A Novel Fault-Location Method for Radial Distribution Systems

Ye Lei, You Dahai, Yin Xianggen, Tang Jinrui, Li Baolei, Yin Yuan

State Key Laboratory of Advanced Electromagnetic Engineering and Technology Huazhong University of Science and Technology

Wuhan, China

Abstract- This paper presents a novel fault-location method for

distribution systems based on direct circuit analysis. In order to

provide a unique fault distance result, an algorithm is proposed to

by an effective iterative and traversal procedure and is applicable

for all types of faults. The method is one-end impedance based

method using the substation voltage and current quantities. The

fault-location equations use line impedance matrix, load impedance

matrix and fault admittance matrix. The method is developed in

phasor domain, assuming that the topology of distribution network

and the fault type are known. Simulation studies have demonstrated

that the proposed method has high accuracy in radial distribution

system.

Keywords–fault location, distribution systems, fault admittance

matrix, iterative method, traversal method

I. INTRODUCTION

In electric power systems, distribution networks are susceptible to faults. Prompt and accurate fault location can

reduce outage time, save losses and improve power supply reliability and continuity. But distribution systems have several

laterals/sublaterals, nonsymmetrical lines, intermediate loads and time-varying loads and always are in unbalanced operation,

which make fault location in distribution systems more

challenging[1][2]. There are various fault location techniques in the past. These

methods can be divided into two main types by locating manner,

This work was supported by GE (China) Research and Development Center

Co., Ltd..

impedance based method and traveling-wave method [3][4].

Because of the particular characteristics of distribution network, traveling-wave phenomenon in distribution network is complex,

which makes it is difficult to obtain wanted information in fault traveling wave. The traveling-wave method has rough

fault-location accuracy. Recent researches [5] ~ [9] on impedance based methods have developed some effective

techniques to improve the accuracy of fault location in distribution lines.

An approach using direct circuit analysis(DCA) is discussed in [5] and [6], which provide a fault-location equation for

phase-to-ground fault, and consider intermediate loads in radial distribution system. The method based on DCA provides

accuracy result in nonsymmetrical or unbalanced distribution systems. Reference [7] proposes a fault-location equation for

phase-to-phase fault later, which takes load variation into consideration. Iterative methods have been used for fault location

in [8] and [9]. Reference [9] proposes and discusses an extended fault-location formulation to be used in general distribution

systems. The method is based on DCA and fundamental quantities, which is capable of locating faults in distribution

systems with intermediate loads and laterals/sublaterals. But iterative methods to converge at a wrong result which is

influenced by initial iteration value. In this paper, a generalized fault location formulation based on

DCA is suggested. Through utilizing fault admittance matrix, a

fault-location formulation has been derived by Kirchhoff formula, which is effective for distribution systems. And the paper

proposes a novel fault-location algorithm to solve the fake root

978-1-4577-0547-2/12/$31.00 ©2012 IEEE

problem of iterative method. Section II discusses the details of generalized fault-location

formulation and algorithm. Section III describes the details of simulations, followed by the conclusion.

II. IMPEDANCE BASED FAULT LOCATION

In the following subsection, a detailed derivation of fault-location formulation is given. Then, the paper provides the

fault-location algorithm.

A. Generalized fault-location formulation

Fig. 1. Three-phase system.

Consider the three-phase system with a fault in Fig. 1, the following equations are obtained by Kirchhoff law.

(1 ) ( )s l s l r LV x Z I xZ Z I= − + + (1)

1(1 )s l s f fV x Z I Y I−= − + (2)

s f LI I I= + (3)

where

[ ]Ts sa sb scV V V V= ; phase voltage vector at substation end;

T

f fa fb fcV V V V⎡ ⎤= ⎣ ⎦ ; phase voltage vector at fault point;

[ ]Ts sa sb scI I I I= ; phase current vector at substation end;

[ ]TL La Lb LcI I I I= is phase current vector after the fault

point;

T

f fa fb fcI I I I⎡ ⎤= ⎣ ⎦ ; fault current vector ;

laa lab lac

l lab lbb lbc

lac lbc lcc

Z Z ZZ Z Z Z

Z Z Z

⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠

; line impedance matrix;

raa rab rac

r rab rbb rbc

rac rbc rcc

Z Z ZZ Z Z Z

Z Z Z

⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠

is the load impedance matrix;

fY ; the fault admittance matrix;

x is the fault distance from the other end.

By eliminating phase current vector fI and LI in (1) ~ (3),

the generalized fault-location formulation is derivate as (4)

( ) ( ) [(1 ) ]s l r s l r f l s sV Z Z I xZ Z Y x Z I V− + = + − − (4)

Formulation (4) has three equations in three phases. Each equation in fault phase can be used for fault location.

B. Fault admittance matrices

Fig. 2. Simple equivalent circuits for other faults: (a) LG fault, (b) LL fault, (c)

LLG fault, (d) LLL fault, (e) LLLG fault

As Fig. 2 shows, the fault admittance matrices of all faults are as follow:

1 0 0

0 0 00 0 0

R f

fY

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

; the fault admittance matrix of LG fault

1 1 0

1 1 0

0 0 0

R Rf f

R Rf fY

f

⎡ ⎤−⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥−⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

= ; the fault admittance matrix of LL fault

2 1 0

1 2 0

0 0 0

R Rf f

f R Rf fY

−

−

⎡ ⎤⎢ ⎥

= ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

; the fault admittance matrix of LLG fault

2 1 1

1 2 1

1 1 2

R R Rf f f

f R R Rf f f

R R Rf f f

Y

− −

− −

− −

⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

; the fault admittance matrix of LLL fault

3 1 1

1 3 1

1 1 3

R R Rf f f

f R R Rf f f

R R Rf f f

Y

− −

− −

− −

⎡ ⎤⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

; the fault admittance matrix of LLLG

fault. The coefficients in formulation (4) can be calculated by the

voltage and current data in substation end and relevant impedance data.

C. Fault-location algorithm

In the three-phase formulation (4), three equations can be obtained. These equations which are all in complex number

form provide real part equations and imaginary part equations. For specific fault, each equation in fault phase is available to

locate fault. The unknown parameters are fault resistances and fault distance. The number of equations which can be used to

locate fault point is adequate to obtain a solution by Newton-Raphson iterative method.

The fault location procedure is as follow: Step 1) according to a specific fault, calculate the Jacobian

matrix of fault-location equations. Step 2) choose initial fault resistance value, and initial fault

distance is 0. Step 3) obtain a solution by iterative procedure. The result

must be in the limitation condition of0 1

0f

xR< <⎧⎪

⎨ >⎪⎩. Otherwise,

back to Step 2), and change the initial fault distance with a small increment.

Step 4) if there is not available result, the fault may be out of the section.

The proposed algorithm above is an iterative and traversal algorithm. Iterative method is fast to solve nonlinear equations,

but it is susceptible by the initial value and may converge at false root. Trough traversing all value of fault distance, the

algorithm eliminates the effect of initial value. The proposed algorithm is a fault-location method for a single

section, but it is also practical for fault location in general feeder by substituting the proposed single section fault-location

algorithm to the same part of fault-location method in reference [9].

III. SIMULATION STUDY

To validate the proposed method, an unbalanced three-phase system as Fig. 1 is modeled by PSCAD.

The percentage error is calculated by (21) | |

% 100%x xestimated actualError

l

−= × (21)

where

estimatedx estimated fault distance;

actualx actual fault distance;

l total line length. This simulation considers 10 different fault distances (varying

0.1~0.9 p.u.) and 4 different fault resistances (0, 20Ω, 50Ω and 100Ω). The simulation does not consider the parallel parameter of line.

The simulation results in Fig. 3 show that the proposed method has a high accuracy eliminating the effect of unbalance

system and false root.

(a)

(b)

(c)

(d)

(e) Fig. 3. Simulation results of case 1 for five fault types. (a) LG fault; (b) LL fault;

(c) LLG fault; (d) LLL fault; (e) LLLG fault.

The simulation results show that the estimated fault distance is

unique and accurate. The results show that the fault-location method is not affected by fault resistance, fault distance and

fault types.

IV. CONCLUSION

This paper proposes and discusses a novel fault-location

method in distribution systems. The method is based on DCA and fundamental quantities and has good accuracy in unbalance

distribution systems. Furthermore, the method is suitable for all types of fault and general feeders and overcomes the defect of

iterative method, being capable to pinpoint a unique and accurate fault location. Analysis of the fault-location algorithm in general

distribution network will be furthered through future work.

REFERENCES

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