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.
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