A new method for identifying a fault in T-connected lines based on multiscale S-transform energy entropy and an extreme learning machine

Due to the characteristics of T-connection transmission lines, a new method for T-connection transmission lines fault identification based on current reverse travelling wave multi-scale S-transformation energy entropy and limit learning machine is proposed. S-transform are implemented on the faulty reverse traveling waves measured by each traveling wave protection unit of the T-connection transmission line, the reverse travelling wave energy entropies under eight different frequencies are respectively calculated, and a T-connection transmission line fault characteristic vector sample set are thus formed. Establish an intelligent fault identification model of extreme learning machines, and use the sample set for training and testing to identify the specific faulty branch of the T-connection transmission line. The simulation results show that the proposed algorithm can accurately and quickly identify the branch where the fault is located on the T-connection transmission line under various operation conditions.


Introduction
With the continuous development of the social economy, the complexity of the power grid has gradually increased. Considering the investment savings and other restrictions on objective conditions, T-connection transmission lines are increasingly appearing in high-voltage and ultrahigh-voltage power networks due to the uniqueness of their modes of connection. However, these lines are often accompanied by large power plants and systems, whose transmission lines have high transmission power and heavy load. When the line fails, it may cause largescale blackouts. Therefore, when a fault occurs, it is required to be able to quickly and accurately identify the fault [1][2][3][4][5].
At present, researches on T-connection transmission line fault identification domestic and foreign scholar have carried out are mainly based on the voltage, current and transmission line distribution parameter model. In reference [6], faults occurred within and outside of the protection zone are identified by using the ratio of the phasor sum of T-connection line three-  [7] uses the sum of the three-terminal current fault components of the T-connection transmission line and the vector difference between the maximum current in the three-terminal current fault components and the sum of the currents of other two terminals to establish a criterion to identify internal and external faults, but the selection of the braking coefficient in the criterion will have an impact on the sensitivity and reliability of fault identification. Aiming at addressing the problems in reference [7], reference [8] utilized the maximum current in the three-terminal fault current components of the T-connection transmission line with the other two ends and the remaining string angles to establish a criterion to identify internal and external faults, but did not analyze the performance of the algorithm under the influence of noise. Based on the criteria presented in references [7][8], reference [9] establishes a comprehensive criterion to identify faults occurred in the photovoltaic T-connection high voltage distribution network. However, in reference [9], data loss is not discussed in the process of simulation analysis of the algorithm. In reference [10], by using the information of the voltage, current and transmission line positive sequence impedance parameters of each side of the T-connection transmission line, the T-connection voltage is obtained from each side, and then the faulty branch is identified by using the obtained T-connection voltage amplitude information. Reference [11] provides the voltage and current signals measured by the T-connection transmission line protection terminal to the second-order Taylor-Kalman-Fourier (T2KF) filter to estimate the instantaneous values of the voltage and current signals, and then calculates the positive sequence impedance to identify the faulty section. In reference [12], the positive sequence voltage at the T-connection is calculated at the three ends of the T-connection transmission line, and internal and external faults are identified by comparing the maximum amplitude of the Tconnection positive sequence voltage superposition component with the maximum amplitude of the three-terminal positive sequence voltage superposition component. In reference [13], the maximum value of the T-connection positive sequence superimposed voltage calculated by the three ends of the T-connection transmission line is used to determine whether the line is faulty, and the phase difference between the positive sequence superimposed voltage and the current at a particular terminal is then used to identify internal and external faults. Reference [14] uses the voltage amplitude difference and measured impedance characteristics of the three sides of the T-connection transmission line to establish the main criterion of the integrated voltage amplitude difference, and with the combination of adaptive distance auxiliary criterion, internal and external faults can be identified. However, the performance of the algorithm has not been simulated. In [15][16], wavelet transform is applied to T-connection transmission line fault identification, but the high-frequency noise signal will affect the identification of faults occurred on T-connection transmission line. In reference [15], the bior3.1 wavelet is used to decompose the three-terminal raw current signal of the T-connection transmission line, the decomposed signal is reconstructed, and then the reconstructed signal is used to calculate the running current and the suppressing current of each phase. Finally, internal and external faults are identified by comparing the relationship between the three-phase corresponding phase running current and the suppressing current. Reference [16] distinguishes internal and external faults faults by comparing the polarity of the fault current detected by the Haar wavelet function at each end of the T-connection transmission line. The fault identification algorithm in reference [17] and [18] is mainly based on the distribution parameters of the T-connection transmission line. Reference [17] discriminates internal and external faults by comparing the exponential sum derived from the model of the transmission line, while reference [18] derives the ranging function based on the distribution parameter model of the transmission line, and uses the phase information at both ends of each branch of the ranging function to determine the branch where the fault is located.
In the traditional fault identification research of T-connection transmission line, the T-connection fault identification algorithm can only identify internal and external faults, but fail to  identify the specific branch on which the fault occurred, and the fault identification accuracies  in some algorithms are susceptible to other variables. In terms of fault tolerance, the traditional  T-connection transmission line fault identification algorithm does not simulate the fault data loss, and cannot verify the fault tolerance of the algorithm. In terms of noise impact, the traditional T-connection transmission line fault identification algorithm does not conduct an indepth study on it. In order to overcome the shortcomings that the traditional T-connection transmission line fault identification algorithm have in identification precision, accuracy, fault tolerance and effects from noise, this paper further studies the T-connection transmission line fault identification algorithm.
In recent years, S-transformation and information entropy theory have frequently been applied in power systems [19][20][21]. Reference [22] uses the S-transformed sample entropy ratio of the fault current traveling wave at both ends of the transmission line within a period of time after the fault occurred to identify internal and external faults. Reference [23] established the criterion based on the energy entropy change characteristics obtained by the reverse traveling wave S transform after the faults occurred on each associated line of the busbar to identify internal and external faults.
Based on the theory of directional traveling wave and information entropy expounded in reference [21][22][23] and with the application of S transform in power system [22][23], this paper proposes a new fault identification method for T-connection transmission line based on the multiscale S transform energy entropy and limit learning machine of current reverse traveling wave. On the basis of S transformation of fault reverse traveling waves at each end of T-connection transmission line, energy entropy of the reverse traveling waves at 8 different frequencies is calculated to form a sample set of fault characteristic vectors of T-connection transmission line. Combined with the limit learning machine fault intelligent identification model, training and testing are conducted to identify fault branches of T-connection transmission line. Simulation results show that the proposed algorithm can accurately identify the T-connection transmission line branch where the internal or external fault is located under various operating conditions.

Fault current traveling wave characteristics analysis
The basic theory of fault traveling waves The connection transmission line is composed of internal branches AO, BO, CO and the external branches AD, BE, and CF. The traveling wave protection units TR1~TR3 are installed at the three ends of the branches near A, B, and C, respectively. When a fault occurs at F1 on branch AO, the traveling wave propagates from the fault point along the transmission line to both sides, and refraction occurs at the discontinuity of the wave impedance of the transmission line. For any point on the line whose distance to the fault point is x, the transient voltage and current traveling wave at this point are [24]: Identifying a fault in T-connected lines In the equations above, t is the observation time; L and C are the inductance and capacitance of the transmission line per unit length; Δu + (Δu − ), Δi + (Δi − ) are the voltage and current forward (backward) traveling wave propagating along the positive (negative) direction of x.
According to the traveling wave propagation theory, the time at which the initial traveling wave reaches the three ends A, B, and C is t 0m (m = 1, 2, 3), respectively, and the second time the traveling wave reaches the three ends of A, B and C after catadioptric reflection occurs is TR m (m = 1, 2, 3); within the time period t 0m~t1m , the fault traveling wave obtained by the traveling wave protection unit TR m (m = 1, 2, 3) at the three ends of the branches near A, B, and C is called the initial voltage and the current traveling wave. Δu m (m = 1, 2, 3) is the initial voltage traveling wave measured by the three-terminal traveling wave protection unit of the internal branch near A, B and C, respectively, and Δi m (m = 1, 2, 3) is the initial current traveling wave measured by the three-terminal traveling wave protection unit of the internal branch near A, B, and C, respectively. The wave impedance of the transmission line is z c .

Analysis of the fault current traveling wave propagation process
Characteristics of the current traveling wave when an internal fault occurs on the Tconnection transmission line. It can be seen from the analysis that the transient voltage and current at any point of the transmission line are the superposition of forward and backward traveling waves. From Eq (1), it can be concluded that the forward and backward traveling waves of the current are respectively [24]: In the equations, Δu and Δi are the voltage and current fault traveling wave components measured at the point R of each branch; and Z c is the wave impedance of the transmission line.
It can be seen from the propagation characteristics of the traveling wave that the traveling wave will be deflected at the discontinuity of the transmission line wave impedance (fault point, bus bar, etc.) [24]. According to Fig 1, the positive direction of the traveling wave is defined as the transmission line that the busbar points to. When F 1 on internal branch AO of the T-connection transmission line fails, the propagation direction of the current backward   wave; within the time period [t 02 , t 02 + 2d min /v], protection unit TR 2 of the traveling wave can only detect the forward traveling wave.

Calculating S-transform energy entropy based on the backward traveling wave
In the three-phase transmission power system, the coupling between the phase voltage and the phase current affects the voltage and current. Therefore, the phase voltage and phase current need to be decoupled. In this paper, the phase voltage and phase current are decoupled with the implementation of'Clark phase-mode transformation, and the combined modulus method is used to reflect the various fault types of the T-connection transmission line [25].
In this paper, the method used in reference [26] is applied to perform discrete S-transformation on the fault current traveling wave modulus after phase-mode transformation, and the multiscale backward traveling wave energy entropy is calculated by selecting the wave front information of the current backward traveling wave at multiple frequencies after the fault occurs.

S transform principle
S transform is an extension of the principle of wavelet transform and short-time Fourier transform, which avoids the selection of a window function and break through the limitations of fixed window width. At the same time, the feature quantity extracted by the S transform is not susceptible to noise [27].
Set the continuous time signal as h(t), then the continuous S transformation S(τ, f) of the time signal h(t) is defined as: In the equations above, τ is the parameter that controls the position of the Gaussian window on the time axis, f is the continuous frequency, t is the time, i is the imaginary unit, σ = 1/|f|, and g(τ-t, f) are Gaussian windows, which are susceptible to the change of frequency.
If h[kT](k = 0, 1, 2, � � �, N − 1) is a discrete time series obtained by sampling signal h(t), T is the sampling interval, and N is the number of sampling points, then the discrete Fourier transform function of h[kT] is: In the equation, n = 0, 1,� � �, N−1.

Then the discrete S transform of signal h(t) is:
The complex matrix after the implementation of S transformation reflects the time-domain and frequency-domain characteristics of the signal, as well as the amplitude information and phase information of the traveling wave in the time domain.

S transform energy entropy
Information entropy is a kind of information measure to the system, which can measure the degree of system disorder, signal uniformity and complexity [20]. The concept of entropy provides a great deal of new ideas for power system fault diagnosis.
Based on the analysis of S transform energy entropy in reference [28], S-transform is applied to the current reverse traveling wave signal Δi m-(t)(m = 1, 2, 3) detected by the mth traveling wave protection unit. The energy entropy values W mn of time signal sequences at eight different frequencies f n (n = 1,2,3,4,5,6,7,8) are calculated respectively. The eigenvectors W m = [W m1 W m2 � � � W m8 ] of the energy entropy of the reverse traveling wave at these eight frequencies are defined as Multi-scale S-transform energy entropy vector of signal Δi m-(t).
In this paper, the data of the reverse traveling wave S-transformation energy entropy is calculated by selecting the data within 0.5ms after the fault occurred on the T-connection transmission line (i.e., the data of 50 sampling points before and after the wavefront of the reverse traveling wave). Taking the reverse-traveling wave signal Δi m− (t) corresponding to a specific frequency f n of the m-th traveling wave protection unit TR m as an example, the calculation steps of the energy entropy are given as follows: 1. Apply S-transform on the reverse traveling wave signal Δi mn− (t) and a complex time-frequency matrix is thus obtained, which is denoted as an S matrix. The modulus of each element of S matrix is calculated, and the modulus time-frequency matrix D is obtained.
2. Let the total energy E mn (m = 1, 2, 3) of the signal Δi mn− (t) at the specific frequency f n be equal to the sum of the energy E mn(j) (j = 1, 2, 3,� � �,100) of 50 sampling points before and after the initial traveling wave head of the signal, that is, is the current data of the m-th traveling wave protection unit at the j-th point at frequency f n ), and the total energy of the signal is E ¼

Extreme learning machine
Feedforward neural network is one of the artificial neural networks [29]. In this kind of neural network, each neuron starts from the input layer, receives the first input, and inputs to the next level until the output layer. There is no feedback throughout the network, and a directed acyclic graph can be used. Feedforward neural network is the earliest proposed artificial neural Identifying a fault in T-connected lines network and the simplest type of artificial neural network. According to the number of layers of the feedforward neural network, it can be divided into a single layer feedforward neural network and a multilayer feedforward neural network. Among them, common feedforward neural networks include BP neural network [29], radial basis function (RBF) neural network [29] and extreme learning machine (ELM) neural network [30].
An ELM is an easy-to-use and effective single-hidden layer feedforward neural network (SLFN) learning algorithm [30]. The network consists of an input layer, an implicit layer, and an output layer. The neurons of the input layer and the hidden layer, and the neurons of the the hidden layer and the output layer are fully connected. Among them, the input layer has n neurons, corresponding to n input variables; the hidden layer has 1 neuron; the output layer has m neurons, corresponding to m output variables. ELM only needs to set the number of hidden layer neurons in the network. It does not need to adjust the input weight of the network and the bias of the hidden element during the execution of the algorithm. Compared with the traditional neural network [31][32], it changes the idea that Identifying a fault in T-connected lines BP neural network should be based on the gradient descent learning and does not need to update the network parameters iteratively. It changes the feature that the learning performance of SVM depends too much on parameter adjustment, and has the advantages of fast learning speed and good generalization performance, and only produces the unique optimal solution. N different training samples ( is given, the output containing L hidden layer nodes can be expressed as: where j = 1, 2,. . .,N; a i = [a i1 , a i2 , � � �, a in ] T is the input weight of the input node and the i-th hidden layer node; b i is the neuron offset of the i-th hidden layer node; and is the output weight of the i-th hidden layer node and the output node.
where H ¼ N�m . The implicit layer node excitation function selects the sigmoid function: 2. In the new feature space, as specified in Eq (11), the least square method is used to calculate the optimal output weightb, whereb ¼ H þ T, and H + is the Moore-penrose generalized inverse of H.

Simulation and experiments
The PSCAD/EMTDC electromagnetic transient simulation software is used to establish a 500kV T-connection transmission line simulation model shown in Fig 12. The model adopts the frequency dependent distribution parameter model that can accurately reflect harmonic and transient responses. TOWER:3H5 pole tower is selected as the type of the line. The    The data of 6 branches of T connection transmission line different from the fault types of training samples are taken as test samples respectively, which are input into the trained intelligent fault identification model of the limit learning machine, and the fault branches are identified and tested.

Extreme learning machine intelligent fault identification model establishment and training sample test analysis
The fault characteristic training sample is input into the limit learning machine for training, and a trained extreme learning machine T-connection transmission line intelligent fault identification model is obtained. The optimal number of neurons in the hidden layer of the extreme learning machine obtained by the trial and error method is 70. The fault characteristic training samples are input into the trained extreme learning machine intelligent fault identification model for testing, and the comparison of the predicted results is shown in Fig 14. The above figure shows that the test sample data in the ELM fault intelligent identification model have a correct rate of 100%.  Table 3.  The above chart shows that the test data in the ELM fault intelligent identification model have a correct rate of 100%. When different types of faults occur on each branch of the T-connection transmission line, the faults occurred within and outside the protection zone can be identified, and the fault branch can be accurately identified. Thus, the protection algorithm is not susceptible to type of faults.

Test sample test analysis
Analysis of different transitional resistance tests. The fault characteristic test samples of different transitional resistances within and outside the protection zone are input into the Tconnection transmission line intelligent fault identification model of limit learning machine for testing. A comparison of the prediction results is shown in Fig 16, while the simulation verification result corresponding to the fault conditions is shown in Table 4.
The above chart shows that the test sample data have a correct rate of 100% in the ELM intelligent fault identification model test, and the method can accurately identify internal and external faults and faulty branches when different transitional resistance faults occur on each branch of the T-connection transmission line. Therefore, the fault identification algorithm is not susceptible to the transitional resistance.
Analysis of different fault distance tests. The fault characteristic test samples of different fault distances with and outside the protection zone are input into the T-connection transmission line intelligent fault identification model of the limit learning machine for testing. The comparison of the output prediction results is shown in Fig 17, and the simulation verification results corresponding to the fault condition are reported in Table 5.
The above chart shows that the test sample data have a correct rate of 100% in the ELM intelligent fault identification model test and that the internal and external faults and faulty    Table 6.
The above chart shows that the test sample data are 100% correct in the test of the intelligent fault identification model of the ELM and that the internal and external faults and faulty branches can be accurately identified at different fault initial angles, so the protection algorithm is basically not susceptible to fault initial angles. Fig 19, and the simulation verification results corresponding to the fault condition are reported in Table 7.

Identification results when the fault is near point O. The fault characteristic test sample at the fault near point O is input into the limit learning machine T-connection transmission line intelligent fault identification model for testing. A comparison of the predicted results is shown in
The above chart shows that using the test sample data in the ELM intelligent fault identification model test results in a correct rate of 100%, so the protection algorithm can accurately identify the branch on which the fault occurs near point O of T-connection transmission line.
Other fault condition identification results. In order to further verify the effectiveness of the algorithm, two sets of fault conditions different from the previous ones are selected from each branch of the T-connection transmission line, and 12 sets of fault characteristic vectors are obtained by simulation, and the obtained fault characteristic test samples are input into the  Fig 20, wherein Table 8 is the simulation verification result corresponding to the fault condition. The above diagram shows that under various fault conditions, the result of the test sample data is 100% correct in the extreme learning machine intelligent fault identification model test,

T-connection transmission line fault branch identification performance analysis
The protection speed of the traditional T-connection transmission line traveling wave is very fast, and the anti-CT saturation ability is relatively good. The impact of the capacitor current is  Identifying a fault in T-connected lines theoretically eliminated, but there have been problems with reliability. One of the main reasons is that when a small initial angle fault or a large transitional resistance fault occurs, the generated transient traveling wave signal is relatively weak, and only using the wavefront information of the initial traveling wave may cause the decrease of reliability and sensitivity of the protection. As to the T-connection transmission line fault branch identification method constructed only by using the wavefront information of the initial traveling, peak information loss may occur, and the fault branch identification can easily fail. In this paper, a performance analysis of the T-connection transmission line fault branch identification algorithm in terms of random data loss, anti-CT saturation and noise impact is performed. Analysis of the impact of data loss. In actual engineering operation, data information may be lost. To verify the performance of the algorithm in this case, take the data information loss at the frequency of 40 kHz after the implementation of S-transformation of the reverse traveling wave signal Δi 1− (t) measured by the traveling wave protection unit TR 1 as an example. Simulation verification analysis is carried out on the fault identification algorithm.  Table 9 presents the specific simulation verification result under the data loss of the corresponding internal branch AO and the external branch BE.
➁ Analysis of 2 Fault Identification Algorithms for Random Loss of Sample Points.    The fault characteristic test sample is input into the ELM intelligent fault identification model for testing, and a comparison of the predicted results is shown in Fig 26. The specific simulation verification results under the data loss of the regional branch BO and the outer branch CF are shown in Table 10.
It can be seen from the above chart analysis that the algorithm can 100% identify the faulty branch when the external branch in the T-connection transmission line fails, and the data near the traveling wave head is lost and the sampling point data is randomly lost, which is less susceptible to data loss.
Analysis of anti-CT saturation ability. To verify the anti-CT saturation performance of the protection algorithm proposed in this paper, the CT saturation of each branch of the T-  Identifying a fault in T-connected lines is carried out in the model, and a comparison of the test set prediction results is shown in Fig  27. Table 11 shows the simulation test results of the CT saturation protection algorithm of the T-connection transmission line. It can be seen from the above chart analysis that when the CT of the branch BO in the Tconnection transmission line region is CT saturated, the algorithm can identify the faulty branch 100%, which is less susceptible to CT saturation.
Noise impact analysis. 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 TR m (m = 1, 2, 3) of the T-connection transmission line, and the signal-to-noise ratio (SBRs) is 30 dB~70 dB. Fig 28 is the current-dependent traveling wave waveform measured by the BO fault traveling wave protection unit TR 1 in the T-connection transmission  Identifying a fault in T-connected lines line zone, and Fig 29 is the current-dependent traveling wave waveform measured by the traveling wave protection unit TR 1 when the AD branch is outside the T-connection transmission line zone. (The current traveling wave measured by the traveling wave protection unit TR 1 is taken as an example when the signal-to-noise ratio is 30 dB and the frequency after S conversion is 40 kHz). In the regional BO branch and the out-of-zone AD branch, a set of faults different from the training samples are selected, noise is added to the voltage and current signals, and the signalto-noise ratio (SBRs) are 30 dB, 40 dB, 50 dB, 60 dB, and 70 dB, respectively. The simulation results show 10 sets of T-connection transmission line fault eigenvectors, and the fault characteristic test sample matrix is input into the ELM intelligent fault identification model for testing. A comparison of the predicted results is shown in Fig 30 below. Table 12 shows the regional branch BO and the outer branch. The simulation test results of the road AD under different SNR faults are provided. According to the analysis of the above chart results, when the regional branch BO and the outer branch AD are under different SNR faults, the algorithm can identify the faulty branch 100%, which is only slightly susceptible to noise.

Motion speed analysis
At present, the traditional power frequency T-connection transmission line fault identification algorithm is widely used in the full-circumference or half-cycle Fourier algorithm. To ensure the accuracy of the calculation, the full-cycle Fourier algorithm requires a data window of 20 ms, and the half-cycle Fourier algorithm requires 10ms. The data window required by the proposed algorithm is 0.5 ms, which greatly shortens the data window length compared with the traditional power frequency T-connection transmission line fault identification algorithm. Identifying a fault in T-connected lines Therefore, the proposed algorithm will have higher speed. In the traditional power frequency T connected to the line outside the fault identification algorithm.

Fault tolerance analysis
At present, the traditional T-connection transmission line fault identification algorithm in the T-connection transmission line does not simulate the data loss, and can not verify the fault tolerance of the algorithm. In this paper, the influence of fault electrical data loss on the proposed algorithm is simulated. When the data near the traveling wave head is lost and the sampling point data is randomly lost, the simulation results show that the algorithm can identify the fault quickly and accurately.

Identification accuracy analysis
At present, the traditional T-connection transmission line fault identification algorithm can identify the faults in the T-connection transmission line, but it can not identify the specific branch of the fault in the zone and outside, and does not analyze the influence of noise on the accuracy of the algorithm identification. Moreover, the selection of the braking coefficient in the traditional current differential protection criterion based on the fault component is especially important for the sensitivity and reliability of fault identification in the T-connection transmission line. For example, for the protection criteria mentioned in [7], when braking if the coefficient is too large, the sensitivity of the internal fault action is not guaranteed. When the brake coefficient is selected too small, the reliability of the external fault brake is bound to decrease. The new method of T-line fault identification based on S-transform energy entropy and extreme learning machine proposed in this paper, using the advantages of high learning efficiency and generalization ability of extreme learning machine to identify fault branch of Tconnection line. In the process, not only can the faults in the area and outside be accurately and effectively identified, but also the specific branch of the fault can be identified. Compared with the traditional fault identification algorithm, this paper proposes a new method of T-connection transmission line fault identification based on S-transform energy entropy and an extreme learning machine, which utilizes the advantages of high learning efficiency and generalization ability of the extreme learning machine. Road identification, in the process of fault identification, not only can accurately identify the faults inside and outside the zone, but can also identify the specific branch of the fault. And in the simulation experiment under the influence of 30-70 db of noise, the faulty branch can be identified quickly and accurately.