Power Electronics in Electricity to IEC61000-3-13

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University of Wollongong Thesis Collections

University of Wollongong Thesis Collection

University of Wollongong Year

Contributions towards the development

of the Technical Report IEC/TR

61000-3-13 on voltage unbalance emissionallocation

Prabodha ParanavithanaUniversity of Wollongong

Paranavithana, Prabodha, Contributions towards the development of the Technical ReportIEC/TR 61000-3-13 on voltage unbalance emission allocation, PhD thesis, School of Elec-

trical, Computer and Telecommunications Engineering, University of Wollongong, 2009.http://ro.uow.edu.au/theses/834

This paper is posted at Research Online.

http://ro.uow.edu.au/theses/834


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Contributions Towards the Development of the

Technical Report IEC/TR 61000-3-13 on Voltage

Unbalance Emission Allocation

A thesis submitted in fulfilment of the

requirements for the award of the degree

Doctor of Philosophy

from

University of Wollongong

by

Prabodha Paranavithana, BSc(Eng)

School of Electrical, Computer and Telecommunications

Engineering

March 2009


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Dedicated to my parents...


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Acknowledgements

It is a pleasure to be able to thank many people to whom I am indebted for the

development of this thesis.

First and foremost, I wish to express my utmost gratitude to my principal super-

visor, Associate Professor Sarath Perera of the University of Wollongong (UoW), for

enabling me to pursue postgraduate studies at the University of Wollongong and the

support given throughout the study period in many ways. Your dedication, patience,

knowledge and experience could not have been surpassed. I admire your guidance

towards growing me up academically and personally over last few years.

Thanks to my co-supervisor, Professor Danny Sutanto of the UoW, for the assis-

tance provided. I would also like to offer many appreciations to Dr. Duane Robinson

of Beca, Australia for proofreading this thesis. To Mr. Robert Koch of Eskom

Holdings Limited, South Africa and Dr. Zia Emin of National Grid Electricity Trans-

mission, United Kingdom go many thanks for their insightful technical contributions

and helpful attitude. LATEX assistance received from Dr. Timothy Browne, previ-

ously with the Integral Energy Power Quality and Reliability Centre (IEPQRC) at

the UoW, is much appreciated.

Funding for this project was provided by SP AusNet, Victoria and the IEPQRC.

I am grateful to Mr. Dhammika Adihetti, Mr. Shiva Bellur and Mr. Sanath Peiris of

SP AusNet for arraigning this. Many thanks to Mr. Jeff Sultana, Mr. Shem Cardosa

and Mr. Mahinda Wickramasuriya of SP AusNet for the support given in collecting

the required data for Chapter 7 of this thesis.

Thanks to Dr. Vic Smith and Sean Elphick of the IEPQRC who have graciously

responded to many administrative and software related requests. My thanks also go to

Roslyn Causer-Temby of the School of Electrical, Computer and Telecommunications

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Engineering (SECTE) at the UoW, Tracey O’Keefe and Maree Burnett who are

former members of the SECTE staff, and Esperanza Riley of the IEPQRC for solving

many administrative problems and providing perspective. The SECTE workshop

staff have cheerfully provided the technical assistance.

Very special thanks go to my friend Dr. Sankika Tennakoon, previously with the

IEPQRC, for being generously supportive especially during hard times along the way.

Your contribution to my PhD experience is also appreciated.

My heartiest gratitude goes to my parents Mithrananda and Manike for all encour-

agements, guidance and sacrifices made on behalf of me to come this far. Finally, my

thanks go to the rest of my family and friends particularly Pinky, Dimuthu, Radley,

Matthew and Nishad for being supportive in many ways.


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Abstract

Although voltage unbalance is a well understood concept, its presence as a power

quality problem in electricity transmission and distribution networks has continued

to be an issue of concerns primarily due to difficulties found by some network service

providers in maintaining acceptable levels. This emphasises the lack of recommenda-

tions on engineering practices governing voltage unbalance that would facilitate the

provision of adequate supply quality to connected customers.

The International Electrotechnical Commission (IEC) has recently released the

Technical Report IEC/TR 61000-3-13 which provides guiding principles for coordi-

nating voltage unbalance between various voltage levels of a power system through

the allocation of emission limits to installations. Although the IEC report is based

on widely accepted basic concepts and principles, it requires refinements and original

developments in relation to some of the key aspects. This thesis primarily focuses on

making contributions for further improvements to the IEC report so as to present a

more comprehensive voltage unbalance allocation procedure.

Similar to the counterpart IEC guidelines for harmonics (IEC 61000-3-6) and

flicker (IEC 61000-3-7) allocation, IEC/TR 61000-3-13 also apportions the global

emission allowance to an installation in proportion to the ratio between the agreed

apparent power, and the total available apparent power of the system seen at the

busbar where it is connected. However, noting that voltage unbalance at a busbar

can arise as a result of both load and system (essentially lines) asymmetries, IEC/TR

61000-3-13 applies an additional factor which is referred to as ‘Kue’ to the appor-

tioned allowance. This factor Kue represents the fraction of the global emission

allowance that can be allocated to customers, whereas the factor K ue (= 1 − Kue)accounts for voltage unbalance which arises as a result of line asymmetries. Although

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IEC/TR 61000-3-13 recommends system operators to assess the factors Kue and

K ue for prevailing system conditions, a systematic method for its evaluation is not

provided other than a rudimentary direction. This thesis initially examines, employ-

ing radial systems, the influence of line asymmetries on the global emission levels

in medium voltage (MV) and high voltage (HV) power systems in the presence of

various load types/bases including three-phase induction motors. It is shown that

the factor K ue is seen to be dependant not only on line parameters as evident from

IEC/TR 61000-3-13, but also on the downstream load composition. In essence, the

global emission levels in HV power systems is seen to arise as a result of both the localHV lines and the downstream MV lines in the presence of considerable proportions of

induction motor loads. Eventually, generalised methodologies, covering both radial

and interconnected networks, for the assessment of the global emission in MV and

HV power systems which arises due to line asymmetries are proposed.

In allocating voltage unbalance based on the IEC/TR 61000-3-13 recommenda-

tions, quantitative measures of its propagation from higher voltage to lower voltagelevels in terms of transfer coefficients, and from one busbar to other neighbouring bus-

bar of a sub-system in terms of influence coefficients are required. IEC/TR 61000-3-13

gives a method for evaluating the MV to LV transfer coefficient suggesting a value

less than unity for industrial load bases containing large proportions of mains con-

nected three-phase induction motors, and a value of unity for passive loads in general.

Upon detailed examination, it is noted that a transfer coefficient > 1 can arise in the

presence of commonly prevailing constant power loads. Incorporating these different

influences exhibited by various load types under unbalanced supply conditions on the

propagation, comprehensive methods for assessing the MV to LV and HV to MV

transfer coefficients are proposed. A systematic approach for estimating influence

coefficients for interconnected network environments taking their dependency on the


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downstream load composition into account is developed.

The IEC allocation policy with regard to harmonics and flicker has been found not

to guarantee that the emission limits allocated to customers ensure non-exceedance

of the set planning levels. This thesis reports that the above is an issue with voltage

unbalance as well. Overcoming this problem, an alternative allocation technique

referred to as ‘constraint bus voltage’ (CBV) method which closely aligns with the

IEC approach has been suggested for harmonics and flicker. The work presented in

this thesis extends the suggested CBV method to voltage unbalance allocation adding

appropriate revisions to address the additional aspect of the emission which arises as

a result of line asymmetries.

In the application of the IEC/TR 61000-3-13 principles to better manage existing

networks already experiencing excessive voltage unbalance levels, the initial develop-

ment of insights into the influences made by various sources of unbalance is required.

Employing an existing 66kV interconnected sub-transmission system as the study

case, deterministic studies are carried out in a systematic manner considering each of

the asymmetrical elements. Approaches for studying the voltage unbalance behaviour

exhibited by various sources which exist in interconnected network environments are

established. These are employed to identify the most favourable line transposition

options for the study system. Further, this knowledge that facilitates the identifi-

cation of contributions made by individual unbalanced sources forms a platform for

developing techniques to assess the compliance with emission limits, which is another

subject of relevance to future editions of IEC/TR 61000-3-13.

As an essential tool for carrying out the studies, an unbalanced load flow program

based on the phase coordinate reference frame incorporating the component level load

flow constraints and the three-phase modelling of system components is developed.


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List of Principal Symbols and Abbreviations

a,b,c refer to the three phasesα summation law exponent

CBV constraint bus voltage

CIGRE International Council on Large Electric Systems

CIRED International Conference on Electricity Distribution

E s:x emission limit of any busbar x of any sub-system S [VUF]

E s:x− j emission limit of any installation j to be connected at any

busbar x of any sub-system S [VUF]

EHV extra high voltage

hm refers to a HV-MV coupling transformer

HV high voltage

I refers to a constant current load

[I ] matrix of nodal currents

I λ:t λ (= 0, +, −) sequence current in any line t [A]I λ:x λ (= 0, +, −) sequence component of I x [A]

I x nodal current at any busbar x [A]I −:c/e negative sequence current in any system element e (e = t, tf, busbar x)

caused by any source of unbalance c (c = t, td,lines,U x) [A]

IEC International Electrotechnical Commission

IEEE Institute of Electrical and Electronics Engineers

IM refers to a three-phase induction motor load

ka allocation constant

ki−x influence coefficient from any busbar i to any other busbar x

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klv fraction of LV loads supplied by any higher voltage (MV, HV) busbar

km ratio between the rated motor load (in MVA) and the total

load (in MVA) supplied by an LV system

kmmv ratio between the rated motor load (in MVA) and the total

load (in MVA) supplied by an MV system

k pq ratio between the constant power load (in MVA) and the total


k pqmv ratio between the constant power load (in MVA) and the total


ks ratio between the positive and negative sequence impedances of the

aggregated motor load supplied by an LV system

ksc−s ratio between the short-circuit capacity (in MVA) at any busbar S

and the total load (in MVA) supplied by the busbar S

kz ratio between the constant impedance load (in MVA) and the total


kzmv ratio between the constant impedance load (in MVA) and the total


Kues:x fraction of the busbar emission allowance at any busbar x of anysub-system S that can be allocated to installations

K ues:x fraction of the busbar emission allowance at any busbar x of any

sub-system S that accounts for the emission arising as a result of

system inherent asymmetries

LF load flow

LV low voltage

ml refers to a MV-LV coupling transformer

MV medium voltage

NECA National Electricity Code Australia

NEMA National Equipment Manufacturer’s Association

PCC point of common coupling

P Q refers to a constant power load

P S refers to a passive load


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rec receiving end busbar of any line t

S represents any sub-system (S = HV, MV, LV)

S sc:s short-circuit capacity at any busbar S [MVA]

S s:x total apparent power to be supplied by any busbar x of any

sub-system S [MVA]

S s:x−ds part of S s:x supplied at the downstream (DS) [MVA]

S s:x− j agreed apparent power of any installation j to be connected

at any busbar x of any sub-system S [MVA]

S s:x−local part of S s:x supplied locally [MVA]

S s:x−total total apparent power, as seen at any busbar x of any

sub-system S, to be supplied by the sub-system S [MVA]

send sending end busbar of any line t

t any radial local line of any sub-system under evaluation

td any radial downstream line of any sub-system under evaluation

tij any line between busbars i and j of any sub-system

under evaluation

tf refers to a coupling transformer

T us−s US to S transfer coefficientθ pf :x power factor angle at any busbar x [deg.]

θ pf :z, θ pf : pq power factor angle of the constant impedance and constant

power loads respectively supplied by an LV system [deg.]

θ pf :zmv , θ pf : pqmv power factor angle of the constant impedance and constant

power loads respectively supplied by an MV system [deg.]

θY −+:x phase angle of the admittance Y −+:x [deg.]

θZ −+:td phase angle of the impedance Z −+:td [deg.]

θZ λ∆:t phase angle of the impedance Z λ∆:t [deg.]

θI λ:t phase angle of the current I λ:t [deg.]

U g/s global emission allowance of any sub-system S [VUF]

U g/s:x emission allowance of any busbar x of any sub-system S [VUF]

U loadsg/s:x global emission arising as a result of unbalanced installations

at any busbar x of any sub-system S [VUF]


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U linesg/s:x global emission arising as a result of system inherent asymmetries


U j/s:x emission level caused by any source of unbalance j


U results:x resultant emission level at any busbar x of any sub-system S [VUF]

U x voltage unbalance at any busbar x [VUF]

UIE International Union for Electricity Applications

US represents any upstream system of any sub-system S

(US = EHV, HV, MV)

[V ] matrix of nodal voltagesV λ:x λ (= 0, +, −) sequence component of V x [V]V λ:s−us λ (= 0, +, −) sequence voltage, referred to US, at any busbar S [V]V n−s nominal line-line voltage of any sub-system S [V]

V x voltage at any busbar x [V]

V lines−:g/s:x global negative sequence voltage arising as a result of line

asymmetries at any busbar x of any sub-system S [V]

V −:U i/x negative sequence voltage at any busbar x caused by

the voltage unbalance U i that exists at any other busbar i

V Rt voltage regulation of any line t

V Rtd voltage regulation of any line td

VUF voltage unbalance factor [%]

[Y ] matrix of nodal admittances

Y λ∆:xy λ − ∆ (λ, ∆ = 0, +, −) sequence coupling admittancecomponent of Y xy [S ]

Y xy nodal admittance between any busbar x and anyother busbar y [S ]

Y −−:x−im downstream negative sequence admittance seen at any

busbar x taking only induction motors into account [S ]

Y −+:x downstream negative-positive sequence coupling

admittance seen at any busbar x [S ]


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Z refers to a constant impedance load

Z λ∆:t λ − ∆ (λ, ∆ = 0, +, −) sequence coupling impedanceof any line t [Ω]

Z λλ:x downstream λ (λ = 0, +, −) sequence impedance seenat any busbar x [Ω]

Z λλ:tf −s λ (λ = 0, +, −) sequence impedance, referred to S, of anycoupling transformer [Ω]

Z −−:x−im downstream negative sequence impedance seen at any

busbar x taking only induction motors into account [Ω]

Z −+:td negative-positive sequence coupling impedance

of any line td [Ω]

Z −+:td−us negative-positive sequence coupling impedance, referred

to US, of any line td [Ω]

0, +, − refer to zero, positive and negative sequences respectively


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Publications Arising from the Thesis

1. Prabodha Paranavithana, Sarath Perera, and Danny Sutanto. Impact of Un-

transposed 66kV Sub-transmission Lines on Voltage Unbalance. In Proc. Aus-

tralasian Universities Power Engineering Conference (AUPEC 2006), paper 28,

Melbourne, Australia, December 2006.

2. P. Paranavithana, S. Perera, and D. Sutanto. Analysis of System Asymmetry

of Interconnected 66kV Sub-transmission Systems in relation to Voltage Unbal-

ance. In Proc. IEEE Power Engineering Society Conference and Exposition in Africa (PowerAfrica ’07), Johannesburg, South Africa, July 2007.

3. Prabodha Paranavithana, Sarath Perera, Danny Sutanto, and Robert Koch.

A Systematic Approach Towards Evaluating Voltage Unbalance Problem in In-

terconnected Sub-transmission Networks: Separation of Contribution by Lines,

Loads And Mitigation. In Proc. 13th IEEE International Conference on Har-

monics and Quality of Power (ICHQP 2008), Wollongong, Australia, September-October 2008.

4. Prabodha Paranavithana, Sarath Perera, and Robert Koch. An Improved

Methodology for Determining MV to LV Voltage Unbalance Transfer Coeffi-

cient. In Proc. 13th IEEE International Conference on Harmonics and Quality

of Power (ICHQP 2008), Wollongong, Australia, September-October 2008.

5. Robert Koch, Alex Baith, Sarath Perera, and Prabodha Paranavithana. Volt-

age Unbalance Emission Limits for Installations - General Guidelines and Sys-

tem Specific Considerations. In Proc. 13th IEEE International Conference

on Harmonics and Quality of Power (ICHQP 2008), Wollongong, Australia,

September-October 2008.

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6. Prabodha Paranavithana, Sarath Perera, and Danny Sutanto. Management of

Voltage Unbalance Through Allocation of Emission Limits to Installations. In

Proc. Australasian Universities Power Engineering Conference (AUPEC 2008),

paper 017, Sydney, Australia, December 2008.

7. Prabodha Paranavithana, Sarath Perera, and Robert Koch. Propagation of

Voltage Unbalance from HV to MV Power Systems. In Proc. 21st International

Conference on Electricity Distribution (CIRED 2009), paper 0497, Prague, June

2009.

8. Prabodha Paranavithana, Sarath Perera, and Robert Koch. A Generalised

Methodology for Evaluating Voltage Unbalance Influence Coefficients. In Proc.

21st International Conference on Electricity Distribution (CIRED 2009), paper

0500, Prague, June 2009.

9. Prabodha Paranavithana and Sarath Perera. Location of Sources of Voltage Un-

balance in an Interconnected Network. In Proc. IEEE Power Engineering So-

ciety General Meeting (panel session on “Developments in Determining Power

Quality Disturbance Sources and Harmonic Source Contributions”) , Calgary,

Alberta, Canada, July 2009.

10. Prabodha Paranavithana and Sarath Perera. A Robust Voltage Unbalance

Allocation Methodology Based on the IEC/TR 61000-3-13 Guidelines. In Proc.

IEEE Power Engineering Society General Meeting , Calgary, Alberta, Canada,July 2009.

11. P. Paranavithana, S. Perera, R. Koch, and Z. Emin. Global Voltage Unbalance

in MV Power Systems due to Line Asymmetries. Accepted for publication in

IEEE Trans. on Power Delivery .


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12. P. Paranavithana, S. Perera, R. Koch, and Z. Emin. Global Voltage Unbalance

in HV Power Systems due to Line Asymmetries: Dependency on Loads And an

Evaluation Methodology. Accepted for publication in IEEE Trans. on Power

Delivery .

13. Prabodha Paranavithana, Sarath Perera, and Danny Sutanto. Management

of Voltage Unbalance Through Allocation of Emission Limits to Installations.

Accepted for publication in Australian Journal of Electrical and Electronics

Engineering (reproduction of Proc. AUPEC 2008 ).


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Table of Contents

1 Introduction 11.1 Statement of the Problem . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Research Objectives and Methodologies . . . . . . . . . . . . . . . . . 41.3 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Literature Review 102.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Definition of Voltage Unbalance . . . . . . . . . . . . . . . . . . . . . 112.3 Sources of Voltage Unbalance . . . . . . . . . . . . . . . . . . . . . . 132.4 Effects of Voltage Unbalance . . . . . . . . . . . . . . . . . . . . . . . 142.5 Mitigation Techniques of Voltage Unbalance . . . . . . . . . . . . . . 17

2.6 Measurement and Indices of Voltage Unbalance . . . . . . . . . . . . 182.7 Limits of Voltage Unbalance . . . . . . . . . . . . . . . . . . . . . . . 21

2.7.1 Compatibility Levels . . . . . . . . . . . . . . . . . . . . . . . 212.7.2 Voltage Characteristics . . . . . . . . . . . . . . . . . . . . . . 222.7.3 Planning Levels . . . . . . . . . . . . . . . . . . . . . . . . . . 252.7.4 Customer Emission Limits . . . . . . . . . . . . . . . . . . . . 26

2.8 Guiding Principles of IEC/TR 61000-3-13 [1] for Voltage UnbalanceEmission Allocation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.8.1 Basic Concepts Used in IEC/TR 61000-3-13 . . . . . . . . . . 282.8.2 Emission Limits: Stages 1, 2 and 3 . . . . . . . . . . . . . . . 302.8.3 Development of Stage 2 Emission Limits . . . . . . . . . . . . 312.8.4 Voltage Unbalance Transfer Coefficients . . . . . . . . . . . . 392.8.5 Factor K ue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.9 A Revised Harmonics/Flicker Allocation Technique Based on the IECGuidelines - A Preamble to Voltage Unbalance Allocation . . . . . . . 43

2.10 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3 Global Voltage Unbalance in MV Power Systems due to System InherentAsymmetries 493.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.2 Influence of Line Asymmetries on the Global Emission and its Depen-

dency on Load Types/Bases . . . . . . . . . . . . . . . . . . . . . . . 523.2.1 Constant Impedance (Z ) Loads . . . . . . . . . . . . . . . . . 543.2.2 Constant Current (I ) Loads . . . . . . . . . . . . . . . . . . . 553.2.3 Constant Power (P Q) Loads . . . . . . . . . . . . . . . . . . 553.2.4 Induction Motor (IM ) Loads . . . . . . . . . . . . . . . . . . 563.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2.6 Mixes of Passive and Induction Motor Loads . . . . . . . . . . 58

3.3 Methodology for Evaluating the Global Emission Arising Due to LineAsymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

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3.4 Verification of the Methodology . . . . . . . . . . . . . . . . . . . . . 663.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4 Global Voltage Unbalance in HV Power Systems due to System Inherent Asym-metries 704.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704.2 Influence of Line Asymmetries on the Global Emission in the Presence

of Induction Motor Loads . . . . . . . . . . . . . . . . . . . . . . . . 744.3 Methodology for Evaluating the Global Emission Arising Due to Line

Asymmetries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4 Verification of the Methodology Using a Three-bus Test System . . . 854.5 Verification of the Methodology Using the IEEE 14-bus Test System . 894.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5 Propagation of Voltage Unbalance 945.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.2 Voltage Unbalance Transfer Coefficients . . . . . . . . . . . . . . . . . 97

5.2.1 MV to LV Transfer Coefficient, T mv−lv . . . . . . . . . . . . . 1035.2.2 HV to MV Transfer Coefficient, T hv−mv . . . . . . . . . . . . . 110

5.3 Voltage Unbalance Influence Coefficients . . . . . . . . . . . . . . . . 1175.3.1 Preliminary Investigations - Dependency of Influence Coeffi-

cients on Load Types/Bases . . . . . . . . . . . . . . . . . . . 1175.3.2 Methodology for Evaluating Influence Coefficients . . . . . . . 1215.3.3 Verification of the Methodology Using a Three-bus MV Test

System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1255.3.4 Verification of the Methodology Using the IEEE 14-bus Test

System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.4 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

6 A Revised Voltage Unbalance Allocation Technique Based on the IEC/TR61000-3-13 Guidelines 1316.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1316.2 Examination of the IEC/TR 61000-3-13 Approach . . . . . . . . . . 132

6.2.1 Calculation of Individual Emission Limits . . . . . . . . . . . 1346.2.2 Resulting Busbar Emission Levels and Examination Remarks . 138

6.3 A Revised Voltage Unbalance Allocation Technique Based on the CBVAllocation Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.4 Examination of the Revised Voltage Unbalance Allocation Technique 142

6.4.1 Calculation of Individual Emission Limits . . . . . . . . . . . 1426.4.2 Resulting Busbar Emission Levels and Examination Remarks . 144

6.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146


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7 Analysis of the Problem of Voltage Unbalance in Interconnected Power Sys-tems 1477.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

7.2 Voltage Unbalance Behaviour of Line Asymmetries . . . . . . . . . . 1507.2.1 Impact of the Line Asymmetries of the Study System on the

Voltage Unbalance Problem . . . . . . . . . . . . . . . . . . . 1507.2.2 Voltage Unbalance Behaviour of the Individual Lines of the

Study System - as Standalone Lines . . . . . . . . . . . . . . . 1527.2.3 Voltage Unbalance Behaviour of the Individual Lines of the

Study System - as Elements in the Interconnected Network . . 1557.2.4 General Outcomes - Representation of the Voltage Unbalance

Behaviour of an Asymmetrical Line as an Element in an Inter-connected Network . . . . . . . . . . . . . . . . . . . . . . . . 160

7.2.5 General Outcomes - Representation of the Interaction of AllAsymmetrical Lines . . . . . . . . . . . . . . . . . . . . . . . . 160

7.3 Voltage Unbalance Behaviour of Load Asymmetries . . . . . . . . . . 1677.3.1 Impact of the Load Asymmetries of the Study System on the

Voltage Unbalance Problem . . . . . . . . . . . . . . . . . . . 1677.3.2 Voltage Unbalance Behaviour of the Individual Loads of the

Study System - as Elements in the Interconnected Network . . 1697.3.3 General Outcomes . . . . . . . . . . . . . . . . . . . . . . . . 174

7.4 Combined Voltage Unbalance Behaviour of Line and Load Asymmetries1767.4.1 Combined Impact of the Line and Load Asymmetries of the

Study System on the Voltage Unbalance Problem . . . . . . . 176

7.4.2 Representation of the Voltage Unbalance Behaviour of the En-tire System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176

7.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

8 Conclusions and Recommendations for Future Work 1848.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1848.2 Recommendations for Future Work . . . . . . . . . . . . . . . . . . . 191

Appendices

A Derivation of (3.5) 204

B Radial MV-LV Test System(Fig. 3.2) 207

C Derivation of (3.14) 209

D Y −−:x−im for an MV Network 212

E Application of the Methodology Given by (3.25) to the Three-bus MV TestSystem (Fig. 3.7) 214


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F Derivation of (4.7) 218

G Derivation of (4.9) 221

H Test Case Description of the Radial HV-MV-LV System (Fig. 4.2) 224

I Y −+:x for an HV Network 227

J Application of the Methodology Given by (3.22) to the Three-bus HV TestSystem (Fig. 4.6) 229

K Data of the IEEE 14-bus Test System (Fig. 4.9) 233

L Derivation of (5.18) 237

M Application of the Methodology Given by (5.37) to the Three-bus MV TestSystem (Fig. 5.16) 240

N 66kV Sub-transmission Interconnected Study System (Fig. 7.1) - AdditionalData/Information 243N.1 Operating Conditions at the Considered Time Stamp . . . . . . . . . 243N.2 Line Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246N.3 An Explanation on the Influence of the Location of an Asymmetri-

cal Line of an Interconnected Network on the Voltage Unbalance Be-haviour of the Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

N.4 A Demonstration of the Linearity of Negative Sequence Voltages . . . 247

O Development of a Method for Unbalanced Load Flow Analysis 249O.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249O.2 Symmetrical Component Versus Phase Coordinate Reference Frames

for Unbalanced Load Flow Analysis . . . . . . . . . . . . . . . . . . . 250O.3 Special Considerations in Developing an Unbalanced Load Flow Program250O.4 Representation of System Components . . . . . . . . . . . . . . . . . 251

O.4.1 Synchronous Generators . . . . . . . . . . . . . . . . . . . . . 251O.4.2 Passive Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . 254O.4.3 Overhead Lines . . . . . . . . . . . . . . . . . . . . . . . . . . 255O.4.4 Capacitor Banks . . . . . . . . . . . . . . . . . . . . . . . . . 256O.4.5 Three-phase Voltage Regulators/Transformers . . . . . . . . . 256O.4.6 Three-phase Induction Motors . . . . . . . . . . . . . . . . . . 256O.4.7 Network Interactions . . . . . . . . . . . . . . . . . . . . . . . 280

O.5 Load Flow Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280O.6 Related References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281


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List of Figures

2.1 Derating of three-phase induction motors (UIE) . . . . . . . . . . . . 15

2.2 Statistical interpretation of the compatibility level (IEC 61000-2-2,IEC 61000-2-12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Statistical interpretation of the planning level (IEC 61000-2-2, IEC 61000-2-12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Interpretation of the emission level (IEC/TR 61000-3-13) . . . . . . . 302.5 Illustration of the global emission allowance (IEC/TR 61000-3-13) . . 352.6 Interconnected sub-system S . . . . . . . . . . . . . . . . . . . . . . . 372.7 System representation of any busbar x of the system S shown in Fig. 2.6 372.8 Variation of T mv−lv with km established using (2.17) for various com-

binations of ks and ksc−lv values . . . . . . . . . . . . . . . . . . . . . 40

3.1 Simple MV network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2 Radial MV-LV system . . . . . . . . . . . . . . . . . . . . . . . . . . 533.3 Variation of |V t−:g/mv:rec| with |I +:t| (V Rt values corresponding to vari-

ous |I +:t| are also indicated) for the four basic load types . . . . . . . 573.4 Variation of U tg/mv:rec with km for the cases where klv = 1, klv = 0.5

and klv = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.5 Interconnected MV sub-system . . . . . . . . . . . . . . . . . . . . . 613.6 System representation of any busbar x of the MV system shown in

Fig. 3.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623.7 Three-bus MV test system considered for applying the proposed method-

ology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.8 Emissions U linesg/mv:x for the three-bus MV test system for the two cases

where km:2 = 0 and km:2 = 1 . . . . . . . . . . . . . . . . . . . . . . . 68

4.1 Simple HV network . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Radial HV-MV-LV system . . . . . . . . . . . . . . . . . . . . . . . . 754.3 Variation of U t+tdg/hv:rec with klvr for the two cases where kmr = 0 and

kmr = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4 Interconnected HV sub-system . . . . . . . . . . . . . . . . . . . . . . 804.5 System representation of any busbar x of the HV system shown in

Fig. 4.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.6 Three-bus HV test system considered for applying the proposed method-ology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.7 Emissions U linesg/hv:x for the three-bus HV test system for the cases where

km:2 = 0 and km:2 = 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.8 Emissions U linesg/hv:x for the three-bus HV test system for the case where

km:2 = 1 in relation to the Phase arrangements I and II of the MV lines 894.9 IEEE 14-bus test system . . . . . . . . . . . . . . . . . . . . . . . . . 914.10 Emissions U linesg/hv:x for the IEEE 14-bus test system . . . . . . . . . . . 91

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5.1 Variation of T mv−lv with ksc−lv obtained for constant power loads usingunbalanced load flow analysis . . . . . . . . . . . . . . . . . . . . . . 95

5.2 Radial system considered for the illustration of transfer coefficients . 97

5.3 Variation of T mv−lv with ksc−lv for constant current loads: I - 0.99lagging pf, II - 0.9 lagging pf . . . . . . . . . . . . . . . . . . . . . . . 104

5.4 Variation of T mv−lv with ksc−lv for constant power loads: I - 0.99 laggingpf, II - 0.9 lagging pf . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.5 Variation of T mv−lv with ksc−lv for induction motor loads with ks = 6.7and pf = 0.9 lagging . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

5.6 Variation of T mv−lv with ksc−lv: I - for a load base dominated by in-duction motors, II - for a load base dominated by passive elements . . 108

5.7 Variation of T mv−lv with km for ksc−lv ≈ 25 and ksc−lv ≈ 10: I - forload mixes of Z and I M loads, II - for load mixes of P Q and I M loads 109

5.8 Variation of T mv−lv with km established using the IEC method, (5.19),(5.20) and unbalanced load flow analysis . . . . . . . . . . . . . . . . 110

5.9 Variation of T hv−mv with klv for ksc−mv = 12 (loads are supplied directlyat the MV busbar): I - for load mixes of Z and IM loads, II - for loadmixes of PQ and IM loads . . . . . . . . . . . . . . . . . . . . . . . . 115

5.10 Variation of T hv−mv with klv for ksc−mv = 4 (loads are supplied directlyat the MV busbar): I - for load mixes of Z and IM loads, II - for loadmixes of PQ and IM loads . . . . . . . . . . . . . . . . . . . . . . . . 116

5.11 Variation of T hv−mv with klv (LV loads are supplied through MV lines):I - for ksc−mv = 12, II - for ksc−mv = 4 . . . . . . . . . . . . . . . . . . 116

5.12 Radial MV-LV system (reproduction of Fig. 3.2) . . . . . . . . . . . . 117

5.13 Variation of ksend−rec with km for the cases where klv = 1, klv = 0.5and klv = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

5.14 Interconnected sub-system S (reproduction of Fig. 2.6) . . . . . . . . 1225.15 System representation of any busbar x of the MV system shown in

Fig. 5.14 (reproduction of Fig. 3.6) . . . . . . . . . . . . . . . . . . . 1245.16 Three-bus MV test system considered for applying the proposed method-

ology (reproduction of Fig. 3.7) . . . . . . . . . . . . . . . . . . . . . 1275.17 Variations of k1−2 and k1−3 with km:2 for the three-bus MV test system 1275.18 IEEE 14-bus test system (reproduction of Fig. 4.9) . . . . . . . . . . 1285.19 Influence coefficients k4−x (x = 1 − 14, x = 4) for the IEEE 14-bus

test system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

6.1 Three-bus HV test system considered for examining the IEC/TR 61000-3-13 approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

6.2 A comparison of the influence coefficients for the test system derivedusing the proposed method: (5.37), and unbalanced load flow analysis 135

6.3 A comparison of the K uex factors for the test system derived usingthe proposed method: (4.16), and unbalanced load flow analysis . . . 138


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6.4 Comparison of the busbar emission limits E hv:x derived according toIEC/TR 61000-3-13 and the revised method for the test system: I -for Case 1, II - for Case 2 . . . . . . . . . . . . . . . . . . . . . . . . 144

6.5 Comparison of the resulting emission levels U reultg/hv:x derived accordingto IEC/TR 61000-3-13 and the revised method for the test system: I- for Case 1, II - for Case 2 . . . . . . . . . . . . . . . . . . . . . . . . 145

7.1 66kV sub-transmission interconnected system under study . . . . . . 1487.2 Measured nodal VUF values for the study system . . . . . . . . . . . 1497.3 Nodal VUF values (load flow results) which arise as a result of the line

asymmetries, in comparison to the measured values . . . . . . . . . . 1517.4 Variation of |V t−:rec| with |I +:t| for the individual lines . . . . . . . . . 1537.5 Variation of θV t

−:recwith |I +:t| for the individual lines . . . . . . . . . . 154

7.6 Nodal VUF values arising as a result of the individual lines . . . . . . 157

7.7 Phase angles of the nodal negative sequence voltages introduced by theindividual lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

7.8 Global emission vectors of the individual lines (drawn approximatelyto a scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

7.9 Resultant influence of the interaction of all asymmetrical lines (drawnapproximately to a scale) . . . . . . . . . . . . . . . . . . . . . . . . . 162

7.10 Nodal contributions made by the individual lines to the resultant volt-age unbalance levels . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

7.11 (I) Deduced from Fig. 7.8 (II) Effect of the transposition of line Fonly (III) Effect of the transposition of lines A and F together (drawn

approximately to a scale) . . . . . . . . . . . . . . . . . . . . . . . . . 1657.12 Effects, obtained using unbalanced load flow analysis, of the transpo-sition of line F only, and lines A and F together . . . . . . . . . . . . 166

7.13 Nodal VUF values which arise as a result of the load asymmetries, incomparison to that of the line asymmetries . . . . . . . . . . . . . . . 168

7.14 Nodal VUF values which arise as a result of the individual loads . . . 1707.15 Phase angles of the nodal negative sequence voltages introduced by the

individual loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1717.16 Global emission vectors of the individual loads (drawn approximately

to a scale) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1737.17 Resultant influence of the interaction of all unbalanced loads (drawn

approximately to a scale) . . . . . . . . . . . . . . . . . . . . . . . . . 1757.18 Nodal VUF values which arise as a result of both the line and load

asymmetries, in comparison to that of the line asymmetries alone, andthe load asymmetries alone, and also to the measured values . . . . . 177

7.19 Resultant influence of the interaction of all lines and loads (drawnapproximately to a scale) . . . . . . . . . . . . . . . . . . . . . . . . . 178

7.20 Nodal contributions made by the line and load asymmetries to theoverall voltage unbalance levels . . . . . . . . . . . . . . . . . . . . . 179


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7.21 Nodal contributions made by the individual sources of unbalance tothe overall voltage unbalance levels . . . . . . . . . . . . . . . . . . . 181

O.1 Synchronous generator model . . . . . . . . . . . . . . . . . . . . . . 252O.2 Load model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255O.3 Equivalent circuit of a voltage regulator/transformer . . . . . . . . . 257O.4 Three-phase induction motor model proposed in [4, 5] . . . . . . . . . 257O.5 Variation of the real (P) and reactive (Q) power with the supply voltage

level for a typical three-phase induction motor . . . . . . . . . . . . . 259O.6 Variation of the real (P) and reactive (Q) power with k p (motor loading

levels corresponding to various k p is also given as a percentage to therated output power) for a 2250hp induction motor . . . . . . . . . . . 260

O.7 Variation of the speed with k p (motor loading levels corresponding tovarious k p is also given as a percentage to the rated output power) for

a 2250hp induction motor . . . . . . . . . . . . . . . . . . . . . . . . 261O.8 Impedance type induction motor model . . . . . . . . . . . . . . . . . 261O.9 PQ type induction motor model . . . . . . . . . . . . . . . . . . . . . 262O.10 Sequence equivalent circuits of a three-phase induction motor: I - pos-

itive sequence, II - negative sequence . . . . . . . . . . . . . . . . . . 263O.11 Variation of |Y im:s| cos(−θim:s)|Y nim:s| cos(−θnim:s)

of P

x−xx with ωrt

ωnrtfor the 3hp, 220V motor 270

O.12 Variation of |Y im:m2| sin(−θim:m2−1200)

|Y nim:m2| sin(−θnim:m2−120

0) of Q

x−xz with ωtωnrt

for the 3hp, 220V

motor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271O.13 Variation of ηim with ωrt for the 3hp, 220V motor . . . . . . . . . . . 275O.14 Variation of the per phase input active and reactive power with the

motor loading level for the 3hp, 220V motor excited at the rated voltage(balanced) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277

O.15 Variation of the per phase input active and reactive power componentswith the motor loading level for the 3hp, 220V motor excited at reducedand unbalanced voltages . . . . . . . . . . . . . . . . . . . . . . . . . 277

O.16 Variation of the per phase input active and reactive power componentswith the motor loading level for a 2250hp, 2.3kV motor excited atreduced and unbalanced voltages . . . . . . . . . . . . . . . . . . . . 278

O.17 Variation of P im:a with k p for the existing and proposed induction motormodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278

O.18 Variation of Qim:a with k p for the existing and proposed inductionmotor models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279


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List of Tables

2.1 Requirements of background disturbances in assessing the uncertainty

of Class A instruments for the measurement of voltage unbalance (IEC61000-4-30) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Indicative planning levels given in IEC/TR 61000-3-13 . . . . . . . . 292.3 Indicative values for the factor K ue given in IEC/TR 61000-3-13 . . 42

6.1 Influence coefficients for the test system shown in Fig. 6.1 . . . . . . 1356.2 S hv:x, S hv:x−total and U g/hv:x for the test system shown in Fig. 6.1 . . . 1356.3 U linesg/hv:x, K

uex and K uex for Case 2 of the test system shown in Fig. 6.1137

6.4 E hv:x according to IEC/TR 61000-3-13 for the test system shown inFig. 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137

6.5 U reultg/hv:x arising as a result of the IEC/TR 61000-3-13 allocation proce-

dure for the test system shown in Fig. 6.1 . . . . . . . . . . . . . . . 1396.6 Values of the RHS of (6.8) in relation to the test system shown in Fig.

6.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1436.7 ka for the test system shown in Fig. 6.1 . . . . . . . . . . . . . . . . . 1436.8 Kuex and E hv:x according to the revised allocation method for the test

system shown in Fig. 6.1 . . . . . . . . . . . . . . . . . . . . . . . . . 1436.9 U reultg/hv:x arising as a result of the revised allocation procedure for the

test system shown in Fig. 6.1 . . . . . . . . . . . . . . . . . . . . . . 144

7.1 Ranking of the sub-transmission lines based on the associated degreeof asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

7.2 Parameters, operating features and emission levels of the individuallines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

7.3 Distribution of the active and reactive power across the three phasesat each of the load busbars of the study system . . . . . . . . . . . . 167

7.4 Operating features and emission levels of the individual loads of thestudy system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171

H.1 Values of ksc−lvragg and σ for various klvr . . . . . . . . . . . . . . . . 226

K.1 Voltage controlled bus data . . . . . . . . . . . . . . . . . . . . . . . 233K.2 Static capacitor data: susceptances . . . . . . . . . . . . . . . . . . . 233

K.3 Generator and load bus data: three-phase MW and MVAr values . . 234K.4 Transformer data: impedances and secondary tap settings (1st and 2nd

bus numbers refer to the primary and the secondary respectively) . . 234K.5 Nodal positive sequence voltages . . . . . . . . . . . . . . . . . . . . . 235K.6 Transmission line data: lengths and impedances . . . . . . . . . . . . 236

L.1 Replacement factors for a mix of various load types . . . . . . . . . . 239

N.1 System details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

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N.2 Voltage controlled bus data . . . . . . . . . . . . . . . . . . . . . . . 244N.3 Generator and load bus data: three-phase MW and MVAr values . . 244N.4 Voltage regulator data: impedances and secondary tap settings . . . . 245

N.5 Static capacitor data: susceptances . . . . . . . . . . . . . . . . . . . 245N.6 Generator impedance data . . . . . . . . . . . . . . . . . . . . . . . . 245N.7 Lengths and impedances (Z −+ and Z −+) of the sub-transmission lines 246N.8 Negative sequence voltages V t−:S 2 caused by the individual lines A - N

at the busbar S2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248N.9 Resultant negative sequence voltage V lines−:S 2 at the busbar S2 . . . . . . 248

O.1 Parameters of a 60Hz, 3hp, 220V induction motor . . . . . . . . . . . 270O.2 Power components P nx−xx - Q

nx−xz for the 3hp, 220V motor . . . . . . 270

O.3 Speed coefficients corresponding to the power components P x−xx -Qx−xz for a range of induction motors . . . . . . . . . . . . . . . . . 272

O.4 Efficiency coefficients for a range of induction motors . . . . . . . . . 275


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Chapter 1

Introduction

1.1 Statement of the Problem

Excessive voltage unbalance1 levels in electrical power systems arising as a result of

unbalanced installations and system inherent asymmetries can cause damage to, and

degradation and maloperation of, customer and utility equipment. Despite the exis-

tence of voltage unbalance regulatory codes, some network service providers are facing

difficulties in complying with stipulated levels. This emphasises the need for recom-

mendations based on well researched engineering practices governing the management

of the problem of voltage unbalance, which this thesis aims to fulfil.

The IEC, one of the world’s leading organisation for standardisation on power

quality, has recently released the Technical Report IEC/TR 61000-3-13 [1] which

provides guiding principles for coordinating voltage unbalance between various voltagelevels of a power system through the allocation of emission limits to installations.

The philosophy of this voltage unbalance allocation process is similar to that of the

counterpart IEC approaches to harmonics (IEC 61000-3-6 [2]) and flicker (IEC 61000-

3-7 [3]) allocation. The absorption capacity or the allowed global emission of a sub-

1In the context of the thesis, this is limited to negative sequence unbalance.

1


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2

system of a power system is established such that the total emission level derived using

the general summation law, taking the upstream contribution in terms of a transfer

coefficient into account, at any point is maintained at or below the set planning

level. The global emission allowance of the sub-system is allocated to its busbars in

proportion to the ratio between the total apparent power to be supplied by the busbar

under evaluation, and the total available apparent power of the sub-system as seen

at the busbar. Voltage unbalance contributions from neighbouring busbars are taken

into account using influence coefficients in determining the total available apparent

power of the sub-system as seen at the busbar. This busbar emission allowance is thenapportioned to individual customers in proportion to the ratio between the agreed

apparent power, and the total apparent power supplied by the busbar.

In the case of voltage unbalance, the global emission at a busbar generally arises

not only as a result of unbalanced installations but also as a result of system inherent

asymmetries (essentially lines). Thus, the apportioning of the total headroom to

installations as in the case of harmonics and flicker can lead to exceedances of theset planning levels. Hence, IEC/TR-61000-3-13 applies an additional factor which is

referred to as ‘Kue’ to the apportioned allowance. This factor Kue represents the

fraction of the emission allowance that can be allocated to customers, whereas the

factor K ue (= 1 − Kue) accounts for the emission which arises as a result of systeminherent asymmetries. It is recommended that system operators assess the factors

Kue and K ue for prevailing system conditions in their specific networks. However,

a systematic method for its evaluation is not provided other than a rudimentary

direction together with a set of indicative values.

The Technical Report IEC/TR 61000-3-13 gives a method for estimating the MV

to LV transfer coefficient considering the system and load characteristics and the

downstream load composition. This suggests a value less than unity for the trans-


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fer coefficient in the presence of industrial load bases containing large proportions

of mains connected three-phase induction motors, and a unity transfer coefficient in

relation to passive loads in general. Although a transfer coefficient of unity is math-

ematically trivial for constant impedance loads, its validity has not been cautiously

examined in relation to constant current and constant power loads which may exhibit

different behaviours under unbalanced supply conditions. Further, systematic meth-

ods for assessing the HV to MV and EHV to HV transfer coefficients and influence

coefficients are yet to be developed.

The IEC allocation policy with regard to harmonics and flicker has been found not

to guarantee that the emission limits allocated to individual customer installations

ensure non-exceedance of the set planning levels [4, 5] 2 . Overcoming this problem, an

alternative allocation technique that is referred to as ‘constraint bus voltage’ (CBV)

method which closely aligns with the IEC approach has been suggested for harmon-

ics and flicker [4, 5]. Being based on a common philosophy, the above problem is

anticipated to be experienced also by the recently introduced voltage unbalance allo-cation approach of IEC/TR 61000-3-13. Thus, it is vital to examine the application

of IEC/TR 61000-3-13 which also involves an additional aspect, i.e. the emission aris-

ing due to system inherent asymmetries. Extension of the CBV method to voltage

unbalance allocation requires revisions addressing this new aspect.

In the application of the IEC/TR 61000-3-13 principles to better manage existing

networks already experiencing excessive voltage unbalance levels, the initial develop-

ment of insights into the influences made by various sources of unbalance is required.

In some circumstances, especially in sub-transmission networks where line transposi-

tion is not a usual practice, the emission which arises as a result of system inherent

asymmetries would not allow an equitable share of busbar emission allowances to in-

2References [4, 5] are the only sources which provide evidence in support of this statement.


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carried out in relation to radial power systems. A basis towards the development

of methodologies for evaluating the global emission in MV and HV power systems

which arises as a result of line asymmetries is established through the extension of the

nodal equations [I ] = [Y ][V ] to the sequence domain. This basis is integrated with the

outcomes obtained from the preliminary studies for ascertaining the methodologies.

Development of a systematic approach for the assessment of influence coefficients is

also facilitated by an approach similar to above. Verification of the methodologies is

accomplished using unbalanced load flow analysis3.

Dependency of the propagation of voltage unbalance from MV to LV and HV to

MV levels on specific load types is initially examined through the development of

theoretical bases which describe the behaviour of these load types under unbalanced

supply conditions. Employing these, the impact of a load base which consists of

various load types on the propagation is established in terms of transfer coefficients.

Examination of the IEC/TR 61000-3-13 principles is achieved through two steps

employing a simple three-bus test system. Consideration to cases both with and with-

out the inclusion of the influence of system inherent asymmetries is given. Firstly, the

emission limits to installations are calculated using the prescribed approach together

with some of the methodologies proposed in this thesis. Secondly, the resulting bus-

bar voltage unbalance levels are established using the general summation law when

all installations inject their allocated limits, and examined against the set planning

level. Extension of the suggested CBV allocation technique to voltage unbalance is

accomplished by introducing its principles while addressing the emission which arises

as a result of system inherent asymmetries according to IEC/TR 61000-3-13.

3This is a program developed in M ATLABR. This, which is described in Appendix O, is basedon the phase coordinate reference frame and incorporates the component level load flow constraintsand the three-phase modelling of power system components.


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To develop theoretical bases which provide an insight into the problem of voltage

unbalance in interconnected network environments, deterministic studies supported

by unbalanced load flow analysis are carried out employing a 66kV sub-transmission

system that is known to experience excessive voltage unbalance levels. Using a new

concept termed ‘voltage unbalance emission vector’ which is derived based on IEC/TR

61000-3-13, the behaviour of each of the lines treating as standalone lines and also as

elements in the interconnected system, and of each of the loads operating in the inter-

connected environment is observed. Through an extensive analysis of these results,

approaches for ascertaining the influence of an unbalanced source, in a global sense,in terms of a single emission vector (which is referred to as ‘global emission vector’)

are established. Employing the linearity of negative sequence variables, these global

emission vectors of individual unbalanced sources are added forming a basis which

provides a comprehensive understanding of the voltage unbalance behaviour of the

entire system.

1.3 Outline of the Thesis

A brief description of the contents of the remaining chapters is given below:

Chapter 2, a literature review, provides an overview on various general aspects

of voltage unbalance, and a critical discussion on IEC/TR 61000-3-13 on which the

thesis is primarily based. A basic introduction, followed by a review on sources, ef-

fects and mitigation techniques of voltage unbalance is given. Various standards anddocuments governing measurement and evaluation procedures, indices and limits of

voltage unbalance are reviewed. The key section of this chapter describes concepts,

principles and related aspects prescribed in IEC/TR 61000-3-13 establishing the back-

grounds for Chapters 3 - 6. The last section discusses fundamental deficiencies of,

and suggested revisions to, the IEC allocation policy with regard to harmonics and


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dency of the MV to LV and HV to MV transfer coefficients on specific load types

which include different passive components and three-phase induction motors, gen-

eralised expressions for their estimation are proposed. Ranges of variation of these

transfer coefficients are demonstrated. The accuracy of this new method for esti-

mating the MV to LV transfer coefficient is compared with the respective method

given in IEC/TR 61000-3-13. Secondly, the propagation from one busbar to other

neighbouring busbars of a sub-system in terms of influence coefficients is addressed.

Preliminary studies carried out employing a radial network on the dependency of

these influence coefficients on various load types is presented. A systematic approachfor the evaluation of influence coefficients for interconnected network environments is

proposed. Results established using this method for a three-bus test system and also

for the IEEE 14-bus test system are compared with those obtained using unbalanced

load flow analysis.

Chapter 6 firstly examines the IEC/TR 61000-3-13 voltage unbalance allocation

principles employing a three-bus test system. The calculation procedure of the emis-sion limits to installations using the prescribed formulae together with some of the

above proposed methodologies is described. The resulting busbar voltage unbalance

levels when all installations inject their allocated limits are derived, and examined.

Secondly, the principles of the suggested CBV allocation policy are introduced to

voltage unbalance ensuring a robust allocation. These new allocation principles are

examined employing the above three-bus test system.

Chapter 7 establishes theoretical bases for studying the problem of voltage un-

balance in interconnected network environments. Deterministic studies carried out

employing a 66kV interconnected sub-transmission system in relation to its line and

load asymmetries are separately described. Outcomes from these studies are presented

in a generalised form such that a systematic approach which allows a comprehensive


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Chapter 2

Literature Review

2.1 Introduction

This chapter provides an overview on various general aspects of voltage unbalance,

and a critical discussion on IEC/TR 61000-3-13 on which the thesis is primarily based.

A brief introduction to voltage unbalance, followed by a review on various methods

used in different standards and documents for its quantification is given in Section 2.2.

Sections 2.3 - 2.5 cover sources, effects and mitigation techniques of voltage unbalance

respectively as reported in the literature. The widely used IEC 61000-4-30 and other

standards/documents governing measurement and evaluation procedures and indices

of voltage unbalance are examined in Section 2.6. Various categories of voltage unbal-

ance limits: compatibility levels, voltage characteristics, planning levels and customer

emission limits are discussed, and a review on limiting values is given in Section 2.7.

The key section of this chapter, Section 2.8, describes concepts, principles and related

aspects prescribed in IEC/TR 61000-3-13 establishing the backgrounds for Chapters

3 - 6. Section 2.9 discusses fundamental deficiencies of, and suggested revisions to, the

IEC allocation policy with regard to harmonics and flicker forming the background

for Chapter 6. The chapter is summarised in Section 2.10.

10


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V UF = V −V + (2.1)

Reproducing from IEC 61000-4-30 [19], IEC/TR 61000-3-13 gives a practical method

for establishing the VUF using the three fundamental line-line rms voltage magni-

tudes as:

V UF =

1 − √ 3 − 61 +

√ 3 − 6 (2.2)

where,

=

|V ab|4+|V bc|

4+|V ca|4

(|V ab|2

+|V bc|2

+|V ca|2

)2

V ab, V bc and V ca - fundamental line-line rms voltages

Alternative methods for the quantification of voltage unbalance are given by the

National Electricity Manufacturer’s Association (NEMA)3 and the Institute of Elec-

trical and Electronics Engineries (IEEE)4. The NEMA definition which is known

as ‘line voltage unbalance rate’ (LVUR), and the IEEE definition which is known as

‘phase voltage unbalance rate’ (PVUR) that exists in two different forms (P V U R1 and

P V U R2) are given by (2.3), (2.4) and (2.5) respectively. However, the recent IEEE

power quality monitoring standard IEEE 1159 [23] lists both the P V U R1 and the VUF.

LV U R = Maximum voltage deviation from the average line-line voltage

Average line-line voltage (2.3)

P V U R1 = Maximum voltage deviation from the average phase voltage

Average phase voltage (2.4)

P V U R2 = Difference between the maximum and the minimum phase voltages

Average phase voltage

(2.5)

3NEMA MG1 [20].4IEEE 112 [21] and IEEE 100 [22].


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Although angle unbalance is excluded, the LVUR which does not take the presence

of zero sequence voltage into account is similar to the VUF or the true value for

more realistic levels of voltage unbalance [22, 24]. However, the PVUR which is

influenced by the presence of zero sequence voltage deviates significantly away from

the true value in the presence of zero sequence voltage even at lower levels of voltage

unbalance [24]. Among the two IEEE definitions, the P V U R1 is reasonably close to

the true unbalance in the absence of zero sequence voltage [24].

Although the absolute value of the ratio V −V +

or the VUF is the parameter in general

use, it is worthwhile noting that voltage unbalance is also associated with a phase

angle. One may, in the same way, define this phase angle as the angle between the

fundamental negative and positive sequence voltage components [25]. This concept

of voltage unbalance as a vector is also applied in IEC/TR 61000-3-13 in defining the

emission level5 introduced by an unbalanced installation at a particular point.

2.3 Sources of Voltage Unbalance

Voltage unbalance is caused mainly by the uneven distribution and/or the uneven

connection of single-phase and dual-phase loads6 across the three phases and the op-

eration of unbalanced three-phase loads7 through the injection of unbalanced phase

currents or negative sequence currents into the system. Unequal mutual impedances

which arise as a result of the asymmetrical electromagnetic coupling between the

conductors of untransposed/partially transposed single circuit [29]/multi circuit [30,

31, 32] transmission and distribution [33, 34] overhead lines, which lead to unbal-

anced voltage drops across the three phases, is also a well known source of voltage

unbalance. Although limited, electrostatic unbalance of untransposed/partially trans-

5See Section 2.8.1.6e.g. LV appliances, electric traction motors [26, 27], induction furnaces.7e.g. arc furnaces [28, 16].


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posed overhead transmission lines [30, 35] and asymmetrical transformer banks [36]

in particular open-wye open-delta transformer banks [37] have also been reported as

additional sources of voltage unbalance.

2.4 Effects of Voltage Unbalance

The influence of voltage unbalance on the adverse performance of three-phase induc-

tion motors is well documented [38, 39, 40]. When an induction motor is exposed to

unbalanced voltages, the negative sequence voltage component produces an air gap

flux that rotates against the rotor which is forced by the positive sequence torque,

thus generating an unwanted reverse torque. This results in a reduction of the net

motor torque and speed, in addition to torque and speed pulsations and increased

motor vibration and noise. Further, due to the relatively small negative sequence mo-

tor impedance, unbalance in phase currents drawn by a motor can be 6 to 10 times

the supply voltage unbalance [20] causing increased motor losses and heating. On the

whole, the motor efficiency and lifetime (primarily as a consequence of the prolonged

overheating) will be reduced. To be able to deal with this extra heating, the motor

must be derated, or a motor of a large power rating may be required. According to

the International Union for Electricity Applications (UIE) [16]8, an induction motor

has to be derated depending on the prevailing degree of voltage unbalance as depicted

by Fig. 2.1.

Power electronic converters having uncontrolled diode rectifier front-ends9

[42,

43] and arc furnaces [42] produce uncharacteristic triplen harmonics in addition to

the characteristic harmonics in the input current in the presence of supply voltage

8The derating curve given in [16] is preferred, as it uses the VUF in quantifying voltage unbalance,in comparison to other recommendations such as given in the standards NEMA MG1 [20] (whichuses the LVUR) and AS 1359.31 [41]/IEC Report 892 (which uses the P V U R1).

9e.g. adjustable speed drives.


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Figure 2.1: Derating of three-phase induction motors (UIE)

unbalance. Significant third harmonic currents can increase harmonics and resonance

problems in power systems, and require large filter ratings. As the degree of voltage

unbalance increases, the input current drawn by a converter becomes significantly

unbalanced and changes from a double pulse waveform to a single pulse waveform as

a result of the asymmetric conduction of the diodes. This results in excessive currents

in one or two of the phases10, which can lead to the tripping of overload protection

circuits, under voltage and increased ripple on the dc-link, and decreased lifetime of

the diodes and the dc-link capacitor.

Modern ac drive systems comprising synchronous pulse width modulated (PWM)

rectifier front ends generate a second order harmonic component on the dc-link whenthey are exposed to supply voltage unbalance [45]. This results in increased ripple

on the dc-link affecting the life and size of the dc-link capacitor. Further, this second

order harmonic component reflects in the input current and also in the inverter output

10Measurements taken on an adjustable speed drive system has shown 50% over-current for asupply voltage unbalance where the highest voltage magnitude was 3.6% higher than the lowestvoltage magnitude [44].

Please see print copy for image


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voltage by generating a third harmonic component and sub-harmonic components11

respectively.

The impact of some fault conditions (other than the traditionally studied three-

phase fault) on the transient stability of synchronous generators has been seen to

be more severe in the presence of voltage unbalance [46, 47]. This indicates the

requirement of advanced algorithms and computer programs for power system stabil-

ity studies.

Power system components such as synchronous generators, transmission and dis-

tribution overhead lines and cables and transformers can also be affected by voltage

unbalance, which is intensified by the fact that a small degree of unbalance in phase

voltages can cause a disproportionately large unbalance in phase currents as discussed

earlier. Synchronous generators exhibit a phenomenon similar to that in induction

motors in the presence of negative sequence current resulting in excess machine losses

and heating and possible hazards to structural components [48]. According to the

Australian standard AS 1359.10112 [49], synchronous machines shall be capable of

operating continuously in unbalanced systems if none of the phase currents exceeds

the rated current and the ratio of the negative sequence current component and the

rated current does not exceed a value between 5% and 10% depending on the type

of construction, the method of cooling and the machine capacity. Flow of negative

sequence currents in overhead lines, cables and transformers increases power losses

lowering their capacity [50, 51]. From a more theoretical point of view, current un-

balance affects the definitions and the measurement techniques of apparent power

and power factor [52, 53] influencing the aspects of the power system economics. In

addition, current unbalance has been seen to result in a degraded power factor [53].

11These sub-harmonics will be replaced by a dc component when the inverter output frequency isequal to twice the system frequency.

12This is based on IEC 34-1: Rotating electrical machines - part 1 - rating and performance.


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voltage unbalance. Series connected static compensators14 which provide an active

correction through the injection of a compensating voltage signal in series with the

supply have also been reported as a means for mitigating voltage unbalance. Com-

prehensive techniques such as unified power quality conditioners (UPQC) [66, 67]

and hybrid active and passive filters [68] which are capable of compensating various

power quality disturbances simultaneously have been further advanced also to handle

voltage unbalance.

The principle of the representation of an unbalanced three-phase load (three-wire)

using an equivalent balanced section and a two-phase section has been employed in

reducing the influence of large unbalanced loads (e.g. traction loads) by the use of

special transformer connection topologies such as Scott, V and Le-Blance at their

supply sub-stations [16, 26, 69]. Installation of Steinments compensators consisting

of inductive and capacitive elements at supply sub-stations of large unbalanced loads

is also a well known technique of load unbalance reduction [69].

2.6 Measurement and Indices of Voltage Unbalance

Purpose of the measurement of a power quality disturbance which is stochastic in na-

ture is to obtain statistical information on the performance of the supply or connected

equipment. Site indices are used to provide a statistical description of the disturbance

at a particular site. System indices which are derived using site indices of various

sites15

based on a certain statistical criteria are representatives of the disturbance

over a part of the power system. This section discusses measurement procedures and

indices of voltage unbalance described in various standards and documents16.

14e.g. static synchronous series compensators (SSSC) [62, 63, 64], dynamic voltage restor-ers (DVR) [65].

15Typically of a particular voltage level, or a group of similar voltage levels.16IEC/TR 61000-3-13 [1] is excluded here. This will be reviewed in Section 2.8 covering all related

aspects.


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The widely accepted standard IEC 61000-4-30 [19] for the measurement of power

quality disturbances prescribes also the voltage unbalance measurement and evalu-

ation procedure for instruments with Class A17 performance. Measurement of the

fundamental component of the three line-line rms voltages over 10-cycle and 12-cycle

intervals for 50Hz and 60Hz systems respectively is specified. A minimum mea-

surement period of one week is recommended. Aggregated values are obtained over

standard time intervals of 3-second, 10-minute and 2-hour18. The method of quan-

tification is as per (2.2). For instruments with Class B19 performance, the above

specifications are to be provided by manufacturers.

Due to the concurrent existence of various power quality disturbances in typi-

cal power systems, the measurement of a particular disturbance can be affected by

the presence of other background disturbances in the input electrical signal to the

measuring instrument. Thus, IEC 61000-4-30 defines limits for the uncertainty of

instruments with Class A performance when each background disturbance is within

a specified range of variation. For the measurement of voltage unbalance, when otherdisturbances exist in the input signal fulfil the requirements given in Table 2.1, except

for voltage unbalance levels in the range of 1% to 5% of the declared input voltage

(U din), an instrument shall present an uncertainty less than ±0.15%. For instrumentswith Class B performance, the uncertainty is specified by manufacturers.

Derivation of site indices using a high percentile (e.g. 95%, 99%) of the aggre-

gated values (3-second, 10-minute, 2-hour) is preferred in general in most standards

and documents [9, 10, 12, 19]. The 95% percentile of the 10-minute aggregated val-

ues over a measurement period of one week is seen to be strongly recommended

for most power quality disturbances including voltage unbalance. This is the only

17That is, precise measurements such as for the verification of compliance with standards.18A 2-hour value is obtained by combining twelve number of 10-minute values.19That is, less precise measurements such as for statistical surveys.


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Table 2.1: Requirements of background disturbances in assessing the uncertainty of Class A instruments for the measurement of voltage unbalance (IEC 61000-4-30)

Disturbance RequirementPower frequency f n ± 0.5Hz (f n - nominal frequency)

Voltage magnitude U din ± 1%Flicker P st < 1 (P st - short-term flicker severity index)

Harmonics 0% to 3% of U din

Inter-harmonics 0% to 0.5% of U din

index used in the European standard EN 50160 [9]. IEC 61000-4-30 proposes a num-

ber of voltage unbalance site indices for contractual applications including the 95%

percentile of the 10-minute and 2-hour aggregated values over a week. The issue

of voltage unbalance indices has also been addressed by the CIGRE/CIRED Joint

Working Group C4.07 [12], and the above index together with the 95% percentile of

the 3-second values over a day has been recently recommended. The South African

standard NRS 048-2 [10] uses the highest of the 10-minute values over a week in

addition to the above index as preliminary site indices. Site indices over long mea-

surement periods are typically calculated as the highest of the daily or weekly indices

(e.g. NRS 048-2).

Among various methods of calculating system indices [25], the choice of a high

percentile of site indices is seen to be popular [12, 70, 71]. The IEC electromagnetic

compatibility standards IEC 61000-2-2 [70] and IEC 61000-2-12 [71] use the 95%

percentile of the 95% site indices as the system index. In addition to the above system

index, [25] recommends the highest of the 95% or 99% site indices as a system index

for voltage unbalance. An alternative approach is given by the CIGRE/CIRED Joint

Working Group C4.07 [12] for a system index in assessing a set voltage unbalance

limit as a low percentage of sites (e.g. 1% and 5%) that exceeds the limit.


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2.7 Limits of Voltage Unbalance

2.7.1 Compatibility Levels

Connection of equipment to a power system requires that it be able to withstand

any disturbance to which it is subjected by itself and other equipment. Alternatively,

the emission of the disturbance must be limited to a level which is tolerable by the

connected equipment. The primary mechanism defined by the IEC20 to achieve a

balance between the emission and the immunity is the compatibility level. Equip-

ment must be designed to ensure the immunity to the disturbance at least up to

the compatibility level, and utilities are required to maintain the disturbance at or

below the compatibility level. Due to the stochastic nature of the power quality phe-

nomenon, an absolute limit or an expectation of 100% compliance at all times and

locations with a set limit is not sensible. Thus, the compatibility levels are generally

set allowing a small exceeding probability (e.g. 5%) as illustrated in Fig. 2.2 where

the probability density function21 of the disturbance level which represent both time

and space variations and the probability density function of the equipment immunity

level are shown.

The IEC compatibility standards IEC 61000-2-2 [70] and IEC 61000-2-12 [71] give

a value for the voltage unbalance compatibility level in LV and MV power systems

respectively of 2% allowing an excursion up to 3

Documents

Power Electronics in Electricity to IEC61000-3-13