Phase Selection and Location Method of Generator Stator Winding Ground Fault Based on BP Neural Network

Abstract

The phase selection and fault location methods of generator stator winding single-phase grounding fault are greatly affected by the transition resistance. A new phase selection and generator stator ground fault location approach based on the BP neural network is proposed in this research from a data-driven angle. This method uses a neural network to calculate the probability of three-phase fault occurrence to identify the fault phase and directly calculate the fault location that takes the amplitude and phase angle characteristics of zero-sequence voltage as input. The simulation results show that the stator ground fault phase selection and location algorithm based on the neural network can achieve correct phase selection and small positioning error, which has verified the effectiveness of the method.

1. Introduction

The heart of the power system is a sizable generator, and the foundation for the power system’s reliable functioning is its safe operation. At present, the proportion of large-capacity generators is increasing, and the current of stator single-phase ground fault increases with the increase in capacity. As the most common fault in generators [1,2], if it cannot be handled in time, it is easy to cause core burns or develop into phase-to-phase faults, which pose a huge threat to the unit itself and the power system.

Machine learning has emerged in recent years. In reference [3], they presented robust artificial intelligence techniques for inter-turn short circuit (ITSC) fault detection of the stator in three-phase induction motors. Reference [4] focused on three numerical techniques: finite element analysis, signal analysis, and artificial neural networks in the diagnosis of a squirrel cage induction machine under inter-turn short circuits in stator windings. The one-dimensional convolutional neural network was applied to the detection and classification of induction motor faults [5]. In reference [6], this paper presented an application of the growing curvilinear component analysis (GCCA) neural network aided by the extended park vector approach (EPVA) for the purpose of transforming the three-phase current signals. Reference [7] proposed a method to discriminate between different types of faults in the stator and rotor windings of wound rotor induction machines. In recent years, a large number of scholars have proposed their methods for fault diagnosis of stator/rotor winding faults. Reference [8] proposed a novel robust diagnosis design for the possible incipient stator/rotor winding faults. Reference [9] analyzed modeling, diagnosis, and detection of broken bar faults and inter-turn short circuit faults in open-end winding induction motors based on the motor current signature analysis method by the fast Fourier transform. In reference [10], the harmonic components of the stator current generated by the rotor turn-to-turn short circuit were analyzed based on the wavelet decomposition method.

At present, the generator stator ground fault protection mainly adopts the basic zero-sequence voltage criterion [11], the third-order harmonic voltage criterion [12], the low-frequency injection criterion [13], the fault current criterion [14], and so on. The above criteria can reliably detect and isolate ground faults. But for transient grounding faults, the generator still needs to be shut down, and power supply reliability cannot be guaranteed. For permanent ground fault, even if the generator is isolated from the system and the excitation current is reduced to zero, the residual magnetic field in the stator winding still exists for a long time, and the ground fault current cannot disappear [15]. Excessive grounding fault current will damage the stator core and cause maintenance difficulties. Therefore, a reliable fault suppression strategy is very necessary.

In reference [16], a stator ground fault location method based on injection protection was proposed. The low-frequency information of the injection equipment was used to measure the transition resistance, and then the fault location was realized. In reference [17], the grounding capacitance and the ground-fault resistance were estimated online by the Kaman filtering method with the measurements provided by the low-frequency injection protection equipment. In reference [18], the loop current method was used to construct the third harmonic equivalent circuit after the fault, and the fault position and transition resistance were solved based on the third harmonic voltages measured at the neutral point and generator terminal. For the above fault location methods, the phase-band distribution characteristics of the stator winding potential have been neglected, resulting in certain theoretical errors.

Phase selection can be realized by using the terminal voltage of the generator [14]. The voltage of the fault phase is the lowest. Reference [19] proposed a phase selection method using the phase characteristics of the zero-sequence voltage. For the above methods, which both consider the phase angle between the winding potential and the phase potential, these methods malfunction or are not sensitive when there is a high-resistance ground fault. Aiming at this problem, reference [20] re-divided the phase selection zone and used the transition resistance measured by the injection protection.

The fault location method based on the amplitude of the zero-sequence voltage is greatly affected by the transition resistance, so calculating the transition resistance correctly is the key to the fault location. The transition resistance can be calculated by using the additional injection signal for the unit with injection protection [21], but it cannot be applied to the generator without injection protection. The transition resistance can also be calculated by the three-phase voltage offset characteristics [22], but this method does not consider the phase angle of the winding potential.

Phase selection and fault location are difficult for a high-resistance ground fault. To solve the problem from a data-driven perspective, this paper proposes a new idea of phase selection and location for generator stator single-phase ground fault based on the BP neural network. Phase selection is realized by comparing the probability of three phases, and at the same time, the neural network model is used to calculate the fault location. For the fault phase selection in the fuzzy area, the phase characteristics of the zero-sequence voltage of the generator are considered, and the amplitude characteristics of the zero-sequence voltage are added as auxiliary criteria in the information source for phase selection and localization. The proposed method no longer requires calculating the transition resistance in advance and applies to generator units with different winding structures. And finally, simulation results verify the feasibility of the algorithm.

2. Theoretical Basis of Phase Selection and Location of Stator Ground Fault

2.1. Zero-Sequence Voltage Characteristics of Stator Single-Phase Ground Fault

Assuming that the generator neutral point is grounded by high resistance, the three phases are symmetrical before the fault, i.e., the three-phase stator winding ground capacitances C_A, C_B, and C_C are equal. When a single-phase ground fault occurs in phase A, ignoring the resistance and inductance of the stator winding, the generator stator winding phase-A ground fault diagram is shown in Figure 1. In the diagram, ${\dot{U}}_0$ represents the zero-sequence voltage of the neutral point, α represents the percentage of the winding from the fault point to the neutral point in the phase A winding, ${\dot{E}}_{\mathrm{B}}$ and ${\dot{E}}_{\mathrm{C}}$ represent the phase potential during normal operation, $\dot{E}\left(\alpha \right)$ represents the winding potential of phase A from the fault point to the neutral point, R_N represents the neutral point ground resistance of the generator, and R_f represents the transition resistance of the fault point.

When the fault occurs, using the idea of fault component, the zero-sequence voltage is

$${\dot{U}}_0=-\frac{\dot{E}(\alpha )}{\frac{R_{\mathrm{f}}}{R_{\mathrm{N}}}+1+\mathrm{j}\omega C_{\mathrm{G}\Sigma }{R}_{\mathrm{f}}}$$

(1)

In the formula, C_G∑ is the three-phase total ground capacitance of the generator, C_{G ∑} = C_A + C_B + C_C.

Usually, there are two branches in each phase of the stator winding for a large non-salient pole generator, and the winding potential is distributed with a 60° phase band, so the phase of the winding potential should be considered. Taking the QFSN-600-2YHG generator as an example, there are seven turns per branch and its electrical angle $\beta =8.57°$. It is assumed that the first branch winding potential leads the phase A potential, and the second branch winding potential lags the phase A potential. The turn potential distribution is shown in Figure 2.

The winding potential $\dot{E}\left(\alpha \right)$ can be calculated as

$$\dot{E}\left(\alpha \right)=\alpha {\dot{E}}_{\mathrm{A}}{e}^{\mathrm{j}\theta }$$

(2)

where θ is the angle of the winding potential that represents the phase potential. The relationship between the phase angle of the first branch winding potential θ and the fault location α is $\theta =30°(1-\alpha )$, and the second branch is $\theta =-30°(1-\alpha )$.

2.2. Theoretical Basis of Fault Phase Selection Algorithm

There are two main methods for phase selection of stator ground fault: low voltage phase selection and phase selection based on zero-sequence voltage phase characteristics.

Taking the phase A ground fault as an example, the criterion of the low voltage phase selection algorithm is U_A ≤ U_B and U_A ≤ U_C. The equivalent phase criterion is

$$120°\le \arg ({\dot{U}}_0/{\dot{E}}_{\mathrm{A}})\le 240°$$

(3)

Reference [20] proposed a phase selection method based on the phase characteristics of zero-sequence voltage. Firstly, the phase angle $\psi =\arg ({\dot{U}}_0/{\dot{E}}_{\mathrm{A}})$ of zero-sequence voltage and A-phase potential is calculated, and the fault phase is selected according to the phase angle $\psi$. The phase selection criterion is:

When $90°\le \psi \le 210°$, it is phase A ground fault;

when $-30°\le \psi \le 90°$, it is phase B ground fault;

when $-150°\le \psi \le -30°$, it is phase C ground fault;

Taking the ground short circuit of generator A phase winding as an example, it can be obtained by Formulas (1) and (2) that

$$\begin{array}{l}\psi =\arg \frac{-\alpha \times e^{\mathrm{j}\theta }}{R_{\mathrm{f}}/R_{\mathrm{N}}+1+\mathrm{j}{R}_{\mathrm{f}}/X_{\mathrm{C}\Sigma }}\\ ={180}^{°}+\theta -\arg \left(\frac{R_{\mathrm{f}}}{R_{\mathrm{N}}}+1+\mathrm{j}\frac{R_{\mathrm{f}}}{X_{\mathrm{C}\Sigma }}\right)\end{array}$$

(4)

where X_C∑ is the total three-phase ground capacitive reactance of generator stator winding.

From Formula (4), we can see that the phase angle $\psi =\arg ({\dot{U}}_0/{\dot{E}}_{\mathrm{A}})$ shifts to the fault zone of phase B with the increase in transition resistance R_f ground, so the sensitivity of phase selection is not high when a high-resistance ground fault occurs. Considering the most unfavorable situation, the high resistance ground fault occurring in the second branch of phase A ground is analyzed.

The neutral ground resistance is generally selected as no more than three-phase total capacitive reactance to limit transient overvoltage multiples. However, to limit the short-circuit current, some generators increase the neutral ground resistance. Considering the limitation of short-circuit current and the transient overvoltage multiple, R_N = 3X_C∑ [23] is taken for the most unfavorable situation. The maximum transition resistance is selected according to the setting of the fundamental zero-sequence voltage which is 0.05 rated voltage, that is

$$U_0=\frac{\alpha E_{\mathrm{A}}}{\left|\frac{R_{\mathrm{f}}}{R_{\mathrm{N}}}+1+\mathrm{j}\frac{R_{\mathrm{f}}}{X_{\mathrm{C}\Sigma }}\right|}=0.05E_{\mathrm{A}}$$

(5)

Based on the above most unfavorable conditions, the maximum transition resistance multiple that can be tolerated at different α positions and the minimum value of $\psi$ at that position can be obtained, as shown in

Table 1. Angle values at different fault positions.

$\mathit{\alpha }$	${\mathit{R}}_{\mathbf{f}}/{\mathit{X}}_{\mathbf{C}\mathbf{\Sigma }}$	$\mathit{\psi }$
0.1	1.37	109.75
0.2	3.38	98.15
0.3	5.32	96.53
0.4	7.23	97.24
0.5	9.14	98.87
0.6	11.04	100.96
0.7	12.95	103.32
0.8	14.85	105.
0.9	18.75	108.45
1	18.65	111.15

.

It can be seen from Table 1 that when the fault location α is 0.3, $\psi$ is the minimum value of 96.53°. The low voltage phase selection criterion will malfunction in this case.

When a metallic ground fault occurs in the first branch of phase B, the phase angle of the winding potential is ahead of the phase B potential, and the angle limit of the ψ angle is 90 degrees, close to the action boundary. Considering the measurement error, when only using the phase characteristics of zero-sequence voltage, it is difficult to distinguish between a high-resistance ground fault in the second branch of phase A and a metallic ground fault in the first branch of phase B.

Therefore, this paper divides the angle into six zones, including three determined areas and three fuzzy areas. The determined area is:

When $120°\le \psi \le 180°$, it is phase A ground fault;

when $0°\le \psi \le 60°$, it is phase B ground fault;

when $-120°\le \psi \le -60°$, it is phase C ground fault.

The remaining areas are fuzzy. For example, $60°\le \psi \le 120°$ is the fuzzy area of a high resistance ground fault in the second branch of phase A and a metallic ground fault in the first branch of phase B. When the fault is in the fuzzy area, the amplitude of the zero-sequence voltage is considered in this paper. Based on the pattern recognition idea of artificial intelligence, the BP neural network is used to realize fault phase selection in the fuzzy area.

2.3. Theoretical Basis of Fault Location Algorithm

The amplitude of zero-sequence voltage is approximately $E(\alpha )\approx \alpha E_{\mathrm{A}}$, so the stator ground fault location α can be obtained by Formula (1)

$$\alpha =\left|\frac{U_0}{E_{\mathrm{A}}}\right|\left|\mathrm{j}\omega C_{\mathrm{G\Sigma }}{R}_{\mathrm{f}}+1+\frac{R_{\mathrm{f}}}{R_{\mathrm{N}}}\right|$$

(6)

The amplitude of zero-sequence voltage, the phase potential, and the ground capacitance of stator winding can be obtained by measurement. It can be seen from Formula (6) that the fault location is greatly affected by the transition resistance, so it is difficult to locate the fault only by using the amplitude of the zero-sequence voltage. Therefore, the key to fault location is an accurate calculation of the transition resistance. For the generators with injection stator ground fault protection, the transition resistance can be measured by the additional injection signal. For generators not equipped with injection protection, a method for calculating the transition resistance is proposed based on phase voltage offset characteristics, briefly described as follows:

When phase A ground fault occurs, the phase voltage offset factor k is calculated first, and then the transition resistance R_f is calculated. This method ignores the phase characteristics of the winding potential when calculating the transition resistance, so the calculation error is large.

When the stator single-phase ground fault occurs, the amplitude and phase of the zero-sequence voltage change with the transition resistance. Therefore, from the perspective of data-driven and artificial intelligence technology, a new idea of phase selection and location for stator ground fault is proposed based on the BP neural network, which can realize correct phase selection and fault location.

3. Phase Selection and Location Method of Stator Ground Fault Based on BP Neural Network

A neural network is a mathematical model for information processing which can imitate the behavior characteristics of biological neural networks. The model is composed of an input layer, a hidden layer, and an output layer [24]. In this paper, a new phase selection and location method based on the BP neural network for stator ground fault is proposed that uses zero-sequence voltage amplitude and phase information as input layer data.

3.1. Phase Selection Method of Stator Ground Fault Based on BP Neural Network

Existing studies have shown that the BP neural network with a single hidden layer can approximate any nonlinear continuous function with arbitrary accuracy, which meets the requirements of the phase selection and localization algorithm in this paper when the numbers of the input layer and output layer are small. Therefore, a single hidden layer BP neural network fault phase selection model with two inputs and three outputs is developed, as shown in Figure 3. In Figure 3, X₁ and X₂ represent the two neurons of the input layer, and the input information sources are the amplitude U₀ and the phase ψ of the zero-sequence voltage; Y₁, Y₂, and Y₃ represent the neurons of the output layer, and the output information Y_A, Y_B, and Y_C represent the probability of fault occurrence in the A, B, and C phases. w and u represent the connection weights between neurons, and b represents the offset of neurons; because the single hidden layer can deal with the triple output data well and ensure the accuracy of the model, the single hidden layer is selected. The number of hidden layer neurons m is determined by comparing the training results.

There is an order of magnitude difference between the zero-sequence voltage amplitude U₀ and phase $\psi$. To reduce the effect of the order of magnitude difference on the MSE and to improve the convergence speed of the algorithm. The raw input data are mean normalized. Taking the $\psi$ data set as an example:

$${\psi }_i{}^{\prime }=\frac{{\psi }_i-{\psi }_{\mathrm{avg}}}{{\psi }_{\max }-{\psi }_{\min }}$$

(7)

In the formula, ${\psi }_i$ is the ith data in the data group, ${\psi }_{\mathrm{avg}}$ is the average value of the $\psi$ data group, ${\psi }_{\max }$ is the maximum value of the $\psi$ data group, ${\psi }_{\min }$ is the minimum value of the $\psi$ data group, and ${\psi }_i{}^{\prime }$ is the ith normalized value of the $\psi$ data group.

The training process of the neural network is mainly divided into two stages: the first stage is the forward propagation of the signal from the input layer to the hidden layer, where the input $ne{t}_{{\mathrm{M}}_1}$ of the hidden layer neuron M₁ is

$$ne{t}_{{\mathrm{M}}_1}=w_{1,1}{p}_1+w_{2,1}{p}_2+b_{1,1}$$

(8)

In the formula: p represents the output value of the neurons in the input layer.

The output of the jth neuron n_j in the hidden layer processed by the Sigmoid activation function is

$$n_j=S\left[{\displaystyle \sum _{i=1}^2\left(w_{i,j}{p}_i\right)}+b_{j,1}\right], j=1,\cdots ,m$$

(9)

In the formula: w_i,j is the weight of the ith input layer data to the jth neuron in the hidden layer; b_j,1 represents the offset of the jth neuron in the hidden layer; S(x) represents the Sigmoid activation function.

From the hidden layer to the output layer, the input z_j of the output layer neuron Y₁ is

$$z_j=u_{1,1}{n}_1+u_{2,1}{n}_2+\dots +u_{m,1}{n}_j+\dots +b_{1,2}$$

(10)

The output layer function selects the SoftMax function, which is more suitable for pattern recognition, and outputs the probability of fault occurrence in the A, B, and C phases. The output y_j of the jth neuron in the output layer is

$$y_j=e^{z_j}/{\displaystyle \sum _{j=1}^3{e}^{z_j}}, j=1,2,3$$

(11)

At this time, the forward propagation of the neural network has been trained. To ensure the accuracy of the BP neural network, the MSE loss function (the mean square error between the estimated value of the neural network output probability and the real probability value) is used as the main index to evaluate the performance of the algorithm. The calculation formula for the MSE loss function is

$$MSE=\frac{1}{N}{\displaystyle \sum _{n=1}^N{\left[\widehat{P_n}\left(w^l,b^l\right)-P_n\right]}^2}$$

(12)

In the formula: $\widehat{P_n}\left(w^l,b^l\right)$ is the nth output prediction value of the neural network; l represents the number of layers; P_n is the nth real output sample value in the zero-sequence voltage data set; N is the number of outputs of the neural network.

The second stage is the backpropagation of the error, with a certain weight $u_{1,1}$ as an example to calculate its impact on the overall error, obtained by MSE partial derivative

$$\frac{\partial MSE}{\partial u_{1,1}}=\frac{\partial MSE}{\partial y_j}\times \frac{\partial y_j}{\partial z_j}\times \frac{\partial z_j}{\partial u_{1,1}}$$

(13)

The updated weight value is:

$$u^{\text{'}}{}_{1,1}=u_{1,1}-\eta \times \frac{\partial MSE}{\partial u_{1,1}}$$

(14)

In the formula: $\eta$ is the learning step, a small value is generally taken to maintain the stability of the system, in this paper 0.01 is taken.

The output of three-phase fault probability is used to realize the phase selection criterion as follows:

Y_A>> Y_B and Y_A >> Y_C is judged as phase A ground fault;

Y_B>> Y_C and Y_B >> Y_C is judged as phase B ground fault;

Y_C>> Y_A and Y_C >> Y_A is judged as phase C ground fault.

The flow of the phase selection algorithm ground based on the BP neural network in this paper is shown in Figure 4. The specific steps are as follows:

(1)

Establish the phase selection model based on the BP neural network, determine the model training algorithm and the neurons’ number of the hidden layer, and initialize the weight and offset of the neural network. The data to be normalized are then mean normalized.

(2)

The training set data is used to train the BP neural network, and the error of fault probability between the output layer and the expected target is obtained by the forward propagation of the neural network.

(3)

Judge whether the MSE value and error of the model meet the requirements. If the BP neural network model converges, perform step (5); otherwise, perform step (4).

(4)

Backpropagation and weight optimization. The backpropagation algorithm of the BP neural network distributes the error obtained in step (2) to each node layer by layer, updates the weight, and repeats steps (2) to (4) until the MSE value and error of the BP neural network phase selection model meet the requirements.

(5)

Using validation set data to test the effect of the BP neural network phase selection model, such as satisfying the end of model training. If not satisfied, re-execute step (1).

3.2. Stator Ground Fault Location Algorithm Based on BP Neural Network

The stator ground fault location model based on the BP neural network also adopts the BP neural network model with two inputs, three outputs, and a single hidden layer; the model structure is also shown in Figure 3. The input information and hidden layer function are the same as in the phase selection model, but the function of the output layer adopts a linear function that is more suitable for data output. The output information is fault location α_c, transition resistance R_c and winding potential phase angle θ_c. Using the Sigmoid function in the hidden layer and the linear function in the output layer can well fit the multidimensional mapping problem. The specific steps and normalization methods of the BP neural network-based generator stator ground fault location model established in this paper are similar to the phase selection method proposed in this paper.

4. Algorithm Validation

4.1. Acquisition of Training and Test Samples

To obtain the training and test samples, a simulation model for the generator stator winding ground fault is established based on MATLAB/Simulink. The stator winding adopts the distributed parameter model, and each branch is divided into 7-unit circuits, as shown in Figure 5. The parameters of the QFSN-600-2YHG steam turbine generator are adopted as model parameters, including the rated voltage Un = 20 kV, the resistance per phase Rs = 1.488 mΩ, and the inductance per phase Ls = 227.05 μH. The total three-phase capacitance to earth C_GΣ = 0.681 μF. There are two branches in each phase. Take phase A as an example, the potential of A₁ winding leads that of phase A, and the potential of A₂ winding leads that of phase A. The turn potential of the winding is distributed in a 60° phase band, as shown in Figure 2 above.

The fault locations are set at the 1st~7th turns of each branch, with 42 fault points in total. The amplitude and phase information of zero-sequence voltage can be obtained by setting different transition resistors. Taking the fault location model based on the BP neural network as an example, 42,774 sets of data were obtained through simulation. Among them, 2681 sets of fault data are used as test sets, which are obtained from the fourth and sixth turns fault of phase A, and the rest of the data are used for model training. The training data is divided into a training set and a validation set, and the proportion of the training set and validation set is 70%:30%. The training set data is used to establish the model parameters, and the validation set data is used for the preliminary model evaluation.

4.2. Training of BP Neural Network Model

4.2.1. Selection of Training Algorithm

The training algorithm of the BP neural network generally adopts Levenberg–Marquardt, scaled conjugate gradient, and Bayesian regularization. For the phase selection model and fault location model based on the neural network, setting the neurons’ number of the hidden layer to 15, the MSE loss function, and iterations times under the three training algorithms are shown in

Table 2. MSE and iterations under different training algorithms.

Model	The Training Algorithm	Iterations	MSE
Phase selection model	Levenberg–Marquardt	132	0.073
	Scaled conjugate gradient	537	0.251
	Bayesian regularization	239	0.162
Fault location model	Levenberg–Marquardt	497	0.005
	Scaled conjugate gradient	861	0.017
	Bayesian regularization	615	0.008

.

According to Table 2, the MSE value and iterations of the Levenberg–Marquardt training algorithm are smaller than the other two algorithms. Therefore, Levenberg–Marquardt is selected as the training algorithm in this paper.

From a mathematical point of view, the BP algorithm is a local search optimization method. And in this paper, its training algorithm uses the Levenberg–Marquardt algorithm, which automatically tunes the parameters. So, part of the hyperparameters of the BP neural network we do not discuss here.

4.2.2. Determination of the Neurons’ Number

The neurons’ number of the hidden layer plays an important role in the accuracy of the model. To select the appropriate neurons’ number, the influence on the MSE value is analyzed when the neurons’ number is different for the phase selection and location model. MSE values of the phase selection model and location model under different neurons number are shown in Figure 6 and Figure 7.

According to Figure 6, the MSE value is the minimum for the phase selection model when the neurons’ number of the hidden layer is 10. Too few or too many neurons will increase the MSE value, which will greatly affect the accuracy of the model. The neurons number of the hidden layer finally selected is 10.

For the fault location model, when the neurons number is 5–20, all the MSE values are low. The neurons’ number of the hidden layer that was finally selected is 12, and the MSE value is 0.00029.

4.2.3. Model Training Process

According to the determined training algorithm and the number of neurons, the phase selection and location model based on the BP neural network is trained. The model training is the process of continuously adjusting the weight w, u, and offset b of the neuron. The initialization weight and offset are normalized to a random number between 0 and 1. Train the model with the training set data to make the output reach the expected value and determine the weight and offset. Using validation set data to preliminarily evaluate the effect of the model.

In the training process, the change curves of the MSE value and accuracy of the training set and validation set are shown in Figure 8 and Figure 9. The red circle in the figure indicates that the model has met the requirements.

According to Figure 8 and Figure 9, the MSE values of the training set and the validation set gradually decrease and converge with the increase in iterations. When the iteration is greater than 29, the MSE value reaches its best and can be stably maintained at 0.0569, which shows the training model is stable. The accuracy of phase selection increases with the increase in iterations, which can approach 100% infinitely and tend to be stable. The phase selection model based on the BP neural network converges rapidly, and the model training effect is good.

Similarly, the fault location model based on the BP neural network is trained. The change curves of MSE value and accuracy in the training process are shown in Figure 10 and Figure 11.

From Figure 10 and Figure 11, the MSE value of the location model can also achieve the best and remain stable. When location accuracy can infinitely approach 100% and tends to be stable, the model has reached the training effect.

4.3. Verification of Phase Selection and Location Algorithm Based on BP Neural Network

4.3.1. Verification of Phase Selection Algorithm

To verify the feasibility of the phase selection algorithm, the test set data is used to verify that all the results are correct. Considering the unfavorable situation, a high-resistance ground fault occurs in the A₂ branch, whose winding potential lags the phase potential ground, and a metallic ground fault occurs in the B₁ branch, whose winding potential is ahead of the phase potential ground. The analysis results of the phase selection algorithm based on the BP neural network are shown in

Table 3. The result of phase selection.

Fault Condition	Rf/Ω	U0/kV	$\psi$	YA	YB	YC
A2 branch α = 42.86%	19860	0.092	102.484	0.972	0.015	0.013
	28960	0.065	99.180	0.973	0.015	0.002
	38060	0.050	97.377	0.966	0.023	0.011
B1 branch α = 14.29%	0.01	0.134	86.399	0.019	0.976	0.005
	0.1	0.155	85.798	0.011	0.986	0.003
	1	0.155	85.787	0.013	0.986	0.001

.

According to the analysis in Table 3, the phase selection algorithm based on the BP neural network can correctly identify the fault phase in both high-resistance ground fault and metallic fault. The calculated probability of the fault phase is much greater than that of the other two phases, which are above 95%. This method can select the fault phase accurately without being affected by the transition resistance.

4.3.2. Validation of Location Algorithm

The feasibility of the location algorithm is verified by the test set data, and the result shows all the faults can be accurately located. This paper gives the location results when the faults occurred at 57.14% and 85.71% of the location of the A₁ branch, as shown in

Table 4. The result of fault location.

Fault Condition	Transition Resistance Rf/Ω	Arithmetic Resister RC/Ω	Winding Potential Angle θ	Fault Location ${\mathit{\alpha }}_{\mathbf{c}}$	Positioning Error εα
A1 branch α = 57.14% θ = 12.858°	200	202	12.859°	57.16%	0.035%
	2000	2009	12.858°	57.17%	0.053%
	5000	5006	12.859°	57.16%	0.035%
	9980	9973	12.860°	57.19%	0.088%
A1 branch α = 85.71% θ = 4.286°	200	197	4.290°	85.70%	−0.01%
	2000	2003	4.287°	85.71%	0.000%
	5000	5009	4.286°	85.72%	0.012%
	9980	9982	4.288°	85.77%	0.070%

.

According to the analysis of Table 4, the location algorithm based on the neural network can accurately locate under various fault conditions, i.e., it is not affected by the transition resistance or fault location. The location error is less than 2%.

Three stator ground fault location methods are compared under the same fault conditions, and the comparison results are shown in

Table 5. Comparison of fault location errors with different methods.

Fault Location	Rf/Ω	Measuring Resistance/Ω			Measurement Resistance Error/%			Measuring Fault Location/%			Positioning Error/%
		Method 1	Method 2	Method 3	Method 1	Method 2	Method 3	Method 1	Method 2	Method 3	Method 1	Method 2	Method 3
α = 57.14%	200	22.89	195.4	202	−88.56	−2.300	−1.000	44.79	57.13	57.16	−21.61	−0.018	0.035
	1000	345.39	961.35	1004	−65.46	−3.865	−0.400	31.27	55.82	57.15	−45.27	−2.310	0.018
α = 85.71%	200	129.74	197.04	199	−35.13	−1.480	−0.500	78.07	86.17	85.71	−8.900	0.537	0.000
	1000	682.32	988.69	1003	−31.77	−1.131	0.300	66.62	85.81	85.81	−22.27	0.117	0.117

. Among them, the location method using the phase voltage offset feature is denoted as method 1, the location method considering the winding potential phase is denoted as method 2, and the method proposed in this paper is denoted as method 3.

From Table 5, it can be seen that the location error is large when the phase of the winding potential is ignored, which is no longer applicable to non-salient pole generators. Compared with location method 2, the method in this paper is comparable in the calculation of the transition resistance and the positioning error, and the error is slightly smaller than method 2, indicating that the new idea of fault location based on a data-driven perspective is feasible.

5. Conclusions

The method of phase selection and fault location for stator winding single-phase ground fault is greatly affected by transition resistance. From a data-driven perspective, this paper proposes a new idea of phase selection and location of generator stator single-phase ground fault based on the BP neural network.

The amplitude and phase information of zero-sequence voltage is taken as the input of the BP neural network. The phase selection method is realized by calculating and comparing the probability of a three-phase fault, which is simple. The fault location and transition resistance can be directly calculated. The location method is not affected by the transition resistance, and the location result is accurate. Simulation results verify the feasibility of the algorithm. Due to the limitations of the BP neural network itself, the signals that can be processed can only handle simpler and fewer numbers of information sources. For more complex signals, we propose to use deep learning networks to solve them in the future. For the network to perform the BP algorithm, the traditional one-dimensional search method cannot be used to find the step size for each iteration, but the update rules for the step size must be given to the network in advance.

This paper provides a new idea for realizing phase selection and the location of stator ground fault based on a data-driven perspective. However, the BP neural network is a black box and requires a large amount of data, so the application of this method still needs more discussion.