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TSINGHUA SCIENCE AND TECHNOLOGY

I S S N 1 0 0 7 - 0 2 1 4

V o l u m e 10, N u m b e r

19/23

2, April

pp247-253

2005

Application of Six-Sequence Fault Components in Fault

Location for Joint Parallel Transmission Line

FAN Chunju CAI Huarong YU Weiyong (#'HMt)

Department of Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200030, China

Abstract: A new fault location method based on six-sequence fault components was developed for parallel

lines based on the fault analysis of a joint parallel transmission line. In the six-sequence fault network, the

ratio of the root-mean square value of the fault current from two terminals is the function of the line imped-

ance, the system impedance, and the fault distance away from the buses. A fault location equation is given

to relate these factors. For extremely long transmission lines, the distributed capacitance is divided by the

fault point and allocated to the two terminals of the transmission line in a lumped parameter to eliminate the

influence of the distributed capacitance on the location accuracy. There is no limit on fault type and syn-

chronization of the sampling data. Simulation results show that the location accuracy is high with an average

error about 2%, and it is not influenced by factors such as the load current, the operating mode of the power

system, or the fault resistance.

Key words: fault location; joint parallel line; six-sequence components; two-terminal

Introduction

Fault location for transmission line can be classified

into one-terminal method

The location method that uses one-terminal informa-

tion is very difficult to overcome the influence of the

change of the remote-terminal system impedance and

the fault resistance on location accuracy. Suonan et

al.

sound line of the joint parallel line to obtain the infor-

mation of the remote terminal. This method is effective

for single line faults, but not so effective for overline

(one line to another line) faults.

The fault location method that uses two-terminal in-

formation is not influenced by these factors and is ac-

curate in theory, but the asynchronous problem of the

data in these two terminals is difficult to be solved. Ji-

ang et al.

[1_6] and two-terminal method

[7_11l

[ 5 ] proposed a method that makes full use of the

[ 9 ] proposes a new method for fault location in

Received: 2003-03-15

* * To whom correspondence should be addressed.

E-mail: chunjuc@online.sh.cn; Tel: 86-21-62932278

parallel double-circuit multi-terminal transmission

lines. Although one equation can be used for all types

of faults, and classification of faults and selection of

fault phase are not required, the proposed methods do

not have enough accuracy when the fault occurs across

both circuits of a parallel double-circuit line. Saha et

al.

measurement unit device. However, this method is not

economic and the accuracy of fault location is not very

high.

A power system is generally a symmetrical three-

phase system. If the symmetrical component method is

used to decompose the asymmetrical phase measure-

ment, all the calculations can be carried out according

to single-phase condition for the asymmetry caused by

asymmetrical fault and asymmetrical load. For the ex-

tremely long transmission line, especially for the joint

parallel lines, there is zero sequence mutual reactance,

as well as positive and negative sequence mutual reac-

tance between phases

symmetrical component method is difficult, so the

[ 1 0 ] and Ge

[ 1 1 ] proposed a method based on the phase

[12]. Application of the traditional

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Tsinghua Science and Technology, April 2005, 10(2): 247 - 253

six-sequence-component method is applied to imple-

ment fault location for a joint parallel transmission line.

1 Six-Sequence Fault Component

1.1 Concept of six-sequence fault component

The six-sequence component can be produced from

symmetrical component. For the joint parallel line, as-

sume that the system meets the symmetrical condition,

namely, the phase mutual impedance between phases

of one line is same and the phase mutual impedance

between two lines is same. Then, the six phase volt-

ages and currents can be expressed as the superposition

of the six-sequence symmetrical voltages and currents.

According to the superposition theory, sudden-

changing components of all the sequence components

can be obtained, and all the corresponded six-sequence

components networks are passive networks. The posi-

tive, negative, and zero sequence networks for joint

parallel line are shown in Fig. 1. In Fig. 1, Μ and TV are

buses of the power system; F is the fault point;

ZNsi are the equivalent source impedance of side Μ and

N; z-1,2,0, representing positive, negative, and zero

sequence; Z

two lines of the parallel lines.

Ζ

Μý ·>

f

M is the mutual impedance between the

Μ Μ

É-ζí/si

É-ζí/si

3Z.,;,

Ν

(a) Positive sequence fault network (b) Zero sequence fault network

Fig. 1 Positive, negative, and zero sudden-change component networks of joint parallel lines

1.2 Sequence parameters of joint parallel line in

six-sequence network system

The sequence impedance in six-sequence network is

related with the positive, negative, and zero sequence

impedance in traditional symmetrical network. The

same-sequence positive impedance and same-sequence

negative impedance of the joint parallel line are equal

to the traditional positive sequence impedance, and the

inverted-sequence impedance of the joint parallel line

is equal to the traditional positive impedance. As there

is zero sequence mutual impedance between the two

lines, the same-sequence zero impedance is equal to

the traditional zero sequence impedance plus the triple

mutual impedance, and the inverted-sequence zero im-

pedance is equal to the traditional zero sequence im-

pedance subtract the triple mutual impedance. The dis-

tributed capacitance in the six-sequence network is

also changed correspondingly. The corresponding pa-

rameters of the joint parallel line can be seen in Ref.

[12]. Various sequence networks for six-sequence

components are shown in Fig. 2. Γ ι, Γ

same-sequence positive, negative, zero network, re-

spectively; Fi, F2, and F0 are inverted-sequence posi-

2, and T0are the

tive, negative, zero network, respectively.

Figure 2 shows that every network in the six-

sequence network is independent. According to the

given fault terminal condition, six-sequence compound

network can be formed and can obviously indicate the

relationship of the amplitude and phases of various se-

quence components. Applying the six-sequence com-

ponents in fault analysis of joint parallel line is the

same as the traditional symmetrical components.

2 Fault Location Scheme for Joint

Parallel Line Based on Six-

Sequence Components

2.1 Solving of system impedance

All the sequence networks in Fig. 2 are passive net-

work. In Fig. 2b, the subscript "m" represents the zero

mututal reactance between the circuits. If the distrib-

uted capacitance is considered, the sequence network

of joint parallel lines for fault mutation components of

one line can be obtained as shown in Fig. 3. In Fig. 3,

L is the total length of the transmission line, and D is

the distance between Bus Μ and the fault point F.

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FAN Chunju ot al: Application of Six-Sequence Fault Components-

249

Μ

2ZM

\)UkT[

Ν

Μ

2ZM

zV()+3z;

Ν

'Π Ι

2 Z v s o J

(a) Tu T2network

(b) T0 network

Μ

\)Ü

kFX

Ν

Μ

ZM)-3ZL

Zvi)

_3ZL

(c) F\, F2 network (d) F() network

Fig. 2 Six-sequence network of mutation components

Μ Ν

DZi ρ (L-D)Z,-

1 — ^ ——^ — ι Ή

1 1

Τ

\1) UFi

Fig. 3 Sequence network of joint parallel lines for

fault mutation components

Firstly, the sudden-change of the fault component is

obtained. The output of electromagnetic transient pro-

gram(EMTP) or fault recorder can record the prefault

and postfault voltages and currents of Buses Μ and TV.

Subtracting prefault components from postfault com-

ponents can obtain sudden-changes of fault compo-

nents. Assume that the sudden-changes of phase meas-

urements are dt7.

dUNj, and dINj , which

can be transformed into six-sequence components

according to the six-sequence-component method

••τ-

[12]:

1

:Γ - ι

Τ

•aUMj,

•<üMj,

X-dÜ

Nj,

AINl=T-'-dINj,

where ζ indicates the z-th sequence, i.e., positive, nega-

tive, and zero sequence of same-sequence and positive,

negative, and zero sequence of inverted-sequence; j in-

dicates they'-th line; Τ is transformation matrix for six-

sequence components

Every sequence system's impedance of two termi-

[ 1 2 ].

nals of the transmission line by the sudden-change se-

quence voltage and current is:

Z'

AL

7'

AU Ni

Δ /λ 7

Ο )

2.2 Modifying of sequence system impedance

The system impedance of the six-sequence network is

not completely equal to the impedance calculated from

Eq. (1) because of the characteristic of the six-

sequence network.

In the joint parallel line system, since the same-

sequence positive current doubles the current of the

line out of the joint parallel line system, the same-

sequence positive system impedance must be doubled.

The inverted-sequence negative current is the circu-

lating current of the joint parallel transmission line,

and hence, the inverted-sequence negative current is

zero for the line out of the joint parallel line system.

The inverted-sequence system impedance must be zero.

Due to the zero sequence mutual impedance be-

tween two lines, the same-sequence zero impedance is

equal to the traditional zero sequence impedance plus

triple zero sequence mutual impedance, and the in-

verted-sequence zero impedance is equal to the tradi-

tional zero sequence impedance subtracting triple zero

sequence mutual impedance. The zero sequence sys-

tem impedance must be modified by the zero sequence

mutual impedance of the line and is not definite.

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Tsinghua Science and Technology, April 2005, 10(2): 247 - 253

When six-sequence components are used to imple-

ment fault location, components except zero sequence

components are applied.

2.3 Fault location scheme

In Fig. 3, the sequence currents that are flowing in the

fault resistance can be solved from the sudden-change

sequence voltages and currents at Bus Μ (considering

the distributed capacitance by lumped parameters), as

shown in Eq. (2).

) + (L-D)Zi

(AIMl-DY,AUMl)

ι

(L-D)Yi

1

(L-D)Yf

λ ί

+ LZ, + zMSi//

1

DY,

(2)

where "//" means the parallel impedance of two

impedances.

The sequence currents flowing in the fault resistance

can be solved from the sudden-change sequence volt-

ages and currents at Bus Ν (considering the distributed

capacitance by lumped parameters), as shown in

Eq. (3).

(A^-DY^)

1

+ DZ;

1

{L-D)Yl

\ ί

+ LZ, +

ZD

(3)

where Zz is the corresponding sequence impedance

per km of the line, Yi is the corresponding sequence

admittance per km of the line (all the parameters can

be seen in Tables 1, 2, and 3), and D is the distance

from the fault point to the Bus M. If the data of two

terminals are completely synchronous, the current

flowing in the fault resistance calculated from Bus Μ

and Bus Ν must be equal. In fact, the data of two ter-

minals are not completely synchronous, so we assume

that the phase difference is δ , and then Eq. (4) exists.

4=4^

The modulus value of the two items of Eq. (4) is equal,

namely,

ί

(

Γ

zNSi Ii

{ (L - D)Y J

(4)

(AiM,-DY,AÜ

M)

1 Ί

(L-D)Y,) +

NSl

(L-D)Zi

ι Ί

+ LZ, + ( ι Ί

7 II— —

U1i )

V

(AiN,-DY,AÜ

Nl)

'( Ο

' J

ί

7

V

Ί

J

ZMS,II—

Λ

+ zz,. +

+DZ,

( 1 1

zNSi II

ι Ϊ

II— —

1i

L J J

(5)

Equation (5) is a high ordered equation about D

this equation is redundant because it is a complex

equation that can be separated into two equations. Ob-

viously, the modulus value of iFi decreases as D in-

creases; the modulus value of PF i increases as D in-

creases. Therefore, the solution of Eq. (5) must be

unique. When the step length is A d , D can be

searched in the range of 0-Z to get the least differential

value of the modulus value of two terminals of Eq. (5).

[U\ and

3 EMTP Simulation

3.1 EMTP simulation model

The fault location method is verified by electromag-

netic transient program simulation. The simulation

model of the parallel line is shown in Fig. 4.

Μ Ν

Generator

System

Fig. 4 Simulation system of joint parallel lines

3.2 Parameters of simulation model

The system frequency is 50 Hz. The impedance of

transmission line is π equivalent circuit. The resis-

tance, reactance, and capacitance of each π circuit

are shown in Tables 1, 2, and 3. System's impedance is

shown in Table 4.

Table 1 Resistance of each π

parallel transmission line

circuit of the joint

Phase

Resistance (Ω )

1A IB

1C

2A 2B

2C

1A

0.3545

IB

0.2599 0.349

1C

0.2624

0.2599 0.3545

2A

0.2619 0.2595

0.2622

0.3657

2B

0.2615 0.2593 0.2619

0.2624

0.3656

2C 0.2610 0.2588 0.2616 0.2623 0.2624 0.2656

Since this fault location method is based on the

lumped parameter, the distributed model is used in the

simulation model to examine the adaptability of the

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FAN Chunju ot al: Application of Six-Sequence Fault Components

251

Table 2 Reactance of each π

parallel transmission line

circuit of the joint

Phase

Reactance(Q)

1A IB

1C

2Α 2B

2C

1Α

3.2009

IB

1.5430 3.2067

1C 1.4840 1.5430 3.2009

2Α

1.1280 1.1848

1.2824 3.6724

2B 1.0374 1.0834 1.1492

1.5455

3.6724

2C 0.9663 1.0050 1.0540 1.3076 1.5510 3.6724

Table 3 Capacitance of each π

parallel transmission line

circuit of the joint

Phase

Capacitance (μ Ρ )

1A IB

1C

2A 2B

2C

1A 0.0476

IB -0.0088 0.0449

1C -0.0060 -0.0087 0.0479

2A -0.0008 -0.0018 -0.0025 0.0363

2B -0.0004 -0.0020 -0.0011 -0.0052 0.0361

2C -0.0003 -0.0007 -0.0006 -0.0020 -0.0053 0.0360

Table 4 System's impedance (Max load: 600 M W )

Ζ

Μ8 / Ω Z j v s / Ω

Positive

0.54+j 18.25

j90

Zero

1.85+J54

J133

method to long transmission line. In the model, the

studied line is composed by 20 π circuit sections, the

length of each π circuit is 6 km, and the total length

of the line is 120 km. In addition, in order to examine

the influence of asymmetry of the parameters on the

fault location accuracy, asymmetrical parameters of

transmission line model are employed.

3.3 Simulation result

Various types of faults in the joint parallel line have

been simulated, including all the single line faults (sin-

gle phase grounded fault, phase to phase fault, phase to

phase grounded fault, and three-phase fault), overline

fault between different phases, overline fault between

same phases, etc. Fault type classification and relative

representation are shown in Table 5.

Fault points near the bus and in the middle of the

line for all types of the line are simulated by EMTP.

To examine the influence of fault resistance on fault

location accuracy, the fault resistance is set at 10 Ω to

200 Ω for the grounded fault and 5 Ω for the phase-to-

phase fault.

Table 5 Fault type classification and relative

representation

Fault type

Representation

Ground

Single fault

line

fault

Single phase

Two phases

Three phases

1AG

1ABG

1ABCG

Non- Two phases

ground

fault

Three phases

1BC

1ABC

One phase of line 1 to

other phase of line 2

1Α 2Β

One phase of line 1 to other

two phases of line 2

1A2BC

One phase of line 1 to other

Non- three phases of line 2

1A2ABC

ground Two phases of line 1 to other

Over fault two phases of line 2

line Two phases of line 1 to other

fault three phases of line 2

1AB2BC

1AB2ABC

Same One phase

phase to Two phases

phase Three phases

1Α 2Α

1BC2BC

1ABC2ABC

Ground Fault type is same as

fault above

Add "G" after

the representa-

tion of the

above

3.3.1

The single line faults are simulated by EMTP, and the

output fault data is applied to find the fault location.

The fault location result and the corresponding location

error are shown in Table 6.

Table 6 obviously shows that the sudden-changes of

the six-sequence-component method is suitable for sin-

gle line fault and the fault location result is accurate in

various types of fault and various fault resistances.

Fault location result of single line fault

3.3.2

The overline faults are simulated by EMTP, and the

output fault data is applied to locate the fault point.

The fault location result and the corresponding location

error is shown in Table 7. Table 7 shows that the six-

sequence-component method is suitable for overline

fault and the fault location result is accurate in various

types of fault and various fault resistances.

Fault location result of overline fault