The production of residual currents due toharmonic loading

G.E. Littler, B.Eng., M.Eng., M.I.E.(Aust)

Indexing terms: Nonlinear systems, Power systems and plant

Abstract: The connection of nonlinear loads such as thyristor drive systems to the power system creates wave-form distortion due to the harmonic currents which are injected. The propagation of the harmonic currentsthroughout the power system is governed by a number of factors including resistance, inductance and capac-itance of circuit elements and the system load. The harmonic current at the nonlinear load may be substantiallybalanced, but due to asymmetry in overhead line and transformer configurations, in particular, residual harmo-nic currents are produced, which circulate through line capacitance-to-ground and transformer grounded starpoints. These currents, being of zero sequence order, may cause noise interference in neighbouring telephonecircuits. Since the harmonic currents in the power system may become amplified as they progress to the powerfrequency source, the interference could be considerably increased. The paper addresses the basic theoryinvolved and studies particular systems with a view to using simplified manual calculations. From a knowledgeof the residual current magnitude produced by a nonlinear load, noise interference could be determined.

1 Introduction

The application of solid state technology to industrialequipment has led to a considerable improvement in oper-ation and efficiency of loads. However, by controlling theshape and quality of the line current waveform, harmonicsare produced and injected back into the power system withknown effects on consumers and interference with telecom-munication circuits. With regard to the latter, any increasein residual ground circuit harmonic current will increasethe noise level. The paper explores one particular source ofresidual harmonic current, that due to the asymmetry oflines and transformers.

2 Definitions

Balanced quantities: Three phase voltages and currentsequal in magnitude and with a phase displacement of 120°Applies at fundamental and harmonic frequenciesSystem and load elements symmetricalThyristor conduction periods correct

Unbalanced quantities: Voltages and currents departingfrom the above equality of magnitude and phase displace-ment at any frequencyCauses include asymmetry of lines and transformersThe conduction periods of thyristors not the samePower system faults, unbalanced loadingThe theory of symmetrical components provides a veryuseful means of analysing these conditions.

Residual current: If the ground circuit is involved in theunbalanced condition, residual harmonic current may flow,giving rise to noise interference in neighbouring telecom-munication circuitsAsymmetry of line and transformer elements, usuallypresent, gives rise to the production of residual groundharmonic current even if the line harmonic currents arethemselves substantially balanced.

Zero sequence quantities: Voltages and currents equal inmagnitude and in time phase at any frequencyUsually associated with single line-to-ground powersystem faults

Paper 3918C (P9), first received 21st June 1984 and in revised form 22nd February1985

The author is Head of the Department of Electrical Engineering, Queensland Insti-tute of Technology, Brisbane, Queensland, Australia

Triple harmonics generated by power transformers arebasically zero sequence harmonicsZero sequence harmonic voltages occur line-to-groundassociated with zero sequence line capacitance-to-ground.

3 Practical observations of asymmetry

In symmetrical systems, harmonics may be classified as:

balanced sequence order: 5, 7, 11, 13 etc.

and

zero sequence order: 3, 9, 15, 21 etc.

Practical measurements in systems with asymmetry revealthat there are zero sequence harmonics of orders: 5, 7, 11,13 etc. present in line-to-neutral voltages, and line currentsand balanced sequence harmonics of orders 3, 9, 15, 21 etc.present in line-to-line voltages and line currents. Followinga wave analysis, if we analyse the line-to-neutral voltagesfor their sequence components, we can understand thereason for this.

Fig. la illustrates the case for the 13th harmonic, nor-mally of balanced sequence order. There is distortion ofthe voltage triangle leading to both balanced sequence andzero sequence components.

Fig. \b shows the situation for the third harmonic, nor-

a III Yl3 bFig . 1 Sequence components due to asymmetry

a 13th harmonic balanced sequenceb Third harmonic zero sequence

mally of zero sequence order. Owing to distortion of thezero-sequence component arrangement, we can see that aswell as the zero-sequence third harmonic quantities, thereare some balanced sequence third harmonic components.

The residual harmonic ground circuit current may thencontain a full range of harmonic components. Consideringtheir production by a nonlinear load, two cases need to beconsidered:

(a) balanced harmonic load currents(b) unbalanced harmonic load currents

IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985 195

flowing through a power system, where there is asymmetryof line and transformer elements.

The latter case may occur with the connection of single-phase low voltage or electric traction loads, but in the caseof high voltage and the usual industrial loads, should notbe significant.

The paper studies the production of residual harmoniccurrent due to substantially balanced harmonic load cur-rents. It provides the field engineer with a method of pre-diction of the magnitudes of residual harmonic currents,owing to the connection of a nonlinear load, which shouldbe of value when considering noise interference with tele-communication circuits.

4 Model power system study

To understand the distribution of residual harmonic cur-rents in a high voltage system and to produce an approx-imate method for estimation, the author examined a modelpower system in an electrical engineering laboratory at theQueensland Institute of Technology. The system and itszero sequence equivalent circuit are shown in Fig. 2. Any

Z r = leakage impedanceZom = zero sequence excitation impedance

of quantities for power system studiessecondary neutral currentsecondary line currentprimary neutral currentprimary line currentsecondary neutral currentsecondary line currentprimary line currentsecondary neutral currentsecondary line currentprimary line currentresidual capacitive currentresidual capacitive currentresidual capacitive current

4.2 Experimental investigationIt is usual in Codes of Practice to examine harmonic per-formance up to, say, the 25th harmonic. The author choseto study a limited range spread over this spectrum, namely

Definitionhsnhs

chsnhshPhsnhs

uPhlnhln/ , , _

= Tl= T1

= T2= T2= T2= T3= T3= T3= T4= LI= L2= L3

8 0 V 415V 140V 80V

2p '2s >3s

• i s n pLln '2pn '2sn 'L2n

Load

Non- Linear

Gl T l LI T 2 L2 T 3 SI

+ J35 +JI76 +JI76 + JI8 + j 18 +JI85 +JI85

Fig. 2 Equivalent circuits for model study

a Model power systemb Zero sequence diagram n = 23Ohms to 415 V base

balanced sequence line harmonic current may be exam-ined. Here the 23rd harmonic was chosen, one of four har-monics for which measurements were recorded.

4.1 Technical dataGl = Laboratory three phase power supply 415/240 V

50 HzTl = Three phase, three-limb core-type transformer:

2.4 kVA, 80/415 V, ZT ^ 5%, Zom * 64%T2 = Three phase, three-limb core-type transformer:

2.4 kVA, 415/140 V, Z r ~ 5%T3 = Three phase, three-limb core-type transformer:

2.4 kVA, 140 V/80 V, ZT ^ 5%LI = Two air-cored coils in series, each (1.6+;8.0)

Q/phase (50 Hz)Shunt capacitance = 0.4 /iF/phase

L2 = Two air-cored coils in series, each (0.3+70.9)Q/phase (50 Hz)Shunt capacitance = 0.04 ^F/phase

SI = SCR and resistor bank representing a nonlinearload

LI and L2 could be considered to model a sub-transmission system overhead line of 45 km length and adistribution system overhead line of 5 km length, respec-tively, at appropriate voltages

orders 5, 13, 23 and 29. As harmonic currents are con-sidered independently and their effect on the system isbeing examined here, it is not necessary to detail the non-linear load characteristics. The method of analysis wouldbe valid for a variety of loads.

With a fundamental load current, substantially bal-anced, at Sx of 2.1 A/phase and 44 V/phase, Table 1 showsthe average line currents to a 415 V base for comparison.

Table 1: Harmonic current distribution

Order,n

5

13

23

29

Line currents

mA/ph

595856553535

43.7

mA/phase

55541413

4.54.82.62.7

'is-mA/phase

636314144.95.22.12.6

Residual currents

/„„.mA

9.48.73.22.72.571.72.7

kin-

mA

0.220.310.610.772.29.11.83.6

mA

9.08.72.52.70.212.00.250.86

mA

0.0080.0150.0130.020.0080.0610.0030.013

Fundamental n = 1, f - 50 HzCurrents: 415 V basefirst row: balanced line capacitancessecond row: 10% difference in the centre line capacitances

196 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985

Two conditions were examined, the first with balancedshunt capacitance to ground and the second with a differ-ence of 10% shunt capacitance for the centre phase toground for both lines, an unbalanced condition. The read-ings were taken across resistive shunts with a waveanalyser and were carried out as quickly as possible whilethe load remained steady. The supply system harmonicscomprised mainly orders 5 and 7 which would affect thefinal distribution to a limited extent. As the results canonly be regarded as approximate, they provide a usefulguide to the trend in harmonic current distribution.

4.3 Some observations on the experimental systemIn the zero sequence equivalent circuit:

(a) The system transformer T2 grounded neutral couldbe regarded as the reference point with residual currentflowing from T2 to be shared by line LI capacitive circuitto ground and Tl secondary grounded neutral.

(b) As the frequency increases there is a decrease intransformer 2 (I2pn) and an increase in line LI (/Lin)residual currents.

(c) As the shunt capacitive reactance of the short line L2is high, the residual current I2sn (= IL2n) is very low com-pared with the other residual currents, at all frequencies

(d) The effect of unbalance in the line capacitive circuitsto ground is to increase the line residual currents at allfrequencies.

(e) Current amplification occurs with the line current asseen in Table 1 by considering the relative values of/3s, I2sand Ils at a given frequency and, in particular, at the 23rdharmonic which is near a resonant frequency.

(/) An unbalance of line capacitance to ground, of 10%for one phase, has a relatively small effect on the line har-monic currents / l s , I2s and /3s at all frequencies.

5 Power system analysis

There are digital computer programs available for bal-anced and unbalanced harmonic load flow analysis whichare associated with a considerable amount of detailedinput and output data. The author has sought to exploreapproximate methods for residual current analysis, using asymmetrical component technique, which require muchless data and are suitable for manual calculations.

5.1 Approximate methods for calculation of residualharmonic current flow

With reference to Fig. 3, a nonlinear load provides a har-monic current /„ and a line-to-ground voltage Vn, of order

n, at the midpoint P of a distribution system. The balancedequivalent circuit shows that the residual current path isthrough the grounded supply transformer neutral and thecapacitances to ground. With the system elements sym-metrical and with the harmonic load currents balanced,there can be no residual current flow.

5.1.1 Basic theory: If a small capacitor is added in paral-lel to the capacitor from a phase to ground, it is apparentthat a residual current will flow through the pathdescribed. If X'cg = Xcg/ku, it may be shown from thetheory of symmetrical components and Thevenin'stheorem that

h (xln x2n) + (xon + zxjku)whereKL

= voltage at P before X'cg is added= residual ground current= positive sequence reactance= negative sequence reactance= zero sequence reactance= capacitive reactance, line-to-ground= capacitive unbalance factor <̂ 1= VX — Y \I(X~ \

•Jv/Xcj eg average/I \-^ eg)

eg average = average capacitive reactance with unbalanceIf Xln, X2n and Xon are less than Xcg as is usually the casein practice,

xonXegKX

Thus Ig ^ K isThe capacitor currents Ip = VJXcggof the order of 0 to 0.1, it is apparent that a small capac-itive unbalance will have an insignificant effect on the lineharmonic current and therefore the harmonic voltage Vn.

5.1.2 Actual estimation: If Xcg and X'cg are combined intoa single reactance, the residual current lg may be approx-imately determined by taking the individual line-to-groundvoltages Vn, dividing them by the individual capacitivereactances to ground and vectorially adding the phase cur-rents.

In practical systems, the capacitive reactance to groundof overhead power lines is often different for each phaseand there is a small residual current flow through ground.Its value depends principally on the load harmonic volt-ages at a point P, say, and the zero sequence capacitances

Lint

Non- Linear

xc7

b

~xc7 x c g

Sourct

Fig. 3 Residual harmonic current circuits

IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985 197

to ground. The former may be determined from a harmo-nic load flow study including the series unbalance effects,whereas the latter are found from the voltage/charge equa-tions. Unequal zero sequence excitation reactances forthree phase transformers may be treated in a similarfashion.

Having determined the residual current, its distributionis calculated from a knowledge of the zero sequence equiv-alent circuit for each harmonic. Where there are a numberof shunt reactances to ground, remembering that theresidual current is usually much smaller than the harmonicload current, each residual current may be estimated inturn and combined by superposition, for an approximateresultant distribution in the system.

6 Power system study

A radial-type system is considered as these are oftenemployed for reasons of economics and ease of operation,and lend themselves readily to basic calculations. Fig. 4shows one-line diagrams of the network and Appendix10.1 the classes of overhead line construction and technicaldata.

Line data: In each case the inductive reactance and capac-itive reactance per phase were calculated for untransposedlines with the ground return condition.

Transformer data: Transformer harmonics are much lessthan those of the nonlinear load. The shunt excitationcircuit has a very high reactance compared with the systemand was neglected in each case. The leakage reactances ofthe phase windings, primary-secondary (and tertiary), areunequal because of the magnetic circuit, and after consul-tation with a transformer manufacturer and laboratorytests, it was assumed that:

z. = and Z» = 1.05Z.

No data was available on the unequal zero sequence exci-tation reactances and from a knowledge of possible fluxpaths, it was assumed:

7 —7 —

6.1 Network calculationsReactances were referred to a 132 kV base and a unitcurrent of 1.0/CT A/phase for each frequency was injected

!32kV 3 3 kV"3_p "35

i — 'Llnl '2pni — — T>2sn

Tl LI T2

|>L2n j -^ ^ T '3tn

L2 T3

Load

Non- Linear

Fig. 4 Equivalent circuits for a typical radial-typepower system

a Power systemb Zero sequence diagramLI = 30 kmL2 = 5 kmL3 = 5 kmT2 = 30 MVA (Zp = 9%, Zs = 1%, Z, = 10%, Xom = 140%)T3 = 5 MVA (ZT = 7%)T4 = 1 MVA

I I KV

11'L3n

T4

Assumptions made are:(a) short circuit level of the source busbar S would be

typical of a grid supply point, e.g. 2000 MVA with Zx =Zo

(b) the 132 kV transmission line is short: 30 km(c) at the 33 kV busbar B, four additional feeders each of

length 5 km are included(d) at the 11 kV busbar D, two additional feeders each

of length 5 km are included(e) as the inductive reactance increases with frequency to

a much greater extent than the increase of resistance, theresistive component of harmonic impedance has beenneglected

(/) the analysis has been carried out for the conservativecondition of no load

(g) all transformers are three-limb core-type three phaseunits.

at the load busbar representing a nonlinear load. It wasassumed that the three-phase load was substantially bal-anced and a basic harmonic load flow study was carriedout, including the effect of line capacitance. This can beapproximated by considering all elements symmetrical.

The unbalanced line-to-ground voltages due to theunequal series impedances and balanced currents werecalculated at various locations. These voltages, using theThevenin equivalent circuits, were used with the unequalline shunt capacitive and transformer inductive reactancesto determine the line residual current flow, within a zerosequence circuit. An example is given in Appendix 10.2.

The line currents and the resultant residual current flowat designated points, for an injection of 1 A at each fre-quency at the 33 kV load busbar C, are shown in Table 2.It is observed that the residual currents are generally muchless than the line currents. Small changes in the series and

198 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985

Table 2: General harmonic current distribution referred to 132 kV base

Order,n

1*57

11131719232529

/ i s /

A/phase

1.01.11.21.31.82.13.86.6

14.2

l2sr

>4/phase

1.01.01.01.01.01.01.11.10.9

A/phase

1.01.01.01.01.01.01.01.01.0

Up-A/phase

1.01.01.00.980.960.950.930.900.97

mA

18004.67.1

162767

113425

11509990

/ t i n #

mA

2252.45

152771

122476

130611460

kpn-mA

15702.22.01.30.223.99.4

51150

1470

l2sn/

mA

4.10.120.240.620.951.92.66

1251

/mA

0.540.090.160.410.571.01.32.02.71.2

* Fundamental residual current mainly independent of load current, largely dependent on zerosequence shunt reactances.

Table 3: Harmonic current distribution 1 MVA 11 kV load busbar E

Order,n

157

11131719232529

1 MVA:

/ i s /

A/phase132kV

4.370.810.560.360.350.380.370.500.570.62

l3pr

A/phase33 kV

17.53.152.11.221.050.880.70.520.350.17

4.37 A at 132 kV17.5 A at52.5 A at

33 kV11 kV

uP,A/phase11 kV

52.59.446.33.673.072.532.001.450.940.52

/ i s n /

mA132 kV

17903.653.715.027.11

14.619.755.7

100440

/ t i n /

mA132 kV

2201.902.624.637.05

15.521.462.4

114504

kpn>mA132 kV

15701.761.080.390.060.841.656.71

13.364.6

l2snr

mA33 kV

16.30.380.510.760.991.641.853.154.088.97

l3sni

mA11 kV

6.480.811.041.51.82.662.683.132.840.65

shunt unequal impedances would have a very small effecton the line currents.

The calculations were extended to cover the injection of'unit' harmonic currents at the 11 kV load busbar E asshown in Table 2. This method allows the estimation ofharmonic line currents, with transformer neutral and lineresidual capacitive currents, at any desired load kVA, bymultiplication of the results in Table 2 by the load currenton a proportional basis. It also allows harmonic composi-tion of the nonlinear load to be taken into account. Thecomplete results for a 1 MVA load at busbar E are shownin Table 3.

6.2 Observations on the power system analysisThe same general effects may be noted as in Section 4.3 onthe experimental system. With reference to Tables 2 and 3:

(a) Current amplification from the 33 kV to 132 kVsystem line currents, I2p to / l s , respectively, may beobserved for 'unit' current injection and for an actual har-monic distribution for the 1 MVA load. Although the11 kV load harmonic currents decrease with increasing fre-quency, the 132 kV line harmonic currents decrease at first,then increase with frequency.

(b) The residual current in the 132 kV system follows thesame pattern of shifting from the transformer circuitsmainly, to the supply transformer Tl and LI residualcircuit, as the frequency increases. Note the decrease in T2primary neutral current in Tables 2 and 3 with frequencyto the 13th harmonic and then an increase with frequency,due to a resonance effect in the 132 kV system.

(c) The residual current flow is constrained to the zerosequence circuits, so that for the 11 kV system it is notaffected by the zero sequence current flow in the otherparts of the network. In the 33 kV system, due to the lowzero sequence source impedance and the short length of

feeders, the residual current flow depends mainly on thatsystem. In both these cases, the magnitude of residualcurrent flow is predominantly governed by the line zerosequence capacitance.

(d) The residual currents are generally much smallerthan the line currents.

7 Practical application to systems

It has been shown that it is possible to estimate theresidual current by detailed calculations in various sectionsof a radial network as a result of the connection of a non-linear load of known harmonic composition. However, itdoes require some knowledge of the calculation of line par-ameters and power system analysis.

7.1 Approximate calculationsFurther simplification for field study would be subject tothe following considerations:

(a) If the radial system has only one grounded supplypoint and is of short length, the residual current may bedetermined, approximately, by estimating the harmonicline-to-ground voltages at the midpoint of the line from abalanced harmonic load calculation and dividing each bythe appropriate line zero sequence capacitive reactance, i.e.neglecting the source impedances. The vector sum of thecurrents then yields the residual current (Fig. 5a). If thesystem is operating, the residual current can be measureddirectly at the supply transformer/s neutral connection/s.

(b) If the system is of a multiple-grounded nature, it isnot possible to make the above approximate calculationsbecause of the more complex zero sequence circuit. Con-sidering a residual current flow at one end only of a linecould not provide the correct solution (Fig. 5b). For anoperating system, harmonic neutral currents may be mea-sured.

IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985 199

The errors involved in the approximations may be notedby referring to Fig. 5, where a detailed calculation and

IOOO

100

10

<E

(M

<**

V

5 9 13 17 21 25 29a Harmonic Order n

10 000

I 000

100

10

y

*

>/

4

/

j

/

/

/

/

/

5 9 13 17 2! 25 29b Harmonic Order n

Fig. 5 Comparison of methods of calculationa 33 kV line residual currentb 132 kV line residual capacitive current

detailed calculation—•— midpoint voltage VPG: approximate calculation

busbar voltage approximate calculations

approximate calculation as above, are compared. Forlonger lines in the sub-transmission and distributionsystems, at high frequencies, it is necessary to include theeffect of zero sequence source impedance, which wouldrequire a detailed calculation.

8 Transpositions

If the asymmetry of lines and transformers with unequalseries and shunt harmonic impedances gives rise toresidual harmonic ground current, with substantially bal-anced harmonic load currents, it is apparent that introdu-cing transpositions, thus improving symmetry, must give a

reduction in ground current. In subtransmission and dis-tribution systems this is comparatively easy and inexpen-sive to carry out in the case of overhead lines. As mosttransformers are of the three-limb core type in thesesystems, little can be done to improve transformer sym-metry.

Transpositions will also ensure a considerable reductionin electromagnetic induction in neighbouring communica-tion circuits due to balanced sequence harmonics. Theywill not cause further reduction due to the remainingresidual harmonic ground currents as they are of zerosequence order.

9 Conclusions

(a) On untransposed lines, balanced harmonic load cur-rents in the presence of system asymmetry will produceunbalanced harmonic voltages and residual groundcurrent.

(b) Harmonic injection anywhere in a system willproduce residual current in connected systems providedwith neutral grounding.

(c) Approximate methods are available for residualcurrent calculations at any load and harmonic composi-tion, where the lines are short.

(d) Multiple-grounded systems require detailed studiesof residual harmonic currents.

(e) Transpositions on overhead lines should be con-sidered where exposure to telecommunication circuits is aproblem, as improving the symmetry may reduce theresidual harmonic currents significantly.

(/) Current amplification magnifies the line and residualharmonic currents at certain locations in the system.Transposing here does not reduce the magnitude of thisline current as it is due to a resonance effect, but shouldgive a considerable reduction in the residual current.

10 Appendixes

10.1 50 Hz data for untransposed overhead lines

132 kV single circuit transmission line {Fig. 6)Series inductive reactance, Q/km: Xa = 0.428, Xb = 0.407,Xc = 0.428(Positive sequence reactance of transposed line: Xx =0.421)Capacitance-to-ground (zero sequence), pF/km: Cag =6106, Cbg = 5794, Ccg = 6106

Two ground wires

4-572

O

O O

4-572

O-

4-572 w

16-764

7/777T777777777TT7T;metres

Fig. 6 132 kV single circuit transmission line

phase conductors 30/7/18.14 mm ACSRground wires 6/1/3.75 mm ACSR

13-716

200 IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985

(Positive sequence capacitance of transposed line: Cx =8594)Series inductive reactance, Q/km (zero sequence):Xa0 = 0.847, Xb0 = 0.855, Xc0 = 0.847

33 kV single circuit subtransmission line (Fig. 7)Series inductive reactance, Q/km: Xa = 0.405, Xb = 0.383,Xr = 0.405

1-83 •83

9-15

/ / / / / / / / • / / / / / / / /

metres

Fig. 7 33 kV single circuit subtransmission line

19/10.54 mm hard drawn copper

(Positive sequence reactance of transposed line: Xl =0.398)Capacitance-to-ground (zero sequence), pF/km: Cag =4704, Cbg = 4159, Ccg = 4704(Positive sequence capacitance of transposed line:Q =9135)

11 kV single circuit distribution line {Fig. 8)Series inductive reactance, fi/km: Xa = 0.383, Xb = 0.371,Xr = 0.405

0 6 1 1-219

8 1 1

metres

Fig. 8 Si/tg/e circuit distribution line

7/2.03 mm hard drawn copper

(Positive sequence reactance of transposed line: Xx =0.386)Capacitance-to-ground (zero sequence), pF/km: Cag =3971, Cbg = 3640, Ccg = 4365(Positive sequence capacitance of transposed line:Cx = 9422)

10.2 Calculation of line capacitive residual curren t132 kV transmission line

Current injection at 33 kV load busbar C, 1 A/phase, 23rdharmonic

(a) Harmonic load study based on balanced load cur-rents and system elements gives:

/ l s = 3.79 A/phase, I2p = 1.35 A/phase,

ILG = 2.44 A/phase and VLG = 1309 V/phase.

(b) An approximation to the unbalanced voltages at L(mid-point) is found from the products:

VALB = 3.79/0! . 351.3/90! = 1331.4/90! V. 333.5/90! = 1264/330° V. 351.3/90° = 1331.4/210° V

VBL

LG

G = 3.79/240° . 333.5/90! = 1264/330° VVCLC = 3.79/120!

(c) The zero sequence circuit is then used to find theresultant reactance/phase through the line capacitivecircuit.

(d) With reference to Fig. 4, the shunt capacitive phasecurrents at L are:

IAG = 1331.4/907373.1/-90° = 3.57/180° AIBG = 1264/3307406.9/-900 = 3.11/60° AICG = 1331.4/2107373.1/ -90° = 3.57/300° A

(e) Thus, the line residual current

Iun = I IpH = 0.46/240_° A.

and is distributed over the zero sequence circuit as shownin Fig. 9.

As with the experimental system, at this frequency level,very little current flows through T2 primary neutral, whilethe residual currents Ilsn and ILln approach the samevalue.

LI

(0V.+J288I)

6 0 6VALG VBLG VCLG

1 1 1-J755 H796

Fig. 9 Zero sequence circuit

-J755

II 'Lln= 0-462/240° A

IEE PROCEEDINGS, Vol. 132, Pt. C, No. 4, JULY 1985 201