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CURRENT HARM ONICS ANALYSIS OF NON-LINEAR SINGLE-PHASE LO ADS

IN A THREE-PHASE NETWORK

V . Spitsa and A . Alexandrovitz

Department of Electrical Engineering,

Technion-Israel Institute of Technology,

Haifa 32000, Israel

A B S T R A C T

This paper presents results of the current harmonics

analysis in a three-phase network with nonlinear single-

phase loads. In this analys is, typical single-phase nonlinear

loads such as computers, m onitors and printers, were

considered. Simulation results are accompanied with field

measurements. A mutual influence of single-phase loads

connected in different phases .o f the network is studied.

Factors, having an effect on harmonic content of a neutralconductor current, are investigated in the present work.

The c auses for the excessive neutral conductor current are

explored and the dominant role of the triplen harmonics is

highlighted.

1 . I N T R O D U C T I O N

Single-phase nonlinear loads, such as computers, TV sets.

fluorescent lightning and different electronic devices are

the main source of harmonics in commercial and

residential building networks. I n recent years their amount

grows rapidly leading to excessive neutral conductorcurrents [2],[3],[7]. As a result, harmonic analysis of the

single-phase nonlinear load s has an increasing importance.

Pom,er supplies of the single-phase nonlinear loads are

usually implemented according to a switch-mode scheme

with dio de-b ridg e rectifier presented in Fig. I . Its typical

harmonic spectrum consists of odd harmonics only. The

low-order harmonics in this spectrum have especially high

magnitudes which causes a highly non-sinusoidal current

waveform. Influence of the single-phase diode-bridge

rectifier harmonics on electrical network performance and

factors affecting magnitude levels of these harmonlcs are

studied in the present paper. A special attention is devoted

to the problem of the excessive neutral conductor current

resulted from triple harmon ics coupling.

078034427-wO~20.0~2004EEE

Fig. 1. Single-phase switch-mode pow er supp ly.

2. A N A L Y S IS M E T H O D

Single-phase diode bridge rectifier operation can be

described by a se t of differential equa tions with particular

continuity conditions [4]-[6]. As a result, current and

voltage waveforms of the rectifier can be obtained using

the strategy proposed in [ I ] , which exploits a classical

solution method of differential equations. A novel

development presented in this paper is based on

incorporation o f the above mentioned dio de-bridge

rectifier model into a composite load of three-phase

electrical network with neutral conductor. For this

purpose, time-domain simulations were performed using

MatlabiSimulink package. A symmetric sinusoidal three-

phase voltage source was assumed. The obtained phase

currents can be written in the following manner:

iH =ti;z&Ihcos[h . (w ' t 1 20")+9.1 (2 )h= l h=l

m

i1. =ti: c&Ihcos[ h . ,It +120")+p h] (3)h=I h=

where

i A , i H , i c are phase currents in phases A , B and C

respectively.

r A , r B , r l . are currents of the particular harmonic o f order

h in phases A, B an d C respectively,

.I! .I, .I?

329



I h is a currentR M S value of particular harmonic oforder

p h i s a current phase of particular harmonic oforder h ,

m' is a fundamental angular frequency,

1 is a time instant.

These current waveforms and their harmonic spectrumare analyzed using two parameters. The first one is an

R M S value of he harmonic current:

h ,

*"ib, h . l m

R ~ r e Xwim icI$hh nm

,I A A A 4 m -iN-

(4)v h= l

The second parameter is a total harmonic distortion (THD)

definedas

The obtained results are described in the next sections.

3. S I N G L E - P H A S E L O A D S I M U L A T I O N R E S U L T S

A simulation of the single-phase diode-bridge rectifier

operation was performed according to the electrical

scheme shown in Fig. I , where the rectifier load

represented by a constant resistance Rdc. Parameters o f

the scheme elements are given in Appendix. The obtained

input current waveform and its harmonic spectrum are

presented in Fig. 2. An RMS value of this current is

0.929[A] while a magnitude of its fundamental component

is 0.431[A]. I t is obvious that current THD value of

190.82% is extremely high in the present case. This factresults from an existence of low order harmonics with

significant magnitudes. Itshould be noted thata magnitude

of the third harmonic is almost equal to the fundamental

current component. I t will be shown later that this

phenomenon is of special importance in three-phase

electrical networks with neutral conductor.

4. S I M U L A T I O N R E S U L T S OF T H R E E - P H A S E

E L E C T R I C A L N E T W O R K

A three-phase electrical network with neutral conductor

and single-phase non-linear loads is investigated in the

present section. The equivalent scheme of this network is

shown in Fig. 3.

Inspecting an order of the current phase interchangeaccording to ( I ) , one can conclude that harmonics of order

3k+, where k=0,1,2, ..., are composing a positive

sequence system, harmonics o f order 3k+2 are forming a

negative sequence system and harmonics of order 3k are

Fig. 2. Input current ofthe single-phase diodebridge rectifier.

33 0



phase currents. As a result, the neutral conductor is in

more severe conditions than the phase conductors and a

potential danger of its overheat and damage is present

even in the totally symmetric balanced network. Therefore,

a special care should be taken whena cross section area of

the neutral conductor is determined.

5. E X P E R I M E N TA L R E S U L T S

Computer simulations and harmonic analysis using

analytical models are based on assumptions and

simplifications, which are made during solution stages.

Moreover, exhaustive data about an electrical network

contiguration are not always available. Therefore

experimental measurements are very useful for model

validation and determination of harmonics levels in

electrical network elements. In the present section.

experimental results of the harmonic measurements are

given. These results allow one to verify a qualitative

content of harmonic spectrum of the phase and neutral

conductor currents in a three-phase electrical network,which was obtained analytically. A l l measurements were

carried out using power analyzers "Voltech PM100 and

"Fluke 418" in the Energy Conversion Laboratory ofthe

Electrical Engineering Department in Technion.

5.1. C o m p u t e r l o a d h a rm o n i c s .

Computers are a major part of the single-phase

nonlinear loads in the commercial and residential electrical

networks. Therefore, reliable infohation on computer

load harmonics has a primary importance for harmonic

analysis o fthe above mentioned electrical networks. In the

present subsection, measurement results of the computer

load harmonics are given.The computer load is typically a unit consisting of the

following elements: tower, monitor and printer. The

measured waveform and harmonic spectrum of these loads

are shown in Fig. 6-8 respectively. A total current of the

computer unit is treated inFig. 9.

5.2 C u r r e n t h a rm o n i c s in a t h ree-phase e lec t r i ca l

n e t w o r k w i t h n e u t r al c o n d u c to r

The results of the current harmonics measurements at

the input of the distributing board in the PC-farm of the

Electrical Engineering Department are presented in the

present subsection. A three-phase line and neutral

conductor currents are taken into consideration. lheirharmonic spectrums and waveforms are shown in Fig. 10-

13. Comparing Fig. 10-12, it can be concluded that a load

distribution among the phases is unbalanced. Indeed.

Phase Conductor Current Waveform

0.02 Time, [sec] 0.04 0.W

Harmonic Spectrum of Phase Conductor Cur rent

z 0.43- I ,

I .3 -

i! 0.14-'i .M- 1L5 7 9 11 13 15 17 19 21 23 25 27 29 31 33

HamO" i c order

Fig. 4. Harmo nic spectrum of the phase conductor current s.

Neutral Conductor Current Waveform

0.02 Time, [sec] 0.04 0.W

Harmonic Spectrum of Neutral Conduc tor Current

z 1.26- , 10.43-

0 3 15 21 27 33

Fig. 5. Harmonic spectrum of the n eutral conductor cur rent .

Fig. 6. Input current harmonics and waveform

of "Mediatek" computer tower.

331



waveforms o f the currents in phases A and B have a bell-

shape form, which is typical for the computer loads, while

a waveform of the current in phase C is almost sinusoidal.

Hence, a majority o f electrical loads in phase C is linear

(air conditioners). Neutral conductor current is a

geometric sum of the phase currents. Consequently, it

represents an unbalanced part of phase currents togetherwith their triplen harmonic content as it is shown in Fig.

13. In this figure a fundamental component of the

harmonic spectrum has a value, which is almost equal to

the fundamental component of the line current in phase C

which is depicted in Fig. 12. This fact indicates that there

exists a very large unbalance of load powers among the

phases of the electrical network. Moreover, uneven

distribution of the single-phase nonlinear loads between

the phases of the electrical network causes an additional

enhancement of the neutral conductor current due to the

fact that first and fifih-order phase current harmonics are

not compensated in this case.

The third-order current harmonics forma zero-sequence

system, they do not cancel in the neutral wire. This is a

primary reason for a high neutral current in the three-phase

systems with the single-phase rectifier loads. In the present

subsection, a third harmonic o f the neutral conductor

current shown in Fig. 13, has a value. which is 78% of the

current fundamental component in phase B,given in Fig.

11. As a result, the neutral current has the RM S value,

which is greater than the R M S value o f the current in

phaseB.

6. CONCLUSION

In the present paper current harmonics produced by the

single-phase rectifier loads in a three-phase electrical

network were studied. The effects resulted from the

diversity o f the load parameters of these loads were

investigated. The simulation results were verified by

measurements. The main factors. which lead to an

excessive neutral conductor current, were determined. .They are an unbalance of oad powers installed in different

phases, a diversity of the current harmonic spectrums of

the phase loads and a presence of the significant triplen

harmonics in the phase currents produced by single-phase

nonlinear loads. Itwas obtained that RMS valueof neutral

conductor current may be higher than that of phase

currents. Therefore, it is recommended to choose a cross

section area of neutral conductor to be not less thana cross

section area of phase conductors in the three-phaseelectrical networks with a large number of the single-phase

rectifier loads.


of "Packard Bell" monitor.

m-r c u m W*"Cform

I .U- I _ .I< 1117 1111 .* ID. .P _o I Y I .0 0 0 ,m ,m m -,U ,U

n--1.


of "HP Laser Jet Illp " printer.


of a typical computer unit.

332



HarmonicSpeCtNmofPhaseA Current HarmonicSpectrum ofPhaseB Current

.~: ,:.

C U m o . l * l .,

. .

7 , ,,,, ..- ,:., ,wll , ~ .,. .

currm.lAl , --.~,

'. ... i

. ~,.

I ..I \ ~ . ~

. .

-:,, ..,: 1,1 (,," -El. ,~.._.L-.~-

'\ iY

Phase C Current Waveform

C Y r n . l * l .,

T,"E. I-,

Fig. 12. Current in phase C o f the input three-phase line.

c"mm.lA, ,,

:,

10. APPENDIX

Supply voltage: V ' = 2 2 O [ V ] , f' 50 [H;]

Parametersof

electrical wire:c, 0 . 2 [ ~ 1 , L, ,~0 . 4 [ 4

R, , =o.ols[n], L,, = l [ p H ]

Parameters of diodes:

Parameters of the diode-bridge rectitiers

Rdc =lOOO[n], C,,' = 3 7 0 [ p F ]

11. REFERENCES

,'.. , -7 ,\

1 , ",,I : ~ , pI,k~r

.-/ I '

L.'. . ~ . ... . .~.. ~ ~ ~ ~ ~

[ I ] 0. Boix, L. Sainz and J. Pedra, "Harmonic interaction in

capacitor rectifier loads", ETEP, vol. 10. no. 2. MarcW April.2000.

[2] J. 1. M. Desmet. 1. Sweettvaegher. G. Vanalme. K. Stocman

and R. J. M. Belmans, "Analysis of the neutral conductor cumentin a three-phase supplied network with nonlinear single-phaseloads", IEEE Transactions on lndustw Applications.vol. 39, no.3, pp. 587-593, May/June 2003.

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