1 Introduction
The safety and stability of the power system operation is the premise to ensure the development of related industries, showing a profound impact on the development of the national economy [1, 2]. For power system, transmission lines, which transmit the electric energy, is one of the most important components. Its fault can influence the power system operation significantly. Power system collapse accidents in domestic and foreign regions are often caused by failure of transmission lines [3–5]. Therefore, it is essential to diagnose faults of transmission lines [6, 7].
T-connection transmission line with high power and heavy load is widely used in high-voltage or ultra-high-voltage power transmission networks to connect the large systems and power plants because of unique wiring characteristics. Large-scale blackouts are often caused by the fault on these lines, causing economic loss. It is necessary to diagnose the locations of faults timely and accurately, and then eliminate the faults [8].
At present, there are two main kinds of methods based on power frequency and transient frequency to diagnose the faults of T-connection transmission line. For power frequency diagnostic method, it relies on the measured information including voltage power frequency, current power frequency and distribution parament of the protection units near the busbar internal and external of T-connection transmission. Sonan et al. [9] analyses the ratio of respective fault component and vector sums of the three-terminal voltage and current to identify the faults. Gao et al. [10] identify the faults based on the sum of the three-terminal current fault components of the vector difference between the maximum current in the three-terminal current fault component and the sum of the currents at the other two. However, the sensitivity and reliability of this method could be influenced by the choice of braking coefficient. To solve this problem, Li et al. [11] uses the maximum current in the three-terminal fault current component of the T-connection transmission line combined with the sum of the currents at the other two and the cosine angle to identify the faults. According to Reference [10, 11], although Wang et al. [12] established a comprehensive criterion to identify of faults inside and outside the PV T-connection high-voltage distribution network area, this paper still not analyses the performance of the algorithm. Nayak et al. [13] calculates the positive sequence voltage at the T node at the three terminals, and compare the maximum amplitude g1 of the positive sequence voltage superimposed component of the T node and the maximum amplitude g2 of the positive sequence voltage superimposed component of the three terminals to identifies faults. It is diagnosed as an in-zone failure occurred when g1 > g2; or as an out-of-zone failure occurred when g1 < g2. Gaur et al. [14] relies on the maximum value of the positive sequence superimposed voltage of the T node calculated by the three terminals of the T-connection transmission line to identify whether a fault occurs. Then proposes the phase θ between the positive sequence superimposed voltage and current at a specific terminal to identify the fault inside and outside the protection zone. When θ ∈ (0°, 180°), it is diagnosed as a failure occurred in external zone; when θ ∈ (180°, 360°), it is diagnosed as a failure occurred in the internal zone. Zheng et al. [15] uses information such as voltage amplitude difference of three sides of T-connection transmission line, measured impedance characteristics, combined voltage amplitude difference and the auxiliary criterion of adaptive distance to identify faults. On the basis of the original current longitudinal differences, Liu et al. [16] establishes auxiliary criterion to identify the faults in the zone of T-type distributed power supply applied in the power distribution network at both ends. But this only relies on the these information including original voltage and current transformers at both ends of the high-voltage transmission, the positive-sequence compensation voltage difference at both ends of the line, and the phase relationship between the positive-sequence compensation voltage and the positive-sequence differential current. And this algorithm ignores the influence of transient control of distributed power supply. Wang et al. [17] adopts a new current differential protection method based on current research results of current differential protection of double-ended lines. This paper proposed an identification method for T-connection transmission line based on distributed parameter model. To conclude, the fault diagnosis method based on power frequency cannot realize the rapid identification due to the long calculation data window. And its sensitivity of fault diagnosis is also easily affected by other variables.
As for methods based on transient quantity, the voltage (current) traveling wave information were processed to identify faults. Kumar et al. [18] estimates the instantaneous value of voltage and current signal phasor by providing the voltage and current signals measured at the relay end of T-connection transmission line to the second-order Taylor Kalman Fourier filter, and then identify faults inside and outside the protection zone by calculating the positive sequence impedance obtained through the instantaneous voltage and current phasor information. Zheng et al. [19] used the cosine similarity of the three-terminal transient currents of T-connected transmission line to establish the criterion to identify faults inside and outside the zone. Although wavelet transform is applied to fault identification of T-shaped transmission line in the literature [20, 21], high-frequency noise signals will affect the effect of fault identification. Bhalja et al. [20] uses bior3.1 wavelet to process the original current signal of the three terminals of the T-connection transmission line, and compares the relationship between the three-terminal operating current and suppression current then to identify. Eissa et al. [21] compares the fault current polarity detected at each end of the T-connection transmission line by applying Haar wavelet function to identify the faults inside and outside the zone. In conclusion, the fault diagnosis method based on transient quantity has attracted extensive attention because it can realize fast protection action. But most existing methods do not further analyze the performance of algorithm, and the accuracy of fault diagnosis needs to be improved.
In recent years, the intelligent fault diagnosis method of power system has been extensively studied, but fewer involved the research of intelligent fault diagnosis method applied to T-connection transmission line. Random forest is a self-supervised ensemble learning algorithm, which can accurately predict a single problem through the integration of multiple trees. It has excellent performance in training speed, generalization ability and dealing with unbalanced data sets. In order to overcome the shortcomings of the traditional T-connection transmission line fault identification algorithm, our paper draws on the research ideas of reference [22–24], analyzes the electrical characteristics of the T-connection transmission line fault, and conducts relevant research on its fault diagnosis method. A new fault identification method for T-connection transmission line based on multi-scale traveling wave reactive power and random forest is proposed. The algorithm calculates the mean sum of the initial traveling wave reactive power by collecting the initial voltage and current traveling waves of multiple short-time sequences at three end measuring points in the T-connection transmission line area after S-transform, compares the mean sum of the reactive power obtained by each two traveling wave protection units corresponding to the short-time sequence to form the T-connection transmission line fault feature vector sample set, which is trained and tested in combination with the random forest fault branch identification model, so as to realize the identification of the T-connection transmission line fault branch. The simulation results show that the algorithm can accurately and sensitively identify the fault branch under various working conditions. The contributions of this article are as followings:
1. This algorithm combines the analysis of fault power distribution characteristics inside and outside T-connected transmission lines and S-transform of a multi-scale reactive power fault characteristic sample set, enriching the fault representation forms of T-connected transmission lines.
2. The neural network is added into the fault diagnosis of T-connected transmission line to improve the stability of fault diagnosis by using the powerful pattern recognition ability of neural network.
3. Compared with traditional fault diagnosis method of T-connected transmission line [9–21], the proposed algorithm can identify the specific branches of the faults inside and outside the area accurately even with the influence of CT saturation, data loss, noise and other factors.
This paper is structured as followings: Section 2 analyses the initial traveling wave power distribution when the T-connected transmission line is located inside or outside of the fault area; Section 3 introduces the related theory and the algorithm flows; Section 4 shows the test and analysis process of the simulation experiment; Section 5 analyzes the superiority and robustness of the algorithm; Section 6 summarizes the full text.
2. Analysis of the initial traveling wave power of the faulty
As shown in Fig 1, the T-connection transmission line (voltage level is 500 kV) is composed of branches named AO, BO, CO in the internal zone and branches named AD, BE, CF in the external zone. The traveling wave protection unit TR1~ TR3 is installed in the branches which are near the terminal busbars named A, B, C respectively. When the fault occurs at the AO branch in the protection zone, the traveling wave propagates from the fault point to both sides along the line, and refraction occurs at the discontinuity of the wave impedance of the line [25, 26].
[Figure omitted. See PDF.]
According to the traveling wave propagation theory, the assumptions are as following: t0m (m = 1, 2, 3) is the initial traveling wave reaches terminals A, B, and C for the first time, respectively. t1m (m = 1, 2, 3) is the second time that the traveling wave reaches the three terminals A, B, and C after the refraction occurs at the discontinuous impedance of the traveling wave. During the time period t0m ~ t1m, the fault traveling waves obtained by the traveling wave protection units TRm (m = 1, 2, 3) near the A, B, and C ends of the branch circuits in the protection zone are called initial voltage traveling waves Δum (m = 1, 2, 3) and initial current traveling waves Δim (m = 1, 2, 3).
2.1 Initial traveling wave power distribution of fault in the protection zone
Assumed that the current polarity of outgoing bus is positive and of incoming bus is negative. The positive and negative power can be judged according to the current polarity of associated lines of each busbar.
When the fault occurs at F1 of the branch named CO in the T-connection transmission line protection zone, the Peterson equivalent circuit of the T-connection transmission line is shown in Fig 2. is the additional network voltage at the fault point, and and are the initial voltage and current traveling waves of the measured bus A, respectively. The wave impedances of lines named OA, OB, OC, AD, BE, CF are ZC1~ZC6 respectively. According to the fact that the line wave impedance is approximately a real constant [27], and the equivalent capacitance impedance of bus C to ground is ZCC.
[Figure omitted. See PDF.]
According to the definition of the initial traveling wave complex power [24], formula of the initial traveling wave complex power at the C terminal of the line bus is:(1)
When a fault occurs on OC in the protection zone, it can be known from the Peterson equivalent circuit in Fig 2 that:(2)
The complex power measured by the TR3 traveling wave protection unit at terminal C:(3)
In the formula, PC is the active power of the initial traveling wave of the line, and QC is the reactive power of the initial traveling wave of the line. When an internal fault occurs on T-connection transmission line:(4)
2.2 Initial traveling wave power distribution of out-of-zone fault
When a fault occurs at location named F2 of CF branch outside the protection zone of the T-connection transmission line, the Petersen equivalent circuit of the T-connection transmission line is shown in Fig 3.
[Figure omitted. See PDF.]
Fig 3 shows that:(5)
Thus, the complex power measured by the traveling wave protection unit TR3 is:(6)
In the formula, PC is the active power of the initial traveling wave of the line, QC is the reactive power of the initial traveling wave of the transmission line, when a fault occurs outside the protection zone of the T-connection transmission line:(7)
3 Related theory and process of algorithm
In the three-phase transmission system, the coupling between voltage and current of each phase will affect the voltage and current. It is necessary to decouple the voltage and current of each phase. In this paper, Clark phase mode transformation is used to decouple the voltage and current of each phase. And then the combined modulus method is used to reflect various fault types of T-connection transmission line [24, 27],(8)
Where Δuα and Δuβ represent the Clark α and β mode voltages, respectively; Δiα and Δiβ represent the Clark α and β mode currents, respectively.
Because S transform method has good ability to extract signal feature in time-frequency analysis. Referring to reference [28], discrete S-transform method is used to convert current and voltage traveling wave moduli of decoupling fault. Then complex matrix reflecting the time-frequency characteristics of current and voltage signals were obtained after S transform. It is noted that the rows of the matrix are from the frequency information of the traveling wave after discrete S-transform, and the columns of the matrix are from the amplitude information and phase information of each sampling time point in the traveling wave time. Select the information of sampling points near the initial traveling wave head of current and voltage at multiple frequencies after S transform, and calculate the initial traveling wave reactive power of each sampling point.
3.1 S-transform principle
S-transform is an extension of wavelet transform and short-time Fourier transform. The choice of window function is avoided, and the defect of fixed window width is improved. At the same time, the feature quantity extracted by S-transform are insensitive to noise [29]. The continuous S-transform of a time signal h(t) is defined as:(9)(10)
Among them, g(τ-t, f) represents the Gaussian window function; τ represents the parameter that controls the position of the window function on the time axis; f represents the frequency; σ = 1/|f|.
The discrete time series h[kT](k = 0, 1, 2,⋯, N − 1) is obtained by sampling the signal h(t), where T is the sampling interval and N is the number of sampling points, then the discrete Fourier transform function of h[kT] is:(11)
In the formula, n = 0, 1,⋯, N − 1.
Then the discrete S transform of the signal h(t) is:(12)(13)
After transforming the signal S, a complex matrix reflecting the time-frequency characteristics of the signal is obtained. After S-transform, a two-dimensional time-frequency matrix is obtained. The rows of the matrix correspond to the frequency information of the traveling wave after discrete S-transform, and the columns of the matrix correspond to the amplitude and phase information of each sampling time point in the traveling wave time domain.
3.2 Initial traveling wave reactive power analysis of faults of the T-connection transmission line
3.2.1 Analysis of initial traveling wave reactive power of faults occurred in the internal zone.
Assumed that the AC phase-to-ground fault occurs at the CO branch 110km away from the O point in the zone of T-connection transmission line. And the initial fault Angle is 60 degrees and the transitional resistance is 100Ω. Taking the signal corresponding to the frequency of 15kHz after S-transformation as an example, the corresponding waveforms of each traveling wave protection unit TRm are shown in Figs 4–6 respectively, where, △im and △um are the initial traveling current and voltage traveling wave of TRm (m = 1, 2, 3), respectively. Qm is the initial traveling wave reactive power distribution waveform of the traveling wave protection unit TRm (m = 1, 2, 3).
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
As shown in Figs 4–6, when a fault occurs in CO branch of the T-connection line area, the reactive power values were obtained by multiplying the data near head of traveling wave of initial voltage and current from the traveling wave protection unit TRm (m = 1, 2, 3). The results are negative.
3.2.2 Analysis of initial traveling wave reactive power of out of zone fault.
Assumed that a BC phase-to-phase failure occurred 220 km away from the O point on the branch CF outside the zone of the T-connection transmission line, the initial fault angle is 5°, and the transitional resistance is 350 Ω. The corresponding waveforms of each traveling wave protection unit are shown in Figs 7–9 respectively (taking the signal corresponding to 15KHz frequency after s transformation as an example).
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
As shown in Figs 7–9, when a fault occurs on the Branch CF in the protection zone of T-connection transmission line, the reactive power values are obtained from the data near the wave head of the initial voltage and current traveling wave of the traveling wave protection unit TR3.The results are positive. And the reactive power values obtained from the data near the wave head of the initial voltage and current traveling wave of the traveling wave protection unit TRm (m = 1, 2) are negative.
3.3 Calculation of initial traveling wave reactive power after S-transform
Perform S-transformation on the voltage and current traveling waves from each traveling wave protection unit TRm (m = 1, 2, 3) combination of the T-connection transmission line respectively. After S transformation of initial voltage traveling wave and initial current traveling, select the phasors , and corresponding to l sampling points of wave within 0.1ms after fault occurs at 10 different frequencies fn (n = 1,2,…, 10). And the reactive power Qmn (l) at the corresponding frequency of each sampling point are calculated respectively.
The reactive power Qmn (l) obtained at each frequency is intercepted with 11 sampling points as the fixed data window length and 1 sampling point as the sliding scale factor to obtain ki short-time sequences Qmnk (x)(k = 1, 2,⋯, 10; x = 1, 2,⋯, 11).The reactive power mean value of K short-time sequences intercepted at each frequency under the traveling wave protection unit TRm is calculated respectively. And then the sum of the average reactive power mean value of the k-th short-time sequence corresponding to n frequencies of each traveling wave protection unit is calculated respectively. Finally, the ratio Q12 = Q1k/Q2k, Q13 = Q1k/Q3k and Q23 = Q2k/Q3k of the mean sum of reactive power under the corresponding time window k-th sequence of each two traveling wave protection units are calculated. And the ratio of the mean sum of reactive power under the corresponding time window of each two traveling wave protection units is defined as the characteristic vector Q of reactive power of T-connection transmission line. Characteristic vector represents the fault characteristics of T-connected transmission lines. Besides, Q = [Q12, Q13, Q23]1×30.
This section takes the short-term fixed time window sequence reactive power mean value and calculation at a specific frequency fn of the m-th traveling wave protection unit TRm as an example. The specific steps are as follows:
1. Perform S-transformation on the initial voltage and current traveling waves measured by the traveling wave protection unit TRm, respectively. This is used to obtain the complex time-frequency matrices of the initial voltage and current traveling waves, which are denoted as matrix SVm and SIm respectively.
2. Select the traveling wave data of 20 sampling points of initial voltage and current corresponding to the frequency fn after S-transformation, respectively. This is expressed as and , where l = 1, 2,⋯, 20.
3. Use the following formula (15) to obtain the complex power corresponding to each sampling point at frequency fn:(14)
4. Take 11 sampling points as the fixed data window length and 1 sampling point as the slip scale factor for the reactive power Qmn (l) obtained at the frequency fn to obtain 10 short-time series Qmnk (x) (k = 1, 2,⋯, 10; x = 1, 2,⋯, 11). And calculate the mean value of reactive power under corresponding short-time sequence, where ;
5. Calculate the sum of mean value of reactive power of the short-time sequence corresponding to the 10 frequencies of each traveling wave protection unit;
6. Finally, calculate the ratio of the mean value sum of reactive power under the corresponding short-time sequence of each pair of traveling wave protection units Q12 = Q1_k/Q2_k, Q13 = Q1_k/Q3_k, Q23 = Q2_k/Q3_k.
3.4 Random forest
Random Forest (RF) algorithm is a more efficient and flexible machine learning method based on decision tree [30, 31]. This algorithm integrates multiple trees through the idea of integrated learning [32, 33]. The basic principle relies on Bootstrap resampling technology to extracted N bootstrap data sets from the original data set randomly. Then, N decision trees are trained to form a random forest classifier. Finally, the classification decision is made by voting that the minority is subordinate to the majority. Because the training of decision tree classifier follows the rules of random samples and random features. This method shows good characteristics of strong generalization ability, simple model and good classification effect. Random forest mainly includes two processes: model training and decision classification, and the classification process is shown in Fig 10.
[Figure omitted. See PDF.]
Given a training sample set X = {(x1, y1), (x2, y2),⋯, (xN, yN)}, where xm = [xm1, xm2,⋯, xmk]T is the m-th training sample, k is the number of feature values in xm, and ym is the class label corresponding to training sample xm.
Model training: bootstrap sampling is performed on the training sample set X, and the Bootstrap sub-sample set Xj (j = 1, 2,⋯, n) is obtained after sampling n times. For each sub-sample set Xj, CART is used to build a decision tree model hj(x), and finally a classifier {h1(x), h2(x),⋯, hj(x)}(j = 1, 2,⋯, n) composed of a set of decision trees is obtained.
Classification of decision: when the test sample is input into the trained classifier, the category voting is carried out through the established n decision trees, and the category with the highest vote is taken as the reddest output category of the test sample. The classification decision is as follows:(15)
Among them, hj(x) is the j-th decision tree; I{·} is the indicative function, which is 1 when the expression is satisfied, and 0 otherwise; y is the category label.
3.5 Fault identification algorithm
In this paper, the initial voltage and current traveling wave data corresponding to the traveling wave protection unit TRm (m = 1, 2, 3) in the 0.1ms time period after the fault are selected at a frequency of 6-15kHz after S-transformation, and calculate the ratio of the mean sum of reactive power under each corresponding time window of each pair of traveling wave protection units. The ratio of the multi-scale initial traveling wave reactive power mean value and specific fault feature vectors are constituted so as to characterize the fault characteristics of the T-connection transmission line. A sample set that can characterize the fault characteristics including randomly simulate the faults with different fault types, different transition resistances, different fault distances and different fault initial angles in each branch of T-connected transmission lines. The flowchart of the fault branch identification algorithm is shown in Fig 11.
[Figure omitted. See PDF.]
4 Simulation and experiment
PSCAD/EMTDC electromagnetic transient simulation software is used to establish the simulation model of 500kV T-connection transmission line shown in Fig 1. The model of transmission line adopts the frequency related distributed parameter model that can accurately reflect the transient and harmonic response. The tower type of line is: 3H5 [26]. The configuration of transmission line is shown in Fig 12. Among them, the parameters of transmission line are shown in Table 1 [28, 34]. The stray capacitance of busbar is set as Cm = 0.001μF. The simulation sampling frequency is 200kHz, and the length of each branch are as followings: AO = 300km, BO = 200km, CO = 150km, AD = 170km, BE = 150km, CF = 180km. All symbols and terms involved in this paper are explained, as shown in Table 2.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
4.1 Training sample data
In order to verify the validity and reliability of the algorithm proposed in this paper in the identification of faulty branches, 6 branches of the T-connection transmission line are tested under different fault initial angles, transitional resistances, fault types and fault distances. Each branch is simulated by 5 groups of faults. And a total of 120 sets of fault feature vectors are obtained to form a training sample set for fault branch identification.
4.2 Establishment and testing of fault branch identification model
Input the fault characteristic training samples into the random forest neural network for training, and obtain a trained random forest T-connection transmission line intelligent fault identification model. Then input the fault training samples into the trained random forest fault identification model for testing, and the comparison of the prediction results is shown in Fig 13.
[Figure omitted. See PDF.]
It can be seen from Fig 13 that the accuracy rate of the test results of the training samples in the recognition model is 100%. Selection of training sample failure parameters is shown in Table 3.
[Figure omitted. See PDF.]
4.3 Test sample analysis
In order to further verify the reliability of the proposed algorithm to identify faulty branches, this section simulates six branches inside and outside the protection zone of the T-connection transmission line under different initial fault angles, transitional resistances, fault types, and fault distances. Then four groups test sample sets of faults are obtained, which are different from the training samples Each sample set contains 24 sets of fault feature vectors. Finally, the test sample sets are respectively input into the random forest intelligent fault branch identification model for testing.
4.3.1 Fault initial angle test.
The test simulation samples obtained by different initial fault angles testing are input into the random forest fault branch identification model for testing. The prediction results are shown in Table 4 and Fig 14.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
When different initial angle faults occur in transmission lines, the algorithm can accurately identify the specific fault branches of the line. The proposed algorithm is not affected by the initial angle of fault.
4.3.2 Transitional resistance tests.
The test simulation samples of obtained by different transitional resistance obtained by simulation are input into the random forest fault branch identification model for testing. The prediction results are shown in Table 5.
[Figure omitted. See PDF.]
When the transmission line has different transitional resistance faults, the algorithm can accurately identify the specific faulty branch of the lines. The proposed algorithm is not affected by the transitional resistance.
4.3.3 Testing of fault types.
The test simulation samples of obtained by different faulty branches obtained by simulation are input into the random forest fault branch identification model for testing. The prediction results are shown in Table 6.
[Figure omitted. See PDF.]
When different fault types occur in the transmission line, the algorithm can accurately identify the specific fault branch of the transmission line. The proposed algorithm is not affected by fault types.
4.3.4 Fault distance test.
The test simulation samples of obtained by different fault distances obtained by simulation are input into the random forest fault branch identification model for testing. The prediction results are shown in Table 7.
[Figure omitted. See PDF.]
When faults occur at different fault distances of transmission line, the algorithm can accurately identify the specific fault branch of the transmission line. The proposed algorithm is not affected by the fault distance.
4.4 Algorithm performance test analysis
4.4.1 Test and analysis of anti-CT saturation ability.
In order to verify the anti-CT saturation performance of the algorithm proposed, the simulation analysis of CT saturation are made when each branch of the T-connection transmission line fails. The CT saturation of the branch CO in the T-connection transmission line is taken as an example to carry out the simulation of CT saturation. The model adopts a nonlinear time-domain equivalent circuit model with relatively good time-frequency characteristics [35].
Under the condition of CT saturation on the branch CO in the protection zone of the T-connection transmission line, a group of faults is simulated in each branch of the T-connection transmission line. 6 groups of T-connection transmission line fault characteristic vectors are obtained. Then the fault feature test sample matrix is input into the random forest fault branch identification model for testing. And the test set prediction results are shown in Table 8 and Fig 15 to compare the prediction results corresponding to the fault conditions.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
It is seen from the analysis of the above chart that when CT saturation occurs in the branch CO in the protection zone of T-connection transmission line, The algorithm can identify fault branches with 100% accuracy. And it is less affected by CT saturation.
4.4.2 Noise impact analysis test analysis.
In order to verify the reliability of the algorithm under the influence of noise, noise is added to the voltage and current signals measured by each traveling wave protection unit TRm (m = 1, 2, 3) of the T-connection transmission line. And the signal-to-noise ratio (SNR) is 30dB~70dB. Fig 16 is the current-related traveling wave waveform measured by the traveling wave protection unit TR2 when a fault occurs on branch BO of the T-connection transmission line. And Fig 17 is the current-related traveling wave waveform measured by the traveling wave protection unit TR1 when a fault occurs on branch named BE outside the protection zone of the T-connection transmission line. And the current traveling wave measured by the traveling wave protection unit TR1 and TR2 are taken as an example under the conditions that the signal-to-noise ratio is 30dB and the frequency after S-transformation is 15kHz.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
A fault condition different from the training samples is selected for the branch named AO in the protection zone and the branch named BE outside the protection zone. The noise is added to the voltage and current signals. The signal-to-noise ratios (SNRs) are set as 30dB, 40dB, 50dB, 60dB, and 70dB respectively. 10 groups of T-connection transmission line fault feature vectors are obtained by simulation. And the fault feature test sample matrix is input into the random forest fault branch identification model for testing. As shown in Table 9 and Fig 18, a comparison of the prediction results of the corresponding fault conditions is made.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
From the results in the above table, the algorithm can identify fault branches with 100% accuracy when the branch BO in the protection zone and the branch AD outside the protection zone under different signal-to-noise ratio faults. Also, this method is less affected by noise.
4.4.3 Data random loss test analysis.
The protection device may experience data loss in actual operation. In order to verify the algorithm performance in this case, take the random loss of the initial current traveling wave data measured by the protection unit TR1 as an example. The branch BO in the protection zone and the branch AD outside the protection zone are selected for simulation analysis, respectively.
Fig 19 shows the relevant waveform of the reactive power distribution after the random loss of data near the initial current traveling wave head when an ACG fault occurs on branch AO in the protection zone at a distance of 120 km from point O. Fig 20 shows the relevant waveform of the reactive power distribution after the random loss of data near the initial current traveling wave head when the BG fault occurs at a distance of 270km from point O on branch CF outside the protection zone. Take the measurement data TR1 randomly missing 8 sampling points in the data window at a frequency of 15kHz after S-transformation as an example.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
The fault feature test sample is input into the random forest fault branch identification model for testing. And the prediction results are shown in Table 10 and Fig 21 to make a comparison of the prediction results of the corresponding fault conditions.
[Figure omitted. See PDF.]
[Figure omitted. See PDF.]
The analysis shows that the algorithm can also accurately identify the branch where the fault is located when a fault occurs on the branch inside and outside the protection zone of the T-connection transmission line and the sampling point data near the traveling wave head is randomly lost.
5 Discussion
5.1 Comparative analysis with traditional algorithm
For algorithm performance, most traditional fault identification algorithms of T-connection line can not analyze the performance of the algorithm under the conditions of noise, CT saturation and data loss. And they can not identify faults accurately in extreme cases. However, under the conditions of noise, CT saturation and data loss, our method could identify faults well.
In terms of algorithm speed, the data window length of the two fault branch identification algorithms proposed in this paper is 0.1ms. Compared with the data window length (20ms or10ms) by full-cycle (half-cycle) Fourier algorithm, our data window length were shorten. And its action speed of the algorithm was improved, which is higher than that of traditional power frequency T-connection line fault identification algorithm.
As for fault identification accuracy, the traditional T-connection line fault identification algorithm can only identify the faults inside and outside the area. And the effects of algorithm are easily influenced by other variables. But the proposed algorithm can not only identify the faults inside and outside the area, but also accurately identify the specific branches of the faults inside and outside the T-connection line.
5.2 Analysis of fault diagnosis results of different neural networks
Because different neural networks have different recognition accuracy for the same sample set. In order to analyze the fault diagnosis performance of different neural networks under the proposed algorithm fault sample set, the above training set test sample sets are input into SVM, PNN and RF for testing, respectively. The fault recognition accuracy of different neural networks is shown in Table 11. The calculation process of fault identification accuracy of different sample sets is as follows:
[Figure omitted. See PDF.]
It can be seen in the above table that only random forest can achieve accurate identification of training samples among the three networks. In the test samples, the test samples of different fault types, transition resistances, fault distances and fault initial angles can be accurately identified, while the test samples can only be accurately identified by random forest when analyzing the performance of the three categories of the algorithm.
5.3 Reliability analysis of algorithm under different voltage levels and line parameters
To analyze the robustness of the proposed algorithm in different test systems, a simulation model of T-connected transmission line with voltage level of 220kV is established by using PSCAD/EMTDC electromagnetic transient simulation software. And lengths of each branch of T-connected line are AO = 150km, BO = 120km, CO = 140km, AD = 80km, BE = 70km and CF = 80km respectively. The training sample is obtained by randomly simulating five groups of faults in four types of faults with different initial angles, transition resistances, fault types and fault distances of six branches of T-connected transmission lines. The training sample set consists of 120 groups of random fault feature vectors. The test sample is a random simulation of four groups of faults different from the training sample by six branches of T-connection line. The test sample set consists of 24 groups of fault feature vectors. The fault feature sample set is input into RF for training and testing, and the predicted results are shown in Table 12. It can be seen that the algorithm proposed in this paper can also realize the reliable diagnosis of fault branch under this voltage level and line parameters.
[Figure omitted. See PDF.]
6 Conclusion
In this paper, a new fault identification method for T-connection transmission lines is proposed based on multi-scale traveling wave reactive power and random forest network. The characteristics of initial traveling wave reactive power of T-connection transmission line within and outside the fault area are analyzed. Through a large number of simulation experiments, the feasibility of the fault identification method is verified. Theoretical and simulation results show as followings:
1. The proposed fault identification algorithm can quickly and accurately identify the specific fault branch of the T-connection transmission line under various working conditions, and basically overcome the influence of factors such as transitional resistance and fault distance.
2. In terms of algorithm performance, the proposed algorithm can accurately identify the faulty branch under the influence of data information loss, CT saturation and noise (30-70dB), showing good performance and anti-interference ability.
3. In terms of fault identification accuracy, the proposed algorithm can not only identify the faults inside and outside the protection zone, but also can accurately identify the specific branch of the fault, while the traditional T-connection transmission line fault identification algorithm can only identify the faults inside and outside the area, and the recognition effect of some algorithms is easy affected by other variables.
Supporting information
S1 Fig.
https://doi.org/10.1371/journal.pone.0284937.s001
(TIF)
S1 File. Other sample set.
https://doi.org/10.1371/journal.pone.0284937.s002
(XLSX)
S2 File. Test sample set.
https://doi.org/10.1371/journal.pone.0284937.s003
(XLSX)
S3 File. Train sample set.
https://doi.org/10.1371/journal.pone.0284937.s004
(XLSX)
Citation: Zhong Y, Yang J, Wang S, Deng S, Hu L (2023) A new method for fault identification of T-connection transmission line based on multi-scale traveling wave reactive power and random forest. PLoS ONE 18(8): e0284937. https://doi.org/10.1371/journal.pone.0284937
About the Authors:
Yawen Zhong
Roles: Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing
Affiliation: School of Engineering, Southwest Petroleum University, Nanchong, Sichuan, China
Jie Yang
Roles: Investigation, Resources, Software, Supervision, Writing – original draft, Writing – review & editing
E-mail: [email protected]
Affiliation: School of Information Engineering, Southwest University of Science and Technology, Mianyang, Sichuan, China
ORICD: https://orcid.org/0000-0001-7998-4273
Sheng Wang
Roles: Conceptualization, Data curation, Formal analysis, Funding acquisition, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing
Affiliation: Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan University of Science and Engineering, Zigong, Sichuan, China
Sijing Deng
Roles: Conceptualization, Formal analysis, Funding acquisition, Methodology, Resources, Software, Visualization, Writing – original draft, Writing – review & editing
Affiliation: Artificial Intelligence Key Laboratory of Sichuan Province, Sichuan University of Science and Engineering, Zigong, Sichuan, China
Liang Hu
Roles: Formal analysis, Resources, Writing – review & editing
Affiliation: State Grid YiliYihe Electric Power Supply Company, Yining, Xinjiang, China
1. ZHANG Z-G, KANG C-Q. Challenges and Prospects for Constructing the New-type Power System Towards a Carbon Neutrality Future[J]. Proceedings of the CSEE, 2022,42(08):2806–2819.
2. YANG J, WU H, Dong X-X, et al. Transmission line fault type identification based on the characteristics of current fault components and random forest[J]. Power System Protection and Control,2021,49(13):53–63.
3. GAUR V-K, BHALIA B-R, MLADEN K. Novel Fault Distance Estimation Method for Three-Terminal Transmission Line[J]. IEEE Transactions on Power Delivery, 2021, 36(1): 406–417.
4. MA K-Q, CHEN Z, LETH B-C, et al. Novel differential protection using model recognition and unsymmetrical vector reconstruction for the transmission line with wind farms connection[J]. International journal of electrical power and energy systems, 2020, 123.
5. WU H, DONG X-X, WANG Q-M. A new principle for initial traveling wave active power differential busbar protection [J]. IEEE Access, 2019, 7(1): 70495–70512.
6. SHAIK A G, PULIPKA V R. A transient current based busbar protection scheme using Wavelet Transforms[J]. Electrical Power and Energy Systems, 2011, 33, 1049–1053.
7. GAUR V-K, BHALIA B-R, BHALIA M-K. Novel Fault Distance Estimation Method for Three-Terminal Transmission Line[J]. IEEE Transactions on Power Delivery, 2021, 36(1): 406–417.
8. WU H, YANG J, CHEN L, et al. A new method for identifying a fault in T-connected lines based on multiscale S-transform energy entropy and an extreme learning machine[J]. PLOS ONE, 2019,14(8), e0220870.
9. SONAN J-L, DENG X-S, LI R-S, et al. Principle of T-type transmission line pilot protection based on fault component comprehensive impedance[J]. electric power automation equipment, 2009,29(12):4–9.
10. GAO H-L, JIANG S-F. Study on new criterion of current differential protection for Teed lines[J]. Relay, 2001(09):6–9+16.
11. LI B, LUO T, BO Z-Q. A novel differential protection criterion based on super-imposed fault component for T-type transmission line[J]. Power system protection and control, 2011,39(15):1–6+12.
12. WANG T, LIU Y, LI F-T, et al. Research on the current differential protection where PV access to the high voltage distribution network with T-type[J]. Power system protection and control, 2015,43(13):60–65.
13. NAYAK P K, PRADHAN A K, BAJPAI P. A Three-Terminal Line Protection new line Scheme Immune to Power Swing[J]. IEEE Transactions on Power Delivery, 2016, 31(3): 999–1006.
14. GAUR V K, BHALJA B. A new faulty section identification and fault localization technique for three-terminal transmission line[J]. International Journal of Electrical Power & Energy Systems, 2019, 93: 216–227.
15. ZHENG T, ZHAO Y-T, LI J, et al. A Protection Scheme for Teed Lines With Wind Power Based on Voltage Magnitude Difference and Measuring Impedance Characteristics[J]. Power System Technology, 2017,41(05):1660–1667.
16. LIU X-W, LI Y-L, CHEN X-L, et al. An Improved Scheme of Longitudinal Differential Protection for Teed Lines With Inverter-Based Distributed Generations [J]. Power System Technology, 2016, 40(04): 1257–1264.
17. WANG Z-P, LIN F-H. A New Curtrent Differential Protection for Three Terminal Transmission Lines Based on Distributed Parameters Model [J]. Power System Technology, 2009, 33(19): 204–209.
18. KUMAR A, SURESH B-P, PHANENDRA B-N-V. Taylor-Kalman-fourier filter based back-up protection for teed-transmission line[C]. International Conference on Computing, Communication and Networking Technologies (ICCCNT). JUL 03–05, 2017.
19. ZHENG L-M, JIA K, BI T-S, et al. Cosine Similarity Based Pilot Protection of Teed Transmission Line Connected to Renewable Energy Power Plants [J]. Automation of Electric Power Systems, 2019, 43(18): 111–124.
20. BHALJA B, MAHESHWARI R P. New differential protection scheme for tapped transmission line[J]. IET Generation Transmission & Distribution, 2008, 2(2): 271–279.
21. EISSA M-M. A new digital relaying scheme for EHV three terminal transmission lines[J], Electric Power Systems Research. 2005, 73(2): 107–112.
22. NING S-G, HE Y-G, CHENG T-T, et al. Feature Extraction of PD Source with Complex Noise Based on Adaptive S-Transform and TCSVD Decomposition[J/OL].Transactions of China Electrotechnical Society, 2021, 1–13.
23. QUAN W-J, TONG X-Y, ZHANG G-X. Single-end Flexible DC Protection Scheme Based on Similarity of S-transform Energy Spectrum Matrix of Traveling Wave [J/OL]. Automation of Electric Power Systems, 2022, 1–18.
24. WU H, LI Q-Z, LIU W. A new pilot protection algorithm based on traveling wave power for transmission lines [J]. Automation of Electric Power Systems, 2016, 40(2): 107–113.
25. ZOU G-B, SONG S-L, XU C-H,et al. Fast busbar protection based on waveform integral of directional traveling waves[J]. Pro⁃ceedings of the CSEE, 2014, 34(31): 5677–5684.
26. YANG J, WU H, et al. Fault Identification Method for T-connection Transmission Lines Based on Multiscale Traveling Wave Power [J]. Proceedings of the CSU-EPSA, 2021, 33(04):115–126.
27. WU H, DONG X-X, YE R-K. A new algorithm for busbar protection based on the comparison of initial traveling wave power[J]. IEEJ Transactions on Electrical and Electronic Engineering, 2019, 14(4): 520–533.
28. LI X-P, HE Z-Y, WU H, et al. Ultra high speed directional element based on amplitude comparison using S- transform energy relative entropy [J]. Automation of Electric Power Systems, 2014, 38(14): 113–117.
29. WENG H-L, LI H-W, XING J-W, et al. Novel criterion adopting S-transform phase angle difference and energy relative entropy for zero-sequence differential protection of converter transformer[J]. Electric Power Automation Equipment, 2019,39(09):20–26.
30. XIE W-W, SUN Y-L, HUANG Y-X. Research on power line communication optimization algorithm based on improved random forest [J]. Power System Protecti on and Control, 2019, 47(11): 22–29.
31. WANG R-M, WANG H-Y, ZHANG Y-N, et al. Composite power quality disturbance recognition based on segmented modified S-transform and random forest [J]. Power System Protecti on and Control, 2020, 48(07): 19–28.
32. WU H-B, CHEN Y-S, ZHANG T-H, et al. Rolling bearing fault diagnosis by improved multiscale amplitude aware permutation entropy and random forest [J]. Optics and P recision Engineering, 2020, 28(03): 621–631.
33. WANG M, ZHANG X-C, WANG J-Y, et al. Forest resource classification based on random forest and object oriented method[J]. Acta Geodaetica et Cartographica Sinica, 2020, 49(2): 235–244.
34. LI C-C, CHEN Q, ZHANG Y. A fault location method based on the waveform discriminator means and RBF neural networks[C]. IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC), 2016:934–938.
35. SHU H-C, LIN M. Comparative Study On Modeling And Transient Simulation Of Current Transformer[J]. Power System Technology, 2003(04): 11–14.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
© 2023 Zhong et al. This is an open access article distributed under the terms of the Creative Commons Attribution License: http://creativecommons.org/licenses/by/4.0/ (the “License”), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Abstract
Though the traditional fault diagnosis method of T-connected transmission lines can identify the faults inside and outside the area, it can not identify the specific branches. To improve the accuracy and reliability of fault diagnosis of T-connection transmission lines, a new method is proposed to identify specific faulty branches of T-connection transmission lines based on multi-scale traveling wave reactive power and random forest. Based on the S-transform, the mean and sum ratios of the corresponding short-time series traveling wave reactive powers of each two traveling wave protection units at multiple frequencies are calculated respectively to form the fault feature vector sample set of the T-connection transmission line. A random forest fault branch identification model is established, and it is trained and tested by the fault feature sample set of T-connection transmission line to identify the fault branch. The simulation results show that the proposed algorithm can identify the branch where the fault is located inside and outside the protection zone of T-connection transmission line quickly and accurately under various working conditions. This method also shows good performance to identify faults even under the situation of CT saturation, noise influence and data loss.
You have requested "on-the-fly" machine translation of selected content from our databases. This functionality is provided solely for your convenience and is in no way intended to replace human translation. Show full disclaimer
Neither ProQuest nor its licensors make any representations or warranties with respect to the translations. The translations are automatically generated "AS IS" and "AS AVAILABLE" and are not retained in our systems. PROQUEST AND ITS LICENSORS SPECIFICALLY DISCLAIM ANY AND ALL EXPRESS OR IMPLIED WARRANTIES, INCLUDING WITHOUT LIMITATION, ANY WARRANTIES FOR AVAILABILITY, ACCURACY, TIMELINESS, COMPLETENESS, NON-INFRINGMENT, MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. Your use of the translations is subject to all use restrictions contained in your Electronic Products License Agreement and by using the translation functionality you agree to forgo any and all claims against ProQuest or its licensors for your use of the translation functionality and any output derived there from. Hide full disclaimer
Details
; Wang, Sheng; Deng, Sijing; Hu, Liang