IN response to societal requirements, microgrid system has received considerable attention [1], [2]. The reliability of the inverter is considered as an important factor to guarantee the high quality, continuousness, and safe operation of the microgrid. Serious impacts of inverter can be caused by an openswitch fault, and the secondary problems are also generated, which can cause other parts to break down. Hence, openswitch fault diagnosis for the inverter switch is very important for high quality power, safe and stable output of the microgrid system.
The diagnosis methods can be mainly classified into two categories: timedomain analysis method and frequencydomain analysis method. The frequencydomain analysis method is to adopt advanced signal processing technology to get the signal frequency changing law, which can reduce the false signal caused by the noise. In [3], the method is based on wavelet packet transform (WPT) to realize realtime diagnosis of threephase inverter. Additionally, the timedomain analysis method is widely used in the signal processing of diagnosis for its fast detecting ability and simplicity. The timedomain analysis study of fault diagnosis methods of threephase inverter switch is presented in [4][6]. The current or voltage signal is used as the research object to judge the fault. In [5], the method is based on the inherent feature of continuous voltage pulsewidth modulation to realize fault detection. In [4], the radius of the current patterns is considered, and it is shown that it can not only detect the fault but also identify the location of the fault switch. The diagnosis method of [6] is based on the distortion of the input current and torque vibration in the system, in which both the inverter and rectifier switch fault are considered.
Although the inverter fault diagnosis methods are mainly presented in above two forms, the accuracy of the diagnosis method has not been an ideal result. For example, many methods, e.g., [4][10], are based on the distortion feature of the current signal or drive signal, which need to design an algorithm and the related threshold. When the number of switch is large or some interference signals appear, these methods are difficult to realize, which lead to inaccurate fault diagnosis of inverter. So, the switch faults are difficult to be accurately diagnosed.
Motivated by the above discussions, the purpose of this paper is to study fault diagnosis method for the microgrid inverter switch, which can realize an openswitch fault diagnosis. This method can improve the diagnosis accuracy, and is not influenced by threshold setting. The main contributions of this paper are summarized as follows:
1) Multilevel signal decomposition and reconstruction are investigated. The input signals are decomposed into the related coefficients of different frequency bands by the use of multi resolution analysis (MRA). Furthermore, the detailed signal information of the different frequency bands for threephase current are obtained by the reconstruction of the related different level coefficients. It is conducive to express the detailed signal change law and improve the diagnosis accuracy.
2) The absolute average ratio process is investigated to extract the detailed signal change information. The signal decomposed in multilevel is processed by this method to achieve multilevel absolute moving average ratio of fault signal. Because the accurate signal variation laws are obtained, the signal feature of switch fault for any switch of inverter can be accurately distinguished. Additionally, it has the function of normalization and reduces the processes of design.
3) Artificial neural network (ANN) is used for the fault diagnosis of microgrid inverter to classify the signal feature. It is more convenient to be combined with above method and has the adaptive feature, which need not set related threshold of algorithm and has a high applicability.
4) In [6], [8], [11], [12], these methods need to set up the related threshold of algorithm for the threephase current radius to diagnose the inverter switch fault. Compared with it, the proposed method in this paper has adaptive ability. The processes of detection and location are implemented at the same time. The design process is more simple and practical. Additionally, compared with [4][6], the proposed method is based on the multilevel decomposed signal feature extraction for absolute average ratio, which can obviously present the detailed signal change law and accurately distinguish the different switch status. Finally, compared with [13], [14], because of the absolute average ratio, the ANN design on the proposed method does not need the process of normalization, the outputs of ANN are more stable and accurate. The design is more convenient.
The remaining parts of the paper are arranged as follows: In Section Ⅱ, the circuit structure for microgrid is briefly described. In Section Ⅲ, the proposed fault diagnosis method is presented. In Section ⅢA, multilevel signal decomposition and reconstruction are described. The decomposition and reconstruction effect is given. In Section ⅢB, absolute average ratio process is presented. The effect of the extracted signal feature for part switch fault are given. In Section ⅢC, the ANN classification method is introduced. The training and testing results are given. In Section Ⅳ, the overall effect of the proposed fault diagnosis method and the main feature data are given. Finally, the conclusion is provided in Section V.
Ⅱ. MICROGRID STRUCTUREThe structure of the microgrid [15][18] is shown in Fig. 1, which includes DG sources, battery storages, DC/AC inverter, inductance capacitance (LC) filter, transmission line and many loads. In that, the DG sources and battery storages are applied to generate and balance the power. The LC filter is used to filter the output of the inverter. The DC/AC inverter is used to provide flexible operation and is connected to the grid. It consists of 6 insulatedgate bipolar transistor (IGBT) switches, and its driver uses pulsewidth modulation (PWM) technique. The PWM is used to generate the switching pulses for the IGBT devices. It plays an important role in the minimization of harmonics and switching losses in the inverter, especially in threephase applications [19].
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Fig. 1 Microgrid structure. 
In the system of microgrid, the transmission lines are equivalent to resistance (
$ \begin{align}\label{eq1} &\begin{bmatrix}L_f&0 &0 \\0&L_f&0 \\0&0 &L_f\end{bmatrix}\begin{bmatrix}\dot{I}_a\\\dot{I}_b\\\dot{I}_c\end{bmatrix}={\begin{bmatrix}V_a\\V_b\\V_c\end{bmatrix}}{\begin{bmatrix}V_{\rm ao}\\V_{\rm bo}\\V_{\rm co}\end{bmatrix}\quad} \end{align} $  (1) 
$ \left[ {\begin{array}{*{20}{c}} {{C_f}}&0&0\\ 0&{{C_f}}&0\\ 0&0&{{C_f}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{{\dot V}_{{\rm{ao}}}}}\\ {{{\dot V}_{{\rm{bo}}}}}\\ {{{\dot V}_{{\rm{co}}}}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{I_a}}\\ {{I_b}}\\ {{I_c}} \end{array}} \right]  \left[ {\begin{array}{*{20}{c}} {{I_{{\rm{ao}}}}}\\ {{I_{{\rm{bo}}}}}\\ {{I_{{\rm{co}}}}} \end{array}} \right] $  (2) 
$ \begin{align} \begin{split}\label{eq3} \begin{bmatrix}V_{\rm ao}\\V_{\rm bo}\\V_{\rm co}\end{bmatrix}=&\begin{bmatrix}L_l&0 &0 \\0&L_l&0 \\0&0&L_l\end{bmatrix}\begin{bmatrix}\dot{I}_{\rm ao}\\\dot{I}_{\rm bo}\\\dot{I}_{\rm co}\end{bmatrix}+\begin{bmatrix}R_l&0 &0 \\0&R_l&0\\0 &0 &R_l\end{bmatrix}\begin{bmatrix}I_{\rm ao}\\I_{\rm bo}\\I_{\rm co}\end{bmatrix}\\[1mm] &+\begin{bmatrix}Z_l&0&0 \\0&Z_l&0 \\0&0 &Z_l\end{bmatrix}\begin{bmatrix}I_{\rm ao}\\I_{\rm bo}\\I_{\rm co}\end{bmatrix} \end{split} \end{align} $  (3) 
where
$ \begin{align} &I_a=I_m\sin(wt)\nonumber\\ &I_b=I_m\sin(wt120^\circ)\nonumber\\ &I_c=I_m\sin(wt+120^\circ). \end{align} $  (4) 
From the microgrid structure (Fig. 1) and system feature (1)(3), it can be seen that the microgrid outputs are affected by the inverter. There are important relations between the inverter and the output signal. It is an important guarantee for the high quality and safe operation for the microgrid system. The inverter faults usually cause many serious primary effects and some secondary problems. Hence, in this paper, the study of the fault diagnosis method for the microgrid inverter switch is important.
Ⅲ. THE FAULT DIAGNOSIS METHODThe multilevel feature moving average ratio method is shown in Fig. 2, which mainly includes multilevel signal decomposition, signals reconstruction in different frequency bands, absolute average ratio process, and artificial neural network (ANN) classification. The threephase current signal obtained by sampling is used as the process signal. The input signals are decomposed into different frequency bands and the related coefficients are extracted by means of MRA. The detailed signals of different frequency bands are obtained by the reconstruction of the related coefficients. Furthermore, the detailed signals features of the different frequency bands are extracted by the absolute average ratio process. Finally, the ANN is used to identify the different switch status.
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Fig. 2 The structure of the multilevel feature moving average ratio. 
The multilevel signal decomposition and reconstruction are a process of the signal extraction at different levels. Multilevel signal decomposition is realized by the use of MRA to achieve different level decomposition coefficients.
Fig. 3 shows the decomposition principle of MRA. The MRA method has a good timescale representation of a discrete signal at various levels of decomposition. It can decompose the discrete signal
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Fig. 3 The structure of the multilevel feature moving average ratio. 
According to (5) and (6), the lowpass and highpass filters based on the selected wavelet function
$ \begin{equation}\label{eq5} \phi_{j, k}(t)=2^{\frac{j}{2}}\phi(2^{j}tk) \end{equation} $  (5) 
$ \begin{equation}\label{eq6} \psi_{j, k}(t)=2^{\frac{j}{2}}\psi(2^{j}tk) \end{equation} $  (6) 
$ \begin{equation}\label{eq7} a_{j, k}=\sum_{n}h(n2k)a_{j1, n} \end{equation} $  (7) 
$ \begin{align}\label{eq8} d_{j, k}=&\ \sum_{n}g(n2k)a_{j1, n} \end{align} $  (8) 
$ \begin{array}{l} X(n) = \sum\limits_{k = 0}^{{2^{N  j}}  1} {{a_{j,k}}} {2^{  \frac{j}{2}}}\phi ({2^{  j}}t  k)\\ + \sum\limits_{j = 1}^J {\sum\limits_{k = 0}^{{2^{N  j}}  1} {{d_{j,k}}} } {2^{  \frac{j}{2}}}\psi ({2^{  j}}t  k) \end{array} $  (9) 
where
The limits for frequency bands are related with the level of signal and the sampling rate. The upper limit of detail
The ''db3'' of the Daubechies family has been used in a wide range of problems which contributes to the localization and classification disturbances [24]. Hence, in this paper, the ''db3'' wavelet is used to decompose the signal
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Fig. 4 The features of the "db3". 
The process of the signal reconstruction is opposite to the decomposition, and mainly realizes different level coefficient reconstruction to obtain different frequency bands signal. The coefficient adopts the cycle zero padding and is convoluted with the highpass reconstitution filtering and the lowpass reconstitution filtering. The length of the different level signals and the original signal are the same.
The reconstitution results of the different level signals for a periodic normal current signal are shown in Fig. 5. The result indicates that the original signal is decomposed into 11 different levels, and the detailed 11 level signals for threephase current are reflected.
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Fig. 5 The reconstitution results of different levels for a periodic normal signal. 
The detailed signals features for the different frequency bands are extracted by the absolute average ratio process, which can be expressed as:
$ \begin{align}\label{eq10} &\mu_{m, l}(k\tau)=\frac{1}{N}\sum^k_{j=kN+1}i^*_{m, l}(j\tau) \end{align} $  (10) 
$ {\nu _{m,l}}(k\tau ) = \frac{1}{N}\sum\limits_{j = k  N + 1}^k  i_{m,l}^*(j\tau ) $  (11) 
$ \xi_{m, l}(k\tau)=\frac{\mu_{m, l}(k\tau)}{\nu_{m, l}(k\tau)} $  (12) 
where
The results of absolute average ratio process of threephases current signals at normal,
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Fig. 6 The absolute moving average ratio of threephases current signals at normal, S_{1}open and S_{2}open states. 
To improve accuracy and realize the adaptive ability, the artificial neural network (ANN) is used to classify different inverter switch status. Nowadays, ANN is a powerful pattern recognition technique, and can realize many functions by training the laws, such as of pattern recognition or data classification, through a learning process [25], [26]. The structure of ANN is shown in Fig. 7, which has an input layer, a hidden layer and an output layer. The back propagation algorithm is used to minimize the sum of square error (SE) (14).
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Fig. 7 The structure of artificial neural network. 
$ \begin{align}\label{eq13} &e_k =Y_kS_k \end{align} $  (13) 
$ SE = \sum\limits_k {{{({Y_k}  {S_k})}^2}} $  (14) 
where
$ \begin{equation}\label{eq15} W_{{\rm new}}=W_{{\rm old}}\eta\left[\frac{\partial {SE}}{\partial W_{\rm old}}\right] \end{equation} $  (15) 
where
$ \begin{align}\label{eq16} &z_{j}=\sum^{N_I}_{i=1}W^{(1)}_{ij}X_j \end{align} $  (16) 
$ y_{j}=\frac{1}{1+e^{z_j}} $  (17) 
$ l_{k}=\sum^{N_h}_{j=1}W^{(2)}_{jk}y_j $  (18) 
$ S_{k}=\frac{1}{1+e^{l_k}} $  (19) 
where
$ \begin{equation}\label{eq20} \frac{\partial {SE}}{\partial W^{(2)}_{jk}}=\frac{\partial {SE}}{\partial {S_k}}\frac{\partial {S_k}}{\partial {l_k}}\frac{\partial {l_k}}{\partial {W^{(2)}_{jk}}}. \end{equation} $  (20) 
The weights from input to hidden layer are then updated as
$ \begin{equation}\label{eq21} \frac{\partial {SE}}{\partial W^{(1)}_{ij}}=\frac{\partial {SE}}{\partial {S_k}}\frac{\partial {S_k}}{\partial {l_k}}\frac{\partial {l_k}}{\partial {y_j}}\frac{\partial {y_j}}{\partial {z_j}}\frac{\partial {z_j}}{\partial {W^{(1)}_{ij}}}. \end{equation} $  (21) 
The input of the ANN includes the 11 level absolute moving average ratio of threephase current signal. Hence, 33 neurons are used as input for ANN.
The system is sampled with 50 kHz frequency, the 336 sets of data are randomly selected from 7 cases. The 231 sets of the 336 data sets are used for ANN training. The rest of the data is used to test the training effect.
For the structure of neural network, the input layer is the characteristic value of detection signal, and the detection signal is threephase current. Every phase signal is decomposed into 11 levels. So, every phase signal has 11 characteristic values and the number all inputs to neural network is 33. The output layer represents the diagnosis results which has 7 kinds of results. Thus, the output neuron is 7. For the hidden neuron, firstly, the neuron numbers are obtained by the empirical formula
The model of microgrid system is set up by MATLAB/Simulink. The 6 kinds of inverter switch faults are diagnosed by the method mentioned in this paper. The openswitch fault is simulated by sending 0 driving pulse in the model. The main parameters are shown in Table Ⅱ.
In this paper, the presented method belongs to the field of artificial intelligence [13], [14] that uses the characteristic value recognition for different switch status in inverter. Threephase current signals are sampled in real time, the switch state of inverter is updated after every period
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Fig. 8 The threephase current signals and diagnosis results of the S_{1} openswitch fault. 
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Fig. 9 The threephase current signals and diagnosis results of the S_{2} openswitch fault. 
Table Ⅲ shows the output of neurons representing various switch states. The
In [6], [8], [11], [12], the methods need to set up the related threshold of algorithm for the threephase current radius to diagnose the inverter switch fault. Whereas, from the process of the method design in Fig. 2 and the related fault diagnosis result, it is obvious that the proposed method has adaptive ability which needs not set up the related thresholds. The processes of detection and location are implemented at the same time. The design process is more simple and practical. Additionally, compared with [4][6], the proposed method is based on the multilevel decomposition signal feature extraction for absolute average ratio, which can obviously present the detailed signal change law and accurately distinguish the different switch status. Finally, compared with [13], [14], the ANN design of the proposed method does not need process of normalization, and the outputs of ANN are more stable and accurate.
Ⅴ. CONCLUSIONIn this paper, the multilevel feature moving average ratio method for fault diagnosis of microgrid inverter switch has been proposed. The proposed method has accurately detected and located the openswitch fault for any inverter switch in the microgrid. Meanwhile, it has the adaptive features, which does not need to set up the related thresholds of algorithm, and it has a high applicability. Particularly, multilevel signal decomposition and reconstruction has been investigated to obtain the detailed signals information of the different frequency bands for threephase current. Additionally, the absolute average ratio process has been investigated to achieve multilevel absolute moving average ratio of fault signal. It also has the function of normalization and reduces the process of design.
Although the proposed method can be realized by simulation, it is difficult for the shortswitch fault diagnosis in real experiments because the time between the fault initiation and failure is very small. However, if the ANN classification method is written into the hardware and the highperformance IGBT is developed, which has high current ratings and ability to handle shortcircuit currents for longer time, then the shortswitch fault diagnosis is possible to be realized by the proposed method.
[1]  R. Lasseter and J. Eto, "Value and technology assessment to enhance the business case for the CERTS microgrid, " University of Wisconsin, Madison Wisconsin, United States, Tech. Rep. FC0206CH11350, May2010. 
[2]  F. A. Mohamed and H. N. Koivo, "Online management genetic algorithms of microgrid for residential application, " Energy Convers. Manag. , vol. 64, pp. 562568, Dec. 2012. 
[3]  S. A. Saleh, T. S. Radwan, and M. A. Rahman, "Realtime testing of WPTbased protection of threephase VS PWM inverterfed motors, " IEEE Trans. Power Deliv. , vol. 22, no. 4, pp. 21082115, Oct. 2007. 
[4]  U. M. Choi, H. G. Jeong, K. B. Lee, and F. Blaabjerg, "Method for detecting an openswitch fault in a gridconnected NPC inverter system, " IEEE Trans. Power Electron. , vol. 27, no. 6, pp. 27262739, Jun. 2012. 
[5]  T. J. Kim, W. C. Lee, and D. S. Hyun, "Detection method for opencircuit fault in neutralpointclamped inverter systems, " IEEE Trans. Ind. Electron. , vol. 56, no. 7, pp. 27542763, Jul. 2009. 
[6]  J. S. Lee, K. B. Lee, and F. Blaabjerg, "Openswitch fault detection method of a backtoback converter using NPC topology for wind turbine systems, " IEEE Trans. Ind. Appl. , vol. 51, no. 1, pp. 325335, Jan. 2015. 
[7]  U. M. Choi and K. B. Lee, "Detection method of an openswitch fault and faulttolerant strategy for a gridconnected Ttype threelevel inverter system, " in IEEE Energy Conversion Congress and Exposition (ECCE), Raleigh, NC, USA, 2012, pp. 41884195. 
[8]  Q. T. An, L. Sun, L. Z. Sun, "Current residual vectorbased openswitch fault diagnosis of inverters in PMSM drive systems". IEEE Trans. Power Electron. , 2015, 30 (5) :2814–2827. DOI:10.1109/TPEL.2014.2360834 
[9]  S. M. Jung, J. S. Park, H. W. Kim, K. Y. Cho, M. J. Youn, "An MRASbased diagnosis of opencircuit fault in PWM voltagesource inverters for PM synchronous motor drive systems". IEEE Trans. Power Electron. , 2013, 28 (5) :2514–2526. DOI:10.1109/TPEL.2012.2212916 
[10]  U. M. Choi, K. B. Lee, and F. Blaabjerg, "Diagnosis method of an openswitch fault for a gridconnected Ttype threelevel inverter system, " in Proc. 3rd IEEE Int. Symp. Power Electronics for Distributed Generation Systems (PEDG), Aalborg, Denmark, 2012, pp. 470475. 
[11]  P. Duan, K. G. Xie, L. Zhang, and X. L. Rong, "Openswitch fault diagnosis and system reconfiguration of doubly fed wind power converter used in a microgrid, " IEEE Trans. Power Electron. , vol. 26, no. 3, pp. 816821, Mar. 2011. 
[12]  I. Jlassi, J. O. Estima, S. K. El Khil, N. M. Bellaaj, A. J. M. Cardoso, "Multiple opencircuit faults diagnosis in BacktoBack converters of PMSG drives for wind turbine systems". IEEE Trans. Power Electron. , 2015, 30 (5) :2689–2702. DOI:10.1109/TPEL.2014.2342506 
[13]  M. A. Masrur, Z. Chen, and Y. Murphey, "Intelligent diagnosis of open and short circuit faults in electric drive inverters for realtime applications, " IET Power Electron. , vol. 3, no. 2, pp. 279291, Mar. 2010. 
[14]  S. Khomfoi and L. M. Tolbert, "Fault diagnosis system for a multilevel inverter using a neural network, " in Proc. 31st Annu. Conf. IEEE Industrial Electronics Society (IECON), Raleigh, NC, USA, 2005, pp. 10621069. 
[15]  Y. Li and Y. W. Li, "Power management of inverter interfaced autonomous microgrid based on virtual frequencyvoltage frame, " IEEE Trans. Smart Grid, vol. 2, no. 1, pp. 3040, Mar. 2011. 
[16]  Z. Y. Chen, A. Luo, H. J. Wang, Y. D. Chen, M. S. Li, and Y. Huang, "Adaptive slidingmode voltage control for inverter operating in islanded mode in microgrid, " Int. J. Electr. Power Energy Syst. , vol. 66, pp. 133143, Mar. 2015. 
[17]  G. Diaz, C. GonzalezMoran, J. GomezAleixandre, and A. Diez, "Complexvalued state matrices for simple representation of large autonomous microgrids supplied by PQ and Vf generation, " IEEE Trans. Power Syst. , vol. 24, no. 4, pp. 17201730, Nov. 2009. 
[18]  F. Razavi, R. Torani, I. Askarian, A. Asgharizadeh, and N. Masoomi, "Optimal design of islanded microgrid using genetic algorithm, " in International Conference on Genetic and Evolutionary Methods (GEM'12), Las Vegas, Nevada, USA, 2012. 
[19]  D. G. Holmes and B. P. McGrath, "Opportunities for harmonic cancellation with carrierbased PWM for a twolevel and multilevel cascaded inverters, " IEEE Trans. Ind. Appl. , vol. 37, no. 2, pp. 574582. Feb. 2001. 
[20]  J. Kim, "Cell seletion through twolevel basis pattern recognition with low/high frequency components decomposed by DWTbased MRA, " in IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA, 2014, pp. 906911. 
[21]  V. R. Satpute, C. Naveen, K. D. Kulat, and A. G. Keskar, "Fast and memory efficient 3ddwt based video encoding techniques with EZW based video compression mechanism, " in Transactions on Engineering Technologies, G. C. Yang, S. L. Ao, X. Huang, and O. Castillo, Eds. Netherlands: Springer, 2015, pp. 397412. 
[22]  G. F. Ju and A. Luo, "DWT application to realtime compression of power quality disturbance data, " Automat. Electric Power Syst. , vol. 26, no. 19, pp. 6163, Oct. 2002. 
[23]  J. Kim, G. S. Seo, B. Cho, W. Kim, J. Park, and T. Ishikawa, "Discrete wavelet transformbased characteristic analysis and SOH diagnosis for A LiIon cell, " in Proc. 7th Int. Power Electronics and Motion Control Conf. (IPEMC), Harbin, China, 2012, pp. 22182223. 
[24]  K. Maleknejad, M. Yousefi, and K. Nouri, "Computational methods for integrals involving functions and daubechies wavelets, " Appl. Math. Comp. , vol. 189, no. 2, pp. 18281840, Jun. 2007. 
[25]  R. Aggarwal and Y. H. Song, "Artificial neural networks in power systems. Ⅱ. types of artificial neural networks, " Power Eng. J. , vol. 12, no. 1, pp. 4147, Jan. 1998. 
[26]  R. Aggarwal and Y. Song, "Artificial neural networks in power systems. Ⅰ. general introduction to neural computing, " Power Eng. J. , vol. 11, no. 3, pp. 129134, Mar. 1997. 