A fault locating method for multi-branch hybrid transmission lines in wind farm based on redundancy parameter estimation
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Abstract
In order to solve the problem of “abandoned” wind caused by short circuit faults in a wind farm, a wind farm fault locating method based on redundancy parameter estimation is proposed. Using the characteristics of the traveling wave, transmission equations containing the position of the fault point are constructed. Parameter estimation from statistical theory is used to solve the redundant transmission equations formed by multiple measuring points to locate the faults. In addition, the bad data error detection capability of the parameter estimation is used to determine bad data and remove them. This improves locating accuracy. A length coefficient is introduced to solve the error enlargement problem caused by a transmission line sag. The proposed fault locating method can solve the fault branch misjudgment problem caused by the short circuit faults near the data measuring nodes of the wind farm based on the proposed fault interval criterion. It also avoids the requirements to the traveling wave speed of traditional methods, thus its fault location is more accurate. Its effectiveness is verified through simulations in PSCAD/EMTDC, and the results shows that it can be used in the fault locating of hybrid transmission lines.
Keywords
Transmission line Fault location Parameter estimation Wind power Least squares1 Introduction
In recent years, wind power generation is increasing year by year, and the wind power is getting much attention as a form of energy power generation. However, due to the complex structure and the bad operational condition of any transmission line in the wind farm, its faults occur frequently, which reduces the wind power generation. Therefore, it is very important to quickly find the fault point after the line failure. Because there are many branches in a wind farm transmission line, conventional fault locating methods are not practical.
The existing fault locating methods can be mainly classified into two classes: the fault analysis methods [1, 2, 3] and traveling wave methods [4, 5]. The former ones can be further subdivided into single-ended and dual-ended. The single-ended method calculates the fault distance based on voltage and current phasors at one end of the faulty line. However, its accuracy largely depends on the fault type, ground impedance and the line model parameters etc. The dual-ended method uses voltage and current phasors at both ends of the line and is usually more accurate than the single-ended method.
The traveling wave methods can also be further classified into single-ended and dual-ended. The single-ended methods use the first traveling wave and the first reflected wave from the fault point measured by oneline terminal to determine the fault location [6]. They can be further classified into A, C, E, and F fault type locators according to the generation mechanisms of their traveling waves. The dual-ended methods use the time differences between the arrivals of the first wavefronts at both terminals to achieve the fault location [7, 8]. They are classified as B and D fault type locators according to the synchronization mechanism of the line terminals. In general, the locating accuracy of the traveling wave methods is better than that of fault analysis methods.
The above methods are commonly used in end-to-end or simple structured transmission lines. Some new algorithms have been proposed for multi-branch hybrid transmission lines: ① improved methods based on traditional methods [9, 10]; ② fault locating methods based on pattern recognition techniques such as Artificial Neural Networks and K-means clustering algorithms [11]; and ③ a method based on dynamic state estimation is proposed [12, 13]. The principle of the first type of methods is first determining the fault branch and then locating the fault point based on the determined fault branch by the traditional method. The second type of methods often require a large quantity of fault data to constitute a database, which contains historical fault data of a real system or those derived from an accurate simulation system. The third type of methods has reference value in fault locating study. However, it did not consider the hybridity of overhead lines and cables. Although the cables in a wind farm transmission line are short, they can not be ignored, which can be demonstrated by Table A1 in Appendix A.
Aiming at the multiple branches and hybrid characteristics of the wind farm transmission lines, a redundancy parameter estimation method to locate fault points is proposed. Firstly, different from the traditional traveling wave method, this proposed method constructs the transmission equations based on the grid synchronization information. In addition, it comprehensively considers the hybridity of overhead lines and cables, and uses statistical methods to estimate the parameters to locate the fault point. Secondly, the length coefficient, which is the ratio of the fault distance and the total length of the fault branch, is used to indirectly find the position of the fault point on the fault branch. It can avoid the amplification of the locating error caused by the line length changes caused by the seasonal sag variations. Furthermore, as the bad measured data may cause large fault locating error, a bad data detecting algorithm is used. Finally, PSCAD/EMTDC simulation results verify the feasibility of the proposed method.
The proposed method has the following characteristics. ① It realizes the fault location on hybrid transmission lines including overhead and cable segments; ② Compared with the traveling wave method, it does not require the calculation of traveling wave velocity which easily causes a locating error; ③ It takes the line sag effect into the fault locating model; ④ It constructs a fault locating model based on multiple measuring points which are adopted to do parameter estimation to minimize measurement errors; ⑤ The bad data detecting algorithm is used to ensure the correctness of the original data and locating results. The method for the parameter estimation in this paper is completely different with Reference [12] which uses the SCPQDM dynamic model to simulate the power grid and uses a dynamic state estimation to achieve fault location. Reference [12] is suitable for the power grids of lines of two ends and three ends, the proposed method can be used to locate the faults in the complex grids of multi-branch lines and transmission lines containing overhead and cable segments. It can consider the line sag effect and find the bad data to improve the fault locating results.
2 Fault locating method
2.1 Wind farm electric system model
- 1)
Overhead and cable segments are hybridly connected in a wind farm transmission line.
- 2)
The distance between adjacent wind turbines is short, ranging from a few hundred meters to a few kilometers.
- 3)
From Fig. 1b, it can be seen that the wind farm is a typical radial network and a large number of wind turbines are connected. In addition, the total length of a collecting power line is usually no more than 20 km.
The above characteristics of the wind farm lead to difficulty in finding fault points in a wind farm line by the conventional locating algorithms. In addition, the failure near the node are also difficult to locate by the traditional methods.
Capability comparison of fault locating methods
Method | Multi-branch | Hybrid lines | Sag effect | Misjudgement near nodes |
---|---|---|---|---|
M1 | ○● | ○ | ○ | ○ |
M2 | ○● | ○ | ○ | ○● |
M3 | ● | ○ | ○ | ○● |
M4 | ● | ● | ● | ● |
2.2 Construction of transmission line equations
The ratio of the number of independent measurements to the number of independent variables of x is defined as redundancy, then (4) is a set of equations with a high degree of redundancy which are overdetermined equations. The traveling wave velocity and the position of the fault can be obtained through solving (5).
2.3 Solving transmission equations through parameter estimation
Although the equations in (4) or (5) can be used to obtain the independent variables, the solution is not as accurate as solving the whole overdetermined equations in (5). Because making full use of all the transmission equations can eliminate measured data errors, a statistical parameter estimation method based on redundancy is proposed to cope with the situation where the measured data have a high degree of redundancy. It can reduce the locating error and be realized through the parameter estimation algorithm [14]. The formula (5) has sufficient redundancy, which is discussed Section 2.2, to satisfy the preconditions of the statistical parameter estimation method.
Equation (8) is an n-dimensional equations that contains n independent variables. we can obtain the best estimate x′ of x without iterative calculation by solving (8). In the case of measured data without error, the result of the above process is the final locating result. However, it is unavoidable that the measured data in a real system is erroneous. In this case, the fault locating result is deviated or even mistaken. Therefore, the bad data of the sample need to be detected and removed to ensure the reliability of the data after the above model is solved. This paper uses the confidence interval of the sample residual as the judgment of the bad data. The specific judging operations are stated as follows. Firstly, the sample residual confidence interval graph is drawn. Secondly, if the confidence interval for all sample residuals contains the zero value, the conclusion is that there are no bad data in the measured data, indicating that the model’s locating results are reliable. Thirdly, otherwise, the data will be removed as an outlier, thus the corresponding equation in (4) or (5) should be deleted, and then use the parameter estimation method to solve the updated (5) again.
2.4 Bad data detection
In order to ensure the correctness of the data, the transmission equations are solved to find and eliminate the bad data in the measured data by the parameter estimation equations. In the theory of parameter estimation, the measured data are only in a certain interval centering on the estimated values of the measured data at a certain confidence level. The intervals are called the confidence intervals. They can measure the credibility of the measured data. The difference between the measured data and their estimated values are called the residuals. The confidence intervals of the residuals are used to judge the bad data. Bad data detection can be easily achieved by calling the Regress function in MATLAB software. By plotting the residual confidence intervals, of all measuring points, the measuring points out of the intervals are regarded as the bad data.
2.5 Parameter estimation error analysis
- 1)
The mean of the estimated error of the unknown x′ is:
- 2)
In engineering, the covariance matrix of the estimated error is often used to measure the difference between an estimated value and its true value. The covariance matrix is shown in (11):
The diagonal elements of A^{−1} decrease with the increase of the number of the measurement quantity, which means that the more the measurement quantity, the more accurate the estimated values. This proves that the premise of better parameter estimation is under a high enough redundancy.
2.6 Feasibility analysis of length coefficient k
In the conventional methods, the length coefficient k is introduced to reduce the fault locating error caused by the sag change and other factors, which requires that the theoretical line length should not appear in the calculating equation. Compared with the conventional methods, the transmission equations in this paper still contains the theoretical line length, which seems irrationality. The following is used to show the rationality of this methodology.
The sag effect causes t_{Ap} and t_{Ap}′ to be unequal, but the parameter estimation in this research still uses the theoretical length of lines, which results in calculation bias. Comparing (13) and (14), it can be seen that the sag effect changes the calculated value of the traveling wave velocity without affecting the length factor k and the fault time moment t_{0}. In other words, this method obtains the exact k at the expense of imprecise wave velocity results.
2.7 Measuring point configuration in a line
When the error δ is taken into account, the cross solution of the system of equations about s_{1} and s_{2} is shown in the shaded portion shown in Fig. 3b assuming t = 0. If one of the vectors is replaced by the vector s_{3} in Fig. 3a, that is, the orthogonal vector, the shadow portion shown in Fig. 3c is the smallest. This shows that the points that can constitute the most orthogonal vector are preferable to be selected as the final measuring points.
Although the orthogonal vector is ideal, the actual line terminals of measuring points are not constructed according to the orthogonal vector form. Therefore, the terminal which has the vector closest to the orthogonal vector is used as a measuring point. The method to measure the similarity of two vectors can be found in [15].
3 Fault interval determination
The fault locating method based on the parameter estimation needs to first determine the interval where the fault is located in the red area or in the blue area of the network shown in Fig. 4.
3.1 Fault interval criterion
First, the theoretical time required for the first wavefront transmission in each section can be obtained and a theoretical time difference matrix Δt is constructed according to Fig. 4. Δt is a matrix of 3 × r order, where r is the number of collecting power lines in the wind farm. The matrix consists of the following parts: ① The elements of the first row are the theoretical traveling wave time differences between the terminal measuring points and the central measuring points; ② The elements of the second row are the theoretical traveling wave time differences between the middle measuring points and the central measuring points; ③ The elements of the third row are the time difference between the terminal measuring point and the middle measuring point.
Then, the actual time difference matrix Δt′ is established according to the actual measured time at each measuring point and the difference matrix Δ is obtained as the difference between Δt and Δt′. Since Δt uses the theoretical wave velocity, the value of the differential matrix Δ in the non-faulty interval is not zero and there will be a slight deviation. Therefore, it is necessary to set a threshold (the value of which is determined based on the maximum locating error based on the theoretical wave velocity) so that the element is set to zero when the value of the difference matrix element is lower than the threshold. The first row of the differential matrix Δ detects on which collecting power line a fault has occurred, the second row detects whether a fault occurs in the first half of the collecting power line, and the third row detects whether a fault occurs in the second half of the collecting power line.
In the first row of Δ, the nonzero element is only the element corresponding to L_{4}, which indicates that short-circuit fault occurs in L_{4} and the corresponding element in the second row L_{4} is zero, indicating that no short-circuit fault occurs in the first half of the L_{4}. The L_{4} corresponding element in the third row is not zero, indicating that a short-circuit fault occurred in the second half of the L_{4}.
At this point, it is not possible to determine where the failure occurred based on (18).
3.2 Criterion for failure near nodes
The measuring points installed at the nodes can be divided into three types: terminal measuring point, middle measuring point, and central measuring point which is at bus node. Among them, since the terminal measuring point can be intuitively judged by the first wavefront arrival time, this kind of fault situation is easy to judge and need not to be considered in this research. For the middle measuring points (non-terminal points), considering of the simplicity of fault interval criterion, the transmission equation of the measuring point is artificially deleted to eliminate the possibility of misjudgment when a short-circuit fault occurs near a middle node. When a fault occurs near the center node, the criterion cannot be directly obtained because it connects a plurality of the collecting power lines. However, the criterion can be obtained by combining this with the parameter estimation algorithm. Assuming that the short-circuit fault occurs on each of the collecting power lines of wind farm bus in turn, the parameter estimation method is applied to the analyzed line to solve the corresponding locating results.
Fault interval criterion for fault around central node
No | Range of k | ||||
---|---|---|---|---|---|
L _{1} | L _{2} | L _{3} | L _{4} | L _{5} | |
1 | (0, r/l_{1}) | ✗ | ✗ | ✗ | ✗ |
2 | ✗ | (0, r/l_{2}) | ✗ | ✗ | ✗ |
3 | ✗ | ✗ | (0, r/l_{3}) | ✗ | ✗ |
4 | ✗ | ✗ | ✗ | (0, r/l_{4}) | ✗ |
5 | ✗ | ✗ | ✗ | ✗ | (0, r/l_{5}) |
Summarizing the contents of Section 2 and Section 3, we can get the algorithm flowchart of the proposed method. See Fig. A1 of Appendix A.
4 Simulation result and discussion
4.1 Simulation model
We install two measuring points on each collecting power line. In addition, these measuring points are numbered from left to right and from top to bottom according to the transmission line number. Furthermore, a measuring point is installed on the 35 kV bus. In summary, the entire simulation system contains 11 measuring points. We verify the feasibility of the algorithm in the following aspects: ① Demonstration of fault locating algorithm; ② Identification of bad data in measured data; ③ Fault locating results in different fault positions; ④ Identify the fault interval when a fault occurs near the node (or traveling wave measuring point).
Given that most faults in the grid are LG faults, LG faults are more representative. However, the fault locating calculation process of other faults, such as LL faults, is the same as for the LG fault. In addition, results for other faults types are similar. Due to space limitations, we here only present results for the LG fault.
4.2 Fault locating simulation and results analysis
4.2.1 Algorithm demonstration
- 1)
Interval identification
Traveling wave point information
MP | t (ms) | MP | t (ms) |
---|---|---|---|
1 | 30.003 | 7 | 30.044 |
2 | 30.032 | 8 | 30.058 |
3 | 30.048 | 9 | 30.056 |
4 | 30.066 | 10 | 30.082 |
5 | 30.052 | 11 | 30.028 |
6 | 30.074 |
- 2)
Fault location
4.2.2 Identification of bad data in measured data
The above results show that the algorithm can identify bad data in the measurement data. In addition, it can still correctly locate the fault point and have high locating accuracy after rejecting bad data.
4.2.3 Fault locating results for different fault positions
4.2.4 Fault section identification when a fault occurs near the center node
The k of the fault interval criterion in L_{1}-L_{5} and the locating result when a fault occurs on the L_{1}
No | Range of k | Calculated k of L_{1}-L_{5} | ||||
---|---|---|---|---|---|---|
L _{1} | L _{2} | L _{3} | L _{4} | L _{5} | ||
1 | (0, 0.11) | ✗ | ✗ | ✗ | ✗ | 0.070 |
2 | ✗ | (0, 0.20) | ✗ | ✗ | ✗ | −0.689 |
3 | ✗ | ✗ | (0, 0.17) | ✗ | ✗ | −0.499 |
4 | ✗✗ | ✗ | ✗ | (0, 0.33) | ✗ | −1.222 |
5 | ✗ | ✗ | ✗✗ | ✗ | (0, 0.17) | −0.819 |
4.3 Fault locating under sag effect
Fault locating results under sag effect of lines
Sag factor (%) | Real value k | Failure point (km) | L_{1} (km) | Method of this paper k | Method error in this paper (km) | Dual-ended method (km) | Dual-ended method error (km) |
---|---|---|---|---|---|---|---|
+10 | 0.25 | 5.5 | 19.8 | 0.244 | 0.117 | 5.031 | 0.531 |
0.50 | 11.0 | 0.503 | 0.056 | 9.960 | 0.964 | ||
0.75 | 16.5 | 0.751 | 0.011 | 12.189 | 1.311 | ||
−10 | 0.25 | 4.5 | 16.2 | 0.252 | 0.038 | 5.093 | 0.593 |
0.50 | 9.0 | 0.506 | 0.106 | 7.858 | 1.142 | ||
0.75 | 13.5 | 0.756 | 0.108 | 14.539 | 1.039 |
Table 5 shows that if the line sag effect is considered, the locating errors are not substantially affected, whereas the conventional dual-ended traveling wave method has a large error.
5 Conclusion
- 1)
The proposed transmission equations and the optimization of the redundancy parameter estimation can ensure good fault locating accuracy for short lines and hybrid lines consisting of overhead wires and cables in a wind farm. In addition, the bad data detecting capability of the method enhances the reliability of the measured data. Through PSCAD/EMTDC simulations, the feasibility of this method in wind farm fault locating has been verified.
- 2)
The method does not require the traveling wave velocity. This avoids locating errors caused by the calculating errors of the traveling wave velocity.
- 3)
In order to solve the problem of misjudgment caused by faults near the node, a criterion for effectively determining the faulty interval is proposed. The feasibility of the algorithm is verified by PSCAD/EMTDC simulations.
- 4)
The introduction of the length coefficient k solves the problem of poor locating accuracy or misjudgment caused by line sag effects and the correctness of the algorithm has also been verified through simulations.
- 5)
The comparison of fault locating results between this method and the dual-ended traveling wave method show that this method is more feasible in a multi-branch line.
- 6)
Although this paper studies the fault locating of transmission lines in a wind farm, this method is also applicable to a distribution grids with lines of multi-branch that may be a mix of overhead wires and cables. Because of paper space limitation, the relative simulations and their locating results are not described.
Notes
Acknowledgements
This work was supported in part by National Natural Science Foundation of China (No. 51677072).
References
- [1]Li YW, Nejabatkhah F (2014) Overview of control, integration and energy management of microgrids. J Mod Power Syst Clean Energy 2(3):212–222CrossRefGoogle Scholar
- [2]Xu HH, Hui ZB, Lai LZ (2002) A novel principle of single-ended fault location technique for EHV. IEEE Power Eng Rev 22(11):61 Google Scholar
- [3]Weng J, Liu D, Luo N et al (2015) Distributed processing based fault location, isolation, and service restoration method for active distribution network. J Mod Power Syst Clean Energy 3(4):494–503CrossRefGoogle Scholar
- [4]Xu F, Dong X, Wang B et al (2015) Self-adapted single-ended travelling wave fault location algorithm considering transfer characteristics of the secondary circuit. IET Gener Transm Distrib 9(14):1913–1921CrossRefGoogle Scholar
- [5]Lee JW, Kim WK, Han J et al (2016) Fault area estimation using traveling wave for wide area protection. J Mod Power Syst Clean Energy 4(3):478–486CrossRefGoogle Scholar
- [6]Azizi S, Sanaye-Pasand M, Abedini M et al (2014) A traveling wave-based methodology for wide-area fault location in multiterminal DC systems. IEEE Trans Power Deliv 29(6):2552–2560CrossRefGoogle Scholar
- [7]Esau Z, Jayaweera D (2014) Reliability assessment in active distribution networks with detailed effects of PV systems. J Mod Power Syst Clean Energy 2(1):59–68CrossRefGoogle Scholar
- [8]Jafarian P, Sanaye-Pasand M (2010) A traveling wave based protection technique using wavelet/PCA analysis. IEEE Trans Power Deliv 25(2):588–599CrossRefGoogle Scholar
- [9]Das S, Santoso S, Gaikwad A et al (2014) Impedance-based fault location in transmission networks: theory and application. IEEE Access 2:537–557CrossRefGoogle Scholar
- [10]Phadke AG, Wall P, Ding L et al (2016) Improving the performance of power system protection using wide area monitoring systems. J Mod Power Syst Clean Energy 4(3):319–331CrossRefGoogle Scholar
- [11]Mora-Flórez J, Cormane-Angarita J, Ordóñez-Plata G (2009) k-means algorithm and mixture distributions for locating faults in power systems. Electr Power Syst Res 79(5):714–721CrossRefGoogle Scholar
- [12]Liu Y, Meliopoulos APS, Tan Z et al (2017) Dynamic state estimation-based fault locating on transmission lines. IET Gener Transm Distrib 11(17):4184–4192CrossRefGoogle Scholar
- [13]Wu ZJ, Xu JJ, Yu XH et al (2017) Review on state estimation technique of active distribution network. Autom Electr Power Syst 41(13):182–191Google Scholar
- [14]Wang Y, Chao LU, Zhu L et al (2016) Comprehensive modeling and parameter identification of wind farms based on wide-area measurement systems. J Mod Power Syst Clean Energy 4(3):383–393MathSciNetCrossRefGoogle Scholar
- [15]Zhang Y, Liu YD, Ji Z (2009) Vector similarity measurement method. Techn Acoust 28(4):532–536Google Scholar
- [16]Suonan JL, Zhang YN, Jun Q et al (2006) Time domain fault location method based on transmission line parameter identification using two terminals data. Power Syst Technol 30(8):65–70Google Scholar
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