Fault identification in T-connection transmission lines based on general regression neural network and traveling wave power angle

In order to improve the accuracy of internal and external fault identification of T-connected transmission lines, a new method for identifying internal and external faults of T-connected transmission lines based on general regression neural network and traveling wave power angle was studied. The initial voltage and current traveling wave measured by each traveling wave protection unit of T-connected transmission line are transformed by S-transform, and the single frequency power angle after fault is calculated to form the sample set of fault eigenvector of T-connected transmission line. The established general regression neural network intelligent fault recognition model is used to train and test the sample data to identify internal and external faults. The simulation results show that the algorithm can accurately identify the internal and external faults of the T-connected transmission line under various operating conditions.


Introduction
High-voltage transmission lines are the place where the most faults occur in the power system. Finding faults quickly through fault diagnosis and excluding faults are of great significance to the safe and stable operation of the power system [1][2]. With the continuous development of the power system, Tconnection transmission lines have been widely used in power systems due to their small transmission corridors, small footprints, and other objective factors. However, these lines are often connected to large power plants and large systems. When a fault occurs, it is required to be able to diagnose the fault quickly and reliably [3][4][5], and then eliminate the fault.
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 transmission line three-terminal voltage fault component and the phasor sum of the current fault component. Reference [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. In reference [8], in order to improve the sensitivity of the standard in case of internal fault and the reliability in case of external fault, the standard proposed in [7] is improved. The ICAACE 2020 Journal of Physics: Conference Series 1570 (2020) 012054 IOP Publishing doi: 10.1088/1742-6596/1570/1/012054 2 sinusoidal angle between the maximum current in the three-terminal fault current component of the Tconnected transmission line and the current at the other two ends is used as the criterion braking coefficient to identify the faults inside and outside the zone. Reference [9] combined the arrival time of transient traveling waves at each end of the line in pairs to obtain a fault branch discrimination matrix composed of fault distances. However, this method is complicated and difficult to implement. In reference [10], a second-order Taylor-Kalman-Fourier filter is used to process voltage and current signals, and the positive sequence impedance information to obtained from the voltage and current signals is used to identify internal and external faults.
This article is based on the study of the fault power angle when T-connection transmission line occur internal and external fault, proposes a new fault identification method for T-connection transmission line based on general regression neural network and traveling wave power angle. The algorithm uses the initial voltage and current traveling wave sampling point data of the three-terminal traveling wave protection unit in the T-connection transmission line after the S-transformation, obtain the power angle of each traveling wave protection unit at a single frequency and form them into a Tconnection transmission line fault characteristic sample set in a specific order, combined with the general regression neural network to realize the identification of the faults internal and external the Tconnection transmission line. Fig 1 shows a 500-KV T-connection transmission line. The three branches AO, BO and CO in Fig. 1 are defined as the internal branches of the T-connection transmission line, and the remaining branches are the external branches.

2.1The theory of fault traveling waves
500kv T-connection transmission line The traveling wave protection units TR 1~T R 3 are installed at the three ends of the branches near A, B, and C, respectively. When a fault occurs at F 1 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 [11]: In the equations above, t is the observation time; L and C are the inductance and capacitance of the transmission line per unit length; 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    is the initial voltage traveling wave measured by the threeterminal traveling wave protection unit of the internal branch near A, B and C, respectively. And 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. Z . It can be known from the line wave impedance that it is approximated as a real constant [12][13][14],

Fig. 2. Peterson equivalent circuit when OA branch fault in T-connection transmission line internal
According to the definition of the initial traveling wave complex power [16], It can be obtained that the initial traveling wave complex power at the A end of the line bus is: (2) When the the fault in the internal OA branch , the Peterson equivalent circuit in Fig.2 shows: The complex power measured by the 1 TR traveling wave protection unit at the A end of the AO branch can be obtained: In the formula, A P is the initial traveling wave active power of the line, and A Q is the initial traveling wave reactive power of the line.

2.2.2Initial traveling wave power distribution when faults in the external: When a fault 2
F occurs at the AD branch in the T-connection transmission line, the Peterson equivalent circuit of the Tconnection line is shown in Fig.3, The complex power measured by the traveling wave protection unit 1 TR is: In the formula, A P is the initial traveling wave active power of the line, and A Q is the initial traveling wave reactive power of the line.

Calculation of initial traveling wave power angle based on S-transform
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 [15].
In the equations above, u   and u   are Clark's α-and β-modes voltage, respectively; and i   and i   are Clark's α-and β-mode current, respectively. This article refers to the method used in [16], discrete S-transformation will be performed on the phase-mode transformed fault current and voltage traveling wave modulus, select the current and voltage retrograde wave head information at a single frequency after the fault to calculate the initial traveling wave power angle. is:

3.1S transform principle
In the equation, 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. Since the S transform has good signal extraction characteristics in time-frequency analysis, therefore, this article uses S transform to extract the fault current traveling wave and fault voltage traveling wave, based on this, the initial traveling wave power angle is calculated.

3.2S-transformed initial traveling wave power angle
S-transform is implemented on the current and voltage traveling wave data detected by the traveling wave protection unit

General Regression Neural Network
General Regression Neural Network (GRNN) is a nonlinear regression neural network model proposed by Donald F. Specht. It has very obvious advantages in approximation ability and learning rate，Very good classification and prediction results are obtained when the sample data is small. The algorithm has achieved good results in classification, prediction and optimization. GRNN and RBF are very similar in structure, It includes an input layer, a mode layer, a summing layer, and an output layer. The structure is shown in Fig.4.  Fig.4. Structure of general regression neural network GRNN is based on nonlinear regression analysis [17]. Let the joint probability density function of the random variables x and y be   , f x y , The corresponding input is X ，the output is Y and the observed value of A is B, Then the regression of y to X , that is, the conditional mean is : For unknown   , f x y , the estimation obtained by Parzen nonparametric estimation can be applied [18], estimates can be obtained by calculation: is the activation function of the neuron, i X and i Y are sample observations of the random variables x and y , respectively, n is the number of samples,  is the width coefficient of Gaussian function, estimate   Y X is the weighted average of all i Y .

Simulation and experiments
The PSCAD/EMTDC electromagnetic transient simulation software is used to establish a 500kV Tconnection transmission line simulation model shown in Fig.1  . The simulation sampling frequency is 200kHz, and the length of each branch is AO = 300km, BO = 200km, CO = 150km, AD = 170km, BE = 150km, CF = 180km.

5.2Establishing a General Regression Neural Network Intelligent Fault Identification Model
The training samples of the power connection angle fault feature of the T-connection transmission line are input into the general regression neural network for training, and a trained general regression neural network intelligent fault recognition model is obtained. The training samples are then input to the model for testing, and the comparison of the prediction results is shown in Fig.5. Where, the recognition results of the generalized regression fault intelligent identification model are divided into specific branches in the case of internal faults and external AD, BE, CF faults.
As can be seen from the below figure, the test sample data is 100% correct in the general regression neural network fault intelligent recognition model.  As can be seen from the above table, the accuracy of the test sample data in the generalized regression neural network intelligent fault recognition model test is 100%.

Analysis of initial angle test of different faults:
The fault feature test samples with different initial fault angles inside and outside the zone are input to the generalized regression neural network intelligent fault recognition model for testing. The prediction results are shown in Table 3.  external fault As can be seen from the above table, the test sample data is 100% accurate in the test of the generalized regression neural network machine intelligent fault recognition model, so the fault recognition algorithm is not affected by the transition resistance.

Summary
This paper proposes a fault identification method for T-connection transmission lines based on generalized regression neural network and traveling wave power angle. The feasibility of the fault identification method is verified through a large number of simulation experiments. Simulation results show that the algorithm works in various operating conditions. Both can accurately identify the internal and external faults of the T-connection transmission line, and basically overcome the influence of factors such as the transition resistance and the initial angle of the fault.