# Diagnosis and Fault-Tolerant Control of Six-Phase Wind Turbine under Multiple Open-Switch Faults

Authors: Rouhollah Bolbolnia; Karim Abbaszadeh; Mojtaba Nasiri
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

A new open-switch fault diagnosis method is proposed in this paper for the six-phase AC-DC converter based on the difference between the phase current and the corresponding reference using an adaptive threshold. The single and multiple open-switch faults are detected without any additional equipment and complicated calculations since the proposed fault detection method is integrated with the hysteresis controller. The proposed fault-tolerant technique reduces the value of overcurrent and total harmonic distortion on the side phases of the faulty one, by changing the switching signal of one switch in its opposite phase in some regions. This technique is performed without adding any legs, switches, or triode for alternating currents to the circuit. Finally, the proposed fault-tolerant technique is evaluated by MATLAB simulation and the results show its effectiveness.


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## Body

## 1. Introduction

Recently, due to the rapid growth of wind energy and its significant effect on the power grid, the reliability and availability of wind energy systems have become very important [1]. A wind turbine with a permanent magnet synchronous generator (PMSG) has the advantages of high density and efficiency and increased reliability due to the absence of gearboxes [2]. These benefits alleviate the investment concerns in a PMSG wind turbine [3]. On the other hand, using multiphase generators in wind turbine systems provides more advantages such as reducing the amplitude of pulsating torque and increasing its frequency, decreasing the stator copper loss, and lowering the current per-phase for the same rated voltage. Moreover, multiphase generators improve reliability and increase the degree of freedom [4]. Therefore, a six-phase PMSG is one of the best choices for a wind turbine system. A wind turbine equipped with a six-phase PMSG requires a full-scale converter to inject the desired power into the grid. According to recent studies [5], the most vulnerable components of a wind turbine system are its power electronics devices and the most faults are originated from power switches, resulting in 25% of failures. Another survey [6] shows that power electronic converters are responsible for more than 22% of the overall downtimes in wind farms, which is the longest one of all. Generally, power switch faults are categorized into two types of short-circuit and open-switch faults. Unlike the short-circuit fault, the open-switch fault does not cause the system to immediately shut down and can remain undetected for a while [7]. However, it can disrupt the performance and reliability of the system, lead to secondary faults in the converter, eventually resulting in complete shutdown of the system [8, 9]. In order to improve the reliability and availability levels and reduce maintenance costs, both diagnostic and fault-tolerant methods with acceptable performance are needed until the situation is revised [10, 11].In general, diagnostic methods can be categorized into the following three groups: model-based, knowledge-based, and signal-based. By employing an observer in [12, 13], a model-based fault diagnostic approach was implemented. However, the model-based methods require accurate information of the system model and are extremely sensitive to the system parameter variations [7]. In [14], a knowledge-based fuzzy fault diagnosis method for the voltage source inverters was proposed. Nevertheless, the knowledge-based methods need the historic data of the system and require long training and a huge computational effort. The signal-based methods are realized by examining the characteristics of voltage and current signals. A single open-switch fault diagnostic method based on a comparison between the measured voltage and the reference value was presented for a doubly fed wind power system in [1, 15]. Voltage-based diagnostic methods increase the system cost, complexity, and the potential of fault on additional equipment like voltage sensors [16]. Current-based methods are widely used for single and multiple open-switch fault detection since they require neither accurate model of the system, complicated calculations, nor additional equipment [10]. The current Park’s vector and the average current Park’s vector methods were introduced in [17, 18], whereas the open-switch fault was determined by using the phase angle. A comparison between the phase angle slope of the current Park’s vector and a constant threshold was suggested in [19, 20]. The fault diagnosis indicator is normalized to be independent of load changes. In [21, 22], the fundamental component and the average absolute value of the current were considered as normalizing variables. In [23], the instantaneous value of the current was proposed as a normalizing variable. The constant thresholds usually need to be adjusted according to the operating point variation or reference values, which can decrease the reliability of fault diagnosis techniques [24]. In [25], the adaptive threshold is used instead of the constant threshold to increase robustness. These techniques detect open-switch faults in conventional three-phase converters with six switches but they have not been analyzed for multiphase systems, yet.Various structures were proposed for open-switch fault-tolerant. In [26, 27], an additional leg was connected to the converter phases by triode for alternating currents (TRIACs), while in [28], this additional leg was connected to the neutral point of the machine. Besides, in [29] and [30], the additional switches were removed, and only by TRIACs, the capacitors midpoint of DC-link was connected to the converter phases or the neutral point of the machine or grid transformer [31, 32]. Also in [33], both sides (grid/machine) of the back-to-back converter were connected to each other through TRIACs. Additional equipment such as switches and TRIACs increases the cost and complexity of the system. In some researches [8, 34, 35], the fault-tolerant method was implemented by revising the PWM switching pattern, which prevents the system cost to increase. Also, these methods have not been evaluated for multiphase systems.This paper presents a fault diagnosis technique for single and multiple open-switch faults in a six-phase AC-DC converter as part of a multiphase wind turbine system. The novelties of this paper can be classified as follows:(1)
The proposed fault detection method only requires the information given by current sensors and their reference signals(2)
These currents and their reference information are already provided by the main control system and there is no need for additional sensors or complicated calculations(3)
After fault detection, without any additional equipment, the fault-tolerant method is performed by revising the switching pattern of the opposite phase of the faulty ones in some regions(4)
The proposed fault-tolerant method reduces the overcurrent and the total harmonic distortion (THD) of current in healthy phasesThis paper is arranged as follows: The six-phase AC-DC converter model used in the wind turbine is presented in Section2. Fault detection technique and fault-tolerant method for single and multiple open-switch faults are introduced in Section 3 and Section 4, respectively. In Section 5, the performance of the proposed fault-tolerant method is evaluated by utilizing simulation results. Finally, in Section 6, conclusions are presented.


## 2. Description of the Six-Phase Wind Turbine with the AC-DC Converter Model

A wind turbine based on a six-phase PMSG is connected to the grid via a full-scale back-to-back converter. According to Figure1, this converter consists of two parts, machine side converter (MSC) and grid side converter (GSC), which are connected to each other through the DC-link capacitor. As the six-phase MSC has 12 switches (twice the three-phase system), open-switch fault diagnosis and fault-tolerant are very important in this converter. Many fault detection and fault-tolerant methods have been developed for DC-AC inverter; however, there are a few types of research for AC-DC converter [8]. This paper uses a six-phase AC-DC converter without grid connection and considers a local load as a consumer according to Figure 2.Figure 1
The six-phase PMSG-based wind turbine system configuration.Figure 2
Six-phase AC-DC PWM converter.Figure3 demonstrates a hysteresis current controller in a six-phase AC-DC converter to maintain the DC-link voltage at the required value. The main advantage of the hysteresis controller is its simplicity, fast response, and load-independent performance [36]. A proportional integral (PI) controller is used to regulate the DC-link voltage and its reference value [37]. The output of the DC-link voltage controller is considered as the reference current Iref in the hysteresis controller. The reference current waveform is obtained from the voltage waveform of the same phase. Switching signals for each phase are generated by comparing the phase current with its reference value and considering the hysteresis band. If the difference between the reference current and the actual current of the same phase is greater than the hysteresis band, the upper switch of that phase will turn on. Otherwise, the bottom switch of that phase will turn on. The differential equation of the six-phase AC-DC converter is given by(1)usnt=Ldisndt+Risnt+umod−ntn=a,b,c,x,y,z,where us is the voltage source and umod is the converter voltage. L is the filter’s inductance, and R is the resistance. The six-phase converter equations are transferred to the dq rotation frame by considering the T62 matrix.(2)T62=26cosθ−sinθcosθ−2π3−sinθ−2π3cosθ+2π3−sinθ+2π3cosθ−π3−sinθ−π3cosθ−π−sinθ−πcosθ+π3−sinθ+π3,ddtidtiqt=−RLw1−w1−RLidtiqt+−1L00−1Lumod,dtumod,qt+1L001Lus,dtus,qt,where w1 is the angular frequency and id and iq are d-axis and q-axis currents, respectively. usd and usq are d-axis and q-axis voltages, respectively. Source power (Ps) is considered based on equation (3). A part of the source power is dissipated as losses in the converter (Plosses) and the rest is delivered to the load (Pload).(3)Ps=Pload+Plosses=3us,d.id+us,q.iq.Figure 3
Control block diagram of direct current control utilizing hysteresis controller in a six-phase AC-DC converter.


## 3. Diagnosis of Open-Switch Faults

The open-switch faults in the six-phase AC-DC PWM converters have different current patterns compared to the six-phase voltage source inverters. Unlike inverters, these converters do not completely block positive and negative currents during open-switch faults. As shown in Figure2, in normal operation, the positive half-cycle current is established through the bottom switch and the upper antiparallel diode of one phase, whereas the upper switch and the bottom antiparallel diode of that phase establish the negative half-cycle current. Therefore, if an open-switch fault occurs on the upper switch, the negative half-cycle of phase current is distorted but its positive half-cycle is not affected. On the contrary, if an open-switch fault occurs in the bottom switch, the negative half-cycle of phase current is not affected but its positive half-cycle is distorted. Hence, the open-switch faults can be detected by monitoring the lost part of the phase current [32].Open-switch faults include single and multiple faults. Two different cases are considered for the multiple open-switch faults:Case I: the open-switch fault occurs in two switches from two different legsCase II: the open-switch fault occurs in two switches from one leg


### 3.1. Single Open-Switch Fault

Due to the open-switch fault that occurred in the upper or bottom switch, part of the negative or positive half-cycle current of that leg is eliminated, which is different from its corresponding reference signal. Therefore, the difference between the phase current and the corresponding reference is used as a fault diagnosis indicator. This fault diagnosis indicator does not require additional measurements so it is integrated with the control block diagram of converter, as shown in Figure3. The fault diagnosis indicator is normalized to be independent of the load [38].The first fault diagnosis indicator is normalized residual currentNrn. As shown in (4), Nrn is the average value ​​of the absolute current error divided by the absolute current value. in and in∗ are the current and its reference value of each phase, respectively. δ is a small positive quantity.(4)Nrn=in−in∗δ+inn=a,b,c,x,y,z.In normal conditions, the value ofNrn is approximately equal to zero in all phases. When the fault occurs, Nrn of the corresponding phase will change and exceed the threshold value. A good threshold value is essential for a robust fault diagnosis [38]. If the fixed threshold value is high or low, then the fault sensitivity is reduced or the false alarm rate is increased, respectively. Therefore, an adaptive threshold value is the best alternative. According to equation (6), the adaptive threshold value is the average of Rmax and Rmin. In this equation, Rmax is the maximum of Nrn in all phases, and Rmin is the minimum of Nrn in all phases.(5)T=Rmax+Rmin2,Rmax=maxNra,Nrb,Nrc,Nrx,Nry,Nrz,Rmin=minNra,Nrb,Nrc,Nrx,Nry,Nrz.Under normal conditions, the adaptive threshold value is similar to the value ofNrn, which is approximately equal to zero. Nevertheless, in fault conditions, due to a sudden change in the value of Nrn, the value of Rmax increases. As a result, the adaptive threshold value also increases and becomes greater than zero [35]. Since T is the average value of Rmax and Rmin, so it is smaller than Nrn in the faulty phase. Moreover, as Nrn has not changed in other phases, their value has become less than T. The phase with the single open-switch fault is detected by considering the first fault diagnosis indicator Nrn and the adaptive threshold value (T) according to Table 1.Table 1
The different states of the single open-switch fault diagnosis.
Normal conditionNra≈TNrb≈TNrc≈TNrx≈TNry≈TNrz≈TFault in phase aNra>TNrb<TNrc<TNrx<TNry<TNrz<TFault in phase bNra<TNrb>TNrc<TNrx<TNry<TNrz<TFault in phase cNra<TNrb<TNrc>TNrx<TNry<TNrz<TFault in phase xNra<TNrb<TNrc<TNrx>TNry<TNrz<TFault in phase yNra<TNrb<TNrc<TNrx<TNry>TNrz<TFault in phase zNra<TNrb<TNrc<TNrx<TNry<TNrz>TAs shown in Figure2, each phase has two switches. After detecting the faulty phase, it is necessary to determine whether the open-switch fault occurred in the upper switch or the bottom one. Therefore, the average current value <in> is considered as another indicator of open-switch fault diagnosis to distinguish between the upper and bottom switch. If the value of <in> is higher than zero, the open-switch fault has occurred in the upper switch. Hence, the open-switch fault has occurred in the bottom switch when <in> is lower than zero. The block diagram of the open-switch fault based on the two indicators Nrn and <in> is presented in Figure 4.Figure 4
Block diagram of the open-switch fault detection method.


### 3.2. Multiple Open-Switch Faults

Multiple open-switch faults occur in at least two switches of one leg or two different legs. The value ofNrn in the faulty phases is greater than the adaptive threshold while it is smaller in healthy phases. For example in Figure 2, if S2 and S11 are in a faulty state, ia and iz will lose their positive and negative half-cycles, respectively. Accordingly, Nra and Nrz are greater than T whereas Nrb,Nrc,Nrx, and Nry are smaller than T. Similar to the single open-switch fault, the average current value is used to discern the upper switch from the bottom switch in multiple open-switch fault modes. Therefore, <ia> is smaller than zero because S2 is the bottom switch and <iz> is larger than zero because S11 is the upper switch.When multiple open-switch faults occur in the upper and the bottom switches from one leg, only the value ofNrn in that phase is greater than the adaptive threshold, similar to the single open-switch fault. In this case, the average current value is used to distinguish between single and multiple open-switch faults of a leg. In a single open-switch fault condition, the value of <in> in the faulty phase is greater than zero or smaller than zero, while in multiple open-switch faults on both switches of one leg, the value of <in> becomes approximately equal to zero after a considerable fluctuation.


## 3.1. Single Open-Switch Fault

Due to the open-switch fault that occurred in the upper or bottom switch, part of the negative or positive half-cycle current of that leg is eliminated, which is different from its corresponding reference signal. Therefore, the difference between the phase current and the corresponding reference is used as a fault diagnosis indicator. This fault diagnosis indicator does not require additional measurements so it is integrated with the control block diagram of converter, as shown in Figure3. The fault diagnosis indicator is normalized to be independent of the load [38].The first fault diagnosis indicator is normalized residual currentNrn. As shown in (4), Nrn is the average value ​​of the absolute current error divided by the absolute current value. in and in∗ are the current and its reference value of each phase, respectively. δ is a small positive quantity.(4)Nrn=in−in∗δ+inn=a,b,c,x,y,z.In normal conditions, the value ofNrn is approximately equal to zero in all phases. When the fault occurs, Nrn of the corresponding phase will change and exceed the threshold value. A good threshold value is essential for a robust fault diagnosis [38]. If the fixed threshold value is high or low, then the fault sensitivity is reduced or the false alarm rate is increased, respectively. Therefore, an adaptive threshold value is the best alternative. According to equation (6), the adaptive threshold value is the average of Rmax and Rmin. In this equation, Rmax is the maximum of Nrn in all phases, and Rmin is the minimum of Nrn in all phases.(5)T=Rmax+Rmin2,Rmax=maxNra,Nrb,Nrc,Nrx,Nry,Nrz,Rmin=minNra,Nrb,Nrc,Nrx,Nry,Nrz.Under normal conditions, the adaptive threshold value is similar to the value ofNrn, which is approximately equal to zero. Nevertheless, in fault conditions, due to a sudden change in the value of Nrn, the value of Rmax increases. As a result, the adaptive threshold value also increases and becomes greater than zero [35]. Since T is the average value of Rmax and Rmin, so it is smaller than Nrn in the faulty phase. Moreover, as Nrn has not changed in other phases, their value has become less than T. The phase with the single open-switch fault is detected by considering the first fault diagnosis indicator Nrn and the adaptive threshold value (T) according to Table 1.Table 1
The different states of the single open-switch fault diagnosis.
Normal conditionNra≈TNrb≈TNrc≈TNrx≈TNry≈TNrz≈TFault in phase aNra>TNrb<TNrc<TNrx<TNry<TNrz<TFault in phase bNra<TNrb>TNrc<TNrx<TNry<TNrz<TFault in phase cNra<TNrb<TNrc>TNrx<TNry<TNrz<TFault in phase xNra<TNrb<TNrc<TNrx>TNry<TNrz<TFault in phase yNra<TNrb<TNrc<TNrx<TNry>TNrz<TFault in phase zNra<TNrb<TNrc<TNrx<TNry<TNrz>TAs shown in Figure2, each phase has two switches. After detecting the faulty phase, it is necessary to determine whether the open-switch fault occurred in the upper switch or the bottom one. Therefore, the average current value <in> is considered as another indicator of open-switch fault diagnosis to distinguish between the upper and bottom switch. If the value of <in> is higher than zero, the open-switch fault has occurred in the upper switch. Hence, the open-switch fault has occurred in the bottom switch when <in> is lower than zero. The block diagram of the open-switch fault based on the two indicators Nrn and <in> is presented in Figure 4.Figure 4
Block diagram of the open-switch fault detection method.


## 3.2. Multiple Open-Switch Faults

Multiple open-switch faults occur in at least two switches of one leg or two different legs. The value ofNrn in the faulty phases is greater than the adaptive threshold while it is smaller in healthy phases. For example in Figure 2, if S2 and S11 are in a faulty state, ia and iz will lose their positive and negative half-cycles, respectively. Accordingly, Nra and Nrz are greater than T whereas Nrb,Nrc,Nrx, and Nry are smaller than T. Similar to the single open-switch fault, the average current value is used to discern the upper switch from the bottom switch in multiple open-switch fault modes. Therefore, <ia> is smaller than zero because S2 is the bottom switch and <iz> is larger than zero because S11 is the upper switch.When multiple open-switch faults occur in the upper and the bottom switches from one leg, only the value ofNrn in that phase is greater than the adaptive threshold, similar to the single open-switch fault. In this case, the average current value is used to distinguish between single and multiple open-switch faults of a leg. In a single open-switch fault condition, the value of <in> in the faulty phase is greater than zero or smaller than zero, while in multiple open-switch faults on both switches of one leg, the value of <in> becomes approximately equal to zero after a considerable fluctuation.


## 4. The Proposed Fault-Tolerant Method for Open-Switch Faults

Open-switch faults in the six-phase converters do not immediately cause the system to shut down, but they compromise the performance of the converters. To improve the converter’s performance and prevent secondary fault, the fault-tolerant control takes place. Figure5 shows the six-phase currents of the AC-DC converter in the normal operation, which is similar to the voltage waveform due to the unity power factor. The general equation of the current is as follows:(6)ik=Imcosw1t−k−1∗π3k=1,2,…6,where Im is the six-phase current amplitude and w1 is the angular frequency. Every cycle of the currents can be divided into 12 regions, where their corresponding devices with normal operation are presented in Table 2. According to Table 2, under normal conditions in each region, three of the upper switches of each phase and three of the bottom switches of the other phases conduct currents.Figure 5
Six-phase currents of AC-DC converter at normal operation.Table 2
Conducting diodes and switches of the six-phase converter at normal operation.
RegionsConducting switchesConducting diodesReg1:0−π6S2,S3,S5,S8,S9,S12D1,D4,D6,D7,D10,D11Reg2:π6−2π6S2,S4,S5,S8,S9,S11D1,D3,D6,D7,D10,D12Reg3:2π6−π2S2,S4,S5,S8,S9,S11D1,D3,D6,D7,D10,D12Reg4:π2−4π6S1,S4,S5,S8,S10,S11D2,D3,D6,D7,D9,D12Reg5:4π6−5π6S1,S4,S5,S8,S10,S11D2,D3,D6,D7,D9,D12Reg6:5π6−πS1,S4,S6,S7,S10,S11D2,D3,D5,D8,D9,D12Reg7:π−7π6S1,S4,S6,S7,S10,S11D2,D3,D5,D8,D9,D12Reg8:7π6−8π6S1,S3,S6,S7,S10,S12D2,D4,D5,D8,D9,D11Reg9:8π6−3π2S1,S3,S6,S7,S10,S12D2,D4,D5,D8,D9,D11Reg10:3π2−10π6S2,S3,S6,S7,S9,S12D1,D4,D5,D8,D10,D11Reg11:10π6−11π6S2,S3,S6,S7,S9,S12D1,D4,D5,D8,D10,D11Reg12:11π6−2πS2,S3,S5,S8,S9,S12D1,D4,D6,D7,D10,D11According to Kirchhoff’s circuit laws, the sum of the six-phase currents should be zero. Since the faulty switch is unable to conduct its corresponding half-cycle current, this current is imposed to the side phases, thus causing an overcurrent. For each side phase, the overcurrent can be calculated by(7)ifaultk−1=Imcosw1t−k−2∗π3+Imcosw1t−k−1∗π3=3∗Imcosw1t−k−2π3+π6,(8)ifaultk+1=Imcosw1t−kπ3+Imcosw1t−k−1∗π3=3∗Imcosw1t−kπ3+π6,where k is the faulty phase and ifault is the fault current. Therefore, the amplitude of the overcurrent is more than 73% of the rated phase current, which causes terrible stresses on the switches of these phases. Accordingly, there is a high possibility of secondary faults in the converter system, and the proposed fault-tolerant control should limit this overcurrent in other healthy phases.


### 4.1. Fault-Tolerant Method for a Single Open-Switch Fault

According to Figure5 and equation (6), the currents of phases A, B, and C are symmetrical with the currents of phases Y, Z, and X, respectively. In other words, phase Y is the opposite phase of phase A, phase Z is the opposite phase of phase B, and phase X is the opposite phase of phase C. Then, the overcurrent in healthy phases can be limited by turning off the switches in the opposite phase of the faulty ones, in some regions. The fault-tolerant switch and fault-tolerant regions for every single open-switch fault are described in Table 3. For example, in Figure 2, if an open-switch fault occurs on the S11 switch, the negative half-cycle current of phase Z does not pass through this switch and causes overcurrent in phases A and C. According to Table 3, the S4 switch in the opposite phase of phase Z must be turned off in regions 2, 3, 6, and 7 to reduce the overcurrent in healthy phases A and C.Table 3
Fault-tolerant switch and fault-tolerant regions for six-phase AC-DC converter at open-switch fault conditions.
Open-switch faultFault-tolerant switchFault-tolerant regionsS1S10Reg4,Reg5,Reg8,Reg9S2S9Reg2,Reg3,Reg10,Reg11S3S12Reg1,Reg8,Reg9,Reg12S4S11Reg2,Reg3,Reg6,Reg7S5S8Reg1,Reg4,Reg5,Reg12S6S7Reg6,Reg7,Reg10,Reg11S7S6Reg6,Reg7,Reg10,Reg11S8S5Reg1,Reg4,Reg5,Reg12S9S2Reg2,Reg3,Reg10,Reg11S10S1Reg4,Reg5,Reg8,Reg9S11S4Reg2,Reg3,Reg6,Reg7S12S3Reg1,Reg8,Reg9,Reg12


### 4.2. Fault-Tolerant Method for Multiple Open-Switch Faults

After fault detection and localization in multiple open-switch faults, the proposed fault-tolerant control for both faulty switches is simultaneously performed according to Table3. The open-switch fault of switches S1 and S12 in Figure 2 is considered as an example. These multiple open-switch faults cause overcurrent in the negative half-cycle current of phases X and Z and the positive half-cycle current of phases A and C. The overcurrent in healthy phases is limited by turning off S10 in regions 4, 5, 8, and 9 and simultaneously S3 in regions 1, 8, 9, and 12. To evaluate the effectiveness of the proposed fault-tolerant method, an overcurrent indicator (Iov) in the side phases of the faulty one is defined according to equation (9). This method tries to reduce it.(9)Iovk±1=maxifaultk±1−inormalk±1inormalk±1,where k is the faulty phase and k ± 1 are the side phases. ifault and inormal are the phase current in faulty and healthy conditions.


## 4.1. Fault-Tolerant Method for a Single Open-Switch Fault

According to Figure5 and equation (6), the currents of phases A, B, and C are symmetrical with the currents of phases Y, Z, and X, respectively. In other words, phase Y is the opposite phase of phase A, phase Z is the opposite phase of phase B, and phase X is the opposite phase of phase C. Then, the overcurrent in healthy phases can be limited by turning off the switches in the opposite phase of the faulty ones, in some regions. The fault-tolerant switch and fault-tolerant regions for every single open-switch fault are described in Table 3. For example, in Figure 2, if an open-switch fault occurs on the S11 switch, the negative half-cycle current of phase Z does not pass through this switch and causes overcurrent in phases A and C. According to Table 3, the S4 switch in the opposite phase of phase Z must be turned off in regions 2, 3, 6, and 7 to reduce the overcurrent in healthy phases A and C.Table 3
Fault-tolerant switch and fault-tolerant regions for six-phase AC-DC converter at open-switch fault conditions.
Open-switch faultFault-tolerant switchFault-tolerant regionsS1S10Reg4,Reg5,Reg8,Reg9S2S9Reg2,Reg3,Reg10,Reg11S3S12Reg1,Reg8,Reg9,Reg12S4S11Reg2,Reg3,Reg6,Reg7S5S8Reg1,Reg4,Reg5,Reg12S6S7Reg6,Reg7,Reg10,Reg11S7S6Reg6,Reg7,Reg10,Reg11S8S5Reg1,Reg4,Reg5,Reg12S9S2Reg2,Reg3,Reg10,Reg11S10S1Reg4,Reg5,Reg8,Reg9S11S4Reg2,Reg3,Reg6,Reg7S12S3Reg1,Reg8,Reg9,Reg12


## 4.2. Fault-Tolerant Method for Multiple Open-Switch Faults

After fault detection and localization in multiple open-switch faults, the proposed fault-tolerant control for both faulty switches is simultaneously performed according to Table3. The open-switch fault of switches S1 and S12 in Figure 2 is considered as an example. These multiple open-switch faults cause overcurrent in the negative half-cycle current of phases X and Z and the positive half-cycle current of phases A and C. The overcurrent in healthy phases is limited by turning off S10 in regions 4, 5, 8, and 9 and simultaneously S3 in regions 1, 8, 9, and 12. To evaluate the effectiveness of the proposed fault-tolerant method, an overcurrent indicator (Iov) in the side phases of the faulty one is defined according to equation (9). This method tries to reduce it.(9)Iovk±1=maxifaultk±1−inormalk±1inormalk±1,where k is the faulty phase and k ± 1 are the side phases. ifault and inormal are the phase current in faulty and healthy conditions.


## 5. Simulation Results

To evaluate the performances of the proposed fault detection method and fault-tolerant control in the six-phase AC-DC converter, several simulations are carried out by using the MATLAB/Simulink software. The simulation parameters and open-switch fault conditions are given in Table4. Although the fault-tolerant technique can be performed immediately after fault detection, it is performed after a while (at t = 0.3 s) to make its effect more clear. The simulation results are divided into three-time intervals:(1)
Normal condition:t < 0.2 s(2)
Open-switch fault time: 0.2 s <t < 0.3 s(3)
Fault-tolerant time:t > 0.3 sTable 4
Parameters of the six-phase AC-DC converter simulation.
Input voltage6 ph-230 (v)DC-link voltage650 (V)Control formatHysteresis (s)Grid frequency50 (Hz)DC-link capacitance2200 (μF)Fault start time0.2Reactor5 (mH)DC load resistance100 (ohm)Tolerant control start time0.3Firstly, the robustness of the fault detection method against load changes should be evaluated. According to Figure6(a), assume that the load connected to the converter is halved at t = 0.14 s. As shown in Figure 6(b), the load changes affect all the phases and increase the value of Nrn and T, but they stay close to each other. Therefore, the fault detection method correctly identifies such changes as nonfault conditions and it is robust against them.Figure 6
Simulation result to prove the robustness of the fault detection method against load changes. (a) Six-phase currents. (b) Diagnostic variablesNrn.
(a)(b)According to Figure7(a), an open-switch fault has occurred in the switch S11 in at the moment t = 0.2 s, which has caused a disturbance in the six-phase currents. Part of the negative half-cycle current of phase Z is eliminated, while phases A and C suffer 66 percent overcurrent.Figure 7
Simulation result of the AC-DC converter currents before and after open-switch fault inS11. (a) All phases. (b) Faulty phase Z and side phases A and C.
(a)(b)Under normal conditions, the values of the actual and reference currents are close to each other, so the values ofNrn and T are about zero. After the start time of the single open-switch fault, the values of Nrn in the faulty phase will increase, and consequently, the value of T will increase. Since T>Nra,T>Nrb,T>Nrc,T>Nrx,T>NryandT<Nrz, the open-switch fault is detected in phase Z at Tfd = 0.2023 s according to Table 1 and Figure 8. As shown in Figure 9, the value of <iz> is greater than zero, so the open-switch fault occurred in the upper switch of phase Z.Figure 8
Simulation result of the diagnostic variablesNrn, for open-switch faults in phase Z.Figure 9
Simulation result of the diagnostic variablesin, for open-switch faults in S11.After identifying the faulted switchS11, the fault-tolerant control is executed at t = 0.3 s, according to Table 3. As shown in Figure 7(b), during the open-switch fault of the S11, the S4 switch is turned off in regions 2, 3, 6, and 7, to reduce the overcurrent of phases A and C. By applying the fault-tolerant method, in addition to reducing the overcurrent in phases A and C, the THD of current in these phases is also reduced. The THD of phases A and C is presented in Figure 10. The numerical results of the overcurrent indicator and THD for the side phases of the faulty phase at the open-switch fault time and fault-tolerant time are presented in Table 5.Figure 10
Simulation result of the THD of phases A and C, for open-switch fault and fault-tolerant conditions.Table 5
Numerical results of the overcurrent indicator and THD for open-switch fault conditions.
Faulty switchSide phaseFault conditionFault-tolerant controlIovTHDIovTHDS11A0.620.1760.220.035C0.660.220.210.042S1andS12X0.440.0940.240.034C0.660.210.350.038S1andS2X0.600.210.350.036Z0.620.230.330.037Since a fault on any switch may also cause other switches to fail, multiple switch faults are very significant and should be addressed properly. For example, consider the open-switch faults on switchesS1 and S12 that cause an overcurrent in the negative half-cycle of phases X and Z and the positive half-cycle of phases A and C, respectively. As shown in Figure 11(a) and Table 5, the value of overcurrent will be reduced by turning off S10 in regions 4, 5, 8, and 9 and S3 in regions 1, 8, 9, and 12. This reduction in the side phases A and C after implementing the fault-tolerant method is specifically shown in Figure 11(b). According to Figure 12 and Table 5, the THD of current in healthy phases is reduced by executing the fault-tolerant method.Figure 11
Simulation result of the AC-DC converter currents before and after multiple open-switch faults inS1 and S12. (a) All phases. (b) Faulty phases A and Z and side phases X and C.
(a)(b)Figure 12
Simulation result of the THD of phasesX and C, for multiple open-switch fault and fault-tolerant conditions.Multiple open-switch faults occur when the value ofNrn in more than one phase is greater than the value of T while in the other phases it is smaller than the value of T. According to Figure 13, when T>Nrb,T>Nrc,T>Nrx,T>NryT<Nra,andT<Nrz, the open-switch faults occurred in phases A and Z at Tfd = 0.2062 s. The value of <ia> is greater than zero and the value of <iz> is smaller than zero; therefore, the open-switch faults occurred in the upper switch of phase A (S1) and the bottom switch of phase Z (S12), as shown in Figure 14.Figure 13
Simulation result of the diagnostic variablesNrn, for open-switch faults in phases A and Z.Figure 14
Simulation result of the diagnostic variablesin, for open-switch faults in S1 and S12.In cases where multiple open-switch faults occur in both switches of one leg, the value ofNrn in that phase is greater than the value of T. However, unlike a single open-switch fault, the value of <in> does not remain positive or negative and after a significant fluctuation becomes approximately zero again. The values Nrn and in are shown in Figures 15 and 16 for multiple open-switch faults in both switches of phase A. Since only T<Nra, the open-switch fault is detected in phase A at Tfd = 0.203 s, as shown in Figure 15. According to Figure 16, the value of <ia> also came close to zero again at the time of fault.Figure 15
Simulation result of the diagnostic variablesNrn, for open-switch faults in both switches of phases A.Figure 16
Simulation result of the diagnostic variablesin, for multiple open-switch faults in S1 and S2.In fault-tolerant time for open-switch fault in both switches of phaseA, switches S10 and S9 must be turned off in regions (4, 5, 8, and 9) and (2, 3, 10, and 11), respectively. According to Figure 17, Figure 18, and Table 5, by implementing the fault-tolerant method, the value of overcurrent and THD of current in phases X and Z are reduced.Figure 17
Simulation result of the AC-DC converter currents before and after multiple open-switch faults in both switches of phaseA. (a) All phases. (b) Faulty phase A and side phases X and Z.
(a)(b)Figure 18
Simulation result of the THD of phases X and Z, for multiple open-switch fault and fault-tolerant conditions.In both single and multiple open-switch faults, the maximum value of DC-link voltage ripple is 5 volts, which is smaller than 1% of the reference value. Figure19 shows the DC-link voltage ripple for single open-switch fault, multiple open-switch faults in two legs, and both switches of one leg, respectively.Figure 19
Simulation result of DC-link voltage ripple, for fault-tolerant conditions. (a) Single open-switch fault. (b) Multiple open-switch faults in different legs. (c) Multiple open-switch faults in one leg.
(a)(b)(c)


## 6. Conclusion

This paper proposes new fault diagnosis and fault-tolerant methods for the six-phase AC-DC converter for single and multiple open-switch faults. The introduced fault diagnosis approach has a simple process, which was integrated with the hysteresis controller, and requires neither complicated calculations, accurate modeling of the system, nor extra hardware. This method is robust against the load changes since a normalized indicator of the fault and an adaptive threshold are used. The main novelty of this research is tolerance against open-switch faults by changing the switching signals in the opposite phase of the faulty phase, without adding any equipment to the circuit. The proposed technique was able to reduce the overcurrent in the side phases, and the value of total harmonic distortion in these phases was also decreased. According to Table5, in the worst case, at least 20% of the overcurrent value and 6% of the value of total harmonic distortion in side phase (X) were reduced (multiple open-switch faults in S1 and S12). Moreover, the DC-link voltage is stabilized with an acceptable ripple, which is smaller than 1% of the reference value. The effectiveness of the proposed fault detection and fault-tolerant methods is confirmed by simulation results for a few different single and multiple fault cases. Evaluation of other switching techniques in the open-switch fault condition and implementation of modern controllers can be considered as future topics.



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*Source: 9999918-2021-10-07.xml*