Long Transmission Lines Fault Location Based on Parameter Identification Using One-Terminal Data Bin Wang, Jiale Suonan, Heqing Liu, Guobing Song Department of Electrical Engineering Xi'an Jiaotong University Xi'an, Shaanxi, 710049, P.R.China
[email protected] Abstract—In this paper, an accurate fault location algorithm based on parameter identification using single-ended data is presented. It is inferred from the differential equations of fault state network and fault component network based on the R-L transmission lines model. And it takes the resistance and inductance of the system behind the fault point, the fault distance and fault resistance as unknown variables. These four unknown variables can be expressed by the coefficients of fault location equations and, therefore, can be obtained by solving those coefficients. When it comes to the distributed parameter transmission lines, an improved algorithm, combining filtering and compensating, is carried out to reduce the model error. Theoretical analysis and simulation results prove that this algorithm is of high accuracy and low time-consumption. Besides, it doesn’t need iteration and the solution is unique. Keywords- long lines; fault location; parameter identification; distributed parameter; compensation algorithm
I.
INTRODUCTION
With the increase of transmission lines voltage level and transmission capacity, modern power systems become increasingly large and complex. Thus the fault location of high voltage transmission lines is becoming more and more important. Finding the fault distance quickly not only contributes to timely lines repairing and stable power supply, but also plays an important role in the power system security, stability and economic operation [1]. The principle of fault location using single-ended data is easy to implement so that it received widespread attentions. Li and Chen [2] proposed a new method for the impedance fault location algorithm using one terminal data. However, this method fails in interphase short circuit fault. Wang and Dong [3] showed a new method for distance measurement while it is lacking of instantaneity. Quan and Li et al. [4] reported a algorithm based on differential equation. But their assumption, that the current flowing through the fault resistance and the zero-sequence current measured by the protection have the same phase, would cause model errors. Another method for accurate transmission lines fault location algorithm using R-L model was investigated in [5]. This method requires the initial value and iteration to solve the nonlinear equations, which calls for a nonignorable time-consumption. Kang and Suonan et al. [6] explored a principle of parameter identification algorithm in the frequency domain. This method also needs to solve the nonlinear equations. Chen and Lv et al. [7] achieved
a method based on parameter identification, but they ignored the influence of long lines’ distributed capacitance. This paper put forward an accurate single-ended fault location algorithm from R-L line model and then utilized in distributed line model. EMTP simulation results prove that this method has high accuracy and low time-consumption. Variations of source impedance, fault types and fluctuations in power frequency have been proved to have little effect on it. II.
THE DERIVATION OF FAULT LOCATION ALGORITHM
First, a transmission lines fault location algorithm of single-phase system using R-L model is presented. Then, algorithm for three-phase system will be given. Finally, algorithm dealing with distributed parameter lines model will be acquired. A. Single-phase system For the sake of simplicity, R-L model transmission lines will be used at first. According to Superposition Theorem, fault network is made of fault state network and fault component network, shown in Fig. 1. Terminal-m is the point where the relay equipment is installed. According to Fig. 1(a), based on the Kirchhoff’s current law at the fault point one obtains:
(a) Fault state network
(b) Fault component network Fig.1 Equivalent circuit of fault condition in system
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iF = im + in = ( imn + Δim ) + ( −imn + Δin ) = Δim + Δin iF = uF / RF
(1)
(2)
equation and four parameters expressed by coefficients are listed in (9) and (10).
⎡ d ( ima + K L ⋅ 3i0 ) ⎤ uma = x1 ⎢( ima + K R ⋅ 3i0 ) r1 + L1 ⎥ + dt ⎣ ⎦
So the terminal-n’s fault current component is: u Δin = F − Δim RF
⎡ d ( i + K R ⋅ 3i0 ) d 2 ( ima + K L ⋅ 3i0 ) ⎤ x 2 ⎢ ma r1 + L1 ⎥ + dt dt 2 ⎢⎣ ⎥⎦ di du x3 ⋅ im0 + x 4 ⋅ m 0 + x5 ⋅ ma dt dt
(3)
According to the fault component network in Fig. 1(b), based on the Kirchhoff’s voltage law, one obtains: d Δin Ln′ Δin Rn′ + dt d Δim −Δim ( Rm + rp ) − ( Lm + Lp ) = 0 dt
⎧ p = x1 ⎪ ⎪ R ′ = x3 ⋅ ( Lm 0 + L0 p ) − x 4 ⋅ ( Rm0 + r0 p ) n0 x 4 + x3 ⋅ x5 ⎪⎪ ⎨ L ′ = − x5 ⋅ R ′ n0 ⎪ n0 ⎪ x3 ⋅ Rn′ 0 x 4 ⋅ Rn′ 0 + ⎪ RF = 6 ( Rm 0 + r0 p + Rn′ 0 ) 6 ( Lm 0 + L0 p + Ln′ 0 ) ⎪⎩
(4)
Substitute (3) in (4), one obtains: u F Rn′ + +
du F Ln′ = Δim ( Rm + rp + Rn′ ) RF dt
d Δim ( Lm + Lp + Ln′ ) RF dt
(5)
dim Lp dt
(6)
Substitute (6) in (5) the equation can be written as: ⎛ di ⎞ di d 2i ⎛ ⎞ um = x1 ⋅ ⎜ im r + m L ⎟ + x 2 ⋅ ⎜ m r + 2m L ⎟ + ⎜ dt ⎟ dt ⎠ dt ⎝ ⎝ ⎠ d Δim du x3 ⋅ Δim + x 4 ⋅ + x5 m dt dt
(10)
Two-phase short circuit faults represent interphase fault and two-phase-earth-fault. Since they share common fault loops, they can be treated in same ways. So take interphase short circuit faults into consideration. As to two-phase short circuit faults, take mode-1 network as fault component network. The fault location equation is:
In Fig. 1(a), voltage of fault point is： u F = um − im rp −
(9)
(7)
Where x1 − x5 are coefficients of linear equation, the relationship between them and p (fault distance), RF (fault resistance), Rn′ and Ln′ (parameters of remote terminal behind fault) can be written as:
⎡ di di d 2imbc ⎤ ⎡ ⎤ umbc = x1 ⎢imbc r1 + mbc L1 ⎥ + x 2 ⎢ mbc r1 + L1 ⎥ dt dt 2 ⎣ ⎦ ⎥⎦ ⎣⎢ dt d Δimbc dumbc + x3 ⋅ Δimbc + x 4 ⋅ + x5 ⋅ dt dt
(11)
RF should be divided by 2 due to the slight change of fault loop in comparison to the single-phase system. Three-phase short circuit faults can be regarded as twophase short circuit fault, and formula (11) still makes sense.
(8)
C. Distributed parameter transmission lines Still using the algorithm based on R-L model, experiment is conduct to examine the impact of distributed parameter line model: When phase-A to earth fault occurs at 0.205s, the fault point is near the end of the lines (p=260km) and the fault resistance is 200Ω. The calculation results are shown in Fig. 2. It can be seen that this method has a serious error which is caused by distributed capacitance.
According to (7) and (8), solving the five coefficients in (7) can identify the four parameters including fault distance p.
Prefilter is employed to eliminate high-order harmonics. In addition, in order to reduce the model error, long lines compensation is exploited to compensate line on the left side of the fault point. For this purpose, it is needed to acquire an approximate location of the fault from any other less effective algorithm. Detail compensation process is described in [8].
⎧ p = x1 ⎪ ⎪ R ′ = x3 ⋅ ( Lm + Lp ) − x 4 ⋅ ( Rm + rp ) n x 4 + x3 ⋅ x5 ⎪⎪ ⎨ L ′ = − x5 ⋅ R ′ n ⎪ n ⎪ x3 ⋅ Rn′ x 4 ⋅ Rn′ + ⎪ RF = 2 ( Rm + rp + Rn′ ) 2 ( Lm + Lp + Ln′ ) ⎪⎩
B. Three-phase system Single-phase-earth-fault will be discussed first. Suppose phase A is the fault phase, using Clarke matrix to finish the phase-mode transformation and taking mode-0 network as fault component network. Derivation process is similar to that of single-phase system shown in (1)-(8). The fault location
In summary, the algorithm for the distributed parameter is: • • •
Filter the voltage and current data. Calculate the voltage and current at setting point pset . Utilize the algorithm based on R-L lines model to get the relative fault distance p′ .
The fault distance can be calculated by: p = pset + p′ . • This algorithm by its nature is an approximate algorithm. It takes the distributed parameter lines, on the right side of the fault point, as R-L model. And it runs based on an initial fault distance provided by a certain other algorithm.
experiments in cases of different source angles, different fault times and different values of fault resistance have been conduct and indicates that all these changes have no impact on fault location. Tab.1 Simulation results of the parameter identification method-I Fault distance/km
20
100
200
Fig.2 Calculated value of fault distance in distributed parameter lines model based on R-L model’s algorithm
III.
SIMULATION
280
Fault resistance /Ω
Computed location /km A_G
B_C
BC_G
ABC
10
19.990
19.919
20.036
19.918
100
19.995
20.036
20.036
19.981
200
19.996
19.913
20.036
20.073
300
19.997
18.691
20.036
19.921
10
99.983
99.967
99.975
99.967
100
99.989
99.977
99.977
99.995
200
99.984
99.995
99.976
99.977
300
99.966
100.000
99.976
99.982
10
199.976
199.968
199.973
199.969
100
199.981
199.974
199.973
199.982
200
199.988
199.974
199.974
199.978
300
199.990
199.986
199.974
199.729
10
279.971
279.967
279.971
279.967
100
279.976
279.971
279.971
279.977
200
279.977
279.978
279.971
279.958
300
279.975
279.978
279.972
279.786
EMTP and MATLAB are employed to simulate and process data, respectively. Sampled data within 10ms are used and a sliding window analysis is realized. A. Parameter identification algorithm based on R-L model— —method-I
Fig.3 Calculated value of fault distance in single-phase-to-earth fault
It is shown in figure 3 that there is a phase-A earth fault of R-L model lines occurs at 0.2s, while the fault distance is 280km and the fault resistance is 300Ω. It is proved that this algorithm can locate the fault distance rapidly and accurately. The accurate result lasts from 0.2s to about 0.35s, which can be represented by the flat part of the curve. When the lines are regarded as R-L model, the computed fault distance using method-I is shown in Tab.1, while other
Fig.4 The effect of the fault distance
Fig. 4 shows the measured fault distance when singlephase-earth-fault occurs at 20km, 100km, 200km and 280km, respectively, with the fault resistance of 200Ω. It can be concluded from the figure that durations of the accurate fault location result vary: 0.05s, 0.075s, 0.1s to 0.15s.
From the results above, they present a law: The duration of the accurate result increases with fault distance. This law is determined by the time constant of the fault loop response.
• •
Another law can also be found similarly that the duration of the accurate result decreases with the increase of the fault resistance.
• •
B. Parameter identification algorithm based on distributed parameter long line model——the parameter identification method-II Tab.2 Simulation results of method-II Fault distance
Fault resistance
/km
/Ω
60 150 240
A_G
B_C
BC_G
ABC
10
59.747
55.206
55.206
57.461
200
45.793
53.797
55.206
53.495
10
143.802
151.846
148.000
153.811
200
149.332
150.830
153.184
151.427
10
239.957
240.472
240.472
240.441
200
234.474
238.212
240.472
237.778
Tab. 2 shows the result of fault location using the parameter identification method-II. It can be seen that methodII maintains a high accuracy. Its maximum error reaches less than 1% for faults near the terminal end of lines. Tab.3 Fault distance’s impact on method-II Fault distance /km
Fault resistance is10Ω/km
Fault resistance is 200Ω/km
60
61.087
90
93.291
70.739
120
124.322
102.795
210
210.981
220.345
300
301.982
308.196
55.893
Tab. 3 reflects the impact of the fault distance’s change on fault location in case of a phase-A to earth fault. It also indicates that method-II is accurate if the fault occurs at the terminal end of lines. IV.
References [1]
Computed location//km
CONCLUSION
In this paper, a fault location algorithm applicable to long distance transmission lines is proposed. This method has salient features as follows:
It is a time-domain algorithm. This algorithm is of the high accuracy and low timeconsumption. Simulation results prove that this method has a high accuracy and isn’t affected by the variation of system operation modes. This algorithm needs an initial fault distance provided by a certain less effective algorithm.
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