Estimation of Fault Resistance from Disturbance Records

Qingxin (Charles) Shi, Bing (Michael) Xia PDS Lab, Department of Electrical and Computer Engineering, University of Alberta

Introduction

The fault resistance that happens in a short circuit has negative impact on the performance of transmission line protection schemes. Aims of fault resistance estimation Improve the protection relay behavior during faults; Locate the fault accurately. In an line-to-ground fault, the fault resistance RF consists of three parts (shown in the below figure).

Fault Location and Fault Resistance Estimation

Transient Modeling of Electric Arc

Simulation Result

Conclusion

Case Fault

Simulation Estimation

m RF m RF ε = | RF(real)-

RF(estimate) |

Error = 100*

ε / RF(real)

1 A-G 0.5 10 0.499 10 0.00 0.00%

2 A-G 0.35 20 0.349 19.99 0.01 0.05%

3 A-G 0.67 8 0.699 7.86 0.14 1.75%

4 A-G 0.18 5 0.18 5.05 0.05 1.00%

5 B-G 0.5 10 0.498 10.00 0.00 0.00%

6 B-G 0.4 12 0.40 11.90 0.10 0.83%

7 C-G 0.82 15 0.819 14.94 0.06 0.40%

8 C-G 0.55 9 0.55 9.01 0.01 0.11%

00( ) ( ) sgn( )

( )a a b b a

b

Iu t U U x R i t i

i t

There have been many algorithms for fault location and fault resistance estimation utilizing two-end or three-end data. Let’s assume a three-phase-to-ground fault occurs in a double-machine system. The fault recording equipment provides distinct data, and the voltage and current phasors are some of them. As the location of the fault point is unknown, we have two variables in the equation, which means the calculation of fault location requires data from both the sending end and the receive end of the line.

S FL F

S S

V IZ mZ R

I I

The method can also be applied to the unsymmetrical fault. Consider a single-phase-to-ground fault, the negative sequence fault voltages are:

2 2 2 2

2 2 2 2(1 )

F S S L

F R R L

V I Z mZ

V I Z m Z

From the above mathematical derivation, we avoid alignment of data sets in substations S and R. The solution for m is a quadratic equation of the form:

2 0Am Bm C

When the fault position m is known, the fault resistance can be solved.

2 22 2 2 23 3 2 2 0ORR g h I R pg qh p q

Traditional fault location algorithms usually assumed that the fault resistance is constant. However, a short circuit fault often occurs with transient electric arc, which is equivalent to a time-varying resistance. The arc resistance can affect the accuracy of fault location. The modeling of arc is mainly based on the measured data obtained in field tests. Below is a widely used transient arc voltage model – Distorted rectangular model.

Field test circuit Arc voltage and arc current Line terminal voltage

The observed waveform shows that the arc current is almost sinusoidal, while the arc voltage is a distorted rectangular form. The transient arc voltage can be approximated as:

0 0

0

( )( )

( ) ( )

a

b

a a

I i t Ii t

i t i t I

where

Where 𝑈𝑎, 𝑈𝑏, 𝐼0 and 𝑅𝛿 are empirical parameters. They are related to the length of the arc. And 𝜉 is random noise.

B. Result Using EMTP Software (with Electric Arc) The transient arc parameters are simulated with PSCAD/EMTDC. The result Shows that the arc voltage has a distorted rectangular form, while arc current is approximately sinusoidal.

Transient arc resistance Arc voltage and arc current Static arc resistance

Where parameters A, B, C and g, h, p, q are calculated from the local measurement data – voltage, current and line impedance.

In most cases, short circuits fault are followed with an electric arc, so the arc voltage arising at the fault point disturbs the impedance evaluation. For the remote faults on overhead lines, the arc voltage can sometimes be neglected because it is much smaller than the line measured voltage. However, this is not the case for close-in fault. In this project, the proposed algorithm can minimize the impact of arc resistance on the fault estimation, because it uses the voltage and current phasors.

Among them, the modeling of dynamic arc resistance is the most difficult work due to its stochastic and non-linear characteristic.

(1 )

F S L S

F R L R

V V mZ I

V V m Z I

S R L R

L S R

V V Z Im

Z I I

Therefore the fault location is:

The impedance measured at one end is as follow:

Substitute m into the formula above, RF can be solved.

A. Result Using Short-Circuit Software (without Electric Arc) A selection of 132 kV power system is simulated with ASPEN software. The table shows results for 3 faults, in distinct positions and with different fault resistance.