations of bearings (generator upper guide bearingUGB, lower guide bearing LGB, turbine guide bearing TGB, thrust bearing THB), a model is createdto predict bearing temperatures at various operation conditions.

1.2 The hydropower generating unit

Hydro electricity is generated by converting potential energy of water to kinetic energy by its turbines.A typical arrangement of a vertical shaft driven turbine, generator unit is shown in Fig.1.2 [5].


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Fig.1.2 Overview of a hydropower generatingunit

1.3 Bearing arrangement of Hydropower unit

A typical arrangement of the bearings in a vertical shaft generator-turbine unit of a hydropower plantis shown in Fig.1.3.

Fig.1.3 Turbine-Generator bearing arrangement

1.4 Purpose and contribution of the thesis

The purpose of this thesis is to develop a model to predict the temperatures of bearings for differentoperating conditions. The model is developed using previously measured temperatures, loads, andcooling water flow data. To achieve these, following principle systems are stated.


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Choose the inputs and outputs.

Determine the appropriate method for this system considering the nature of the problem. It

is suggested to use a neural network model for this problem as justified in the next section.

It is suggested to decompose the system into sub models to identify the heat transfer charac-

teristics of the system.

In this work, Matlab neural network tool box, and Matlab scripts are used.

1.5 Organization of dissertation

The rest of the chapters of this dissertation are organized as,

Describes the overview of the modelling strategy approach to the modelling method includ-

ing the selection of modelling method and selection of input variables.

About application of neural network and the theory behind it.

Describes how to approach to developing the model by considering the heat transfer pattern,

the interaction within system variables and implementing the model.

Presents the results obtained by simulating the model with comparison to the past actual

characteristics of the system.

Discusses the performance of the model and concludes the work carried out by this study.


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2Overview of the Modelling

This section is devoted to describing the problem under investigation, importance of it to the energysector, aims of the research, its scope and limitations, formulation of the research problem and theapproach.

2.1 The research problem

Monitoring the temperature of a bearing is an important task for ensuring continues running of hy-dropower generating. Old hydropower plants are frequently failed due to bearing temperature rise orstop when they reach to recommended temperature levels. This may causes frequent power failuresor damagers to turbine-generator system.

2.1.1

A im and scopeIt is aimed to model and simulate the dynamic variation of temperatures of the bearings (generatorguide bearing, turbine guide bearing, thrust bearing) of an in-service hydropower unit.

2.1.2

The research questionOne research question has been formulated for focusing the work:

Howshould multi-physical interactions in a hydropower bearing-heat exchanger systembemodelled, simulated, in ordertopredict thebearingtemperaturevariation?

2.2Approach

HE3, HE4 LGB, TGB oil coolers, HE1 THB and UGB oil cooler, HE2 Stator cooler

Fig.2.0 Bearings-heat exchanger system,


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A simplified diagram that illustrate the physical arrangement of different types of heat exchangers,bearings, generator stator and cooling fluids flow directions of a hydropower plant is shown in

Fig.2.0. The bearings (UGB, LGB, THB, and TGB) and generator stator are considered as heat

sources and cooling water as well as ambient air act as heat sinks. Pictures of the TGB oil cooler and

THB oil cooler are shown in Fig 2.1 and Fig. 2.2, respectively.

Fig.2.1 A picture of TGB-heat exchanger arrangement

Fig.2.2 A picture of THB & UGB heat exchanger arrangement

THB and UGB oil cooler consists of shell-and-tube type two parallel heat exchangers. Heat from theoil is transferred to the circulating cooling water. Interactions of system variables with each other areshown in heat transfer diagrams in Fig. 2.3 and Fig. 2.4.


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Load variation

0

10

20

30

40

50

1 611

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

101

106

111

116

121

126

131

136

141

146

Time/ hours

MW,M

Var

Load MW

Load Mvar

Fig 2.5 Bearing metal / oil/ cooling water/electrical load and circulating air temperature variation

When the plant started from stand still, the temperatures of the bearings rise rapidly and stabilize at acertain level for the given generator load profile is shown in Fig. 2.6. Sampling rate of the tempera-ture values are selected at 10-minute intervals. (Sample data record 1365 to 1465 Appendix D)


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Fig. 2.6 Variation of bearing metal and oil temperatures

When the external parameters such as cooling water flow rate and cooling water or ambient air tem-perature varies, the heat absorption rate of the bearing oil coolers varies. Data relevant to these dif-ferent operating conditions are given in table 2.1. According to this data, when the cooling watertemperature is high (29C) the bearing temperatures are also at a higher value.


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Table 2.1 Temperature variation of the bearings with load and cooling water temperature.Load Temperature C / Alar MW MVar Cwin UGBm THBm LGBm TGBm UGBo LGBo TGBo

77

78767676747576

9

10121314162025

24.8

24.824.824.724.724.724.724.7

50/85

50/8550/8550/8550/8550/8550/8550/85

71/85

71/ 8572/8572/8572/8572/8572/8572/85

62/85

62/8563/8563/8563/8563/8563/8563/85

56/75

56/7557/7557/7557/7557/7557/7557/75

54/70

54/7055/7055/7055/7055/7055/7055/70

54/ 70

55/ 7055/ 7055/ 7055/ 7055/ 7055/ 7055/ 70

54/70

54/7055/7055/7055/7055/7055/7055/65

737372767679

353535323435

24.824.824.824.824.824.8

53/8553/8553/8554/8557/8557/85

81/8582/8582/8582/8583/8583/85

71/8572/8575/8575/8575/8576/85

63/7563/7564/7564/7565/7565/75

60/7060/7061/7061/7062/7061/70

60/ 7061/ 7061/ 7061/ 7061/ 7062/ 70

60/7060/7061/7061/7062/7062/70

30303030101010

42444445454440

29292929292929

65/8565/8565/8565/8565/8565/8565/85

78/8578/8578/8578/8578/8578/8578/85

77/8577/8577/8577/8577/8577/8577/85

72/7572/7572/7572/7572/7572/7572/75

60/7060/7060/7060/7060/7060/7060/70

65/ 7065/ 7065/ 7065/ 7065/ 7065/ 7065/ 70

64/7064/7064/7065/7065/7065/7064/70

When one of the bearing temperatures reaches to the alarm level of the machine, the plant has to bestopped or automatic shut down takes place. A failure that occurred due to bearing over heating isshown in Fig. 2.7. It was observed that the THB temperature reached to 83C with an increasingtrend when the machine was running at a load of 77 MW, 37MVar and then the machine was manu-ally stopped.


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Fig.2.7 Failure due to bearing temperature rise

The bearing temperature variations show a clear relation to electrical load (both MW and MVars) andcooling water flow rates.Bearing metal temperaturesdepend on the initial conditions of the bearing,external conditions such as cooling water flow rate, cooling water temperature (ambient temperature)and electrical load of the generator. Parameters involved with system are shown in Fig.2.8.


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Fig. 2.8 Representation of the system: HE1, HE3, HE4 - bearing oil coolers, HE2 stator air cooler.

From first principles of thermodynamics,

Considering heat transfer from bearing metal to oil,

UGBoUGBmUGB TTAUQ 11 ( 1 )

Considering heat transfer in heat exchanger 1 (HE1),

cwoutcwindotcwwUGBOOutUGBOindotoilOil TTmCTTmC 1 ( 2 )

For HE2,

cwoutcwindotcwWAir

TTmCQ 22 ( 3 )

Where AirQ is the heat absorbed from circulating air,

For HE3,


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cwoutcwindotcwwLGBOOutLGBOindotoilOil TTmCTTmC 333 ( 4 )

For HE4,

cwoutcwindotcwwTGBOOutTGBOindotoilOil TTmCTTmC 444 ( 5 )

Again, heat absorbed by circulating air can be written as,

ELLGBUGBAir QQQfQ ,, ( 6 )

Where, ELLGBUGB QQQ ,, are the heat generated by upper Guide bearing, Lower guide bearing and

due to Electrical Load of the generator, respectively. Also CWAirOil CCC ,, are the specific heat ca-

pacities of bearing oil, air and cooling water, respectively and1,2,3,4are the efficiencies of heatexchangers.

UGBOilUGBUGBUGBUGB TTAUQ ( 7 )

LGBOilLGBLGBLGBLGB TTAUQ ( 8 )

Also, heat generated at TGB also can be expressed as,

TGBOilTGBTGBTGBTGB TTAUQ ( 9 )

Where TGBLGBUGBTGBLGBUGB AAAUUU ,,,,, are the heat transfer coefficients and surface areas

of the Upper guide bearing, Lower guide bearing and turbine bearing, respectively.

Heat generated due to electrical load can be written as,

LefQEL ( 10 )

Where,Leis the electrical load.

Again, heat transfer coefficients,Ualso a complex non-linear function of temperatures, cooling waterflow rates, thermal conductivity of the material, the individual convection heat transfer coefficient foreach fluid and wall thickness as given in equation (11) [6].

221

1111

AkAdx

AUAwall

(11)

Therefore, the system under investigation has multiple time dependent inputs and multiple outputs.Multiple input, Multiple output (MIMO) and interaction within the system are complex and non lin-ear in nature. So that, all the inputs has to be parallel processed to obtain the output. This type ofcomputation can not be implemented by using conventional modelling techniques based on sequen-tial computer programs and based on first principles of thermodynamics. This topic will be discussedin detail in section 4.0 under developing of the model.

Hence, neural network (NN) approach is the best to model systems which exhibits the followingcharacteristics. Due to the fascinating characteristics and capability of NNs, most of the models de-

veloped in the past using other techniques are now being converted to NN model [7][8].


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Inputs and out puts have a cyclic repetitive pattern of variation over the time.

Input/output past data of the system which describes the characteristics of the system is

available.

The NN has the capability to identify the patterns exist in a given data set. The NNs can map the input data to the output data in a nonlinear system.

The NNs can process data in parallel, so it can be applied to MIMO system easily.

Dynamic systems can be modelled using time delay inputs to the network to represent previ-

ous time series values.

NN need to know little about the theory behind the process of the system.

The approach is described with the following steps:

1) As the system consists of several heat exchangers, which has different inputs and outputbearing temperature variables, first the inputs (which characterize the behaviour of the sys-

tem) and outputs of the model are clearly identified.

2) Then the past historical data over a period is collected from past operation data records.

3) Then an artificial NN is formed to model the system by mapping the input to known out-puts. The system is modelled using MATLAB neural network tool.

4) The simulated results are compared with past actual outputs and necessary adjustments aredone to get the required accuracy.

5) The model and results are discussed with an objective perspective.


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3Neural Networks

Neural networks (NN) play a vital role in the field of modelling and identifying characteristics of nonlinear systems. Hence, this section describes the capabilities of NN and mathematical theory behindit. In section 3.5.1, it is shown by an example, how NN technology can be used to solve a nonlinearproblem.

3.1 Introduction

Neural networks are capable of modelling complex MI-MO systems with non linear characteristics.So that NNs are a powerful tool in system modelling and identification field compared to conven-tional modelling techniques. NNs imitate the function of human brain or biological nervous systemmade up of small units called neurons. The network is formed by connecting the neurons with eachother by adjustable weights between neurons. Neural network can be trained or adjusted to get a de-

sired output or target for a given input. Hence, when the input, output characteristics of a system;historical data is available we can train a NN to model the system. NNs have the capability of identi-fying the patterns exist in the input/ output data, if a pattern exists. In section 3.2 gives a formal defi-nition of NN.

3.2 Formal definition

The following formal definition was proposed by Hechi-Nielson [9] which describes the functionalityof neural network.

An artificial neural network is a parallel distributed information processing structure consisting ofprocessing units (which can posses a local memory and can carry out localized information process-ing operations) interconnected via unidirectional signal channels called connections. Batch processing

unit has a single output connection that branches (fans out) into as many collateral connections asdesired: each carries the same signal the processing unit output signal. The processing unit outputsignal can be of any mathematical type desired. The information processing that goes on within eachprocessing unit can be defined arbitrarily with the restriction that it must be completely local: that is,it must depend only on the current values of the input signals arriving at the processing element viaimpinging connections and on values stored in the processing units local memory.

3.3 Biological Neuron

Human nervous system consists of about 1.3 x 1010of neurons [10]. They are distributed among thehuman brain and the other parts of the body. It is found that about 1 x 1010[10] neurons contain inthe human brain itself. The basic building block of the nervous system is the neuron which containsfour main parts. Normally it has a spherical shape. The cell body is called the Soma and is sur-rounded by tree like branches called Dendrites which receive signal from other neurons as shown inFig. 3.1. The out of the neuron passes through the Axon which has a length varying from fraction ofmm to 1 m in human body [10][11].


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Fig 3.1 Biological Neuron

(source: Artificial Neural Networks, ch1, EE543 Lecture notes ,

METU EEE, Ankara , by Urgu Halici)

At the end of the Axon it is divided into branches called Synapses which transmits the signals toother neurons. There are about 103-104number of Synapses at each Axon end. The incoming signalsto the cell body or Soma create an electrical potential due to the chemical changes takes place in thecell body. When this potential called action potential exceeds a certain threshold that neuron firesand transmits pulse through the Axon [10].

These neurons form a parallel distributed network in the nervous system which helps to transmit in-formation gathered in the system to the brain to maintain a communication link. Signal transmissionis caused by electric pulses. The pulses passing through the Axon has approximately constant ampli-tude but different time spacing decided by the statistics associated with the incoming signals fromsynaptic junctions of other neurons [10][11].

3.4 Mathematical Model of a neuron

Characteristics of a biological neuron in mathematical form can be represented as shown in Fig. 3.2.The main three aspects of the biological neuron needed to be represented are the, synapses and theactual activity taken place inside the neuron. The weight w models the synapse. The value of theweight determines the strength of the connection. Then an adder adds up all the inputs.

Fig.3.2 neuron as a model

)( bwpfa (12 )

Typical characteristics of a neuron can be expressed as in equation (12). Wherea, pandnareoutputof the neuron, inputof the neuron and input totheactivation functionof the neuron, respectively. The

output of neuron a, is the outcome of a function f called as activation function. Activation func-

tion acts as a transforming function such that the output of a neuron should lie in between two de-


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fined values. Normally the lower and upper limits of the outputs are in between 0 to 1 or -1 to 1. Ac-tivation functions used in neural networks can be in several forms [12].

Generally there are three types of activation functions commonly used. The first type of function actsas a threshold function. If the summed up value exceeds a certain threshold value it is considered as 1

otherwise 0 which is called the step function. In mathematical form it can be shown as, given inequation (13).

nf 1 if 0n

0 if 0n (13)

First type of activation function characteristic is shown in Fig. 3.3

Fig. 3.3 Step function

Second type is the piecewise linear function. Output of this function lies in a linear region dependingon the amplification factor, which can be expressed as shown in equation (14). A graphical form isshown in Fig. 3.4.

1 21n

nf n 2121 n

0 21n (14)

Fig. 3.4 Piecewise linear function


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The third type is Sigmoid function which can take two forms, logistic Sigmoid or tangential Sig-moid. The logistic sigmoid function is also called as logsig, whose characteristics are shown in Fig.3.3.

Fig. 3.3 Logsig function

The Logsig functionfcan be expressed as in equation (15),

nenf

1

1)( (15)

The tangential sigmoid function is also called as tansig, whose characteristics are shown in Fig. 3.4.

Fig. 3.4 Tansig function

The tansig functionfcan be expressed as in equation (16),

nn

nn

ee

eenf

)( (16)

The tangential sigmoid has the advantage due to its ability to deal with negative numbers whichtransforms output in between -1 and +1, while the logsig function normalizes the output in between

0 and1. In our case we are using logsig function as the activation function as we do not deal withnegative numbers.

3.4.1

Neuron with multi -inputsWhen there are several inputs to the same neuron, the model can be represented as shown in Fig. 3.5.p1, p2, . pRare the input value and while w11,w12,..w1Rrepresents the corresponding weights.


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Fig. 3.5 neuron with multi inputs(source: neural network toolbox user guide)

Mathematically this can be represented in vector form as,

nbwww

p

p

p

R

R

11211

2

1

.. (17)

1 x R R x 1 1x1 1x1

3.4.2

Layer of NeuronsSimilarly a number of inputs also can be modelled as shown in Fig. 3.6 by layer of input neurons.

Fig. 3.6 Layer of neurons with multi inputs(source: neural network toolbox user guide)


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3.4.3

Muli -layer neurons

Fig. 3.7 Multi layer neurons (source: neural network toolbox user guide)

In a multi-layer neural network the relationship between inputs and the outputs can be expressed as,

bwfa pL 11111 (18)

For layer two as,

)212122 bawfa L (19)

Similarly for the 3rdlayer,

bawfa L 323233 (20)

From equation (19)(20) and (21),

bbbwfwfwfa pILL

3211112123233 (21)

General Structure of NN

Followings are the typical major aspects common to any NN model.

A set of input processing units

A state of activation for each unit

An output function for each unit

Topology of the network that describes pattern of connectivity among processing units.

A rule defined to propagate or combine activities of processing units through out the net-

work.

A defined rule to activate and update values received from input neurons.

External data input that provides information of the environment.

A rule to modify connectivity pattern based on the data which describes the environment.


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3.4.4

Training a neural networkGenerally neural networks trained by adjusting the weights. At the beginning of the training processthe bias values (b) and weights are initialized randomly (random values are selected)

The training method can be classified in to several categories based on the method used by the net-work to learn behaviour of the actual system by adjusting the weights of the network so as to obtainthe desired output. These methods can be classified into two main types called supervised-learning

and unsupervised-learning.

Fig.3.8 Training process (source: Matlab user guide)

3.4.4.1 Supervised learningIn the process of supervised learning, the network is allowed to adjust its weights by comparing theinput and corresponding outputs. The inputs are fed to the network input nodes batch by batch andthe actual output is compared with target. The error is used as a feedback to adjust the bias valuesand weights. This process is repeated until an accepted preset value is reached. The process can bepictorially depicted as shown in Fig. 3.8 which is called the supervised learning as the network is self-supervised during the training process. This method needs to have the historical data which repre-sents the behaviour of the system

3.4.4.2 Unsupervised learningIn this method, when the inputs are fed into the network it creates its own outputs to represent thoseinputs. When the same inputs are fed to the network it produces the same out puts as earlier. In thisway network classified the inputs into several categories or identifies the inputs. Compared to theprevious method this training does not need any external supervision.

Our problem under investigation falls into the first category where historical data is used to train thenetwork.

3.4.5

Training processSteps of the training process can be given as follows,

Feed first training sample to the NN. Initialize the threshold and weights for the input hid-den and output nodes of the network and set small random values.

For each hidden unit calculate,

i

R

i

jij pwn

1

(22)


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njj ea 1/1 for j=1.2N (23)

For each output calculate,

N

j

jkjk awO1

* (24)

For each neuron calculate a scaling factor in order to adjust the difference between net-

work actual output and the desired output. In other words, actual and the target.

Adjust the weights of each neuron to reduce the local error,

kjkjkj ww (25)

Move to the next training sample, and repeat the procedure for all training samples. At theend compare the actual output with the target for each output neuron. Then calculate themean square error.

The mean squared error is calculated by calculating difference between target and the actualoutput, squaring it summing over all the trials. Then by dividing by the number of trials M, to

get the mean value as given in equation (26).

2

1

.1M

j

jj taMdErrorMeanSquare (26)

When the mean squared error reaches the possible minimum value the corresponding trained net-work is saved. This is used to test the performance of the network for new data.

3.5 Demonstration of developing a NN by example

In this section a demonstration is done to explain how a problem is solved using NN technology.This problem is related to the modelling of non linear thermodynamic characteristics, to show thecapability of NNs.

3.5.1

ProblemThe problem selected is related to representation of thermodynamic properties of steam. Enthalpy,

entropy characteristics of steam is non-linear. For different value of x (steam quality) characteristiccurves can be represented as shown in Fig. 3.9, for different values of x, x=0.8, 0.85, 0.9 and for 0.95

respectively. These characteristics can not be modelled by using mathematical models due to its com-

plexity and non-linear nature. Hence, some other method has to use to model these characteristics.


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Enthalpy vs Entropy for Steam

2000

2100

2200

2300

2400

2500

2600

2700

2800

2900

5.00

5.40

5.80

6.20

6.60

7.00

7.40

7.80

8.20

8.60

9.00

Entropy S

Enthalpyh

/KJ/Kg

Enthalpy x=1.0

x=0.95

x=0.90

x=0.85

x=0.80

Fig 3.9 Enthalpy vs Entropy for Steam

Capability of modelling non-linear characteristics of a system in NNs can be useful in modelling asystem of this nature. This system can considered as a model with 2 inputs, steam quality x and en-tropy s and enthalpy h as the output as shown in Fig. 3.10.

3.5.2

System as a NN model

Fig 3.10 NN model (inputs/ outputs)


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3.5.3

Data usedEntropy, enthalpy data used to model the system is shown in the table 3.

Table 3: Data of Entropy and enthalpy for different values of x , steam quality

Entropy S

Enthalpy fo

x = 1. x = 0.9 x = 0.90 x = 0.8 x = 0.80

5.0 2461 2461 2446 2446 2423

5.2 2561 2561 2534 2515 2450

5.4 2653 2630 2600 2538 2438

5.6 2723 2684 2630 2538 2400

5.8 2769 2715 2623 2500 2330

6.0 2800 2715 2600 2446 2265

6.2 2808 2693 2561 2400 2215

6.4 2793 2661 2523 2346 21656.6 2769 2638 2475 2300 2123

6.8 2746 2600 2446 2261 2076

7.0 2719 2569 2400 2230 2038

7.2 2692 2542 2369 2200 2015

7.4 2669 2507 2338 2176

7.6 2650 2476 2318 2146

7.8 2623 2453 2293 2130

8.0 2600 2438 2276

8.2 2576 2423 2261

8.4 2553 2400

8.6 2538 2384

8.8 2523

9.0 2515

This data has to be normalized in order to make the data range in between 0-1. We take normalized s= S/10 and h=H/ 10000 to feed into the NN model as inputs and targets in the training process.

3.5.4

TrainingTraining data set consists of 63 set of input/ output data values (s, x), where s and x are the entropyand steam quality respectively. Entropy (s) is ranging from 5 to 9 for different values of x rangingfrom 0.8 to 0.95. As the system has two inputs (x, s); input layer consists of two neurons and the out-

put layer one neuron to represent the output (h). In this case two hidden layers are selected whichcomprises of 3 neurons and 2 neurons for the hidden layer 1 and hidden layer 2, respectively, asshown in Fig. 3.11. Initially, number of hidden layers and number of neurons in each layer are se-lected randomly. Later, they are changed so as to get the optimized performance of the model byminimizing the error.


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Fig. 3.11 NN model

In the implementation of this network in Matlab, it can be represented in Matlab code as,

nnet =newf f ( pr , [ 2321] , {' t ansi g' ' t ansi g' ' t ansi g' ' t ansi g'}, ' t r ai nbr ' ) ;

which represents

newff, Create a feed-forward back propagation network.

pr, represents the input data

2321, number of neurons in each layer (input, hidden layer 1, hidden layer 2, output layer etc)

tansig, is a transfer function. Transfer functions calculate a layer's output from its net input.

Trainbr, is a network training function that updates the weight and bias values according to Leven-berg-Marquardt optimization. It minimizes a combination of squared errors and weights and, thendetermines the correct combination so as to produce a network which generalizes well. The processis called Bayesian regularization [13].

Full code listing of the Model training program is given below.

% develops a model to steam entropy enthalpy Characteristics (10 jun 2010)% Trains ,validates and tests new dataclose all;clear all;tic;file=xlsread('steam','a23:c86'); % loads xl data filetoc;tic;B=file(:,1:2); % loads inputs x, sC=file(:,3:3); % loads outputs hp=B'; % inputst=C'; % targets

Q=6;n=63;dtst=14:Q:n; % divides data for training validation

dval= [ 13:Q:n ]; % and testingdtrn=[1:Q:n 2:Q:n 3:Q:n 4:Q:n 5:Q:n 6:Q:n 7:Q:n 8:Q:n 9:Q:n 10:Q:n 11:Q:n 12:Q:n ];

val.P=p( : , dval); % validation dataval.T=t( : , dval);test.P=p( : , dtst); % test datatest.T=t( : , dtst);ptr=p( : , dtrn); % training data


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ttr=t( : , dtrn);nnet=network; % creates networkpr=minmax(p);nnet=newff(pr,[2 3 2 1 ],{ 'tansig' 'tansig' 'tansig''tansig' },'trainbr');nnet.trainParam.epochs = 1000;nnet.trainParam.show = 1;

nnet.trainParam.lr = 0.01 % SETS ETA learning rate[nnet,tr]=train(nnet,ptr,ttr,[],[],val,test);plot(tr.epoch,tr.perf,tr.epoch,tr.vperf,tr.epoch,tr.tperf)legend('Training' , 'Validation' , 'Test', -2);

ylabel('Squared Error');xlabel('Epoch ');title(' Model Performance');a = sim(nnet,p); % simulatesfigure(1)t1=t(1:1,1:63); % targeta1=a(1:1,1:63); % simulated outputplot(2:64,a1,'.',2:64,t1,'r-')

ylabel('Output');

xlabel('Entropy S ');title(' Predicted vs Actual');% writes data into xl fileSUCESS=XLSWRITE('steam_op.xls',a1','b2:b64')SUCESS=XLSWRITE('steam_op.xls',t1','c2:c64')toc;

% regresson analysisfigure(2) %[m(1),b(1),r(1)]=postreg(a1,t1);

% end

In the training process the training is done iteratively for a number of epochs (iterations) until the er-ror (in this case SSE; sum of squared error) reaches to a predefined value. Variation of performance,

training, validation and testing errors during the training process is shown in Fig 3.12. At the end ofaround 260 epochs (iterations), training, validation and testing errors have reached to 1.59084e-005,1.40373e-006 and 6.53338e-007, respectively.


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Fig.3.12 Training error of the model

3.5.5

SimulationSimulation is done in order to test the trained model to see whether it performs well for the new data(unseen data) fed to the model. In this case data relevant to x=1.0 was selected as the new data to testthe model.

Model simulation (testing) matlab code listing

% Tests the model for new data% of steam x= 1.0 (13 Jun 2010)close all;clear all;tic;

A=XLSREAD('steam'); % loads xl data fileload model; % trained network modelnet1= model;toc;% column 1 and 2 is input datarec_start=2;rec_end=22;n=rec_end-rec_start; % no of recordstic;B=A(2:22,3:3); % loads data output (entropy,h)C=A(2:22,1:2); % loads inputs ( x, s)p=C';t=B';toc;

pr=minmax(p);tic;a = sim(net1,p); % simulate the modelfigure(1) % graph 1t1=t(1:1,1:n); % expected targeta1=a(1:1,1:n); % simulated targetplot(1:n,a1,'bx',1:n,t1,'r-')

ylabel('Enthalpy / KJ/Kg Pu')xlabel('Entropy, S / KJ/Kg')legend('simulated ' , 'actual ');title('Entropy vs Enthalpy for steam x =1.0')% end

3.5.6

ResultsSimulation results of the model shown in Fig.3.13 illustrate the characteristic curves relevant differentsteam qualities. The simulated characteristics generated by the NN model in comparison to actual

values are almost same. This result shows how the model has modelled the characteristics of the

given data set for training.

The NN has satisfactorily modelled the characteristics of steam. Regression analysis for the simula-tion is shown in Fig.3.14 proves the performance of the model.


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Fig.3.13 Simulated vs Actual characteristics

Fig. 3.14 Regression analysis result for the model

The simulated results for unseen (new) data to the model which corresponds to x=1.0 is shown inFig.3.15. It compares actual characteristics with the simulated result. So the model accurately simu-lates the steam characteristics where the corresponding regression analysis results are shown in Fig.3.16.

Hence, using this model any other characteristics curves corresponding to intermediate values of x

such as x=0.775, 0.825, 0.875, 0.925, 0.975 can be obtained is shown in Fig 3.17

.


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Fig.3.15 Simulated (predicted) characteristics for new data for x=0.1

Fig.3.16 regression analysis results for x=1.0

Fig.3.17 Predicted characteristics for new data x=0.775, x=0.825,X=0.875, x=0.925, x=0.975 and x=1.0


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4Developing the model

This section describes the approach and steps followed to develop a dynamic model to simulate hy-dro-electric power generating unit bearing temperature variation with time, electrical load, with theduration of operation and other environmental factors.

4.1 Selection of input variables

Input variables which affect to the characteristics of the system under investigation are listed out be-low.

TLGBm Lower guide bearing metal temperatureTUGBm Upper guide bearing metal temperatureTTGBm Turbine guide bearing metal temperatureTTHBm Thrust bearing metal temperatureTLGBoil Lower guide bearing oil temperatureTUGBoil Upper guide bearing oil temperatureTTGBoil Turbine guide bearing oil temperatureTTHBoil Thrust bearing oil temperatureTcoolingwater Cooling water temperatureTair Circulating air temperaturemdotCW Cooling water flow ratemBCW Bearing cooler water flow rateLe Electrical load (MWs)

Lvars

Electrical load (Vars)

The main concern is to simulate the temperature variation pattern of,

TLGB,TUGB,TTHB,TTGB,TLGBoil,TUGBoil,TTGBoiland TTHBoil. But,values ofthe above variables depend notonly on the instantaneous values of them, but current values as well as the previous values. It can beillustrated more general form as shown in Fig. 4.1, where, Xias temperature related inputs, miasflow rate related inputs andLias load variable related inputs .


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Fig.4.1 System as a static model

Where,

Xi = { TUGBm(0), TTHBm(0), TLGBm(0), TUGBO(0), TLGBO(0), TTGBO(0), TUGBm(t-2T),TUGBm(t-T), TUGBm(t), TTHBm(t-2T), TTHBm(t-T), TTHBm(t), TLGBm(t-2T),TLGBm(t-T), TLGBm(t), TTGBm(t-2T), TTGBm(t-T), TTGBm(t), TUGBo(t-2T),TUGBo(t-T), TUGBo(t), TLGBo(t-2T), TLGBo(t-T), TLGBo(t), TTGBo(t-2T),TTGBo(t-T), TTGBo(t), TCW(t-2T), TCW(t-T), TCW(t), TCA(t-2T), TCA(t-T), TCA(t), } Mi = { mdot1(t-2T),

mdot1(t-T), mdot1(t), mdot2(t-2T), mdot2(t-T), mdot2(t) } Li = { Lmw(t-2T), Lmw(t-T), Lmw(t), Lmv(t-2T), Lmv(t-T), Lmv(t), }

4.2 Selection of data

As a case study, a set of data records were obtained from the Victoria hydro power station, Sri Lanka.It is a vertical shaft turbine generator unit which has an electrical power generating capacity of 71

MW. The data set was extracted from eight channels of the DAQSTANDARD R8.11 data recorder,

which contains bearing metal temperatures, oil temperatures, cooling water flow rates and generator

electrical load. The data set consists of 3623 data records as given in Appendix D. The sampling pe-

riod of data was 10 minutes intervals.

4.3Approach of developing a dynamic model

In section 4.3.1 up to 4.3.4, it is described the approach and how the model is developed in step bystep by starting from the selection of variables to developing a model to characterize the system.

4.3.1

Developing a static NN modelAs discussed earlier, in section 4.1 and as shown in Fig. 4.1, there are two types of input variables tothe model, temperature dependent variables ( bearing metal temperatures, bearing oil temperatures,cooling water temperature and circulating air temperature) as denoted byXi. Second, type of inputsis the bearing water flow rates that do not change due to the performance of the system and the elec-trical load that directly affect to the bearing metal and bearing oil temperatures.


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The variables that interact with system can also be classified into two categories. They are externalvariables and internal variables. Electrical load, cooling water temperature, circulating air tempera-tures are acts as external factors while initial bearing metal temperature, bearing oil temperature act asinternal variables of the system. In a system of this nature, output values depend on the present statusas well as previous status of the system.

In mathematical form, general behavior of the system can be defined as,

State equation,

)),(),(()( wtXtSfTtS (27)

Output equation,

)),(()( wtShty (28)

Where, Srepresents the state vector, xexternal input vector and wneural parameter vector synapticconnection vectors and operational parameters,f(.) is the function that represents the structure of theneural network, and h(.) is a function that represents the relationship between state vector S(t) andoutput vectory(t) [13].

The output of the system does not depend on the current inputs but also on the previous values.Therefore, previous time series values also have to be considered. Some times in order to get a rea-sonable accuracy several previous states have to be considered. Therefore, some sort of memory ca-pability has to be introduced to the model. The variation of temperatures are continues varying func-tions. But, as we consider sample inputs at a chosen time interval the model becomes a discrete sys-tem. Hence, the memory capability can be incorporated by giving a series of time delay inputs to rep-resent previous states [14].

Fig 4.2 Representation of a NN for prediction

Selection of time delay, inputs to represent the previous states in a NN structure and predicting theoutput can be shown in Fig. 4.2, where one time dependent variables is shown there. Equations (27)and (28) describe behavior of a first order system which takes into account the previous state (withone step time delay) of the variables. In generally nthorder system can be described as,

State equation,

)),()]1[().........2(),(),(()( wtXTntSTtSTtStSfTtS (29)

Output equation,


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)),(()( wtShty (30)

We have developed two models; second order and third order. Then by comparing the performanceor output error, the better model with the lowest error can be selected. But, higher the number oftime series values or degree of the network, number of hidden layers, and number of neurons in eachlayer the computing power (memory and processor speed) required is higher. Hence, a compromiza-tion between accuracy and computing power is needed.

In a second order system we have to consider the two previous states. Therefore, in order to predictthe bearing temperature value at timet, bearing temperatures at time, (t-T)and(t-2T)also has to con-sidered. Then, with the bearing metal temperature, bearing oil temperature, cooling water tempera-ture, circulating air temperature and electrical loadMWs, MVarsaltogether makes 32 inputs to themodel. Our intention is to predict the four bearing metal temperatures but as bearing oil tempera-tures, cooling water temperature and circulating air temperatures also affect to it, altogether the num-ber of outputs become 9 (TUGBm,TTHBm,TLGBm,TTGBm,TUGBOil,TLGBOil,TTGBOil,Tcw, TCA). So that, the ini-tial architecture of the NN takes shape of 32 input nodes, and 9 output nodes as shown in Fig. 4.2.Lets arbitrarily select two hidden layers. This can be changed if necessary during the process oftraining the network. [15][16][17].

Then, the initial architecture becomes (32, 24, 15, 9), where number of inputs and outputs are a fixed

value and the number of input also can be changed according to the consideration of previous statusof inputs at interval such ast-T, t-2T, etc depending on the accuracy or the error of training. Training,

validation and testing errors explain to what extent that the model fit to the actual system behavior.

Fig 4.2 General NN architecture

4.3.2

Training the network and training resultsFor training the network 500 data records which consists of past data inputs and outputs were used.Initially, time interval t, time intervals t, t-T, t-2Twas considered 23 input 9 outputs and 32 inputs, 9outputs, respectively. Four different architectures were selected by varying the number of previousstatus considered, number of hidden layers and number of nodes in hidden layers etc. For trainingthe model four different architectures were considered as shown in Table 4.1

Table 4.1: Model Architecture

Model no Architectur1 23,15,12,9 second order 4 Layers2 32,21,9 third order 3 Layers3 32,28,16,9 third order 4 Layers4 32,25,15,9 third order


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Training, testing and validation results are shown in Table 4.2 for models 1,2,3 and 4, respectively.The model with the (32, 25, 15, 9) architecture gives the performances giving the lowest training errorof 0.0689 SSE.

Table 4.2: Model Performance

Model no Architecture Training Error (SSE)1 23, 15, 12, 9 second order 1.46342 32, 21, 9 third order 0.24783 32, 28, 1 6, 9 third orde 0.1189

32, 3 , 1 , 9 third order 0.06895 32, 40, 26, 9 third order 0.0011

In order to improve the training performance of the model, the whole system was divided into twosub units and two separate models are developed for the individual sub units. The new approach isshown in Fig 4.3.

Fig 4.3 Sub models to represent the system

Decomposed model with two sub models shows better training performance compared to singlemodel. The architecture selected for the sub models are (19, 50, 25, 5) and (17, 50, 30, 6) respectively.

Where, UGBm, THBm, UGBo, CW, CA with delayed time series inputs and MW, Mvar, coolingbearing water flow rate act as inputs to the model 1. Then, similarly LGBm, TGBm, LGBo, TGBo,with delayed time series inputs and MW, Mvar,cooling bearing water flow rate act as inputs to themodel 2. The training performance of the model is shown in Table 4.3 for model 1 and model2, re-spectively.

Table 4.3. : Sub Model PerformanceModel no Architecture Training Error (MSE)

1 19, 50, 25, 5 3.04 X 10-72 17, 50, 30, 6 3.80 x 10-7

Graphical representation of the performance and convergence of the errors to a minimum value dur-ing the training process is shown in Fig. 4.4.


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Fig. 4.4 Training Performance of Model 1

4.3.3

Static model simulation resultsOur approach is to develop (training) a static model to simulate the behavior of the real system andthen to convert it to a dynamic model by arranging a feedback of internal variables as inputs to themodel. The simulated outputs are compared with the actual outputs to evaluate the performance ofthe static model.

4.3.4

Developing the dynamic modelAs described in the previous section in order to model the temporal nature of the system as well asthe effect of the internal variables the general architecture of the model should be as shown in Fig.4.5 where Xi(0) denotes the initial conditions.

Fig 4.5 NN Dynamic model


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Algorithm of the simulation:

Read

Xi ( 0) , i ni t i al condi t i ons ( bear i ng met al and oi lt emperature)

r ead Xi ( t ) , Xi ( t - T) , Xi ( t - 2T) , bear i ng met al and

oi l t emper ature

Mi ( t ) , Li ( t ) cool i ng wat er f l ow r at es, ci r cul at i ng ai r

t emper at ur e and el ect r i cal l oad,

make i nput mat r i x

l oad t r ai ned neur al network

deci de t i me dur at i on n

l oop up t o n r ecor ds

si mul ate and get out put of Xi ( t +T)

update i nput sr ecor d out put

end

pl ot gr aph of Xi ( t ) si mul at ed & act ual

For corresponding Matlab implementation (Matlab codes) see appendix C.

Next section presents the dynamic simulation results obtained from the model.


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5Results

5.1 Static model simulation results

5.1.1

Static model simulation results for bearing metal temperature

Fig. 5.1. Simulation results of the static model


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Out put results obtained from the static model are shown in Fig. 5.1. It represents the UGB, LGB,THB and TGB metal temperature variation with time for a given generator load profile.

5.1.2

Co-relation coefficient of the static simulation resultsCorresponding correlation coefficient results for bearing metal temperatures for UGB, LGB andTHB and TGB are shown in Fig 5.2.and Fig. 5.3 respectively.

Fig.5.2. Co-relation results for UGB and LGB metal temperature

Fig.5.3. Co-relation results for THB and TGB metal temperature


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5.1.3

Static model simulation results for bearing oil temperature

Fig 5.4. Simulation results of static model for bearing oil temperature

Simulation results of static model for bearing oil temperature for UGB, THB and TGB and corre-sponding co-relation coefficients graphs are shown in Fig. 5.4. and Fig. 5.5, respectively.


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5.1.4

Correlation coefficients of simulation on bearing oil temperature.

Fig.5.5. Correlation coefficients of simulation on bearing oil temperature

Summary of the static model simulation results are shown in Fig.5.6 and Fig.5.7 for bearing metal andbearing oil.


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5.1.5

Summary results of static model

Fig. 5.6. Simulation results of static model for all four bearing metal temperatures

Fig. 5.7Simulation results of static model for bearing oil temperatures


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5.2 Dynamic simulation results

5.2.1

Dynamic simulation results for bearing metal temperature

Fig. 5.8 Dynamic simulation results for bearing metal temperature


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5.2.2

Dynamic simulation results for bearing oil temperature

Fig 5.9 Dynamic simulation results for bearing oil temperature

Dynamic model simulation results for bearing metal temperature variation and bearing oil tempera-ture variation for new data (unseen data) for the model are shown in Fig.5.9 and Fig.5.10 respectively.

5.3 Dynamic simulation results for reduced flow rate

5.3.1

Bearing metal temperature variation


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Fig 5.10 Dynamic simulation results of bearing metal temperature rise for reduced cooling water flowrate

A new input data set, which represent a different operating environment (i.e. reduced cooling waterflow rate) were presented to the trained model. The simulated out put given by the model is shown inFig.5.10 for bearing metal temperature variation and in Fig.5.11 for bearing oil temperature respec-

tively.

Both the bearing metal and oil temperatures show a temperature rise over the normal operating con-ditions due to reduced cooling effect of heat exchangers as results of reduced (10%) cooling waterflow rate.

5.3.2

Bearing oil temperature variation

Fig 5.11 Dynamic simulation results of bearing oil temperaturerise for reduced cooling water flow rate


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6Discussion

In this research work Neural Network modelling approach was used to model the bearing heat ex-changer system of a hydro electric power generating unit. The results shown in section 5 consist ofperformance obtained from the static model for bearing metal temperature. Static simulation wasdone in order to test the accuracy of the static model. Correlation coefficient results shown in Fig. 5.2and 5.4 respectively show the accuracy of actual verses simulation results.

Then, as discussed in section 4.3.4, dynamic simulation model was developed using the above results.The results obtained for the dynamic simulation for the untrained on untested data are shown in Fig.5.7 and 5.8 for bearing metal temperatures and bearing oil temperatures respectively. Those resultsshows with accuracy of 1.0 C for bearing metal temperature and 2.0 C variation for bearingmetal temperature with compared to the actual past performance of the system.

For improving the accuracy, more past data needs to feed to cover all possible input combinationsand also several previous values of inputs. Higher number of inputs of the NN model, number of in-put layer neurons and intermediate layer neurons increase. Therefore, higher computing capacity isneeded in terms of memory and processor speed to train the network.

In section 5.3, it was tested the behavior of the heat exchanger system due to a reduced cooling waterflow rate for the same load profile, as it usually happens in operation of power plants. In section 5.3,as shown in Fig.5.10 and 5.11, both the bearing metal temperatures and the bearing oil temperatureshave risen over the normal stabilized temperature level due to the reduced heat absorbing rate causedby the reduced (10%) cooling water flow rate.


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7Conclusions

Continuous operation of old hydropower plants have constrained with the failures due to bearingoverheating. The objective of this work was modelling and simulation of dynamic variation of tem-peratures of bearings (generator guide bearing, turbine guide bearing, thrust bearing) of a hydro elec-tric generating unit. The temperature of a bearing is depends on multiple variables such as ambientair temperature, cooling water temperature, cooling water flow-rate, initial bearing temperatures, du-ration of operation and generating unit electrical load.

As the problem under investigation was a multi-input (MI) and multi-output (MO) system, conven-tional first principles based model approach and sequential computer programs could not be applied.So that the neural network (NN) method was selected as the best where past input and output data isavailable, and the input characteristics can be mapped in order to develop a model. The NNs capa-bility of parallel processing was used to develop a model the system. This was implemented in MAT-

LAB environment. According to the simulation results, it demonstrates a reasonable (2 C) accuracyto predict the temperature variation for a given generator load profile.

Hence, this model can be used to predict the temperature variation characteristics of the system.Temperature increase in ambient air, or cooling water (due to reduced cooling water flow rate) wouldincrease the temperature level of bearing metal and oil. Using this model, it is possible to predict thetemperature increase for a given generator load profile for a given period. It will help to determinemaximum safe load level, while maximizing the plant factor minimizing the sudden failures due tobearing overheating.


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8References

[1] www.eia.doe.gov/ Energy Information Administration international statics database, visited 04-03-2010[2] Renewable Global Status Report 2006 Update,REN21, published 2007, accessed 04-03-2010;see Table 4, p. 20[3] Statistical Digest 2009, Ceylon Electricity Board, Sri Lanka[4] http:/ / www.machinerylubrication.com/Read/367/ temperature-stability, Machinery Lubrica-tion, asaccessed 2010-03-02[5] R.K.Sharma, T.K.Sharma, A text book of Water Power Engineering, S.Chand & CompanyLtd, pp 450-455, 2000[6] http:/ / www.engineeringtoolbox.com/overall-heat-transfer-coefficient- d_434.html,The Engi-neering Tool Box, as accessed 22-10-2010[7] Girish kumar Jar, Artificial neural networks and its applications, IARI, New Delhi- 100-012, pp

41-42,[8] Ral Rojas, Neural network a systematic introduction, Sprinter -Verlag, Berlin, New-York, pp5-27, March 1996.[9] Heichi Neilson R. [1990], Neurocomputing, Addison-Wesley, Reading, Mass.pp 18, 1990[10] Ugur Hlici, Artificial Neural Networks, EE543 Lecture notes, METU EEE, Ankara.[11] http:/ /www.learnartificialneuralnetworks.com/, Artificial Neural network tutorial as accessed24-06-2010[12] Matlab Neural Network Users Guide, The Mathworks inc, 1992-2010[13] Stuart Russel, Peter Norvig, Artificial Intelligence A Modern Approach Persons Inc, pp24,693-695,727-736,1995,[14] G. Bekely and K. Goldberg, Eds, Norwell , MA Kluwer , Stable nonlinear system identificationusing neural network models in Neural Networks in Robotics, pp 147-164,1992[15] http:/ /www.obitko.com/tutorials/neural-network-prediction/prediction-using-neural-

networks.html, Prediction using Neutal Networks, as accessed 17-11-2010[16] Madan M Gupta, Liang jin and Noriyasu Homma, Static and Dynamic Neural Networks FromFundamental to Advanced theory, John Wiley& Sons Inc, Hobokan New Jersey,pp 27-31,297-387,2003[17] James A Freeman, David M Skapura, Neural networks Algorithms, Applications, and pro-gramming techniques, Pearson Inc, pp 12-30,89-93,1999


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Appendix A : NN initial weight andbias values (NN example)

nnet =Neur al Net work obj ect:ar chi t ectur e:

numI nputs: 1numLayer s: 4

bi asConnect : [ 1; 1; 1; 1]i nput Connect : [ 1; 0; 0; 0]l ayer Connect : [ 4x4 bool ean]

out put Connect : [ 0 0 0 1]t ar getConnect : [ 0 0 0 1]

numOut put s: 1 ( r ead- onl y)numTar gets : 1 ( r ead- onl y)

numI nput Del ays: 0 ( r ead- onl y)numLayerDel ays: 0 ( r ead- onl y)

subobj ect st r uct ur es:

i nput s: {1x1 cel l } of i nput sl ayers : {4x1 cel l } of l ayer s

out put s: {1x4 cel l } cont ai ni ng 1 out putt ar get s: {1x4 cel l } cont ai ni ng 1 t ar getbi ases: {4x1 cel l } cont ai ni ng 4 bi ases

i nput Wei ght s: {4x1 cel l } cont ai ni ng 1 i nput wei ghtl ayer Wei ght s: {4x4 cel l } cont ai ni ng 3 l ayer wei ght s

f uncti ons:

adapt Fcn: ' t r ai ns'i ni t Fcn: ' i ni t l ay'

per f or mFcn: ' mse't r ai nFcn: ' t rai nbr '

parameters:

adapt Par am: . passes

i ni t Par am: ( none)per f ormPar am: ( none)

t r ai nPar am: . epochs, . show, . goal , . t i me,. mi n_grad, . max_f ai l , . mem_r educ, . mu,. mu_dec, . mu_i nc, . mu_max, . l r

wei ght and bi as val ues:


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I W: {4x1 cel l } cont ai ni ng 1 i nput wei ght ma-t r i x

LW: {4x4 cel l } cont ai ni ng 3 l ayer wei ght ma-tr i ces

b: {4x1 cel l } cont ai ni ng 4 bi as vect or s

ot her:

user dat a: ( user st uf f )


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Appendix B: Training record ( NNexample)

TRAI NBR, Epoch 0/ 1000, SSE 18. 3133/ 0, SSW 1279. 74, Gr ad4. 87e+001/ 1. 00e- 010, #Par 2. 60e+001/ 26



TRAI NBR, Epoch 3/ 1000, SSE 0. 0269173/ 0, SSW 135. 249, Gr ad 8. 41e-001/ 1. 00e- 010, #Par 3. 66e+000/ 26







TRAI NBR, Epoch 10/ 1000, SSE 0. 00455401/ 0, SSW 133, Gr ad 3. 08e-001/ 1. 00e- 010, #Par 8. 08e+000/ 26







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TRAI NBR, Epoch 18/ 1000, SSE 0. 00260062/ 0, SSW 131. 324, Gr ad 7. 59e-

004/ 1. 00e- 010, #Par 9. 14e+000/ 26












TRAI NBR, Epoch 30/ 1000, SSE 0. 000989142/ 0, SSW 131. 784, Gr ad9. 98e- 002/ 1. 00e- 010, #Par 1. 41e+001/ 26







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TRAI NBR, Epoch 38/ 1000, SSE 0. 0001153/ 0, SSW 131. 909, Gr ad 5. 99e-

002/ 1. 00e- 010, #Par 1. 65e+001/ 26

TRAI NBR, Epoch 39/ 1000, SSE 9. 4329e- 005/ 0, SSW 131. 778, Gr ad3. 31e- 002/ 1. 00e- 010, #Par 1. 67e+001/ 26

TRAI NBR, Epoch 40/ 1000, SSE 8. 36614e-005/ 0, SSW 131. 578, Gr ad1. 58e- 002/ 1. 00e- 010, #Par 1. 69e+001/ 26

















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TRAI NBR, Epoch 58/ 1000, SSE 4. 28702e-005/ 0, SSW 128. 382, Gr ad

2. 55e- 003/ 1. 00e- 010, #Par 1. 81e+001/ 26



















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3. 28e- 003/ 1. 00e- 010, #Par 1. 92e+001/ 26



















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1. 85e- 004/ 1. 00e- 010, #Par 1. 94e+001/ 26



















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