Error-Voltage-Based Open-Switch Fault Diagnosis Strategy for Matrix Converters with Model Predictive Control Method

This paper proposes an error-voltage-based open-switch fault-diagnosis a strategy for a matrix converter (MC). A finite control set model predictive control method is used to operate the MC. The MC system performances under normal operation and under a single open-switch fault operation are analyzed. A fault-diagnosis strategy has also been implemented in two steps. First, the faulty phase is detected and identified based on a comparison of the reference and estimated output line-to-line voltages. Then, the faulty switch is located by considering the switching states of the faulty phase. The proposed fault-diagnosis method is able to locate the faulty switch accurately and quickly without additional voltage sensors. Simulation and experimental results are presented to demonstrate the feasibility and effectiveness of the proposed strategy.

M ATRIX converters (MCs) are a promising family of direct ac-ac power electronic converters. Compared with the conventional power converters, the MC possesses the advantages of bidirectional power flow with full four-quadrant operation, sinusoidal input, and output currents, controllable input power factor, high-power density and no dc-link energy storage elements [1]- [3]. Nevertheless, the components of MC may suffer several kinds of electrical faults. These components include capacitors, printed circuit boards, semiconductor devices, solder joints, and connectors [4], [5]. Among them, the power device module is the most vulnerable component, reportedly accounting for 34% of failures in converter systems (21% of semiconductor and 13% of solder joint) [6]. The failure of power device can be classified as open-circuit failure and short-circuit failure [7]. As a protection circuit is always installed in an MC system, a fast fuse in series with each of the switches can be employed 0093-9994 © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications standards/publications/rights/index.html for more information.  Fig. 1, the clamp circuit has to conduct the current that originally flowed through the faulty phase, and then the clamp voltage will be enlarged. This would accelerate the damage in a normal switch and lead to the occurrence of a secondary fault. If the faulty switch is not located in time, fault-tolerant operation of the MC [8], [9] cannot follow the isolating of the faulty switch. Therefore, issues, including real-time monitoring of the operating state and fault diagnosis of the MC, are gradually brought into sharp focus due to the demands for high reliability and lifetime.
In the existing literature, the methods for diagnosing an openswitch fault in power converters can be divided into two types: The signal processing-based approach and the analytical modelbased approach [10]. For the signal processing-based approach in an MC system, the discrete wavelet transform analysis of measured output current is an example of a fault-diagnosis method [11]. However, the diagnosis time is long if the fault occurs near the zero crossing of the faulty phase current. The analytical model-based approach for MC systems can be seen in [12]- [17]. In [12], the faulty phase is identified under the condition when the load current is equal to zero for 30 consecutive sampling periods. Then, an additional algorithm is used to locate the faulty switch. In [13], the fault-diagnosis method is proposed for Alesina-Venturini (AV). The diagnosis approach utilizes the special feature of the AV method, such as the load currents, the angles of the input and output voltage space vectors, and the duty cycles of the switches. However, these fault-diagnosis methods in [12] and [13] require relatively long detection times. In [9], a fault-diagnosis method based on the analysis of the currents circulating through the drive system is presented. This method can detect the faulty switch within a minimum of one switching period, in the example given about 0.08 ms after the fault occurs. However, an additional current sensor is needed to monitor the clamp current.
To reduce the detection time and avoid additional sensors, the fault-diagnosis method in [14] moves the load current sensors ahead of the clamp circuit connection. This arrangement detects and locates the faulty switch according to the information from the current sensors during the zero vectors. The accurate detection of the current sensor depends on an adequate zero vector time. This method is therefore not fit for MC applications, where a high-voltage transfer ratio is needed as the zero vector time will be small.
In [15], the proposed fault recognition method can detect and locate the faulty switch with voltage error signals dedicated to each switch, based on a direct comparison of the input and the output voltages. In [16] and [17], the differences between the measured and predicted output voltages are used as the criterion for the diagnosis. However, the diagnosis methods in [15]- [17] require additional voltage transducers and analog-todigital converters (ADC) with a very high bandwidth, which adds the system cost.
The finite control set model predictive control (FCS-MPC) has been shown to be a very interesting alternative for the modulation and control of MCs [18]- [20]. It uses the time-discrete model of the MC topology to predict the future values of, for example, the load currents and decides the most suitable switching state for the next sampling period. The FCS-MPC possesses several advantages, such as fast dynamic response, easy inclusion of nonlinearities and constraints of the system [21]- [23]. Currently, the fault diagnosis for the MC with FCS-MPC has not been considered in depth.
In [24], a fault-diagnosis method for MCs is proposed, which monitors the load currents and considers the switching state to locate the faulty switch. It is simpler to diagnose the exact location of the open-circuit switch in an MC with FCS-MPC. However, it is difficult to diagnosis the open-circuit fault switch when the following two conditions are satisfied simultaneously.
1) The frequency of the load current is same with the frequency of the input voltage. 2) The phase difference between the input voltage and the output current is π. The current-based fault diagnosis [24] has been proposed for MC with FCS-MPC. However, voltage-based fault-diagnosis strategy for MC with FCS-MPC has not been considered but may have some important advantages. Ideally, the fault-diagnosis strategy should be accomplished without increasing the overall system cost and complexity. Thus, this paper uses the load model to estimate the actual output line-to-line voltage. The reference output line-to-line voltage is obtained from the input voltage and the switching states. Then, the difference between the estimated output line-to-line voltage and the reference output line-to-line voltage is used to detect an open-circuit fault. The switching state is utilized to locate the faulty switch. Therefore, the additional hardware and large computational burdens are avoided. In addition, the advantages of voltage-based fault diagnosis, such as fast detection and an inherent high immunity to the false alarms, are inherited. The proposed fault-diagnosis method in this paper has been described in [25], more principle details and experimental results are added in this paper. This paper is organized as follows. In Section II, the normal operation based on FCS-MPC is presented. In addition, the MC performance under open-switch fault operation is analyzed. Then, in Section III, the fault-diagnosis method is described in detail. Finally, simulation and experimental results are presented to demonstrate the feasibility of the proposed strategy.

II. MC SYSTEM
The MC topology is shown in Fig. 1. The circuit consists of nine bidirectional switches, an input filter, and a clamp circuit. The bidirectional switches connect a three-phase voltage source to a three-phase resistance-inductance load for bidirectional energy flow. The input filter filters the switched input current of the converter to attenuate the switching frequency harmonics. The clamp circuit consists of 12 fast-recovery diodes to connect the clamping capacitor between the input and output terminals, to avoid overvoltage coming from the grid side and the load side.
For the safety operation of the MC topology: The open circuit is prohibited across the load connection and a short circuit is prohibited between the input lines, respectively. The switching states of each load phase must satisfy where S X y (X ∈ A, B, C, y ∈ a, b, c) equals to "1" when switch S X y is turned ON and equals to "0" when switch S X y is turned OFF, respectively. So the MC can generate 27 valid switching states. The reference output line-to-line voltages and input currents can be obtained as follows: For the sake of completeness of this paper and for an easy understanding of the faulty operation of an MC, the FCS-MPC that rules the normal operation of an MC will be presented first. Then, the faulty operation of MC with an open-switch fault is analyzed.

A. Normal Operation With FCS-MPC [26]
The continuous-time models of input filter and load are given as follows: where Then, the discrete models are achieved as To obtain the desired load currents and unity power factor for the MC, the following cost function is used where the weighting factor λ is empirically adjusted [27]. The predicted values of the load currents i P o and the source currents i P s can be obtained according to (7) and (8), respectively. The reference value of load current is given by (11) The reference value of source current is given as follows: (12) The input and output active powers are calculated from (13) to (15) (15) where η denotes the system efficiency. Hence, the amplitude of the expected source current I * sm can be calculated as [26] At each sampling period, the cost function values of 27 valid switching states are calculated. Finally, according to the following equation, the switching state N that produces the minimum value is applied in the next sampling period: [1], g [2], . . . , g[i], . . . , g [27]}.

B. Single Open-Switch Fault Operation
On the basis of the FCS-MPC, the effect of an open-switch fault on MC performance is discussed. Assume the sampling period is T s , the switch S Aa is applied at the kth sampling period T k s and the switch S Aa is suffering an open-switch fault as shown in Fig. 1. This means that the actual switching functions of S Aa will always be zero, hence leading to desired values do not correspond to the real ones. Since the voltage drop of the input filter is small compared with the input source voltage, the input filter is ignored to simply the analysis in the equivalent circuit. The arrow in Fig. 1 specifies the direction of positive load phase current flow. Assume that switch S Aa is suffering an open-switch fault and is applied. When the direction of load phase-A current is positive, the output terminal of load phase-A will be connected to the negative terminal of the capacitor in clamp circuit. The corresponding equivalent circuit is shown in Fig. 2(a). When the direction of load phase-A current is negative, the output terminal of load phase-A will be connected to the positive terminal of the capacitor in clamp circuit. The corresponding equivalent circuit is shown in Fig. 2(b). Thus, the actual output phase voltages are expressed as follows: The actual output line-to-line voltages are achieved as (19) shown at the bottom of this page.
Meanwhile, since the load phase-A current charges the capacitor of the clamp circuit, the capacitor voltage of the clamp circuit u cp is larger than the maximum input line-to-line voltage. Under normal operation, the actual output line-to-line voltage u oX Y will be same with the reference value u oX Y 1 . If S Aa is suffering an open-switch fault and is applied, the actual output line-to-line voltage u oAB and u oC A will be different from the reference value u oAB 1 and u oC A1 according to (2) and (19). This feature can be exploited later for fault detection.
To obtain the output line-to-line voltage without requiring extra voltage sensors, the load model is built as follows: 20) where u N is the voltage between the load neutral point and the ground point of the power supply.
According to (20), the actual output line-to-line voltage can be estimated if the derivative part of the load current is known. In order to obtain an accurate derivative part of the load current, the load currents are sampled four times in a sampling period, as shown in Fig. 3. The sampling values at T k s and the known switching state S k at kth sampling period are used for calculation of variables at T k +1 s . Then, all switching states are applied for prediction of variables at T k +2 s . The switching state making the cost function minimum will be applied in the (k+1)th sampling period. The sampling values at T k +1/4 s , T k +1/2 s , and T k +3/4 s are used for estimation of the output lineto-line voltage. Since the switching state stays the same from T k s to T k +1 s , the sampling values will not be disturbed by the four-step current-based commutation [28]. Assume output load current is According to Taylor's formula, the following equations can be obtained: When the high-order part n =3,5... f (n ) (kT s + T s 2 ) * ( T s 4 ) n is neglected, the derivative part of the load current is obtained as follows: Compared with the common method, (23) is more accurate to the true value with consideration of the second-order part of the load current. The actual output line-to-line voltages are estimated by substituting (23) into (20) as follows: By the way of monitoring the load currents based on (24), the actual output line-to-line voltages under faulty operation are estimated without additional voltage sensors.
In addition, the reference output line-to-line voltage is obtained from the input voltage and the switching states according to (2). Note that to suppress the disturbance, the mean value of input voltage in (2) is obtained as follows:

III. FAULT-DIAGNOSIS METHOD
From the discussion in the Section II, the output line-to-line voltages under faulty operation are not equal to the reference values. Based on these observations, this section proposes a fault detection algorithm, which uses two steps to identify the fault. The first step detects the occurrence of the fault and identifies the faulty phase. The second step locates the faulty switch.

A. Step 1: Detection and Identification of the Open-Circuit Phase
Three error voltagesε AB , ε B C , and ε C A are defined as the residuals, which are shown as Under normal conditions, the output line-to-line voltages equal to their reference values. As a result, the residuals of the output line-to-line voltage are ideally zero (in practical cases, they are expected to be a very small value due to the voltage drop across the insulated gate bipolar transistors (IGBTs) in a conducting state, the dead time of switch commutation, etc.). The residuals are within a small threshold. When single open-switch fault occurs at the switch S X y , the value of the output phase voltage u oX with respect to the supply neutral will change. It will be equal to either the positive or the negative dc-bus voltage of the clamp circuit according to the direction of the output phase current. The residuals related to the faulty output phase are shown as where X, Y ∈ {A, B, C}, XY , y ∈ {a, b, c}. The residuals related to the faulty output phase will exceed a threshold. While the residual of the two normal output phases preserves a low value.
Based on the analysis above, the residual related to normal output phases remains a low value, while the residuals related to the faulty output phase are a large value. This feature can be used to locate the faulty phase. The fault detection is achieved by monitoring the residual and comparing it with the predefined threshold ε th . The value of ε th is determined empirically. The algorithm to locate the faulty phase is summarized in Table I. The residuals (ε AB , ε B C , and ε C A ) under normal and faulty situations are illustrated. F X (X ∈ {A, B, C}) equals to "1" when the load phase-X is faulty and equals to "0" when the load phase-X is normal.

B. Step 2: Location of the Open-Circuit Switch
After the detection and recognition of faulty phase, the opencircuit switch must be located. For the MC with FCS-MPC, the switching state taken in a sampling period is clear and constant. In addition, only one switch is turned ON for connecting each output phase to the input phase. Therefore, the switch that connects the faulty phase to the input phase is located as the open-circuit switch. The algorithm to locate the open-circuit switch after identifying the faulty phase is presented as follows: where F X y (X ∈ {A, B, C}, y ∈ {a, b, c}) equals to "1" when S X y is open-circuit and equals to "0" when S X y is normal. For example, if (ε AB > ε th )&&(ε B C < ε th ) &&(ε C A > ε th ), from Table I, F A = 1, F B = 0, F C = 0, and the current switching state is S Aa = 1, S Ab = 0, S Ac = 0. According to (29), F Aa = 1. As a result, S Aa is regarded as the open-circuit switch.
The described technique employs a direct comparison between the reference and estimated output line-to-line voltages to locate the open-circuit switch, without any requirement of additional voltage sensors. Thus, for the improvement of the MC reliability, based on the proposed detection and identification of the failed switch, fault-tolerant operation of the MC drive systems can be followed by isolating the faulty devices.

IV. SIMULATION RESULTS
To verify the effectiveness of the proposed fault-diagnosis method, some numerical simulations are carried out by using MATLAB/Simulink. All the components of the MC topology used in the simulation are chosen from the power system block set in the Simulink and the dead time of the device is not taken account. The corresponding component parameters are indicated in Table II. To make the fault-diagnosis method more robust and to minimize the possibility of the false alarms, a positive threshold is selected, which is 60 V in the simulation.   Fig. 4, during normal operation, the MC system is operated with FCS-MPC, which employs a time-discrete model of the MC topology and a cost function to select the best switching state for the next sampling period. Three load currents are seen to be sinusoid with low distortions. In addition, the estimated line-to-line voltage is nearly equal to the reference output line-to-line voltage. During faulty operation, the fault is simulated by imposing permanent zero gate signals to both IG-BTs belonging to switch S Aa . The load phase-A current i oA is distorted and rapidly decreased to zero after the open-circuited fault of S Aa occurs at t = t 1 , the load phase-B current i oB and load phase-C current i oC are also affected. In addition, since the actual line-to-line voltage is not the reference output line-to- line voltage, the estimated output line-to-line voltage is different from the reference output line-to-line voltage. As shown in Fig. 5, during normal operation, three residual errors ε AB , ε B C ,and ε C A are all below the threshold value. During faulty operation, residual error ε B C is below the threshold value, while residual errors ε AB and ε C A are above the threshold value when predictive controller intends to give "ON" signal to S Aa . This phenomenon above is used for the fault diagnosis.
Figs. 6 and 7 show the simulation results of the MC system with I * om = 10 A, f o = 30 Hz during normal and S Aa faulty operation when the fault-diagnosis and tolerant methods are activated. The fault-diagnosis method in Section IV is applied while the fault-tolerant strategy in [24] is applied. The faulttolerant strategy selects the appropriate switching state for the remaining eight switches to minimize the error between the load current and the reference current. As shown in Fig. 6, during normal operation, three residual errors ε AB , ε B C , and ε C A are all below the threshold value, and the fault detection signal F Aa remains zero. During faulty operation, when predictive controller intends to give "ON" signal to S Aa , a "OFF" signal is imposed to switch S Aa instead to simulate the open-circuit failure. Therefore, the load current i oA flows through both the MC and the clamp circuit. The actual output line-to-line voltage is different from the reference output line-to-line voltage. As a result, the residual errors ε AB and ε C A exceed the threshold. Three residual errors and the switch signal satisfy (S Aa = 1)&&(ε AB > ε th )&&(ε B C < ε th ) &&(ε C A > ε th ), the fault detection signal F Aa reveals S Aa fault in a sampling period. This phenomenon can be seen more clearly from the enlarged drawing in Fig. 7.

V. EXPERIMENTAL RESULTS
The error-voltage based fault-diagnosis method is further evaluated on an experimental prototype. The experimental setup    comprises nine bidirectional switches FF200R12KT3_E and a controller, whose core control chip is TMS320F28335 and EP2C8T144C8N. The load current is obtained by the current sensor LT208-S7. The ADC chip in the control board is MAX1308. The actual sample instant is about 100 ns later than the desired sample instant. The impact of the delay during the ADC conversion process can be nearly neglected. The other parameters of the experimental setup are same as the simulation parameters given in Table II.
In order to ensure the load current regulation and unity power factor operation, the FCS-MPC technique is adopted to control the MC under normal condition. The experimentally measured result under normal condition is shown in Fig. 8, where the Ch1 trace is the actual source voltage u sa ; the Ch2 trace is the actual source current i sa ; the Ch3 trace is the actual output line-to-line voltage u oAB ; and the Ch4 trace is the actual load current i oA . As shown in Fig. 8, when the reference load current changes from 6 A/30 Hz to 12 A/60 Hz, the unity input power factor is obtained and the actual load current tracks the reference load current. Fig. 9 also shows the experimentally measured results under the same condition as Fig. 8. In Fig. 9, the Ch1 trace is the actual load current i oA ; the Ch2 trace is the reference output line-to-line voltage u oAB 1 ; the Ch3 trace is the estimated output line-to-line voltage u oAB 2 ; the Ch4 trace is the error voltage ε AB . It is clear that the reference output line-to-line voltage and estimated output line-to-line voltage are almost coinciding, and error voltage is less than 20 V. In addition, there is no misdiagnosis, regardless the change of reference load current.
The error voltages ε AB , ε B C , and ε C A in normal and faulty operation are compared in Fig. 10. Where the Ch1 trace is the actual load current i oA ; the Ch2, Ch3, and Ch4 traces are error voltages ε AB , ε B C , and ε C A , respectively, as indicated in Fig. 10. Under normal operation, the error voltages ε AB , ε B C , and ε C A are all less than 20 V. Under faulty operation, when predictive controller intends to give "ON" signal to S Aa , an "OFF" signal is imposed to switch S Aa instead to simulate an open-circuit failure. Therefore, the load current i oA flows through both the MC and the clamp circuit. The error voltages ε AB and ε C A are both larger than 100 V, while the error voltage ε B C is less than 20 V. Thus, the different features of the error voltages under normal and faulty operation can be used for the fault detection and location. The threshold error voltage ε th is set as 60 V according to the above analysis.
According to the above analysis, the fault-diagnosis method in Section IV is applied. As shown in Fig. 11(a), an open-circuit fault is imposed on the switch S Aa at t = t 1 . The load current i oA in Ch1 is distorted after t = t 1 . Ch2, Ch3, and Ch4 show three residual errors ε AB , ε B C , and ε C A between u AB 1 , u B C 1 , u C A1 based on known switching states and u AB 2 , u B C 2 , u C A2 based on the load model. Since (S Aa = 1)&&(ε AB > ε th )&&(ε B C < ε th ) &&(ε C A > ε th ), the switch S Aa is diagnosed as the faulty switch. This phenomenon can be seen more clearly from the enlarged drawing of a dotted box in Fig. 11(b). As indicated in Fig. 11(b), the diagnosis time is only a sampling period time (100 μs). To obtain the better quality of the load current under faulty operation without additional hardware, the fault-tolerant strategy in [24] is applied. To validate the universality of the proposed fault-diagnosis method, the reference load current frequency is set as same as the source voltage frequency. The open-circuit fault switch in this condition is difficult to be detected for the fault-diagnosis method in [26]. The experimental result for the proposed fault-diagnosis method in this paper is shown in Fig. 12, where the Ch1 trace is the actual load current i oA ; the Ch2, Ch3, and Ch4 traces are error voltages ε AB , ε B C , and ε C A , respectively. The faulty switch is also detected and located during a sampling period.

VI. CONCLUSION
An error-voltage-based open-switch fault-diagnosis strategy for MCs controlled with a FCS-MPC method has been investigated. The error-voltage is obtained by comparing the reference output line-to-line voltage and the estimated output line-to-line voltage. The reference output line-to-line voltage is obtained based on the input voltage and known switching state, whereas the estimated output line-to-line voltage is obtained based on the load model. The proposed fault-diagnosis strategy is cost-saving and space-saving because no additional voltage sensor is needed. In addition, compared with the fault-diagnosis time 1.4 ms in [25], the detection time of the proposed fault-diagnosis strategy is only a sampling period (100 μs). Meanwhile, the high immunity to the false alarm is also guaranteed. Finally, simulation and experimental results demonstrate the feasibility and effectiveness of the error-voltage based open-switch fault-diagnosis strategy.