Open circuit fault diagnosis of wind power converter based on VMD energy entropy and time domain feature analysis

Aiming at the shortcomings of feature extraction and fault identification in fault diagnosis of wind power converters, a novel method for open circuit fault diagnosis of wind power converters based on variational mode decomposition (VMD) energy entropy (EE) and time domain feature analysis (TDFA) is proposed. Primarily, the three‐phase output current at the grid side of the wind power converter is collected as the original signal, and the VMD is used to decompose the original signal into a series of intrinsic mode functions (IMF). To reduce noise interference as much as possible, the Pearson correlation coefficient between each mode component and the original signal under different fault states is analyzed, and the IMF component containing the major failure features is selected to calculate the energy entropy of each component; afterward, according to the Pearson correlation coefficient results, the modal components of the first layer are selected for time domain feature analysis; finally, the feature matrix that combines energy entropy and time domain feature analysis is inputted into the long short‐term memory neural network for training and fault identification. The simulation and experimental results show that the open circuit fault diagnosis method proposed in this paper has high accuracy and robustness.


| INTRODUCTION
In recent years, to relieve the global warming and carbon emissions caused by the consumption of traditional fossil energy, countries around the world are vigorously developing renewable energy technologies.Among them, wind energy has become one of the renewable energy sources with rapid growth because of its large reserves, easy access, and good economic benefits. 1,2However, as shown in Figure 1, in the past 20 years, with the continuous increase of the single-unit capacity of wind turbines, the structure of each part of the unit has become more complex, leading to an increase in fault types and failure rates.And most wind turbines operate in harsh natural environments, which further aggravates the frequency of their component failures.The occurrence of the fault will reduce the productivity of the wind farm and increase the production cost, which may pose a threat to the power grid and even personal safety in serious cases.Therefore, fault diagnosis of the wind turbines is of great significance. 3he power converter plays the role of power transformation and transmission between the wind turbine and the power grid.Poor working conditions of the power converter, high temperature, vibration, corrosive gas, dust, and other factors will cause converter fault.According to the investigation of the research institute, the power converter has the highest failure rate and the longest annual shutdown time among the core components of the wind turbine. 4,5IGBT module fault is mainly considered in the fault of the wind power converter, and the fault types include short circuit faults and open circuit faults. 6The short circuit fault is caused by the excessive current in the main circuit.The short circuit fault causes a sharp increase in the current during the transient process, which leads to a transient rise in the temperature of conductors and semiconductor switching devices, causing damage to conductors and insulation layers.The converter will cause irreversible damage to the equipment if it operates in the short-circuit fault state for a long time.Therefore, protective devices are generally added to the main circuit to cut off the main circuit at the moment of short circuit fault, so that it can turn into an open circuit fault, to avoid further damage to the converter and other parts of the wind turbine.However, when the power converter has an open circuit fault of the IGBT module, a large number of harmonics and inter-harmonics will be generated, resulting in a decline in grid connected power quality and affecting the reliability of grid operation. 7he open circuit fault diagnosis methods for wind power converters are divided into three categories: mathematical analytic model-based methods, signalbased methods, and data-driven methods. 8ault diagnosis methods based on analytical models need to utilize specific knowledge of the electrical structure and physics of the wind power converter to establish an accurate analytical model of the system from its essence.Through the residuals between the actual operating values of the converter and the observed values, the residual values generated between different fault types are differentiated and analyzed to realize the fault diagnosis of the converter. 9Although such methods can reflect the essence of the system and have a faster diagnosis speed, the accuracy of the mathematical model has a greater impact on the diagnosis effect.The signalbased method eliminates the influence of modeling accuracy on the fault diagnosis performance, analyzes the operational characteristics of wind power converters in the event of faults in different components, and uses Park coordinate transform, Fourier transform, and other methods to obtain the signal spectrum, amplitude, frequency, variance, average value, and wavelet coefficients through the current, voltage and other signals, and selects the representative feature quantities that can describe the fault information to carry out diagnosis and identification.To realize the fault detection and fault localization of wind power converter. 10,11Threshold setting in signal-based methods depends on the a priori knowledge of the system, and is less robust when the load changes suddenly or external disturbances occur.The data-driven fault diagnosis method gets rid of the problems of mathematical analytical modeling and threshold setting, and uses intelligent algorithms to analyze the difference relationship between different faults in current and voltage data for fault diagnosis, which is more suitable for realizing the identification and classification of multiple fault types compared to analytical model-based and signal-based methods. 12,13urrently, there are numerous data-driven fault diagnosis methods based on the process usually contains three steps 13 : signal acquisition, feature extraction, and fault classification.Literature 14 uses a combination of FFT and PCA, first, the inverter output voltage signal is FFT transformed, the transformed data are PCA dimensionality reduction and fault features are extracted, and finally input into the support vector machine (SVM) for identification and classification.FFT for signal analysis can only obtain the frequency components contained in the signal, and lacks the time-domain description of the signal, such as PCA, and other dimensionality reduction and feature extraction algorithms, which is difficult to accurately implement for the selection of dimensions.feature extraction algorithms, and it is difficult to realize accurately for the selection of dimensions, resulting in the lack of recognition and classification.The literature 15 proposed a fault diagnosis method with LMD-multiscale sample entropy and support vector machine, which achieved better results, but the feature extraction method using multiscale sample entropy has a greater sensitivity in the face of different faulty signal samples, and thus has poor generalization ability.Literature 16 addresses the problem of similar fault features and low diagnostic efficiency caused by IGBT open-circuit faults in mmc inverters.A weighted-amplitude permutation entropy and DS evidence fusion theory fault diagnosis method is proposed, and it is verified that weighted-amplitude permutation entropy possesses better feature extraction capability.Literature 17 decomposes the converter voltage signal into EEMD, extracts the parameter entropy features from the decomposed intrinsic modal components, and inputs the feature vector composed of the parameter entropy into a support vector machine, which has a high accuracy rate and good robustness.However, this method adopts the paradigm entropy for feature extraction, and the paradigm lacks a certain direction when facing the IGBT fault localization of the upper or lower bridge arm of the converter.Literature 18 proposed a feature extraction algorithm with VMD and trend feature analysis by analyzing the waveform characteristics of the three-phase output voltage of the wind power grid-side converter, which is input into the DBN to achieve fault identification and classification, and improve the fault diagnosis accuracy.Although the method can better distinguish the upper and lower faulty bridge arms of the IGBT module by using trend feature analysis, the robustness is weakened by the fact that all the VMD components are used in the feature extraction, and some of them are interfered by harmonics in the noisy environment.With such special topologies as converters, with a wide variety of faults and high feature similarity, incomplete fault feature extraction is prone to misjudgment of fault localization, poor robustness, and other problems.Comprehensively analyzing the above, while the data-driven approach has better fault diagnosis performance, feature extraction, as the key to fault diagnosis, determines the effect of fault diagnosis by whether it can comprehensively and effectively describe the characteristics of fault signals.
To improve the accuracy of fault diagnosis and the ability of antinoise interference, this paper proposes an open circuit fault diagnosis method for wind power converters based on VMD energy entropy and time domain feature analysis.First, the three-phase output current of the grid side converter is collected as the diagnostic signal.According to the distortion features of the three-phase output current of the grid side converter under different fault states, the three-phase output current signal is decomposed into multilayer IMF components with different feature frequency scales using VMD.By analyzing the Pearson correlation coefficient of each IMF component under different fault states, the IMF components containing the main fault features are selected to solve their energy entropy features; second, the modal components of the first layer with high correlation coefficient are analyzed in time domain; Finally, the feature matrix composed of energy entropy and time-domain feature analysis is used as the fault feature, which is input into long short-term memory (LSTM) network for training and testing, so as to achieve single open circuit and double open circuit fault diagnosis of IGBT module of wind power converter.

| Topology of PMSG
In the early days of wind turbine, the doubly fed asynchronous wind turbine has a high market share because of its variable-speed constant frequency operation, small converter capacity, low cost, and high system efficiency.However, with the emergence of the demand for large-capacity wind turbines, PMSG wind turbines are mainly used.Because of their low maintenance frequency, good grid side performance, strong fault traversal capability, and other advantages, more and more wind power operators tend to use PMSG wind turbines, which have become the mainstream of the current wind power market. 19he topology of PMSG system is shown in Figure 2, which is composed of fan blades, permanent magnet synchronous generator, back-to-back dual PWM converter, and a transformer.Among them, the wind energy captured by the fan blade is transferred to the permanent magnet synchronous generator in the form of mechanical energy through the drive shaft, and the permanent magnet synchronous generator is used to realize the conversion of mechanical energy and electrical energy.The power converter is composed of a generator side converter, a DC link, and a grid side converter.The generator side converter (MSC) is responsible for realizing the decoupling control of generator speed, torque and excitation, realizing the maximum wind energy tracking, and rectifying the AC generated by the permanent magnet synchronous motor that changes with the wind speed and has unstable frequency and amplitude into DC; the grid side converter converts the DC power into the AC power with the same frequency as the grid, stabilizes the DC bus voltage, and makes it have good dynamic response capability to ensure the power quality; finally, the transformer is connected to the grid after boosting to feed power to the grid. 20

| Fault analysis of grid side converter
In this paper, the open circuit fault diagnosis method of grid side converter is studied.The topology of grid side converter is shown in Figure 3.The grid side converter is mainly composed of six IGBT modules.Through PWM control strategy, the DC voltage generated by the DC link is converted into AC with the required amplitude and frequency.After that, it is filtered by a filter and fed to the power grid after being boosted by a transformer.
When the converter operates normally, the current is in balance, and the three-phase output current is expressed as where the i i i , , ga gb gc represent three-phase output current, I m is the current amplitude, ω is the angular frequency, and θ is the initial phase angle.
The three-phase output current waveform of the converter under normal state and open circuit fault state is analyzed.Under normal state, as shown in Figure 4A, the three-phase current waveform fluctuates steadily, and the three-phase output current i i i , , ga gb gc presents a three-phase symmetrical current waveform with equal amplitude frequency and phase angle difference of 120°: open circuit fault.Taking the T1 open circuit fault as an example, as shown in Figure 4B, the T1 module of phase A upper bridge arm F I G U R E 2 Topology graph of permanent magnet synchronous generator wind turbines.
F I G U R E 3 Topology graph of grid side converter.fails, causing the positive half-cycle waveform of phase A output current to disappear.The open circuit fault of IGBT module of the converter will directly affect the three-phase output current at the grid side, and the open circuit fault will cause the disappearance of the sinusoidal features of the three-phase output current of the converter, and the current waveform will be distorted to varying degrees.Therefore, the three-phase output current on the grid side is selected as the original input signal of the fault diagnosis model. Single

| FAULT DIAGNOSIS METHOD BASED ON VMD ENERGY ENTROPY AND TIME DOMAIN FEATURE ANALYSIS
Before fault signal is input into LSTM neural network for diagnosis, feature extraction algorithm combining VMD energy entropy and time-domain feature analysis provides more detailed features for LSTM classification and recognition, and then fault diagnosis is completed.

| Signal analysis method based on VMD
The three-phase output current i t i t i t ( ), ( ), ( )  frequency-domain distribution features of the signal will be lost, resulting in lower extraction accuracy and affecting the accuracy of fault diagnosis.
VMD is an adaptive and non-recursive signal analysis algorithm for nonstationary signals proposed by Dragomiretskiy et al. in 2014. 21By constructing and solving the variational problem, the complex original current signal i t i t i t ( ), ( ), ( ) . This process solves the problem that FFT only deals with signals in the frequency domain and lacks description in the time domain; at the same time, it avoids the generalization limitation of signal analysis because different types of fault data in wavelet analysis are applicable to different wavelet basis functions.Due to the harmonic features of different frequencies in the fault current signal, VMD obtains several eigenmode function components through time-frequency decomposition, which not only enhances the data features but also solves the problem of single data dimension.The main steps are as follows: The purpose of VMD is to decompose the original signal into multiple eigen modal components.The number of eigen modal components k is preset.The finite bandwidth parameter α and the initial center angular frequency ω k value are used to obtain various modal functions u t ( ) , which is expressed as where envelope A t ( ) is the instantaneous phase.The frequency center and bandwidth of each modal function are determined by iteratively searching to construct the extreme value of the variational mode, which realizes the frequency domain division of the signal and the effective separation of each component.VMD algorithm decomposes three-phase output current signal i t i t i t ( ), ( ), ( ) into k eigen modal components with different frequency scales by constructing and solving variation.

| Energy entropy feature extraction
If the grid side converter has an open circuit fault of IGBT module, the three-phase output current i t i t i t ( ), ( ), ( ) ga gb gc will be distorted, resulting in a large number of harmonics and inter-harmonics.The IMF component of three-phase current signal decomposed by VMD contains fault information in time and frequency domains of each distorted signal.If the multidimensional IMF component is directly used as the feature input classifier for diagnosis, it will not only increase the training time but also reduce the diagnosis efficiency due to the large data dimension.To obtain the feature information of A, B, C, three-phase current IMF components under different states, the "entropy" principle in the nonlinear method is introduced into the fault diagnosis research.
Under different fault states of the converter, there are differences between IMF components in different frequency bands, and the energy value of IMF components changes accordingly.In information theory, "entropy" can express the degree of chaos of the system.Energy entropy is used to describe the difference of current signals in different states at different scales.Energy entropy feature extraction is carried out for IMF components.The IMF components of each phase in A, B, and C three-phase current signals are IMF 1 , …, IMF k in turn.Each IMF component is divided into s component segments and recorded as IMF, and the ratio p of signal segment energy in its IMF component is calculated.At the same time, to prevent false alarm and false alarm from affecting the diagnostic accuracy when the in-phase double open circuit fault current is 0, the minimum real number σ that does not affect the classification result is added, 20 and the energy entropy formula is introduced: (5) where x = 1, 2,…, 22 state codes; = A/B/C  is three phase signal; imf s is component fragment.
After energy entropy feature extraction, the expression of energy entropy feature matrix .
Energy entropy uses the energy complexity between components of different frequency bands to extract the energy features of the distorted signal.Although it can be used as a feature input to diagnose some open circuit fault types, because the wind power converter has a symmetrical topology and the energy does not have directionality, it is difficult to accurately locate the upper and lower IGBT modules of the phase bridge arm by using energy entropy alone for feature extraction, such as T1 or T4 modules in a single open circuit state, T1&T3 and T4&T6 modules under the double circuit.
To improve the accuracy of fault diagnosis and improve the robustness of fault diagnosis methods, according to the decomposition features of VMD algorithm, Pearson correlation coefficient is used to carry out correlation analysis on each component, and it is obtained that the first layer IMF 1 (t) component has a large correlation, which can avoid noise interference as a low-frequency signal, and meet the waveform features of the original current, so the time domain feature analysis is carried out on the first layer IMF 1 (t) mode coefficient.
The time domain feature parameters are divided into dimensional features and nondimensional features.The dimensional features mainly include average value, standard deviation, and so forth; nondimensional features are composed of time-domain feature operations, including peak coefficient, waveform coefficient, and pulse factor. 10To avoid the influence of current amplitude fluctuation caused by sudden change of wind speed on the time domain feature parameters, the time domain feature parameters.Therefore, time domain feature parameters, namely normalized location coefficient, standard deviation, and waveform coefficient, are selected for time domain feature analysis.

| Normalized positioning coefficient
Due to the distortion of three-phase output current caused by the IGBT open circuit fault, the current waveform will shift within a period.The sum of the modal coefficient sequence is made a ratio with the sum of the absolute values of the modal coefficient sequence, then the fault location is carried out by positive and negative values and numerical values.
where N A/B/C is the three-phase normalized positioning coefficient of A, B, C; m is the number of samples in a period; and λ is the minimum real number that does not affect the positioning parameters.

| Standard deviation
The standard deviation is used to indicate the dispersion of data in a period.Under normal states, the average value of current tends to zero, so the standard deviation is large.When an open circuit fault occurs, the degree of waveform distortion varies according to different open circuit states, resulting in differences in the standard deviation.The standard deviation of the non-fault phase is large, and the standard deviation of the fault phase is small, and the feature V A/B/C is obtained by normalizing the standard deviation where is the standard deviation value, and m is the number of samples in a cycle.

| Waveform coefficient
As a nondimensional feature, the waveform coefficient is composed of the ratio of the root mean square value and the average value.To measure the features of the current waveform distortion, the quantitative index of the waveform coefficient is used to characterize the degree of current waveform distortion caused by the opencircuit fault of the IGBT module, and the waveform coefficient of the three-phase IMF 1 (t) component where S A/B/C is the three-phase normalized waveform coefficient of A, B, C, x A/B/C sf _ is the waveform coefficient value, m is the number of samples in a period, and λ is the minimum real number that does not affect the positioning parameters.
Therefore, the time domain analysis feature matrix A between different faults is obtained by synthesizing the above analysis.
The VMD energy entropy feature H x in Section 3.2 and the time domain analysis feature T x in Section 3.3 are fused to obtain the feature matrix M x that can provide the classifier with diagnostic details in 22 states.

| LSTM neural network
LSTM is an improved model of recurrent neural network.The network structure is shown in Figure 5.The special gate structure makes it more advantageous in processing time series data and can effectively learn the nonlinearity of time series. 22The forgetting gate structure solves the problem of RNN in dealing with gradient disappearance and gradient explosion of long time series, and is widely used in the field of fault diagnosis.
To retain the spatial feature of "phase to phase" of feature matrix M x after VMD-EE-TDFA feature extrac- tion of three-phase output current on the grid side.According to the input features of the multi-dimensional sequence matrix, LSTM is used as the classifier in this paper for training, recognition and classification.
The LSTM neural unit is composed of the forgetting gate, input gate, and output gate, and its structure is shown in Figure 5.The special network structure makes it capable of training and learning information that has been relied on for a long time, and its calculation process is as follows: (1) First, the forgetting gate f t uses the external state h t−1 of the previous time and the current time input x t to send the sigmoid function to judge whether the last neuron information C t−1 is retained.If the output of the sigmoid function in the forgetting gate f t is 0, the neuron information C t−1 at the last moment will be deleted; if the output is 1, the neuron information C t−1 at the last moment will be retained and deleted.
(2) Second, the input gate (3) Finally, the output gate o t is used to determine the output information of the current neuron.The Sigmoid function determines the part of the current state information that needs to be output.The internal state information is transferred to the external state h t by multiplying the current state information C t activated by tanh.
The whole network formula is simply described as  7 in two cycles, and 1, 2, …, 21, 22 output labels are added to each fault type.The total number of fault data samples is 22 × 100 = 2200 groups.

| VMD of three phase current signal
To obtain fault information in different frequency bands, VMD algorithm is used to decompose the three-phase output current i i i , , ga gb gc on the grid side of the wind power converter in layer k.First of all, when using VMD for decomposition, it is necessary to pre-set the number of decomposed modes k.Too small a value of k results in under-decomposition of the signal; too large a value of k results in over-decomposition, which triggers the phenomenon of modal aliasing.The center frequency observation method is used to determine the number of modes k according to the different characteristics of the center frequency ω of each mode, 23,24 as shown in Table 3.The k value ranges from 4 to 8. When the number of decomposition layers are 4 to 6, the value of the center frequency ω of the last layer increases with the increase of the number of decomposition layers, and at that time, the signal decomposition presents the underdecomposition state; when the value of k is 7, the center frequency of the last layer reaches the maximum for the first time and there will be no decomposition problem; when k value reaches 8, the difference between ω 7 and ω 8 center frequency is small, resulting in overdecomposition causing modal aliasing phenomenon; comprehensive center frequency and according to the relevant literature analysis, it is considered that the decomposition effect is the best when k = 7, so this paper carries out 7-layer decomposition of the three-phase output current signals in 22 states. 19cording to the analysis of relevant literature, it is believed that the decomposition effect is the best at k = 7, so in this paper, three-phase output current signals in 22 states are decomposed in seven layers. 19he original current signal is decomposed into IMF modal components of different frequency bands.Figure 8 shows the breakdown diagram of three-phase current VMD under single open circuit fault condition of T1 module.

| Energy entropy and time domain feature analysis
After VMD of original signal i i i , , gax gbx gcx , each phase current signal has seven IMF components, each of which contains fault information of different frequency bands.To reduce noise interference and improve the robustness of fault diagnosis, Pearson correlation analysis is conducted between the seven modal components and the original current signal.
where X and Y are two groups of data to be determined, with m elements, respectively; X and Y are the average values of the two groups of data, respectively; ρ X Y ( , ) is Pearson correlation coefficient, and the value range is [−1,1].The larger the ρ X Y | ( , )| value is, the higher the correlation degree of X and Y data is.In the formula, X represents the kth IMF component, and Y represents the original signal f t ( ).Take the VMD results of phase A current under five types of states, namely, normal state, T1 fault, T2&T5 fault, T1&T3 fault, and T1&T2 fault, as an example, Pearson correlation analysis is carried out, as shown in Figure 9. Pearson correlation coefficient shows a The collected data samples are decomposed in seven layers using VMD algorithm, and the first four layers of IMF components after decomposition are selected for feature extraction.Table 4 shows the fault feature matrices of six types of faults (Normal, T1, T1&T4, T1&T3, T2&T4, and T1&T2) by examples.Because threephase current under normal states presents sinusoidal waveform, energy fragment values are randomly distributed, with large uncertainty.Therefore, the energy entropy value is greater than the energy entropy value under fault conditions.Because the energy entropy values of different faults under single open circuit and double open circuit faults are different, the energy entropy can be used as the vector to represent some fault features.
Due to the special topology of the converter, there is symmetry similarity between some fault states, and the single use of energy entropy feature extraction results in the misjudgment of some in-phase upper and lower bridge arm faults.Therefore, time domain feature analysis is required to increase the accuracy of fault diagnosis.As shown in Figure 8, the IMF 1 component after VMD has a high waveform similarity to the original current signal.The normalized coefficient N x , standard deviation V x , and waveform coefficient S x are used to analyze the time domain feature of the three-phase IMF 1 (t) component to obtain the 3 × 3 time domain feature matrix T x .
Finally, the energy entropy feature H x of three-phase current signal is fused with the time domain analysis feature T x to form the 3 × 7 feature matrix M x that can describe different converter fault states.The radar chart visualization of feature values is shown in Figure 10.
The feature matrices of 22 fault types are converted into data feature vectors of dimension 1 × 21 for the visual representation of radar chart, as shown in Figure 10A.Figure 10B shows the feature values of six major types, and the fault feature values vary with the changes of different types of faults.Figure 10C shows the feature values of the single open circuit fault of the IGBT module.For instance, the T1 fault belongs to the upper arm and the T4 fault of the lower arm.Figure 10D shows the feature values of the double open circuit of the same half bridge T1&T5 and T2&T4.Figure 10E shows the feature values of the double open circuit of the different half bridge T1&T2 and T4 &T5.The above pictures show that the proposed strategy has good effect in expressing the fault of upper arm or lower arm, and has good distinguishing details in judging the difference of similar fault types.
Although feature extraction has effectively mined the features between different faults, it is difficult to accurately and quickly identify each fault type in many fault types through artificial observation.Therefore, it is necessary to input the feature matrix into LSTM network for fault identification and classification.

| LSTM network training and testing
Feature extraction provides a more detailed feature matrix for the classification network.To avoid setting After many experiments and analysis, the optimal parameters of the LSTM network are shown in Table 5.
The changes of each index in the network training process are shown in Figure 11 With the increase of the number of training rounds, the accuracy rate starts to increase gradually, and the loss function decreases gradually.The feature matrix after feature extraction can be used as LSTM input to reduce the original data dimension, and the training and diagnosis speed is fast.After eight rounds of training, the accuracy and loss function gradually becomes stable until the training is completed.At this time, the accuracy rate reaches 100%, and the loss function reaches 0.0015, indicating that the network fitting degree is good at this time, and the trained network model is saved.
Six hundred and sixty sets of fault samples from the test set are input into LSTM to test the accuracy of fault diagnosis after being extracted by VMD-EE-TDFA features.LSTM confusion matrix and classification results are shown in Figure 12.From the confusion matrix, it can be seen that 22 fault diagnosis methods for grid side IGBT module of wind power converter based on VMD-EE-TDFA-LSTM can be accurately judged, and there is no misjudgment of classification samples.According to the sample classification results, the accuracy rate of 660 samples in the test set reached 100%.It is verified that the fault diagnosis method proposed in this paper has a high accuracy of fault diagnosis.

| Robustness test of three classifiers and seven fault diagnosis methods
Feature extraction and classifier are two key links of fault diagnosis methods, which have a great impact on the final diagnosis results.To further verify that the fault diagnosis method based on VMD-EE-TDFA-LSTM has good antinoise interference capability, 10 db, 15 db, 20 db, and mixed noise (70% noise free, 10 db, 15 db, and 20 db each accounting for 10%) different decibels of high white noise are added to the original three-phase output current signal.The signal-to-noise ratio addition method, as shown in Formula (25), simulates noise interference to the original signal, and verifies the robustness of the VMD-EE-TDFA-LSTM method compared with other fault diagnosis algorithms.where P signal is the original signal energy and P noise is the noise energy.
First of all, to verify the robustness of LSTM network.Three classifiers, LSTM, BP, and SVM were selected for the robustness test.Among them, the maximum iteration number of BP neural network MaxEpoachs = 100, learning rate lr = 0.01, error item goal = 0. 001, and the number of hidden layer neurons n = 43; penalty factor C = 0.0819, and kernel function parameter g = 62.94 in SVM.After 20 tests for each of the three classifiers, the line graph of average accuracy under different noise conditions is shown in Figure 13 The LSTM network has the highest accuracy rate compared with the other three classification methods under 10 db, 15 db, 20 db, and mixed noise conditions, and the accuracy rate is higher than 90% under 10 db noise conditions.The results show that the LSTM network has a higher accuracy rate and better antinoise ability under noise data.
Second, to verify the robustness of the VMD-EE-TDFA feature extraction method, seven feature extraction algorithms are used to obtain the training set and test set for the same data in a 7:3 ratio.The seven algorithms are as follows: (1)    6.
(1) It can be seen from the data in Table 5     noisy state, thus better validating the superiority of the proposed method.

| Experimental verification
To verify the effectiveness of the fault diagnosis method of VMD-EE-TDFA-LSTM proposed in this paper under the experimental data, the three-phase AC380V 50 Hz power supply is used to simulate the input of the converter, and the open circuit fault diagnosis experiment of the IGBT module of the converter on the wind grid side is carried out.The converter parameters are shown in Table 7.
In the construction of the experimental data set, the three-phase output current under the fault operation state is collected by removing the IGBT module at the corresponding fault location to simulate the fault phenomenon.At the same time, the same sliding window method as in the simulation analysis is used to expand the data samples, and 100 samples are constructed for each of the 22 states, a total of 22 × 100 = 2200 data samples for experimental verification.
The conclusions obtained through simulation analysis are decomposed into 22 fault states by VMD7 layer, and the decomposition diagram under single open circuit fault state is shown in Figure 14.
The VMD-EE-TDFA feature extraction method is used to extract fault features and input them into LSTM for training and fault recognition.To illustrate the reliability of this method for fault diagnosis, the trained LSTM network is tested 20 times.The test results are shown in Figure 15, with an average accuracy of 99.96%.
At the same time, to show that the method has a high accuracy of fault diagnosis, the performance of the eight methods is tested using the same data set.classification capabilities for time series signals.Due to the certain differences between experimental data samples, this method requires a large number of data sets for training to improve the generalization ability of the model for different samples to achieve good diagnostic results.Due to the targeted nature, strong generalization ability, and robustness of the proposed method for fault features, the accuracy is relatively high.(6) In the fault diagnosis method proposed in this paper, due to the fluctuation of the data collected in the experiment compared with the simulation data, the data samples have a certain degree of differentiation, and due to the interference of the current probe and the influence of the oscilloscope sampling rate, the data collected in the experiment has a certain noise interference compared with the simulation data between different samples, so the diagnosis result in the experiment is 99.96% lower than the simulation result of 99.99%.But at the same time, it also proves that the method has a certain stability in the face of different working conditions, and both simulation and experiment have a high accuracy.
The experimental results and simulation analysis conclusions are consistent, which can effectively improve the accuracy of fault diagnosis of wind power converter.

| CONCLUSION
Aiming at the problem of a single open circuit and double open circuit fault diagnosis of IGBT module of grid side converter for permanent magnet synchronous wind turbine, a novel fault diagnosis method based on VMD energy entropy and time-domain feature analysis is proposed.The feasibility of this method is verified through simulation and experiment, the main work of this paper are summarized as follows: (1) The VMD algorithm is used to decompose the threephase output current of the converter in a nonlinear seven-layer manner.The first four layers of IMF components are filtered by Pearson correlation coefficient for feature extraction, which not only retains useful fault information, but also removes high-frequency interference components, thus improving the antinoise interference ability of the fault diagnosis method.(2) The energy entropy and time-domain feature analysis are combined to make the extracted fault features more comprehensive, which effectively avoids the issues of misjudgment and poor noise robustness of the upper and lower bridge arms of the IGBT module.Therefore, they provide fault details with high discrimination for LSTM classifiers.The diagnostic accuracy of 22 fault types in simulation results reaches 99.99%, and they have better robustness and higher accuracy with other fault diagnosis methods (VMD-MSE-TDFA-LSTM, VMD-ER-TDFA-LSTM, etc.) in 10 db, 15 db, 20 db, mixed noise simulation.(3) The average accuracy of the experimental results is 99.96%, which verifies the effectiveness of the proposed method.
This method is only for the current as the original signal for diagnosis, to further explore the fault characteristics.In the future, the method of multisource information fusion will be applied to the fault diagnosis research of wind power converters.

4
gb gc of the grid side converter is a three-phase one-dimensional time series.If only the three-phase one-dimensional current signal is used for feature extraction, partial time-domain and Waveform of three-phase output current of converter.(A) Waveform of three-phase output current under normal state.(B) T1 module fault three-phase output current waveform.T A B L E 1 Grid side converter IGBT module 22 states coding table.

F
I G U R E 8 Variational mode decomposition of open-circuit threephase current occurred in T1. (A) Phase A. (B) Phase B. (C) Phase C. F I G U R E 9 Pearson correlation coefficient of each modal component and the original signal.

F I G U R E 10
Radar chart of fault feature values.(A) Feature values of 22 fault types; (B) feature values of 6 fault types; (C) feature values of T1 and T4; (D) feature values of T1&T5 and T2T4; (e) feature values of T1&T2 and T4&T5.T A B L E 5 Long short-term memory parameter setting.

FF
I G U R E 11 Long short-term memory network training change curve.(A) Accuracy.(B) Loss function.I G U R E 12 Test set confusion matrix and classification results.(A) Confusion matrix.(B) Classification results.

T A B L E 7 6 ( 2 )
Experimental parameters of converter.In comparison with multi-scale sample entropy, although the effect of feature extraction using energy entropy alone is inferior to MSE, TDFA can effectively express the time-domain features of faults and greatly improve the accuracy of fault diagnosis.(3)In comparison with LMD-EE-LA-SSAE, the VMD in this paper uses the low-frequency features of the signal to extract features.Compared with the LMD method, it reduces the misjudgment and missed judgment caused by noise interference in the original signal, so the accuracy is higher.(4) In the comparative experiment with VMD-EE-LSTM, VMD-TDFA-LSTM, EE-LSTM, TDFA-LSTM, it is analyzed that the fault diagnosis method combining VMD-EE-TDFA can effectively improve the accuracy of fault diagnosis.(5) In the comparative experiment with LSTM, it demonstrated good feature extraction and F I G U R E 14 Decomposition diagram of three-phase experimental current signal VMD for T1 open circuit fault.(A) Phase A. (B) Phase B. (C) Phase C.
i t decides whether to update the current candidate state C ͠ t into the hidden layer neurons.Sigmoid function is used to determine the update degree of the new information needed.Function tanh is used to generate the candidate information C ͠ t of the current neuron, and forgetting gate f t and input gate i t are used to update the current state C t .

Table 2 .
͠ t is the current time candidate state; o t is the output gate; i t is the input gate; f t is the forgotten door; tanh and σ are nonlinear activation functions; x t is the current time input; h t−1 external state at the last moment; W is the network weight; b is the network offset.To solve the problem of single open circuit and double open circuit fault diagnosis of grid side IGBT module of wind power converter, the corresponding IGBT module is removed and the fault phenomenon is simulated.During the experiment, the grid side To prevent the impact of repeated data samples on fault diagnosis, 100 groups of data samples in each state are constructed using the sliding window with step size S = 20 as shown in Figure Structure diagram of long short-term memory network.F I G U R E 6 Flow chart of fault diagnosis of wind power converter.
T A B L E 2 Main simulation parameters of the system.
T A B L E 3 VMD decomposition of center frequencies for different values of k. , including 1540 training sets and 660 test sets, LSTM neural network is inputted to train and test the method in this paper.The setting of the relevant parameters in the LSTM model directly affects the efficiency of model training and the accuracy of identification.
the location threshold and realize intelligent diagnosis of fault features, the LSTM network model is constructed.The 2200-group feature matrixes are constructed as a training set and a test set according to 7:3 This paper proposes VMD, Energy Entropy, Time Domain Feature Analysis, LSTM (VMD-EE-TDFA-LSTM).(2) EEMD, norm entropy, SVM T A B L E 4 Fault features matrix of 6 states.

Table 8
In the comparison of the experimental results of eight fault diagnosis methods, the accuracy of the method proposed in this paper is up to 99.96%.Robustness simulation results of 8 feature extraction algorithms 10-20 db noise and mixed noise.
F I G U R E 15 Long short-term memory recognition accuracy under different test times.T A B L E 8 Experimental comparison results of 8 fault diagnosis methods.