Current Harmonics in Modern Low Voltage Networks

8/6/2019 Current Harmonics in Modern Low Voltage Networks

1/80

Brunel University West LondonDepartment of Mechanical Engineering

Current Harmonics

In Modern Low Voltage Networks

By

Patrick Maguire

(0530673)

Dissertation submitted in pursuance of

MSc Building Services Engineering Management

Brunel University

2010

Dissertation Tutor: Prof. Alan Reynolds

- 1 -


2/80

Abstract

The causes, effects and consequences of current harmonics are not well understood by many

in the Building Services industry. Because of this, many of the indicators of harmonic

problems are ignored or misinterpreted, often until it is too late. The financial cost of this is

inestimable, but industry sources put the cost per individual commercial customer at many

hundreds, or thousand of Euro per year in cable energy losses alone.

This study aims to simplify the science behind current harmonics, such that their sources are

more easily identified, their consequences understood, and costly oversights averted.

Two discrete analysis approaches were taken: simple mono-phase loads were used to illustrate

the concepts, and more complex poly-phase systems were examined to illustrate the effects of

current harmonics in the field.

A simple computer model was developed to aid understating of both harmonic current

magnitudes and the effects of their displacement, and also as a model to help gauge the

benefit of systems and process to eliminate certain harmonics.

Finally, mitigating actions and recommendations will be discussed.

- 2 -


3/80

Acknowledgments

Firstly, I must say a special thank you to the following people:

Professor Alan Reynolds, my dissertation tutor, for his advice, assistance and words of

encouragement.

Mrs. Mary Bridge, the MSc program administrator, who has been incredibly helpful

throughout my years of distance learning at Brunel University.

Mr. Richard Gallagher, my friend and manager who supported my work throughout.

Mr. Ray Walker, my friend and colleague who helped me with the set up many of my

field measurements.

Mr. Liam Carroll for putting me straight on a number of transformer-related issues.

Mr. Pat Waters and Mr. Jimmy Connolly, my friends of many years, for their advice

and suggestions when I need some direction.

Most especially, Karen, Fintan and Bebhinn Maguire, my wife and children, who have

helped and supported me in ways too numerous to count throughout the years, for

without their patience, encouragement and support I could not have completed this.

- 3 -


4/80

Table of ContentsABSTRACT ............................................................... ........................................................... ................................. 2

ACKNOWLEDGMENTS.......................................................... ............................................................... ............ 3

TABLE OF CONTENTS............................................................ .............................................................. ............ 4

TABLE OF FIGURES ................................................................ ............................................................. ............. 5

TABLE OF EQUATIONS................................................................ ................................................................. ... 6

LIST OF TABLES...................................................................... ............................................................... ............ 6

GLOSSARY OF TERMS ........................................................... ............................................................. ............. 7

CHAPTER 1: INTRODUCTION ......................................................... ............................................................. .. 8

Context of the Dissertation Topic .................................................................... .............................................. 8 Aims and Objectives..................................................... ........................................................... ....................... 9 Limitations of study..................... ........................................................... ...................................................... 10Methodology ........................................................... ................................................................ ..................... 11

LITERATURE REVIEW ........................................................ ........................................................... ..................... 12Sources related to Electrical fundamentals................................................................. ............................ 12

Sources related to Causes of harmonics..................................................................... ............................. 12Sources related to Mathematics ........................................................................................................... ... 12Sources related to Harmonic identification and costs........................................................ ..................... 13Sources related to Transformers and Resonance ............................................................ ........................ 13Sources related to Living with harmonics ............................................................. .................................. 14Sources related to Harmonic countermeasures and considerations ....................................................... 15

MEASUREMENT EQUIPMENT: ..................................................... ............................................................ ........... 15Choosing a good quality RMS meter ............................................................ ............................................... 15

EQUIPMENT SETUP: ........................................................... ........................................................... ..................... 17

CHAPTER 2: CURRENT HARMONICS ................................................................ ........................................ 20

WHAT ARE HARMONICS? ................................................... ........................................................... ..................... 20 Basic electrical principles......................................... .............................................................. ..................... 21

Power................................................... ........................................................... ............................................. 21 Active Power...................................................... ............................................................. ............................. 22 Reactive Power ........................................................... ........................................................... ...................... 22 Linear loads ............................................................. ............................................................... ..................... 23 Non-Linear Loads ..................................................... .............................................................. ..................... 26Where are current harmonics generated? ...................................................................... ............................. 26

CHAPTER 3: CASE STUDY........................................................ ......................................................... ............ 31

ANALYSIS EQUIPMENT USED: .................................................... ............................................................ ........... 31LOAD TYPES ANALYSED ................................................... ........................................................... ..................... 31

Bench Tests ........................................................... .................................................................. ..................... 31Field Tests..... ................................................................ ................................................................... ............ 32

OBSERVATIONS ....................................................... ........................................................... ............................... 321phase systems............................................................... .................................................................. ............ 343-phase systems................................................ ................................................................ ............................ 42

CHAPTER 4: MATHEMATICAL MODELLING....................... ................................................................ ... 45

ANALYSIS OF FINDINGS..................................................... ........................................................... ..................... 48Total Harmonic Distortion (THD)............................................................... ................................................ 49

CHAPTER 5: WHY ARE CURRENT HARMONICS A PROBLEM? ......................................................... 51

Electrical Issues ......................................................... ............................................................. ..................... 51 Mechanical issues ...................................................... ............................................................. ..................... 56

CHAPTER 6: COUNTER MEASURES ............................................................... ............................................ 59

Living with Harmonics................................... ................................................................ .............................. 59Reduction .............................................................. .................................................................. ..................... 59 Elimination ............................................................. ............................................................... ...................... 62

- 4 -


5/80

CHAPTER 7: CONCLUSION AND RECOMMENDATIONS............................................................... ....... 66

Conclusions.............................. ................................................................ .................................................... 66 Main Findings...... ................................................................ ............................................................ ............ 66Recommendations ............................................................... .............................................................. ........... 67Suggested Further Reading................................................ .............................................................. ............ 68

Management of Project... ................................................................ .......................................................... ... 69

GANTT CHART ...................................................... .............................................................. ............................. 70COPY OF TOPIC DEFINITION ............................................................... ....................................................... 75

APPENDIX 1 ................................................... ........................................................... ......................................... 76

APPENDIX 2 ................................................... ........................................................... ......................................... 77

REFERENCES........................................................ .............................................................. .............................. 78

Table of FiguresFIGURE 1-THE NEED TO READ TRUE RMS ....................................................... ................................................. 16FIGURE 2-EQUIPMENT SET UP ................................................................................... ......................................... 17FIGURE 3-1PHASE BACKGROUND HARMONICS.......................................................... ......................................... 18FIGURE 4-WAVEFORMA .................................................. ........................................................... ................... 20FIGURE 5-WAVEFORM B ........................................................ ........................................................... ............. 21FIGURE 6-WAVEFORMS A AND B TOGETHER................................................... ......................................... 21FIGURE 7-VOLTAGE AND CURRENT IN PHASE .......................................................... ......................................... 22FIGURE 8-VOLTAGE AND CURRENT OUT OF PHASE.................................................. ......................................... 22FIGURE 9-COMPOSITE LOAD ........................................................................... ................................................... 24FIGURE 10-COMPARISON BETWEEN COS PHI AND DISPLACEMENT FACTOR............................................... .... 25FIGURE 11-HARMONIC CONCEPT ........................................................... ........................................................... . 25FIGURE 12-"SQUARE WAVEFORM" ....................................................... ........................................................... . 27FIGURE 13-CURRENT FLOW .......................................................................................................... ..................... 28FIGURE 14-CHOPPED SINUSOID GENERATED HARMONICS........................................................... ..................... 29FIGURE 15-HARMONICS IN PHASE ................................................................................................ ..................... 32FIGURE 16-HARMONICS OFFSET BY INDEPENDENT VALUES............................................................................. . 33FIGURE 17-SIGNIFICANT NEUTRAL CURRENT IN A BALANCED 3P SYSTEM .................................................. ..... 34FIGURE 18-NEUTRAL IMAX GREATER THAN IMAX PHASE ........................................................... ..................... 34FIGURE 19-RESISTIVE LOAD ..................................................................................... ......................................... 34FIGURE 20-INDUCTIVE LOAD (TRANSFORMER) ........................................................ ......................................... 35FIGURE 21-ENTERTAINMENT CENTRE............................................................. .................................................. 35FIGURE 22-HIGH FREQUENCY LIGHTING ......................................................... .................................................. 36FIGURE 23-COMPACT FLUORESCENT LIGHTING ..................................................... ......................................... 36FIGURE 24-COMPOSITE LOAD OF TRANSFORMER AND ENTERTAINMENT CENTRE......................................... 37FIGURE 25-DOMESTIC DWELLING AT REST DURING EVENING TIME ...................................................... ........... 38FIGURE 26-DOMESTIC DWELLING AT EVENING MEALTIME ......................................................... ..................... 39FIGURE 27-SIMULATED BALANCED APARTMENT BLOCK......................................................... ..................... 39FIGURE 28-UPSDISTRIBUTION BOARD................................................................................................... ........... 42FIGURE 29-COMPONENT HARMONIC CURRENTS AND RESULTANT ........................................................ ........... 45FIGURE 30-3PH UPS LOAD AND RESULTANT NEUTRAL..................................................................................... 46FIGURE 31-PREDICTION OF NEUTRAL CURRENT FOR BALANCED LIGHTING LOAD .......................................... 47FIGURE 32-COMPOSITE LOAD MODELLED AND MEASURED ..................................................... ......................... 47FIGURE 33-INDIVIDUAL COMPONENT HARMONIC CURRENTS .......................................................................... . 49FIGURE 34-DERATING OF TRANSFORMER ACCORDING TO K-FACTOR........................................................... . 54FIGURE 35-NEGATIVE SEQUENCE OF 5TH HARMONIC........................................................ ............................... 57

- 5 -


6/80

Table of EquationsEQUATION 1-RMSVALUE.......................................................................................... ......................................... 16EQUATION 2-TIME FREQUENCY RELATIONSHIP ................................................................. ............................... 20EQUATION 3-REACTIVE POWER FOR CHOPPED SINUSOID ................................................... ............................... 28

EQUATION 4-TOTAL HARMONIC DISTORTION (THD)........................... ........................................................ .... 49EQUATION 5-EDDY CURRENT LOSSES PER GIVEN HARMONIC NUMBER........................................................... . 53EQUATION 6-TOTAL EDDY CURRENT LOSSES................................................... .................................................. 53EQUATION 7-K-FACTOR......................................................................... .......................................................... .. 53EQUATION 8-INDUCTIVE REACTANCE ................................................... ........................................................... . 55EQUATION 9-CAPACITIVE REACTANCE............................................................ .................................................. 55EQUATION 10-LOAD IMPEDANCE ............................................................................................................ ........... 55EQUATION 11-CURRENT VOLTAGE IMPEDANCE RELATIONSHIP ........................................................... ........... 56

List of TablesTABLE 1-HARMONICS ASSOCIATED WITH WAVEFORM ABOVE .................................................... ..................... 16TABLE 2-HARMONIC VOLTAGE LIMITS AS PEREN-61000-3-6......... ........................................................... ...... 18TABLE 3-CURRENT TRANSFORMER SERIAL NUMBERS........................................................ ............................... 31TABLE 4-HARMONIC SUMMARY TABLE...................................................................... ....................................... 40TABLE 5-VSDHARMONICS: SUPPLY SIDE OF FILTER- AND MOTOR SIDE OF FILTER....................................... 43TABLE 6-SAMPLE CALCULATIONS FOR"PEAK" "EQUIVALENT RMS" AND "TRUE RMS"..........................46TABLE 7-FILTER HARDWARE COSTS ...................................................... ........................................................... . 64

- 6 -


7/80

Glossary of terms

Term Description

A Amp (Ampere) - Unit of current

AC Alternating Current

AHF Active Harmonic Filter

Amplitude Measurement of a perioduc waveform from Peak-to-Peak

C/T Current Transformer

CFL Compact Fluorescent Light

Cos Phi Angle by which current leads or lags voltage

DC Direct Current

Eddy Current A ciculating current which produces no effecive work

Frequency Numer of periodic cycles in a given time period - normally measured in

seconds (see also Hz)

Fundemental A base, or reference frequency

Harmonic Waveform that is a in interger multiple of a given reference or

fundemental frequency

Hz Hertz. Number of cycles per second

IEC International Electrotechnical Commission

IEE Institute of Electrical EngineersIEEE Institute of Electrionic and Electrical Engineers

K Factor A compensating factor for Transformers. A higher number is accociated

with operating with greater harmonic currents present

LV Low Voltage (


8/80

Chapter 1: Introduction

Context of the Dissertation Topic

For many years engineers in the Building Services industry have been aware of the existence

of Current Harmonics, and of their reputation as being a bad thing, and with often only

some vague awareness of where they came from. It is generally thought that large

semi-conductor loads create them; loads like Uninterruptible Power Supplies (UPS), motor

variable speed drives (VSDs), fluorescent lighting, computers etc.

What is not generally understood is why these loads appear to create current harmonics, what

effects these harmonic currents cause, and whether all current harmonics are inherently bad.

Most Building Services Engineering managers will know of reported cases of unexplained

catastrophic failures of major items of electrical and mechanical plant. Events such as:

failures of power factor correction banks, large motors wrecking their bearings, and of neutral

conductors overheating. In many cases, where no obvious external agent can be identified,

that mysterious electrical phenomenon current harmonics will field the blame.

Some will point out that current harmonics are unavoidable in the modern world, and that

there is simply nothing that can be done about them. Others are of the opinion that since

current harmonics are so random that if you have enough of them in your distribution system

that eventually they will all cancel each other out, and if not completely, then to some non-

harmful level. Some are of the opinion that harmonic currents can at least be reduced to

manageable levels.

The question is: is it all true, some of it, or none of it?

- 8 -


9/80

Aims and Objectives

As there is so much misunderstanding, myth and supposition, this paper aims to clarify what

really is happening, and what can be done about it. The causes of current harmonics will be

discussed how they are generated, and the kinds of loads and switching types that are

responsible. By knowing how current harmonics are generated, the building services manageris now in a position to put certain failure modes, or previously unexplained events into a new

context.

If the presence of harmonics is indicated, how can they be measured? What are THD and

the K-Factor, and why are they significant? Is it possible to tell if harmonics are a problem

in an installation? By knowing the magnitude of the harmonic currents, what are the effects

they might cause in the system?

What are these effects doing to the network and the connected equipment, and are the

consequences all inherently bad? Can awareness of harmonics be used to predict equipment

failure, or diagnose latent issues, or explain previous failure events? Armed with this

knowledge, can the Building Services manager do anything about it, and if so, what are the

typical clean up methods and costs?

There is an abundance of highly technical literature available on the Internet and in printed

works, a great deal of which is aimed at a learned and specialist audience. Many of these

approach the issue of harmonics as a sub-section of Power Quality, Variable Speed

Drives, or Non-Linear Loads. The technical detail contained in these works is generally

quite comprehensive. However, discussion on the subject tends to develop quite quickly, such

that it can soon become difficult to retain a grasp on that discussion, unless the reader is

already highly competent in the area of electrical engineering.

Finding a source that deals with the matter of harmonics in terms that can be readily

comprehended the non-specialist has always been difficult. Indeed, there are well-respected

Building Services reference books such a Chadderton (2000), which do not address the issue

at all. Yet in practice, it is frequently not the electrical engineer, but the Building Service

Engineer who first encounters the negative influence of current harmonics. How then, can the

matter be made accessible to the Building Service Engineer, who must be conversant in so

many aspects of engineering, and whose background is frequently from one of the mechanical

disciplines?

- 9 -


10/80

It is easy to become overwhelmed by the sheer quantity and variety of results when using

typical Internet search engines. The challenge is deciding which of the information can be

trusted, and whether it is properly referenced. It is therefore advisable to refrain from using

sources unless the primary data can be traced and verified. Therefore where I have referenced

Internet sources they have been from reputable international equipment manufacturers, such

as Schneider Electric, trade associations such as the Copper Development Association (CDA),

as well as academic papers published through institutions such as IEEE, or ELSEVIER.

This dissertation aims to discuss the subject of current harmonics in terms that the Building

Service Engineer is likely to be familiar with. Using and highlighting established reference

sources for further referral by the reader support this approach. The salient points are

presented such that the Building Services Engineer can be comfortable in discussing both thesituation and possible options with an electrical specialist, if the scale of the observed problem

requires that the matter needs to be escalated.

Limitations of study

In-depth study of precisely how certain loads and switching types give rise to current

harmonics could easily form the basis of a Doctoral paper in its own right. However it was

felt that a high-level appreciation of how harmonic currents were generated was important,

and that the switching mode and not simply the load type was also of significant

importance.

Some references to Direct Current or DC are made in this document for completeness, but DC

systems in general are outside of the scope of this work.

Long-term harmonic monitoring of industrial systems were also outside of the scope of thisproject, as was in-depth laboratory scale analysis of load characteristics. Actual case studies

involving the introduction of real active harmonic cancelling systems were outside the budget

of this program, but the data provided as part of the discussion on this topic was provided by

the Vendor of such equipment, was verified in so far as possible and used in good faith.

- 10 -


11/80

Methodology

To measure the effects of harmonics, a number of bench-scale single-phase measurements

were made using a Fluke 434 power quality meter. The intent was to create a reference point

for many typical load types: Resistive, Inductive, and Switch Mode Power Supply (SMPS).

The latter type being typical of many modern electrical loads such as computers, VSDs,UPSs, and high efficiency lighting. Current harmonics change the shape of the supply current

waveform from the ideal sinusoidal shape to something often quite dramatic. By identifying

the harmonic components, the magnitude and displacement of each in the current profile, it

became possible to develop a simple computer simulation using spreadsheet software, such as

Microsoft Excel.

That model was then used to predict the combined effects of similar loads on poly-phase

systems. Those predictions were then field-verified, leading to some modifications being

made to the model. The model can now be used to help predict the effects that the

combination of certain load types can have on the distribution system. Furthermore, the model

can help predict the effects that reducing the magnitude of certain harmonic components can

have on the system. This is particularly useful for future cost-benefit analysis of installing

harmonic reducing equipment. It may also be beneficial in determining the true available

capacity of supply transformers

Additional field studies were made in an industrial / commercial setting to establish whether

the harmonic currents generated by high efficiency lighting, office computers on a poly-phase

system would self-cancel, or sum.

The improvements that the incorporation of inductive chokes made on the supply to a large

VSD were also investigated. A large UPS distribution system feeding SMPSs, mainly in the

form of computers, Programmable Logic Controllers (PLCs) and their associated power

supplies and hardware was also studied.

Attention was focused both in the field and in the computer simulation on those harmonics

that were multiples of 3 the so-called triplens. These are believed to be particularly

harmful in three-phase systems. The negative sequence effect of the 5th harmonic was also

investigated, as to whether it did in fact contribute to a counter rotational force in motors.

- 11 -


12/80

Resonance issues, especially in inductive and capacitive circuits, and in particular power

factor correction systems also received attention.

Literature Review

The literature review for this project was directed largely by the aim of covering the

underlying electrical principles, and finding reliable resources on what were felt to be the key

areas that need to be addressed.

Sources related to Electrical fundamentals

With regard to this dissertation topic, an appreciation of certain fundamental electrical

principles is necessary. It has been my experience that frequently textbooks used for craft

theory training of electricians are well structured. Therefore, examples such as Whitfield

(2009) permit the reader who has some subject knowledge to find their present level and

progress from there. A number of illustrations in relation to AC theory were adapted from

this. In contrast, sources such as Reed Elsevier (2001) is an extremely useful Building

Services general reference guide, but was limited in its electrical technical detail. Although

Wildi (2000) is strongly US influenced in terms of network voltages and frequencies, and the

photo illustrations frequently look dated, the early chapters deal with electrical fundamental

principles very well.

Sources related to Causes of harmonics

The later chapters of Wildi (2000p799 / 830) cover harmonic generation principles concisely

and will also be drawn upon to illustrate how, depending on switching methods, even resistive

loads can be a source of current harmonics. This is a concept not widely discussed in other

texts, where typically the discussion only refers to non-sinusoidal currents arising from non-

linear loads. In such cases, examples cited were switch mode power supplies, and arc furnacesetc. A general understanding of the relationship between periodic non-sinusoidal waveforms,

and harmonics is therefore key to an appreciation of the prevalence of current harmonics in

modern loads.

Sources related to Mathematics

I chose to use Morris (1994) and Bird (2003a) as key reference sources for the sinusoidal and

harmonic mathematical functions that are essential to a fuller appreciation of this dissertation

topic. A number of equations and illustrations to be used in the discussion of Root Mean

- 12 -


13/80

Squared (RMS), and Total Power for complex voltages and currents were adapted from Bird

(2003b).

Sources related to Harmonic identification and costs

For most modern facilities, the presence of current harmonics can be taken for granted.

However the scale and significance of the harmonic condition needs to be explored. I found

the work of Y. Zhao et al (2004) on identification of harmonic current sources by the

existence, or otherwise, of a linear relationship between the voltage and current of a particular

harmonic order to intriguing. However, I feel that changing supply voltages, even in the

manner they describe, is largely outside the scope of the most Building Services engineers. In

practice, the Building Service Engineer will most likely employ a portable power quality

analyser, such as a Fluke 43B, Fluke 434, or similar.

However an understanding of the concept is useful, and Zhao et al (2004) agrees well with

Wildi (2000) in terms of linear loads as potential harmonic sources, but unlike Wildi does not

discuss the principles underlying their creation. The case study by Fluke (2003) provides a

simple harmonics-related example that works progressively through the

observe/measure/analyse/solve process. Additionally, the excellent analysis in Bird (2003b

p631/687) will be used for guidance for predicting the harmonic content of a waveform by

inspection of particular waveform characteristics.

The summary work of Singh G.K. (2007) was particularly useful in bringing together a

well-referenced discussion on not only harmonics, but also more general power quality issues.

Singh G.K. also introduces the IEC 61000 family of standards, and its relevance to Electro

Magnetic Compatibility (EMC), and highlights important differences between US IEEE-519

and IEC-61000.

The work of Key and Lai (undated) provides a useful basis for discussion on the cost of a

harmonic problem in terms of I2R, and on the over-sizing of distribution system components.

Sources related to Transformers and Resonance

The effect of harmonics on transformers forms an important aspect of this work. I had been

referred by a colleague to a transformer book by Heathcote (1998), and found it be a most

useful reference book. The discussion in section Operation and Maintenance (p638) was

- 13 -


14/80

particularly useful in relation to highlighting the considerations of 3rd Harmonics in Star and

Delta connected transformers.

A complimentary paper published by Pacific Gas and Electric Company (1993) clearly

illustrated the concept the negative sequence of the 5th harmonic, and this will be developed

using the work of Heathcote (1998), and Bird (2003b).

Bird (2003b) and Laughton and Warne (2003) introduce the important concept of resonance

in relation to power factor capacitors, a major consideration when dealing with inductive and

capacitive elements in a setting where harmonic frequencies are uncertain.

The discussion on the de-rating of transformers and K-Factor will draw on the published workby the Copper Development Association (2000). Likewise, a complimentary brochure from

Powerlite (2004) explains the basics of harmonic problems and provides guidance in much

simplified terms.

Sources related to Living with harmonics

The paper by Tsujimoto et al (2008) in the use of 3rd harmonic currents in the diagnosis of

XLPE cable was particularly interesting, as it discussed a useful aspect to unwanted current

harmonics. Since their work was not related to Low Voltage cable and transmission, I

considered it to be valuable, but outside of the scope of this document. However the work of

Guldemir (2003) and Wakileh (2003) as they relate to harmonics in Low Voltage

squirrel-cage motors is both useful and relevant. These will be drawn upon in the discussion

on harmonic sources, the diagnostic applications of harmonic currents, and considerations to

bear in mind when making equipment selection.

The works of Radakovic et al (2005) and El-Saadany et al (1997) will be used in relation to

the harmonic generation effects of modern fluorescent lighting, with particular reference to

emergent legislation relating to the phased withdrawal of traditional low efficiency filament

lighting. This will also tie in with my own work in relation to bench-scale lighting study, and

subsequent mathematical simulations. Like Singh G.K., this work also discusses the European

family of standards IEC 61000 in relation to voltage harmonic limits. With that family of

standards, the technical report by the International Electrotechnical Commission [IEC] (2005)

provides a useful history and rationale behind imposing limits on the levels of Total Harmonic

Distortion (THD).

- 14 -


15/80

Sources related to Harmonic countermeasures and considerations

The analysis and predictions of Goughler and Johnson (1999) and Singh B et al (1999) in

their interpretation of the future development and application of active harmonic filters is

largely verified by more recent work by Chaoui et al (2010), and current ready-at-market

Active Harmonic Filter (AHF) products such as AccuSine

from Schneider Electric (2009).Table 1 of Singh B (1999) provides a useful reference guide regarding the suitability of

different types of power quality countermeasures according to the nature of the problem.

The Copper Development Association was identified as a significant online resource. The

website for this non-trading organisation was well laid out, and contained many useful

reference documents on power quality related issues, not simply harmonics. From their

website a number of concise and well-structured papers are available, including a paper by

Fassbinder (2003) on passive harmonic filtering.

Measurement Equipment:

The power quality analysis tool used was a FLUKE 434. Up to 4# clamp-type current

transformers (C/Ts) model no. i400S were used as part of the sampling studies.

Since a good deal of the analysis and discussion in this paper is based upon findings made

using this instrument, it is important that those findings can be relied upon. A copy of the

executive summary of the calibration certificate of the instrument is included in Appendix 2,

which clearly shows that the equipment was in within specification during the analysis.

Choosing a good quality RMS meter

In most industrial electrical distribution systems, the voltage format is AC, or alternating

current. Some Direct Current (DC) distribution systems may exist, such as centralised

emergency lighting systems, but this falls outside of the scope of this document. In terms of

AC systems, this means that the instantaneous voltage value is constantly changing in a

sinusoidal format similar to those illustrated in Figure 1 - The need to read True RMS below. It

is worth remembering that since the values of voltage and current are constantly changing,

most good quality voltage and current meters display their values as calculated Root Mean

Squared or simply R.M.S value.

- 15 -


16/80

In the case of a set of n values {x1, x2 .., xn}, the RMS value is given by:

Equation 1- RMS Value

For pure sinusoidal waveforms a much simpler RMS Equivalent can be applied:

y = a sin (2pi f t)

Where a = peak value, f = frequency, and t = time.

Or even more simply as:

y = a / (2)

However, voltage and current that are distorted by harmonics are no longer sinusoidal.

Therefore values recorded on a test meter that represent values simply by means of the two

simple sinusoidal equivalents may be out by a significant amount compared with true

calculated RMS values. This unrecognised disparity often lies at the root of many adverse

harmonic conditions being overlooked.

-150

-100

-50

0

50

100

150 Distorted Waveform True Sinusoid

Figure 1 - The need to read True RM S

DC Harmonic Harmonic Harmonic Harmonic

Peak 100.2127 1 3 5 7

RMS "Equivalent" 70.86108 current 0.00 current 75.00 current 16.00 current 15.00 current 8.00RMS Actual 55.40 offset 0 offset 30 offset -120 offset -120 offset 50

Table 1 - Harmonics associated with w aveform above

- 16 -


17/80

The RMS equivalent of the Sinusoid is 70.86, where the calculated RMS of the Distorted

waveform is 55.40. It follows then, that any indicated value that is derived from the simplified

equation using only the peak value will be incorrect. In this above example, the reported value

for the distorted waveform will be higher that the True RMS equivalent, but for other

waveforms, the reverse may be equally true. See Figure 15 - Harmonics in Phase. Without

knowing the waveform shape, an observer who is not using a True RMS meter can have no

insight into the likely error in the reported value. (See Appendix 1 for sample calculations)

Equipment Setup:

For single-phase loads the basic set up was as perFigure 2 - Equipment set upbelow, with a

small external modification for most bench-scale analysis. In order to capture the relatively

small currents being drawn by bench-scale loads, a multiplication factor of 10:1 was

introduced into the detection circuit of all single-phase bench-scale studies, by passing the

load cable through the measurement C/Ts ten times. This multiplier was not used in the

analysis of the domestic dwelling, and further reference to this will be made at the appropriate

point in this paper. For 3-phase observations the instrument set up was as illustrated without

any multiplication or correction factors.

Figure 2 - Equipment set up

To eliminate supply voltage harmonics as a contributing factor, an off-load Voltage harmonic

spectrum was taken. See Figure 3 - 1phase background harmonics below. While it was not a

perfect sinusoid, the Total Harmonic Distortion (THD) was 2.5 % and well within the utility

supply tolerance set out in EN50160. EN50160 set limits for the levels of low-frequency

harmonic disturbance, or distortion, based on the level of distortion that the supply networks

can tolerate. BS EN 50160 : 2007 permits a maximum Total Harmonic Distortion of 8% in

the supply voltage.

- 17 -


18/80

Figure 3 - 1phase background harmonics

The table below, taken from BS EN 50106 : 2007 provides information on the limits set for

individual harmonics. It can be quickly seen that Even numbered harmonics and those that are

multiples of 3 have much tighter limits imposed than the remaining Odd numbered

harmonics. Even numbered harmonics indicate the presence of an unwelcome DC component.

Under normal operating conditions, during each period of one week, 95 % of the 10-minute

mean RMS values of each individual harmonic voltage shall be less than or equal to the value

given in Table 2 - Harmonic voltage limits as per EN-61000-3-6

Table 2 - Harmonic voltage lim its as per EN-61000-3-6

In general, it is the Voltage distortion that is of greatest concern to the Supply network, since

this disturbance can be experienced along the supply network. In this way, voltage distortion

caused by excessive harmonic currents in one facility can be experienced at the point of

supply to another. A weak supply network can exacerbate the voltage distortion created in the

- 18 -


19/80

supply network arising from current harmonics - as may be experienced in remote or rural

facilities, or where a facility may be supplied by a local generator.

Supplying a distorted voltage to any load is almost certain to result in current harmonics

even if that load is not of itself a harmonic current generator. Thus the network condition can

rapidly deteriorate.

Individual harmonic currents are generally expressed either as a percentage of the

fundamental current or as an absolute current value.

- 19 -


20/80

Chapter 2: Current Harmonics

What are harmonics?

Harmonics of any kind are integer number multiples of a base, or fundamental frequency. For

example; in the audio world, musical notes that we accept to be an octave apart, and hear as

being harmonious when played together, the higher note has a frequency that is twice that

of the lower note the higher note is therefore a second harmonic of the first.

To understand harmonics, of any kind, it is essential to understand some basic properties of

certain waveforms called Periodic waveforms. Periodic waveforms are those with a regular

repeating rate, normally measured in cycles per second, or Hertz (Hz).

1= T Hzfreq

Equation 2 - Time frequency relationship

The time, or period of a wave is given by Morris (1994) as : time taken between any point on

a wave to the next identical point on the wave It follows that as frequency increases then

wavelength decreases. For the purposes of this document it is the frequency aspect that is of

greatest interest.

-1

0

1

1 unit of time

Wavelength

Figure 4 - Waveform A

In Figure 5 - Waveform Bit can be seen that there are now two wave cycles in the same time

period where previously there had been only one. As the frequency has increased by an

integer number, so B is a harmonic of A

- 20 -


21/80

-1

0

1

1 unit of time

Wavelength

Figure 5 - Waveform B

-1

0

1

1 unit of time

Figure 6 - Waveforms A and B together

It follows then that where a waveform is of a frequency that is an integer multiple n of a

fundamental frequencyff then that frequency can be described as an nth harmonic offf

Basic electrical principles

Power

Based on Whitfield (2009). At its simplest, power may be calculated as Instantaneous Voltage

multiplied by Instantaneous Current:

Poweri = Voltagei x Currenti

- 21 -


22/80

-1.5

-1

-0.5

0

0.5

1

1.5

Power Voltage Active Current

Figure 7 - Voltage and Current in Phase

Active PowerWhen a load current is perfectly in phase with the supply voltage then, even when their values

are negative, their product is a positive value. Consequently the values of instantaneous power

can be seen as series of positive peaks at a rate of twice the fundamental frequency in the

direction supply to the load. Such an instance is called Active Power, is measured in Watts,

and is designated as the letterP. Note that the voltage and current are shown completely in

phase. This is typical of a purely resistive circuit.

Reactive Power

Consider a situation where the voltage and current are out of phase by 90deg, as would be

case where the load was purely inductive or capacitive.

-1.5

-1

-0.5

0

0.5

1

1.5

Power Voltage

Reactive Current Active Current

Current leads voltage by 90deg

Figure 8 - Voltage and Current out of phase

- 22 -


23/80

In this case the current pulses are both negative and positive and no nett work is done. Where

current surges back and forth from source to load like this, it is called Reactive Power, is

measured in VARs, and is designated as Q.

In a purely capacitive circuit as illustrated above, the current leads the voltage by 90deg,

and in an inductive circuit the current would lag the voltage. Both illustrations above

suggest a perfect resistive or capacitive circuit. Most practical circuits will contain some

inductive and / or capacitive elements. Nonetheless, the resultant current waveform for simple

circuits is generally linear.

Since the current waveform is a true sinusoid, as in either case illustrated above, then there are

no harmonic influences. It can accepted therefore that if either the Voltage or Current aredistorted by harmonics away from being a true sinusoid, then the resultant power will also be

distorted.

It was noted earlier that the instantaneous product of in-phase voltage and current was power

in Watts. Fassbinder S. (2003) notes that a condition arises in harmonic rich environments

where there are harmonic currents, for which there is no significant harmonic voltage.

Therefore the nett product of harmonic Voltage and Current is effectively zero. Such currents,

which produce no power, are called Wattless Current

Linear loads

In many instances, linear loads are often presumed to be simply resistive in nature. As shown

in Figure 7 - Voltage and Current in Phase above, resistive loads draw current that is both

sinusoidal and in phase with the sinusoidal supply voltage.

More correctly however, a load is said to be linear when the current remains sinusoidal,regardless of phase displacement. It can be reasonably deduced therefore that if a load

produces a non-sinusoidal current, regardless of phase displacement, then harmonic currents

are present.

Power Factor and Cos Phi

Consider this simple load below comprised of 30% active current, and 70% reactive

current (lags voltage by 90o), as might represent a simplified motor or transformer circuit.

- 23 -


24/80

-1.5

-1

-0.5

0

0.5

1

1.5

Power Voltage

Reactive Current Active Current

Figure 9 - Composite load

Some other quantity must exist to be able to describe the relation ship between power, voltage

and current in this common scenario. As can be seen the power flow is still represented by

positive and negative pulses. However the pulses are not equal, so some nett work is being

done. The effective power is now calculated by Voltage x Current x Cosine of the

displacement angle between Voltage and Current. The greater the angular displacement

between current and voltage, then the lower will be the value of nett effective power.

This quantity is frequently referred to as Power Factor or Cos Phi, where Phi represents

the displacement angle, where the Cosine can take a value of between zero and one, and said

to be either current leading or current lagging. The situation gets a little more complicated

when the load is not linear, and so the current waveform is not sinusoidal. So while Cos Phi

is an acceptable term, Power Factor needs some further qualification, especially when the

waveforms are non-sinusoidal. The term Displacement Power Factor (DF) may sometimes be

used instead of Cos Phi, but is this is only true for sinusoidal waveforms

As the true Power Factor is the total real power (kW), divided by total apparent power (kVA).

It follows then that if harmonic components are not contributing to the real power, then they

must be contributing to the apparent power, and so are influencing power factor. So it may be

that a load, whose non-linear current may largely be in phase with the voltage, may have a

poor power factor. An example of this can be seen in Figure 10 - Comparison between Cos Phi

and Displacement Factorbelow

- 24 -


25/80

Figure 10 - Comparison between Cos Phi and Displacement Factor

It is for such reasons that most power quality analysers will present values for Real and

Apparent power, and Power Factor as well as Cos Phi.

Harmonics currents

Figure 11 - Harmonic concept

When Harmonic components are present, the current waveform is no longer sinusoidal,

although it is may still be periodic. Harmonic currents are currents drawn by the load that are

a multiple of the base or fundamental frequency. It may be useful to imagine the total load as

being broken down into a number of discrete sub-loads, with each sub-load being supplied by

with its own AC voltage, where each of these imaginary AC voltages is of a frequency that is

an integer multiple of the fundamental. As presented by R.A. Alammari (2004), the total

current drawn the system as a whole is the sum of the currents drawn by these notional sub

loads (see Figure 11 - Harmonic concept).

In conclusion: where the supply voltage is not distorted, then any load that is periodic, but has

not a sinusoidal current waveform must be non-linear, and so must have some harmonic

component.

- 25 -


26/80

Non-Linear Loads

Non-Linear loads are those loads that draw a current that is not sinusoidal, whether or not that

current is in phase with the supply voltage. Loads such as battery chargers, variable speed

drives and other switch-mode power supplies are typically cited as being non-linear Figure

23 - Compact Fluorescent Lighting for example.

Their non-linearity typically results in the burst firing of electronic components such as

rectifiers and thyristors. In these instances the component presents to the supply voltage as a

high impendence, restricting or preventing current flow. At a point specified by the

controlling mechanism, these components switch on presenting low impedance to current

flow. In this way current flow is in chunks, with the appearance and disappearance of each

chunk coinciding at a particular point in the supply voltage cycle.

Fundamental voltage and fundamental current produce fundamental useable power. The

product of harmonic currents and their corresponding harmonic voltages produce harmonic

power, which does little or no useful work, but rather is generally experienced as heat in

network components.

As such, the cycle of current draw is periodic, but it is not sinusoidal, therefore it is not linear.

Where are current harmonics generated?

It is convenient to imagine that at the moment of firing of a thyristor, for example, in a power

electronic circuit, that the current immediately flows, and the leading edge of the current

waveform is straight i.e. an instant transition from Off, to the value associated with the

voltage being applied at the moment of On. In effect that is not possible. While the leading

edge of that current rise might indeed be steep, it must, according to Fourier, be a slope

defined by a high frequency component perhaps a very high frequency component.

Fourier has shown that a square periodic wave is a product of many harmonic components,

and the straighter the appearance of the rising and falling edges the higher the frequency of

the components involved.

- 26 -


27/80

-1.5

-1

-0.5

0

0.5

1

1.5

"Square Wave" Fundemental

Figure 12 - "Square Waveform"

The square wave approximation in Figure 12 - "Square Waveform" above can achieved

through relatively small harmonic numbers and magnitudes: up to harmonic #9 in this

instance, where the amplitude of each harmonic relative to the fundamental is 1/n, where nrepresents the harmonic number. It can be extrapolated that for a square wave, the harmonic

numbers may be practically infinite, but as the relative amplitude of successively higher

harmonics becomes less, so too does their significance.

If all the energy in a waveform is contained at the fundamental frequency, then that waveform

is a perfect sine wave. Conversely, if the waveform is not a perfect sine wave, then some

energy is contained in the harmonics. Once this has been accepted, then it becomes clearerthat it is possible to generate harmonics even in linear loads.

Consider the following simple circuit (from Wildi (2000)):

The supply voltage is 1000v 50Hz AC, a resistive load of 10 Ohms, and a synchronous switch

that opens and closes in synchronism with the supply voltage. Presume that the switch closes

for the last half of each half-cycle.

If the switch in Figure 13 - Current flow were closed all the time then the current would be

1000V/10Ohm = 100A, so the power would be P = I2 R = 1002 x 10 = 100kW. When the

switch is only closed half of the time, the circuit power must be only 50kW. This means that

the effective equivalent current must be 70.7A, since:

(70.7 Amps)2

x 10 ohm = 50kW.

- 27 -


28/80

The Chopped fundamental current has an equivalent current of 59.3A, lagging by 32.5deg, or

Cos = 0.843 as shown in Figure 14 - Chopped Sinusoid generated harmonicsbelow. Presume

that the switch does not absorb any active power i.e. it does not get hot. The apparent

fundamental power is 1000v x 59.3 A = 59.3kVA, the active fundamental power is 59.3 kVA

x 0.843 = 50 kW, while the reactive power is:

(59.3)2

(50)2

= 31.9 kVAR

Equation 3- Reactive power for chopped sinusoid

Figure 13 - Current flow

The resistor absorbs P = I2 R = 59.32 x 10Ohm = 35.2kW, therefore the switch must be

absorbing 50kW - 32.2kW = 14.8kW. The source delivers 31.9kVAR and the resistor absorbs

none of that, so the switch must also absorb this too. But since the switch does not get hot, the

14.8kw is immediately converted to harmonic power to be absorbed by the resistor. (WILDI

p806)

- 28 -


29/80

Figure 14 - Chopped Sinusoid generated harmon ics

What this clearly shows is that harmonic currents are not simply generated by the load, but

also by the switching mechanism. A significant clue to existence of harmonic currants in this

instance is the periodic but non-sinusoidal waveform.

Simplified operation of UPS or VSD (from Brown et al (2005))

To appreciate the basic manner in which a polyphase Variable Speed Drive (VSD) operates,

consider the following simple 4-Switch square wave inverter as one output phase. A

common DC source bus is shown here as VD, and switches S1 to S4 operate in pairs to

connect the motor winding to the source, shown here as the Load.

LOAD

1. S1 = on, S4 = on.... giving + VD at the load

2. S2 = on, S3 = on.... giving VD at the load

3. S1 = on, S2 = on.... giving zero volts at the load

4. S3 = on, S4 = on.... giving zero volts at the load

5. S1 = on, S3 = on.... giving a short-circuit fault

6. S2 = on, S4 = on.... giving a short-circuit fault.

- 29 -


30/80

If the load is inductive, when switches S1 and S4 are ON in the first part of the cycle the

current will be initially negative, as the current lags the voltage. Most power electronic

devices cannot conduct in a negative direction, so to avoid damaging the switches this

negative current is generally diverted around them using diodes D1 to D4. This results in the

supply current being drawn from the supply in series off-on-off-on bursts, and so present to

the supply as a non-linear load. See also Figure 23 - Compact Fluorescent Lighting for an

approximation.

Equally, the figure above can also be used to represent a simplified UPS where the DC source

may be a rectifier output or a battery string, In either case the current drawn by the load will

be a broadly triangular or square waveform depending on the resistance or reactance of the

load.

The operation of the switches may be very fast, in the kHz range, and an effective RMS

output voltage may be created by altering the duration of the On and Off times. This

method of pulse variability is known as Pulse Width Modulation (PWM).

As noted earlier, Fourier analysis indicates that any repetitive waveform can be represented as

a summing of a number of sinusoidal waveforms, with one sinusoid at a fundamental

frequency and a number of sinusoidal harmonics at higher frequencies, which are multiples of

the Fundamental frequency. (see Figure 29 - Component harmonic currents and resultant

Consequently the load supplied via this type of arrangement is naturally prone to the effects of

harmonic currents generated by the inverter.

- 30 -


31/80

Chapter 3: Case Study

Analysis Equipment Used:

The power quality analysis tool used was a FLUKE 434 Serial no DM9050162 with a sample

rate of 20.48 kHz. Up to 4# clamp-type current transformers (C/Ts) Model No. i400S were

used as part of the sampling studies. The executive summary of the calibration certificate for

this equipment is copied in Appendix 2.

90100001 90100008

90100015 90100017

Table 3 - Current transformer serial num bers

Load Types Analysed

Bench Tests

Simple Resistive Load: 2kW Electric KettlePurpose: to base line simple inductive load signature and provide bench-test data for

Computer Harmonic model.

Simple isolation transformer (Legrand: #0428 44 / Radionics: #383-302)Purpose: to base line simple inductive load signature and provide bench-test data for


High Frequency Fluorescent Lighting (Compton Moduspec MS6418ZT-4K)

Purpose: to base line a modern fluorescent lighting fixture signature, and provide bench-test

data for Computer Harmonic model.

Compact Fluorescent Light / CFL (Osram Duluxstar 11w)Purpose: to base line a modern Compact Fluorescent Lighting fixture, and provide bench-test

data for Computer Harmonic model.

Electronic Switch mode Power supplied (TV and Entertainment Centre):

Purpose: to observe interaction of multiple electronic loads, and provide bench-test data for


TV and Entertainment Centre and Transformer in parallelPurpose: to observe the harmonic summing effect, if any, of two loads of known harmonic

signatures into a single composite load. To provide bench-test data for Computer Harmonic

model.

- 31 -


32/80

Field Tests

1-Phase domestic situation at evening and mealtime:

Purpose: to observe the swamping effect, if any, of a large linear load introduced into a

known harmonic rich environment.

3-phase 160kW ABB Variable Speed Drive operating at approx 80% speed, without andwithout input filter:Purpose: to determine whether, and to what degree the filter is effective.

3-phase unbalanced harmonic rich electronic equipment fed via UPS source:

Purpose: to observe the effect on the Neutral of an unbalanced 3-phase system in a harmonic

rich environment.

Observations

After conducting bench-scale tests on small individual items of equipment, it became clear

that not only was the magnitude of the harmonic currents important, but so too was their

angular offset. In the two examples below, the harmonic numbers and their magnitude are the

same, however by altering the harmonic phase angle, a completely different waveform can be

constructed. Figure 16 - Harmonics offset by independent values is derived from analysis of

an isolation transformer. It is again clear that the True RMS value and a simple

Equivalent can be very different.

Figure 15 - Harmonics in PhaseDC Harmonic Harmonic Harmonic Harmonic Harmonic Harmonic

Peak 0.845962 1 2 3 5 7 9RMS "Equivalent"0.598186current 0.00 current 0.929 current 0.03 current 0.340 current 0.103 current 0.041 current 0.019

RMS Actual 0.70 offset 0 offset offset offset offset offset offset

-1.5

-1

-0.5

0

0.5

1

1.5

Distor ted waveform Supply voltage

- 32 -


33/80

DC Harmonic Harmonic Harmonic Harmonic Harmonic HarmonicPeak 1.455156 1 2 3 5 7 9

RMS "Equivalent"1.02895current 0.00 current 0.929 current 0.03 current 0.340 current 0.103 current 0.041 current 0.019RMS Actual 0.71 offset 0 offset -82 offset 98 offset -81 offset -79 offset -70 offset -82

-2

-1.5

-1

-0.5

0

0.51

1.5

2

Dis torted waveform Supply voltage

Figure 16 - Harm onics offset by independent values

This finding was especially significant. It was long been believed that harmonic currents that

are 3x multiple of the fundamental were particularly troublesome, as in 3ph systems these 3rd

harmonic components did not cancel out. Instead these so-called triplens would sum, such

that the neutral current could be in excess of the individual phase currents.

This is of particular importance in older installations where it was commonplace to install a

half-size neutral. In more recent times, 1980-1990s, the recommendation was to install a full

size neutral. More recently still, many consulting practices are recommending up to a double

size neutral for certain applications - especially those involving UPS and computer equipment

where it can be presumed, or demonstrated, that the end user equipment will not be provided

with harmonic filtering. However, it can be shown that in mixed loads, it is possible that

while there are triplen harmonic currents being generated, they need not necessarily be in

phase with each other. Even so, neutral currents of at least 1x load at 3x fundamental

frequency can be expected. This puts a significant stress on the cable and other switchgear.

Figure 17 - Significant neutral current in a balanced 3p system predicts a significant neutral

current when 3 single-phase loads similar to the transformer in Figure 20 - Inductive load

(Transformer) are connected to a 3-phase system with 4-wire Star connection. The notional

phase currents in Figure 18 - Neutral Imax greater than Imax phase are roughly equal in

magnitude and are largely sinusoidal. It is their relative displacement, driven by harmonic

elements, that contributes most significantly to the overall resultant neutral current. In both

cases below the True RMS values for phase Imax and neutral are approx 70A.

- 33 -


34/80

-150

-100

-50

0

50

100

150 Phase 1 Phase 2 Phase 3 Neutral

Figure 17 - Significant neutral current in a balanced 3p system

-200

-150

-100

-50

0

50

100

150

200 Phase 1 Phase 2 Phase 3 Neutral

Figure 18 - Neutral Imax greater than Imax phase

Voltage and current waveforms, harmonic spectra and a summary table for each bench scale

test are reproduced below.

1phase systems

Figure 19 - Resistive Load

It can be seen that the current and voltage waveforms are in phase, and the harmonic spectrum

of the off-line voltage Figure 3 - 1phase background harmonics introduced above, and the

current of this resistive device below are indistinguishable. Note also that the K-Factor for this

purely resistive load is 1.0

- 34 -


35/80


36/80

is born out by the increasing value for K-Factor, which is now at 4.9. Again, as small DC

component, measured at 2.1 % is observed.

Figure 22 - High frequency lighting

The Compton Moduspec MS6418ZT-4K was fitted with Tridonic ATCO digital Ballast, and

4x 18W 4000deg K lamps. The observed results in this instance were somewhat surprising,

since high frequency lighting has been long associated with being a significant harmonic

contributor. What is apparent is that while the current waveform shape appears significantly

sinusoidal, the total harmonic distortion is approaching 10%. Significantly the K-Factor is 1.9,

which indicates that there is a relationship between THD and K-Factor. The DC component is

measured in this instance at 4.6%.

Bird (2003b) explains that DC components may sometimes be identified in a waveform by a

lack of symmetry about the horizontal axis of a cycle. In such cases the positive and negative

half-cycles are not equal in area.

Figure 23 - Compact Fluorescent Lighting

- 36 -


37/80

The overall characteristic in Figure 23 - Compact Fluorescent Lighting is clearly non-linear,

even though it is clearly periodic. The Total Harmonic Distortion (THD) value is now

approaching 80%, while the K Factor is over 65. The current waveform shows periods where

no current is being drawn, followed by sharp bursts of current, with a tapering decay. The

sharp rise is indicative of higher order harmonics.

Figure 24 - Composite load of Transformer and Entertainment Centre

Here in Figure 24 - Composite load of Transformer and Entertainment Centre the isolation

transformer and entertainment centre from above were connected in parallel. The THD value

for the combined load is 29.8, and the K-Factor is 4. The waveform shows certain

characteristics of both load types, and this will be used later in Mathematical Modelling.

The entertainment centre was later supplied via the isolation transformer. It will be found that

at a basic level, isolation transformers make rudimentary harmonics filters. This too will be

further discussed in the section Mathematical Modelling. However, from Heathcote (1998),

the degree by which the windings of the transformer present as a filter to certain frequencies

is a function of the winding spacing, core construction, winding air-gaps etc, and this aspect

will be discussed later in section Living with Harmonics

A TYPICAL DOMESTIC HOME WAS SURVEYED IN TWO BASIC STATES:

1) Typical at evening time state. A number of CFL lamps were lit, as were a small

number of traditional filament lamps, which amounted to no more than 100w, a TV

and entertainment centre, and a home office PC were also on. Always-on appliances

such as fridge and freezer were also connected.2) As 1) above but some major kitchen appliances, such as electric stove, oven and kettle

were turned on to simulate evening meal preparation.

- 37 -


38/80

It must be noted that in this domestic dwelling analysis, the power quality analyserwas set up according to the manufacturers recommendations without anymultiplication factors.

-10

-8

-6

-4

-2

0

2

4

6

8

10

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Resultant Supply

Figure 25 - Domestic dwelling at rest during evening time

It was clear that in the lightly loaded evening scenario that the electronic loads dominated

the waveform. These can be modelled to simulate how a number of similar single-phase

dwellings connected to an upstream three-phase supply might behave with respect to the

system neutral. See Figure 27 - Simulated balanced apartment block below.

When the more powerful and essentially resistive kitchen loads were added, the effect of these

was to swamp the effects of the electronic loads. The overall effect was the load appeared

now to be wholly resistive is indicated in Figure 26 - Domestic dwelling at evening mealtime

above.

A summary of the single-phase loads is included in the following pages. When viewing tables

of harmonic numbers, magnitudes and angular offsets, it is possible with some practice to be

able to predict with some degree of confidence the likely current leading or lagging of the

resultant wave form. A rough estimate of the current waveform can also be made.

- 38 -


39/80

-40

-30

-20

-10

0

10

20

30

40

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.60.8

1

Resultant Supply

Figure 26 - Domestic dwelling at evening mealtime

-200

-150

-100

-50

0

50

100

150

200

Phase 1 Phase 2 Phase 3 Neutral

Figure 27 - Simulated balanced apartment b lock

- 39 -


40/80

Table 4 - Harmonic Summ ary Table

Significant

Harmonic

Load type Comment

Number %

Harmonic

Angular

Offset

(Degrees)

Total

Harmonic

Distortion

(THD)

K -

Factor

1 Resistive Current

waveform issinusoidal, andin phase with

voltage

1st 100 0 2.5% 1

2 Inductive Current wave

form is nolonger

sinusoidal,distinctive

pointed crests.Current lags the

voltage

1st

2nd3rd

5th7th

9thDC

92.9

2.834.

10.34.1

1.93.7

-82

98-81

-79-70

-82-

36.6% 2.4

3 Composite

ElectronicLoads

Current

waveform isclearly

distorted.

Underlying

sinusoid withdistinct peaks

occurring

within each

half-cycle.Current is

broadly in

phase with

voltage

1st

3rd5th

7th

9th

DC

95.0

17.321.4

11.1

6.8

2.1

0

-160-4

-176

1

-

31.0% 4.9

4 HiFrequency

Fluorescent

Lighting

Current appearslargely

sinusoidal, with

a sawtooth

superimposedon it. Current

lead the voltage

1st3rd

5th

7th

9th

99.37.0

4.7

2.1

2.7

14-130

-127

-161

-129

9.9% 1.9

- 40 -


41/80

Harmonic summ ary table (Contd)

Significant

Harmonic

Load type Comment

Number %

Harmonic

Angular

Offset

(Degrees)

Total

Harmonic

Distortion

(THD)

K -

Factor

5 Compact

fluorescentlighting

Current is very

distorted. Nolonger

resembles asine wave.

Distinctperiods of on

and off arevisible within

each half-cycle.

Odd number

harmonicspresent up tolimit of

instrument

1st

2nd3rd

5th7th

9th11th

13th..

..

..

49th

61.5

3.846.5

32.226.9

25.219.2

13.5..

..

..

2.2

30

-43-99

15050

-59189

90..

..

..

134

78.3% 65.8

6 Combination

of loads #2and #3 in

parallel

Current

waveformretains certain

elements ofboth

components.Waveform is

non-symmetrical

around currentpeak

1st

3rd5th

7th

9th

23rd

95.5

18.620.0

9.1

5.6

2.6

-15

-136-9

-178-8

-125

29.8% 4.0

7 Combination

of loads #2and #3 in

series

Current

waveformdiffers

significantlyfrom load #6,

and is moresinusoidal.

Waveform

remains non-symmetricalaround current

peak. Current

peaks are less

pronounced

1st

3rd5th

7th9th

11th

98.1

8.814.7

6.13.8

3.5

-17

-186-74

18112

-159

19.1% 2.2

- 41 -


42/80

Harmonic summ ary table (Contd)

Significant

Harmonic

Load type Comment

Number %

Harmonic

Angular

Offset

(Degrees)

Total

Harmonic

Distortion

(THD)

K -

Factor

8 Domestic

EveningTime

Current

waveform islargely

triangular, withsmall crest peaks

1st

3rd5th

7th9th

11th

15th

97.4

17.99.1

5.56.5

4.12.6

-1

-170-33

141-12

-17532

22.6% 3.1

9 DomesticMeal Time

Currentwaveform

indistinguishablefrom purely

resistive load(Load #1)

1st3rd

1002

0-179

2.7% 1

3-phase systems

The effect of harmonic currents on the neutral is of particular interest. In this section an

unbalanced three-phase distribution board is surveyed. The voltage source for this load is a

lightly-loaded dual conversion UPS. Because of this, the source voltage is not polluted by

outside influences; therefore any current distortion is caused by the load rather than from an

already polluted power supply, and provides a control element to the study.

Figure 28 - UPS Distribution board

- 42 -


43/80

It is evident in this situation is that the board is substantially unbalanced in terms of

Amps/Phase, but also that there is clearly a different load profile connected to all three phases,

with the profile of L3 is particularly different. The K-Factor ranges from 3.6 to 4.7

What is also evident is that the neutral current exceeds the current of the most heavily loaded

phase. This may cause unwanted trips on what is clearly a mission-critical distribution board,

given that a UPS supplies it. The neutral current also makes approx 6# zero crossings per

cycle. However, where the supply voltage is distorted by harmonic currents, such that there

are additional zero-crossings, this can create problems for certain electronic loads which use

the zero-crossing of the supply frequency as part of their timekeeping functions.

A 160kW variable speed drive (VSD), which was fitted with an inline filter, was also

analysed. Readings were taken both upstream and downstream of the filter, but in both cases

upstream of the VSD. This was to illustrate the harmonic reduction qualities of the filter.

Since structurally the filter and isolation transformer are similar, it also provided a useful

comparison to the standard isolation transformer as harmonic filter.

Supply / Clean Side Motor / Dirty Side

H1 H3 H5 H7 H1 H3 H5 H7

193.9 amps 7.8 amps 47.5 amps 19.6 amps 182.3 9.7 51 19.4

-19 49 88 143 -17 46 91 148

191.3 amps 7.1 amps 49.2 amps 20 amps 181.2 8.2 52.4 19.8

-136 -117 -151 22 -132 -122 -149 27

203.5 amps 2.5 amps 48 amps 19 amps 194.5 3.3 51.4 19.4

-258 -192 -30 -98 -254 -182 -27 -94

Table 5 - VSD Harmonics: supply side of filter - and m otor side of filter

In this particular instance, there was little appreciable benefit being offered by the filter. The

fundamental current is higher on the Supply side, as might be expected, with modest

improvements in the 3rd and 5th harmonic

What is also apparent is there is a significant 5th harmonic current on both sides of the filter

of approx 20-25% of fundamental. This will be shown later to be acting in opposition to the

normal rotation of the motor, reducing overall efficiency, and generating heat in the motor.

- 43 -


44/80

As the load is a variable speed device, and precautions were taken to monitor the loads during

times of similar demand, some degree of caution must be observed when drawing

conclusions. Nonetheless, a greater degree of improvement was expected beyond what which

was actually observed. Only simultaneous upstream and downstream analysis should be used

in deciding whether there is any thing fundamentally wrong with this installation. Such

simultaneous 3ph analysis is outside of the scope of this paper.

- 44 -


45/80

Chapter 4: Mathematical ModellingBy using the harmonic table of harmonic number, harmonic current and harmonic angular

displacement, a number of loads have been modelled for comparison against those measured

Using the typical formula for each harmonic number

=(SIN((RADIANS((A*B)+C))))*D

where

A is an incremental phase angle with repeating range 0 to 360

B is a fixed value representing the particular harmonic number

C is a fixed value representing the angular offset in degrees

D is a fixed value representing the harmonic current.

The resultant values for each angular degree value, for each of the harmonic values, may be

plotted individually, or summed and plotted as a resultant waveform.

In the case of harmonic currents associated with the Entertainment Centre these are plotted

below in Figure 29 - Component harmonic currents and resultant individually, and as a

resultant waveform. This example clearly indicates the relative phase displacement of each

harmonic current, and their magnitudes relative to each other. By summing the instantaneous

values of each current, and by plotting the result, a new waveform can be plotted. Further, it

shows strong agreement with the observed current waveform associated with the

entertainment centre referred to inFigure 21 - Entertainment Centre.

-20

-15

-10

-5

0

5

10

15

20

Ent Ctr H1 Ent Ctr H3 Ent Ctr H5

Ent Ctr H7 Ent Ctr H9 Resultant

Figure 29 - Component harmonic currents and resultant

The resultant RMS current value is approx 7.5A, whereas a true sinusoid of peak value of

approx 15.9A, as in this example, would be marginally over 11.2A (See Table 6 - Sample

- 45 -


46/80

Calculations for "Peak" "Equivalent RMS" and "True RMS"). Again this highlights the

potential for instrument reading error when not reading True RMS.

DC Harmonic Harmonic Harmonic Harmonic Harmonic

Peak 15.8843 1 3 5 7 9

RMS "Equivalent" 11.23189 current 0.20 current 9.90 current 1.80 current 2.20 current 1.20 current 0.70

RMS Actual 7.50 offset 0 offset 0 offset -160 offset -4 offset -176 offset 1Deg Radians Sin

0 0 0 0.2 0 -0.6156363 -0.1534642 -0.0837078 0.0122167

1 0.017453293 0.017452 0.2 0.1727788 -0.703316 0.0383953 -0.2289708 0.1215537

2 0.034906585 0.034899 0.2 0.345505 -0.7890681 0.2299626 -0.3708204 0.2278977

3 0.052359878 0.052336 0.2 0.518126 -0.8726573 0.4197798 -0.5071419 0.3286301

4 0.06981317 0.069756 0.2 0.6905891 -0.9538547 0.6064022 -0.6359031 0.4212705

5 0.087266463 0.087156 0.2 0.8628419 -1.0324376 0.7884095 -0.7551845 0.5035379

355 6.195918845 -0.08716 0.2 -0.8628419 -0.1568803 -1.0665812 0.6180457 -0.4862609

356 6.213372137 -0.06976 0.2 -0.6905891 -0.2505116 -0.8948206 0.488084 -0.4015035

357 6.23082543 -0.05234 0.2 -0.518126 -0.3434562 -0.7162499 0.350846 -0.3068598

358 6.248278722 -0.0349 0.2 -0.345505 -0.4354594 -0.5322282 0.2083778 -0.2046602

359 6.265732015 -0.01745 0.2 -0.1727788 -0.5262691 -0.3441558 0.0628031 -0.0974212

360 6.283185307 -2.5E-16 0.2 -2.426E-15 -0.6156363 -0.1534642 -0.0837078 0.0122167

Table 6 - Sample Calculations for "Peak" "Equivalent RMS" and "True RMS"

-100

-80

-60

-40

-20

0

20

40

60

80

100 Phase 1 Phase 2 Phase 3

-100

-80

-60

-40

-20

0

20

40

60

80

100 Neutral

When modelling Figure 30 - 3ph UPS load

and resultant Neutral distribution board,

there is also strong agreement in terms of

the observed and modelled waveforms,

when compared to Figure 28 - UPS

Distribution board above.

It becomes clear that phases L2 and L3

cancel each other to a considerable degree,

such that in this instance the neutral is

substantially dominated by L1 in terms of

magnitude and angular displacement.

Figure 30 - 3ph UPS load and resultant Neutral

Figure 31 - Prediction of neutral current for balanced lighting load below represents a

prediction of neutral for a balanced three-phase installation comprising of the high frequency

luminaries analysed above.

- 46 -


47/80

-6

-4

-2

0

2

4

6Phase 1 Phase 2 Phase 3 Neutral

Figure 31 - Prediction of neutral current for balanced lighting load

It was important to determine if, having successfully modelled independent loads, whether it

was possible to sum them in the model, and achieve an agreeable result when measured

against those two loads connected in parallel. Two loads of relatively comparable size, but

with distinctive individual waveforms were chosen. From the Table 4 above Load #2 and

Load #3 were connected in parallel to form a new composite load (Load #6), shown below in

Figure 32 - Composite load modelled and measured. It is immediately clear that the observed

metered result contains distinctive elements from both of the individual loads. The modelled

result, shown below, of the two discrete loads agrees well with the observed value for Trafo

+ Ent Ctr, and the modelled Sum of all Harmonics, and helps to validate the model.

-20

-15

-10

-5

0

5

10

15

20Trafo Ent. Ctr. Trafo + Ent Ctr Sum of all harmonincs

Figure 32 - Composite load modelled and measured

- 47 -


48/80

Analysis of FindingsWhat is now clear is that all

Documents

Current Harmonics in Modern Low Voltage Networks