Open-Circuit Fault Diagnosis of Wind Power Converter Using Variational Mode Decomposition, Trend Feature Analysis and Deep Belief Network

: The power converter is the significant device in a wind power system. Wind turbine will be shut down and off grid immediately with the occurrence of the IGBT module open-circuit fault of power converter, which will seriously impact the stability of grid and even threaten personal safety. However, in the existing diagnosis strategies of power converter, there are few single and double IGBT modules open-circuit fault diagnosis methods producing negative results including erroneous judgment, omissive judgment and low accuracy. In this paper, a novel method to diagnose the single and double IGBT modules open-circuit faults of the permanent magnet synchronous generator (PMSG) wind turbine grid-side converter (GSC) is proposed. Above all, collecting the three-phase current varying with wind speed of 22 failure states including a normal state of PMSG wind turbine GSC as the original signal data. Afterward, the original signal data are decomposed by using variational mode decomposition (VMD) to obtain the mode coefficient series, which are analyzed by the proposed method base on fault trend feature for extracting the trend feature vectors. Finally, the trend feature vectors are used as the input of deep belief network (DBN) for decision-making and obtaining the classification results. The simulation and experimental results show that the proposed method can diagnose the single and double IGBT modules open-circuit faults of GSC, and the accuracy is higher than the benchmark models.


Introduction
The capacity of power converter in recent years has steadily grown in step with increased size of large wind turbines, correspondingly, the load capacity of components of converter improved evidently and the electrical structure is more complex, which is bound to raise the failure rate greatly [1,2]. Meanwhile, the wind farms are mostly built in areas with abundant wind resources and complex weather climate [3,4]. The operational ambient of power converter is extremely harsh, and the failure rate is high [5]. The core device of the power converter of wind turbine is the power switching component--insulated gate bipolar transistor (IGBT) module [6]. A lot of harmonics and interharmonics will be produced if the IGBT module in a power converter has short-circuit or opencircuit, which will impact the power quality and pollute the grid. Then the wind turbine would be shut down and off grid immediately, so as not to seriously impact the stability of grid and even threaten personal safety [7]. The existing researches are matured for the short-circuit fault of power converter, and there are corresponding modules for protection. Though  In the Figure 1, DC-Link is mainly consisted of shunt capacitors (C1 and C2), whose two-terminal provides a stable direct current (DC) voltage to GSC. The GSC is mainly composed of 6 IGBT modules. Every two IGBT modules compose phase A, B and C, respectively. Through PWM control strategy, the DC voltage is transformed into sinusoidal alternating current with required equivalent frequency and amplitude. Afterward, the harmonic and peak are suppressed and filtered by the filter, and the power is fed to the grid via the transformer.
For the full scale power converter of PMSG wind turbine, the key of grid connection is the GSC control strategy, which generally needs to meet two basic principle: first, to maintain the stability of DC-Link voltage. The second is to realize the control of output phase current. The relationship between the output power of the full scale converter and the wind speed can be expressed as follows: Where GSC P is the output power of GSC,  is the air density in invariant. It can be stated that the phase current is random and unstable. Thus, it is difficult to diagnose the open-circuit fault, which is also one of the most significant differences between the wind turbine converter and other converters.  respond in time to cut off the electric energy transmission after the occurrence of  single open-circuit fault. Therefore, this paper is considering the single and double IGBT modules  open-circuit faults of GSC. Then, there are 22 open-circuit failure states including 1 normal operating  state for the 6 IGBT models of GSC. The code of IGBT modules open-circuit fault of GSC is shown in  Table 1. Table 1. Code of open-circuit fault of IGBT modules. T6 T5 T4 T3 T2 T1  Coding  Number  Normal  0  0  0  0  0  0  1 Single open-circuit

VMD Modeling
The target of VMD is to decompose a real valued input signal f into a discrete number of subsignal k u , that have specific sparsity properties while reproducing the input. Assuming each mode k u to be mostly compact around a center pulsation k  , which is to be determined along with the decomposition [22,23]. A scheme to assess the bandwidth of a mode is as follows: 1, for each mode k u , compute the associated analytic signal by means of the Hilbert transform in order to obtain a unilateral frequency spectrum. 2, for each mode, shift the mode's frequency spectrum to "baseband", by mixing with an exponential tuned to the respective estimated center frequency. 3, the bandwidth is now estimated through the 1 H Gaussian smoothness of the demodulated signal, the squared 2norm of the gradient. The resulting constrained variational problem is as follows: In order to render the problem unconstrained, a quadratic penalty term and Lagrangian multipliers  are both used. The augmented Lagrangian L is as follows: Minimization k u and k  , respectively: The decomposition procedure of VMD method is as follows: Step 1. Initialize     Step 2. Update k u , k  and  , 11ˆ( Step 3. Repeat the iterative procedure of Step 2 until, Where  is a given parameter.

Trend Feature Analysis of Decomposed Data
A novel method of trend feature analysis is proposed for extracting trend feature vectors in this part. The three-phase current Where A , B and C denote the each phase of GSC in Figure 1 Where Axk E ,

Bxk E and
The three-phase current vary according to the wind speed. The same varieties occur to the feature energy of each mode. Thus, when the open-circuit happens in the GSC, the varied feature energy vectors would bring difficulties to the following data analysis. It is necessary to normalize the feature energy vectors. Let: Where  is a tiny real number to avoid the erroneous judgment when the phase current is zero, and minimize impact on final classification results. The normalized feature energy vectors can be expressed as: Then, the factors of normalized feature energy vectors can be the function about the part factors of trend feature vectors. Let: Where p is a positive real number. The value of p could be confirm in an optimal range ..
are the coefficient sum of the first level modes of three-phase current. n is the total number of coefficients at each mode coefficient series. Define Then, the trend feature vectors of x -th failure state is: Where 33 K + is the number of factors in each trend feature vectors.

DBN Modeling
In 2006, a DBN model with a efficient learning algorithm proposed by Geoffrey Hinton. This algorithm becomes the main framework of the deep learning algorithm later. It can extract the required features from the training set automatically [24,25] The process of DBN training model can be mainly divided into two steps.
Step 1: Unsupervised pretraining. Each layer of RBM network is trained independently and unsupervised to ensure that as much feature information as possible is preserved when the feature vectors are mapped to different feature spaces. The greedy method is adopted between the layers training, and the process is as follows: 1. The input layer 0 V of the first RBM is also the input layer of the entire network. It typically involves training the first layer RBM by applying contrastive divergence. W0 is the weight in the first RBM. 2. The hidden layer 0 H of the previous layer RBM can be seen as the visible layer 1 V of the back layer RBM, followed by iterative training remaining RBM. W1 is the weight in the back layer RBM.

Simulation Results
The simulation results produced from the proposed method which is addressed to diagnose the open-circuit faults of GSC are evaluated in this section.
Simulink is used to simulate 22 failure states of GSC of PMSG wind turbine, as shown in Figure  3 Table 2 is the parameters of main simulation components.

VMD of Three-phase Current
Considering [26], the whole three-phase current samples under 22 failure states are addressed by VMD at 7 levels. Figure 4 and Figure 5 show the waveforms of three-phase current and the mode coefficient serials under No. 1 (normal operating) and No. 2 failure states, respectively. Where the red, green and blue curves denote the A, B and C phase current in Figure 4 and Figure 5, respectively. 1. No. 1 failure state (normal operating). It can be seen from Figure 4 (a) that there is no phase sequence alteration, meanwhile, threephase current is operating on a stable state. Figure 4  It can be seen from Figure 5 (a) that the value of phase-A current is non positive when T1 IGBT module is open-circuit. This is determined by the electrical structure and working principle of GSC. The currents of phase-B and phase-A are stable but changed in phase sequences, almost reverses for each other. Figure 5

Experimental Results
In this section, experimental results are generated to verify the simulation results and analysis. As the same as simulation, the three-phase current A I , B I and C I are extracted, where the subscripts A , B and C are the each phase. Extracting 1000 samples under each failure state. The length of time of each sample is between T and 1.15T , where T is the period of the phase current.
800 samples out of 1000 samples under each failure state are randomly selected to compose training set, and the remaining 200 samples are used to compose test set. So, the sum of entire samples is 22000, including 17600 in training set and 4400 in test set. Table 6 is the parameters of main components of GSC. Phase difference of each phase 120°

VMD of Three-phase Current
The whole three-phase current samples under 22 failure states are addressed by VMD at 7 levels. Figure 6 and Figure 7 show the waveforms of phase-A current and the mode coefficient serials under No. 1 (normal operating) and No. 2 failure states, respectively. 1. No. 1 failure state (normal operating). It can be seen from Figure 6 (a) that the waveforms of phase is stable as same as each phase in Figure 4 (a). Figure 6  It can be seen from Figure 7 that the waveforms of phase-A is similar (to red curve) in Figure 5. The value of phase-A current is non positive for a large majority. Figure 7
8 compared methods mentioned in the end of Section 4 are used to compare the performance. They are involved to address the same experimental samples. To increase the credibility, every method trains the same training set and tests the same test set at 100 times. Table 9 shows the experimental comparison results between 8 methods. 1.37% 433971 The following conclusions can be analyzed and drawn from Table 9: 1. The method of VMD-TFA-DBN, proposed in this paper, has generated the best classifying capability under the 22 circumstances that the accuracy is 99.99%, the error times is 3. 2. The method of only BP has produced the worst classifying performance, the accuracy is 1.37%, the error times is 433971. 3. When the accuracy of VMD-TFA-DBN is higher than VMD-TFA-BP, TFA-DBN is higher than TFA-BP, VMD-DBN is higher than VMD-BP, and DBN is higher than BP. All of these illustrate the classification accuracy of DBN in higher than BP in the models. 4. The accuracy of each method used proposed TFA is higher than corresponding who does not use TFA, which verifies the great function of TFA for increasing classification accuracy. 5. The accuracy of each method used VMD is higher than corresponding who does not use VMD, which verifies the function of VMD in proposed method.
The conclusions of experimental results are broadly in line with what of simulation results. But the performance of each method of experimental results is worse than corresponding method. The probable causes are summarized as follows: 1. Three-phase current is extracted with error or interference. The samples are varying to indistinct, which lead to the accuracy decreased. 2. The total number of experimental samples in training set may be lack of, which leads to the DBN training model leaky.

Conclusions
This paper proposes a novel method to diagnosis the single and double IGBT modules opencircuit faults of GSC of the PMSG wind turbine. Above all, three-phase current varying with wind speed are extracted under 22 failure states. Afterward, the three-phase current are conducted by VMD at 7 levels to obtain the corresponding modes. Trend feature analysis is proposed to address the corresponding modes data to produce the trend feature vectors under 22 failure states. Finally, input the trend feature vectors to DBN, which is used to train and test and construct the model, and obtain the classification results.
The simulation and experimental results show that the proposed method has the capability to diagnose the single and double IGBT modules open-circuit faults of GSC, and the accuracy is high.