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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON POWER DELIVERY 1

An Interphase Distance Relaying Algorithm for

Series-Compensated Transmission LinesZ. Y. Xu, Senior Member, IEEE, Z. P. Su, J. H. Zhang, A. Wen, and Q. X. Yang

AbstractA new interphase distance relaying algorithm for se-ries-compensated transmission lines is proposed in this paper. Thefault impedance can be correctively calculated using the proposedalgorithm without requirement of the parameters of series capac-

itor device. The series capacitor can be simplified as a linearizedimpedance during the fault period, but its parameters can be usedas variables in fault loop equations. The real-time digital simulatortests show that the proposed algorithm can obtain more accurateresults than other traditional distance relaying algorithms for se-ries-compensated transmission lines.

Index TermsDistance relay, interphase faults, series-compen-sated transmission lines.

I. INTRODUCTION

S ERIES capacitors (SCs) have been widely used in powertransmission to increase power transfer capability, improvetransient stability and damp power oscillations. The metal oxide

arrestor (MOV) was applied as an overvoltage protection de-

vice on the series capacitors itself for years. Distance relay is

widely used as main or backup protection of transmission lines

including series-compensated transmission lines, but the relia-

bility of traditional distance relay is affected by the incorrectly

measured fault impedance caused by highly nonlinear charac-

teristic of MOV[1].To eliminate the influence of nonlinearity caused by MOV a

series of simplified and approximated models of SC/MOV de-

vice for distance relay have been discussed[2][6]. However, in

the methods based on the calculation of voltage across SC/MOV

to eliminate the effect of series capacitor discharging gap (GAP)

was not considered, which must be set to discharge in order to

protect the SC/MOV in severe internal faults on the protected

lines. Actually, GAP is an important part of modern SC/MOV

devices and it is impossible to accurately calculate the voltage

across SC/MOV without considering GAP discharging.

The enhancement for directional and pilot protection on

series-compensated lines has been proposed in [7], [8], but itcannot be used in fault impedance calculation of step distance

Manuscript received April 07, 2013; revised July 07, 2013, August 16, 2013;accepted September 02, 2013. Date of publication September 26, 2013; date of

current version nulldate. Paper no. TPWRD-00382-2013.Z. Y. Xu, Z. P. Su, J. H. Zhang, and Q. X. Yang are with the School of Elec-

trical Electronic Engineering, North China Electric Power University, Chang-ping, Beijing 102206, China.

Z. Y. Xu and Q. X. Yang are also with Beijing Sifang Automation Co. Ltd.,

Haidian, Beijing 100085, China (e-mail: [email protected]).A. Wen is with China Southern Power Grid Co. Ltd., Guangzhou 510623,

ChinaColor versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPWRD.2013.2281067

relay. The wavelet transform technique [9], [10] has also

been presented to improve the performance of protection on

series-compensated transmission lines; in [11] a neural net-

work scheme has been suggested. However, their performance

needs further evaluation and improvement. A scheme based on

high-frequency signals have been proposed in [12], in which

a specialized measurement unit consisting of stack tuner and

line trap is used to capture the high-frequency components of

the fault signal. In order to evaluate the performance of this

scheme more test cases were required.

In this paper a new algorithm is proposed for the distance

relay on series-compensated transmission lines, which is de-

duced from time domain fault location method [13], [14]. In

the proposed algorithm, the effect of series capacitor on mea-

sured fault impedance is avoided because the series capacitor

parameters are only used as variables in the fault loop equations,

which are not required to be known. A significant merit of pro-

posed algorithm is that all operating states of series capacitance

device can be modeled as a linearized equivalent impedance.

Meanwhile, the operating states of SC/MOV/GAP, the parame-

ters of SC/MOV/GAP, the relative fault position with respect to

SC/MOV/GAP and the iterative calculations are unnecessary.

This makes the algorithm simpler and more accurate than other

algorithms. This paper mainly investigates the algorithm for in-

terphase faults. The algorithm for single phase to ground faults

is being reviewed in another paper. Validation tests have been

performed using RTDS to demonstrate the accuracy of the pro-

posed algorithm.

II. MODEL ANALYSIS

The voltage-current characteristics of MOV are designed as

highly nonlinear. This can significantly affect the traditional dis-

tance relaying. The general characteristics of MOV conduction

by IEC standard[15]is expressed by a single exponential curve

as given in theAppendix.Fig. 1shows the structure of modern SC/MOV/GAP device

and its equivalent circuit. Three different operating states incor-

porate the SC/MOV/GAP different protection functions for dif-

ferent fault conditions. The three operating states are as follows:

1) SC/MOV is bypassed by GAP discharging in 23 ms after

fault inception.

2) Capacitor operates without MOV and GAP action.

3) Capacitor operates with MOVaction and without GAP dis-

charging.

Actually, all these three operating states can be represented

as a linearized equivalent circuit in series with resistance

and capacitive reactance for the SC/MOV/GAP as shown

0885-8977 2013 IEEE
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2 IEEE TRANSACTIONS ON POWER DELIVERY

Fig. 1. SC/MOV/GAP equivalent circuit for analysis. (a) FSC, (b) Equivalentcircuit.

Fig. 2. Series-compensated transmission line.

Fig. 3. SC/MOV equivalent circuit for interphase fault.

inFig. 1(b). This is the basis of the proposed algorithm in this

study as shown below:

For thefirst state the fault location is always internal in series-

compensated transmission lines and the fault is severe. The GAP

is set to discharge in order to protect SC/MOV as quickly as

possible after fault inception. It is easy to understand that

and are equal to zero and the linearized model is applicable.

For the second state, the fault is not severe and it is always ex-

ternal. The voltage of SC is below the designed protective level

andthustheMOVdoesnotconduct.The iszeroand isstill

constant during the fault period. Obviously the SC/MOV/GAP

can be represented by a linearized impedance in such state.

For the third state, various simulations on RTDS were carried

out to confirm that a linearized equivalent impedance model is

reasonable for the SC/MOV coordination action during fault pe-

riod. The test model used is a 500 kV 300 km long series-com-

pensated transmission line as shown in Fig.2. The line reactance

of 60% is compensated by two series capacitors C1 (30%) and

C2 (30%) that are located at two ends of protected line. MOVs

are simulated in detail with a single exponential model [15].

Faults are initiated at 0.4 s. The three-line equivalent circuit of

an interphase fault is also indicated in Fig. 3.

Fig. 4. SC/MOV device waveform under CA solid fault at 180 km away frombus M with MOV cond uction. (a) SC voltage. (b) R elay cur rent. (c) MOV cur-

rent. (d) SC current. (e) Calculated SC/MOV equivalent impedance.

Fig. 4shows the current and voltage waveforms in SC/MOV

device for a solid CA fault located at 180 km away from bus

M. In this case the series capacitor operates with corresponding

MOV conducting during fault period, and the GAP is set not to

discharge. As shown inFig. 4(b)(d), the following character-

istics can be found: 1. Voltage across SC is lagging 90 degrees

from its current. When voltage reaches its protective level the

phase angle of current flowing through SC is always in 90 to

180 degree or 270 to 360 degree; 2. For every power frequency

period when MOV conducts the initial phase-angle and magni-

tude of fault current of SC/MOV have already appeared, so that

the initial phase-angle and magnitude of power frequency fault
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XUet al.: AN INTERPHASE DISTANCE RELAYING ALGORITHM FOR SERIES-COMPENSATED TRANSMISSION LINES 3

current flowing through SC/MOV is not affected by MOV con-

duction; 3. When MOV conducts the voltage across SC/MOV is

limited to a constant value and the fault current is transferred to

MOV branch. In this stage because of the nonlinear character-

istic of MOV, the fault current is still a part of sinusoidal wave-

form, as shown in Fig. 4(c), and the power frequency component

of fault current measured by relay is completely sinusoidal due

to that. As shown inFig. 4(a), the initial phase-angle and mag-

nitude of fault voltage across SC are also constant during fault

period. According to the analysis above, the SC/MOV can also

be represented by a linearized impedance regardless of the high

nonlinear characteristics of MOV. Fig. 4(e) shows the calcu-

lated SC/MOV equivalent impedance during such fault period.

It is apparent that the equivalent impedance is a capacitive con-

stant. The transient process of impedanceinFig. 4(e)is caused

by the transient current and voltage.

Meanwhile,Fig. 5shows the current and voltage waveforms

of SC/MOV device for the same fault without MOV conduction.

It is clear from Figs. 4(e) and 5(d) that the transient process

with MOV conduction after fault inception is much shorter than

that of fault without MOV conduction. This is the reason of the

attenuation of MOV/SC equivalent resistance.

In summary, all three operating states of SC/MOV/GAP de-

vice can be represented with a linearized impedance, which is

the basis of the algorithm proposed in this paper.

III. ALGORITHM FORSERIES-COMPENSATED LINES

Based on the analysis above, a new interphase distance relay

algorithm for series-compensated transmission line is proposed

below. The following analysis neglects the shunt capacitance of

transmission lines to simplify the algorithm. The error causedby this will be discussed later. As shown in Fig. 3, when an

interphase fault occurs on the series-compensated transmission

line, the interphase voltage of fault phase at relay location

can be obtained as

(1)

where are resistance and inductance of fault line.

Combining the resistance items,(2)can be obtained

(2)

where .

Differentiating(2)with respects to t, (3)can be obtained

(3)

by applying a simplified notation as follows:

Fig. 5. SC/MOV waveform under CA solid fault at 180 km away from bus M

without MOV and GAP conduction. (a) Relay current. (b) SC voltage. (c) SCcurrent. (d) Calculated SC/MOV equivalent impedance.

Equation(3) can be rewritten as(4)

(4)

where N is a sequence sampling number, (4) should be satis-

fied for each sampling instant. In (4), there are three unknown

variables. It means that arbitrary three discontinuous sampling

points can be selected to satisfy the(5) as follows:

(5)

According to the(5), and because , and are constant

during the fault period, the fault reactance and resistance
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can be obtained from (6) and (7), without any requirement of se-

ries capacitor parameters. is a variable, which is not required

to be solved, and is any phase of AB, BC, or CA.

IV. DIGITAL VERIFICATION

A test model of a 500 kV series-compensated transmission

line is shown inFig. 2. The detailed parameters are presented

in theAppendixof this paper. The studiedfirst-zone interphase

distance relay is set to protect 85% of the 300 km transmission

line (i.e., 255 km). RTDS is used for the simulation of power

system, series-compensated transmission line, CTs and CVTs.

MATLAB is used for the calculations of the new algorithm.

Source M leads source N by the angles between 0 (no load) and

30 (heavy load). Faults are initiated at 0.4 s. The sampling rate

of 80 samples per cycle (for 50 Hz system) is used and Butter-

worth low-pass filter with 120 Hz cut-off frequencies is selected

to filter out the high order harmonic components. Equations(6)

and(7), shown at the bottom of the page, are employed to cal-

culate the fault impedance from the relay location to the faultpoint for interphase faults.

In order to verify and evaluate the new algorithm, some

comparison results are shown between the new algorithm and

the traditional distance relaying algorithm[16]which is widely

used in distance relay of transmission lines. The traditional

algorithm for interphase fault is given as

(8)

Fig. 6 shows the current waveform flowing through

SC/MOV/GAP, the phase voltages, currents and the inter-

phase fault impedance loci measured at two ends for a solidBC fault located at 240 km away from bus M which is inside

the reach offirst-zone. As shown inFig. 6(a), in this case the

series capacitor operates corresponding to MOV conduction

during fault period and the GAP is not triggered. As shown in

Fig. 6(b), for the relay at end M, the calculated fault reactance

using traditional algorithm(8)reached to 28 ohm (100 km) and

instable due to the series capacitor in the fault loop.

For the new algorithm the accurate fault impedance is ob-

tained within a cycle (20 ms) following the fault occurrence.

As shown inFig. 6(c), for the relay at end N MOV/SC is by-

passed by GAP triggering discharge, the series capacitor is not

in the fault loop and the calculated fault impedance with the tra-

ditional algorithm (8) had an error of 10%. However,for thenew

algorithm the accurate fault impedance is obtained in 18 ms fol-

lowing the fault occurrence.Fig. 7shows the currents flowing

through SC/MOV, the impedance loci and the comparison re-

sults between the new algorithm and traditional algorithm(8)

for an ABC three-phase fault, which occurs at 150 km away

from end M within the reach offirst-zone of the distance relay

at both ends. As shown inFig. 7(a), in this test the SC/MOV is

bypassed by GAP discharging in 2.5 ms after fault occurs. As

shown inFig. 7(b)the calculated fault impedances with tradi-

tional algorithm are nearly the same as the proposed algorithm.

This is because the series capacitor in fault loop is bypassed by

GAP. The proposed algorithm can always correctly calculate

the fault impedance.

Fig. 8 shows the currents flowing through SC/MOV, the

impedance loci and the comparison results between the new

algorithm and the traditional algorithm (8) when an ACG

two-phase to ground solid fault occurs at 270 km away from

end N. This point is beyond the reach offirst-zone of the dis-tance relay at end N. As shown inFig. 8(a), the series capacitor

operates with MOV action during fault period, because the

voltage across SC/MOV is too small to conduct MOV in deep

nonlinear zone. As shown in Fig. 8(b) the calculated fault

impedance with traditional algorithm is instable and inside

the first-zone due to the series capacitors in fault loop. The

proposed algorithm can correctly calculate the fault impedance.

The error of the calculated fault reactance is derived by using

(9)

% (9)

where is the actual fault reactance of the line. is the cal-

culated fault reactance.

To further verify the new algorithm, the comparisons between

the new algorithm and the traditional algorithm are given under

various typical fault conditions. Fig. 9shows the comparison

results between the new algorithm and the traditional algorithm

(8), when BCG solid grounded faults occur along the series ca-

pacitor compensated transmission line with MOV conduction.

The faults are simulated with (heavy load, source

M leads source N) under different fault locations. As shown

(6)

(7)
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Fig. 6. SC/MOV/GAP waveform and estimated fault impedance under BCsolid fault at 240 km from bus M. (a) Current waveform through SC/MOV at

end M. (b) Current and impedance loci measured at end M. (c) Current throughSC/GAP and impedance loci measured at end N.

in Fig. 9, the errors of new algorithm are much smaller than

Fig. 7. SC waveform and estimated fault impedance under ABC fault at 150km away from bus M. (a) Current waveform though SC/MOV/GAP and relay.

(b) Fault impedance loci measured at end M and N.

those of the traditional algorithm. The relay with the new algo-

rithm can operate correctly under this condition; however, the
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Fig. 8. SC/MOV waveform and estimated fault impedance under CAG solid

fault at 270 km from bus N. (a). Current waveform though SC/MOV. (b) Fault

impedance loci measured at both ends.

relay with the traditional algorithm may over-reach. As shown

inFig. 9, the maximum error of the new algorithm is less than

3.0%, while the traditional algorithms error reaches 80%. As

shown inFigs. 6(b),8(b)the impedance loci of traditional al-

gorithm is instable in early 0.6 s after the fault occurs due tothe impact of SC/MOV. For the proposed algorithm, the errors

exist due to that the shunt capacitance of transmission lines is

neglected, while the test used the distributed parameter model.

V. REACH SETTINGS FORRESISTANCECOMPONENT

As (1) concerning an interphase fault on a series-compen-

sated transmission line, the measured fault resistance R is ex-

pressed as follows.

(10)

According to the [5], the maximum equivalent resistance

Rcmax equals 0.34Xco when MOV acts. Xco is the original

capacitive reactance of series capacitance. If k is the series

Fig. 9. Estimated fault reactance errors for BCG solid grounded fault with the

condition of under different fault locations.

compensation degree, we have . As for the solid

interphase fault occurring at the end of the series-compensated

line, following equations can be obtained.

(11)

(12)

Here, is the increasing resistance due to the series com-

pensation capacitor.

According to the typical parameters of 500 kV line in the

Appendix, is6.6 ohm. Substituting the parameters into(12)

the increasing resistance can be expressed as

(13)

Even the series compensation degree is 70%, the increasing

maximum resistance willbe 15.7 ohm. The increasing re-

sistance of interphase distance relay should not be neglected for

the reach settings of resistance component when MOV acts in

practical engineering. However, the arc resistance of interphasefault is much smallerthan that of single-phase to ground faults

and 20 ohm interphasearc resistance is the limitation value in

practical engineering[17]. So that 50100 ohm is the suitable

valuefor the reach settings of interphase distance relay. As to the

other two cases theincreasing resistance is zero like singe phase

to ground faults. The equivalent resistance shown in Fig. 4(e)

demonstrates the correct analysis here.

VI. SENSITIVITY ANALYSIS

It is necessary to analyze the sensitivity of the proposed al-

gorithm for the influential factors.

A. Impact of Shunt Capacitance

The proposed algorithm is derived based on neglecting the

shunt capacitance of transmission lines. As shown in Figs.6to9,

the simulation is carried out using distributed parameter line

models. The maximum relative error is less than 3.0%. The re-

sult shows the errors of proposed algorithm including the im-

pact of shunt capacitance is less than 3.0% for the 500 kV typ-

ical series-compensated transmission line, therefore the shunt

capacitance impact on proposed algorithm can be neglected for

practical applications.

B. Impact of Fault Resistances and Load Currents

It can be concluded that the accuracy of the new algorithm can

be affected by the fault resistance and load current according to
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Fig. 10. Estimated fault reactance errors under CA faults with fault resistance

030 at 150 km away from bus M.

Fig. 11. Estimated fault reactance errors under BC solid faults at 80% away of

series-compensated line length from bus M.

the derived formulas(6)(7).Figs. 6 to 8 show the new algo-

rithm functions perfectly for a solid interphase fault. In prac-

tice the fault resistance for the two phases fault may be rela-

tively smaller. A simulation is given under the extreme condi-

tions of (heavy load) and fault resistance 030 for

CA inter-phases fault. As shown in Fig. 10, the errors of the

new algorithm are much smaller than those of the traditional

algorithm.

C. Impact of SIR (System Impedance Ratio)

SIR reflects the ratio of the system equivalent impedance and

the relay reach impedance. For a fault on a series-compensated

transmission line, lower SIR means a larger fault current, which

will cause different equivalent impedance and resistance

. This section will illustrate the impact of SIR for the pro-

posed algorithm. A series of solid interphase faults at 80% away

from end M of the series-compensated transmission line under

different SIRs are simulated. Errors of fault reactance for pro-

posed algorithm are shown inFig. 11. Fig. 11 shows that the

proposed algorithm performances soundly when a solid inter-

phase fault occurs under different SIRs. The simulation is given

under the extreme conditions of (the series ca-

pacitor is included in the line impedance) and (heavy

load). As shown inFig. 11, the maximum errors of the proposed

algorithm is less than %, therefore the SIR impact on pro-

posed algorithm is insignificant.

D. Impact of Low Frequency Components

The proposed algorithm is based on the power frequency

components that satisfy the differential equation (1). In se-

ries-compensated transmission system, sub-harmonic, low

frequency, and sub-synchronous components may appear.

For instance, the capacitance series oscillation with line re-

actance may introduce low frequency transient component,

the capacitance series oscillation with transformer reactance

may introduce sub-harmonic component; and the capaci-

tance series oscillation with turbine generator may introduce

sub-synchronous component. The sub-harmonic, low frequency

transient and sub-synchronous components including decayed

d.c. component also satisfy the differential equation (1). It is

still valid to solve the fault impedance with (6) and (7). Such

kinds of low frequency components have no impact on the

algorithm proposed in this paper. As explained in Section IV

only a butterworth low-pass filter is needed to filter out the

high-order harmonics.

VII. CONCLUSION

A new algorithm has been developed for the distance relay of

interphase faults on series-compensated transmission lines. The

algorithm can eliminate the effect of nonlinear characteristics of

MOV and can satisfy all the operating states of series capacitordevices. The advantage of the proposed algorithm is that it does

not requireany parametersof series capacitor device,and it is not

necessary to know the operating state of SC/MOV/GAP during

fault period. The overreach and under-reach of distance relaying

caused by MOV conduction are eliminated. Another advantage

of the algorithm is that its calculation is simple and non-iterative.

Thestudy hasshown thatthe shunt capacitance does nothave any

impact on proposed algorithm. Theother influential factors such

as fault resistance, load level and SIR effect are also investigated

in this paper. Numerical simulations are carried out on RTDS,

showing that the accuracy and reliability of the new algorithm

proposed in this paper are satisfactory.

APPENDIX

1) Parameters of 300 km, 500 kV Bergeron Model lines:

Positive/negative sequence parameters

Zero sequence parameters

System parameters

Source M parameters: 500 kV

Source N parameters 500 kV
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2) MOV parameters:

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[17] Z. Y. Xu, S. F. Huang, L. Ran, J. F. Liu, Q. X. Yang, and J. L. He,A distance relay for a 1000-kV UHV transmission line, IEEE Trans.

Power Del., vol. 23, no. 4, pp. 17951804, Oct. 2008.

Z. Y. Xu (M08SM10) was born in 1963. He received the Ph.D. degree in

electrical engineering from North China Electric Power University, Beijing,

China, in 1996.

Currently, he is a Professor at North China Electric Power University. When

he was with Sifang Automation Co. Ltd., he designed a series of extremely

high voltage/ultra-high voltage transmission-line protection relays, which have

been widely used on 220 kV1000 kV transmissio n lines in China. His research

interests include power system protection and control.

Z. P. Su was born in China in 1987. He received the M.Sc. degree in electrical

engineering from North China Electrical University and is an Engineer with

Wuhu Power Supply Company, Anhui Electric Power Company, Wuhu, China.

His research interests include power system protection and control.

J. H. Zhangwas born in China in 1983. He is currently pursuing the Ph.D. de-

gree in electrical engineering at North China Electric Power University, Beijing,

China.His research interests include power system protection and control.

A. Wen was born in China in 1965. He received the Ph.D. degree in electrical

and electronics engineering from the University of Manchester, Manchester.

U.K., in 1992.Currently, he is a Senior Technical Specialist with China Southern Power

Grid Co. Ltd., Guangzhou, China. His research interests include power system

protection and control.

Q. X. Yang was born in China in 1937.

Currently, he is a Chinese academician of Engineering and a Professor at

North China Electric Power University, Beijing, China. His research interests

include power system protection and control, and substation automation.

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