Open Fault Detection and Tolerant Control for a Five Phase Inverter Driving System

Abstract

This paper proposes a fault detection and the improved fault-tolerant control for an open fault in the five-phase inverter driving system. The five-phase induction machine has a merit of fault-tolerant control due to its increased number of phases. This paper analyzes an open fault pattern of one switch and proposes an effective fault detection method based upon this analysis. The proposed fault detection method using the analyzed patterns is applied in the power inverter. In addition, when the open fault occurs in the one switch of the induction machine driving system, the proposed fault-tolerant control method is used to operate the induction machine using the remaining healthy phases, after performing the fault detection method. Simulation and experiment results are provided to validate the proposed technique.

1. Introduction

Multiphase machines can reduce the torque ripple and the phase current compared to traditional three-phase machines without the phase voltage change. The output torques of these machines can be increased through the injection of harmonic current, because the five-phase induction machine (IM) is able to increase at least 10% torque compared to its three-phase counterpart of the same active volume [1]. It is worth noting that multiphase machines with an increased number of phases provide more opportunities for the fault-tolerant control [2]. Therefore, these can be applied to the high reliability system such as electric vehicles, aircrafts, ship propulsion, military equipment, and railroad vehicles [3,4,5,6]. The development of special permanent magnet (PM) machines, specifically designed for automotive, naval, and aerospace applications, has provided further advantages for fault-tolerant applications [7,8].

Fault detection methods have been researched in five-phase voltage source inverters [9], electric drives [10,11,12,13], monitoring noise and vibration [14], variation of speed and torque, Park’s vector, and normalized dc current method [15,16,17,18,19]. It is worth noting that the problem of fault detection is usually faced by using the same diagnostic methods as for three-phase systems, although specific solutions for fault detection in multiphase drives are under development [20].

The fault-tolerant control of multiphase machines has been reported in five [21], six [22], and seven phases [23], using permanent magnet synchronous motors (PMSM) and induction machines (IM). A fault-tolerant five-phase machine was investigated in [24,25], whereas in [26], the general problem about the control of a faulted multiphase IM was solved by using the traditional phasor representation of the stator currents in steady-state operating conditions.

This paper proposes a fault detection method and the improved fault-tolerant control scheme for the five-phase IM. The proposed fault detection method can be used to recognize an open fault in the five-phase IM driving system. In addition, the fault-tolerant control is used to operate the five-phase IM under the open fault condition in one phase. It is able to be operated in any phase under the same condition. This fault-tolerant control proposes simple technical skill to use in any case. The analytical approach in a five-phase induction motor has not been introduced. Therefore, this technical skill was performed as an analytical approach in this paper. The performance results of the fault detection and the fault-tolerant control method will be demonstrated through simulation and experimental results.

2. Proposed Fault Detection Method

This paper uses a four-pole five-phase IM with identical quasi-concentrated phase windings, which are evenly distributed with a 72° spatial angle as shown in Figure 1. An open fault type can be divided into two categories: the fault in the one leg of the inverter and the fault in one switch of the machine.

When the open fault occurs in the one switch and one phase, trajectory of stationary frame d-q axis current appears as shown in Figure 2 and Figure 3. These patterns can be used to verify whether the fault occurs or not according to the each switch situation. The result of Figure 2 can be verified in accordance with the speed and current. Although the current is very high, the fault patterns are classified to each phase. In order to detect the open fault, the proposed detection method is used for the five-phase inverter.

The proposed fault detection method uses the d₁-q₁ axis current from the five-phase transformation matrix. The d₁-q₁ axis current can be expressed as:

$$i_{d1ss}=\frac{2}{5}\left(i_a\cos (0)+i_b\cos (\frac{2\pi }{5})+i_c\cos (\frac{4\pi }{5})+i_d\cos (\frac{4\pi }{5})+i_e\cos (\frac{2\pi }{5})\right)$$

(1)

$$i_{q1ss}=\frac{2}{5}\left(i_a\sin (0)+i_b\sin (\frac{2\pi }{5})+i_c\sin (\frac{4\pi }{5})-i_d\sin (\frac{4\pi }{5})-i_e\sin (\frac{2\pi }{5})\right)$$

(2)

where i_a, i_b, i_c, i_d, and i_e are the phase currents. When the five-phase IM is operated in normal mode, x axis and y axis are applied to Equation (1) and (2) as shown in normal operation of Figure 2. At that time, if the open fault of the top switch of phase A occurs in the five-phase inverter, the faulted pattern appears to one side in the trajectory of a stationary frame as shown in Figure 3. As a same result, the faulted patterns of one phase appear to both sides in the trajectory of stationary frame as shown in Figure 2.

Table 1. Detected phase angles of each switching devices under the open-fault condition.

Phase	Open Fault Angle (Fault_θ)		Flag
A	Top	145°–180°	1
	Bottom	325°–360°	2
B	Top	73°–108°	3
	Bottom	253°–288°	4
C	Top	0°–36°	5
	bottom	181°–216°	6
D	Top	289°–324°	7
	Bottom	109°–144°	8
E	Top	217°–252°	9
	bottom	37°–72°	10

depicts in the analysis result of an open fault angle for each switch and leg from Figure 2. Because all switches have an angle region of 36°, the flag signal can be considered in from 1 to 10. Therefore, all open fault switches can be recognized in accordance with the information of switch position.

In order to calculate the average d₁-q₁ axis current during the one cycle, these can be expressed as:

$$i_{d1ss\_mean}={\displaystyle \sum _{k=0}^{Num}{i}_{d1ss}}[k]$$

(3)

$$i_{q1ss\_mean}={\displaystyle \sum _{k=0}^{Num}{i}_{q1ss}}[k]$$

(4)

$$fault\_mag=\sqrt{{(i_{d1ss\_mean})}^2+{(i_{q1ss\_mean})}^2}$$

(5)

where i_{d1ss_mean} and i_{q1ss_mean} are mean values of the stationary reference frame d₁-q₁ axis current during the one cycle. Num is number of arrangement. When the five-phase IM is operating in the normal mode, i_d1ss and i_q1ss are kept at constant sinusoidal waves which have difference of 90°. At this time, the fault_mag remains at zero value, because i_{d1ss_mean} and i_{q1ss_mean} are zero under normal operation. However, when an open fault occurs in the switch of the inverter, the fault_mag no longer remains zero. Therefore, in order to detect the fault switch, fault_mag is compared with a predefined threshold value.

It is important to detect the faulty switch position in the open fault case. Using the stationary reference frame, the fault angle and error can be expressed as:

$$fault\_\mathsf{\theta }={\tan }^{-1}(\frac{i_{q1ss}}{i_{d1ss}})$$

(6)

$$fault\_{\mathsf{\theta }}_{error}=fault\_\mathsf{\theta }-fault\_{\mathsf{\theta }}_{old}$$

(7)

where fault_θ_old is the previous fault_θ. When the five-phase IM is operated in the normal mode, fault_θ_error has almost constant value. However, when the fault occurs in the one switch of the inverter, fault_θ_error changes rapidly. The fault switch can be recognized from the angle of that time. The proposed fault detection method recognizes the open fault of the switch when both conditions of fault_mag and fault_θ_error are satisfied.

3. Proposed Fault-Tolerant Control Method

The five-phase space vector of IM is extended from three-phase IM. In order to improve the performance of the torque density, the five-phase IM has the rectangular current waveform, because of its spatial current density and the airgap flux density of the concentrated windings. Therefore, it can be applied to two space vector combined fundamental d₁-q₁ and third harmonic d₃-q₃ model.

Two space vector of the five-phase IM can be expressed [27]:

$$\begin{array}{ll}{f}_{d1q1s}& =\frac{2}{5}(f_{as}+a_5{f}_{bs}+a_5^2{f}_{cs}+a_5^3{f}_{ds}+a_5^4{f}_{es})\\ & =f_{d1s}+j{f}_{q1s}\end{array}$$

(8)

$$\begin{array}{ll}{f}_{d3q3s}& =\frac{2}{5}(f_{as}+a_5{f}_{cs}+a_5^2{f}_{es}+a_5^3{f}_{bs}+a_5^4{f}_{ds})\\ & =f_{d3s}+j{f}_{q3s}\end{array}$$

(9)

where $a_5=e^{j2\mathsf{\pi }/5}$.

From Equations (8) and (9), orthogonal matrix for the equivalent transformation of five-phase IM including fundamental d₁-q₁ axis and third harmonic d₃-q₃ axis is defined as follows:

$$T(\mathsf{\theta })=\frac{2}{5}\left[\begin{array}{ccccc}\cos \mathsf{\theta }& \cos (\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \cos (\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \cos (\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \cos (\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})\\ \sin \mathsf{\theta }& \sin (\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \sin (\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \sin (\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \sin (\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})\\ \cos 3\mathsf{\theta }& \cos 3(\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})\\ \sin 3\mathsf{\theta }& \sin 3(\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})\\ \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\end{array}\right]$$

(10)

Because of pseudo orthogonal property of Equation (10), inverse transfer matrix can be defined as follows:

$$T{(\mathsf{\theta })}^{-1}=\frac{5}{2}{T}^T(\mathsf{\theta })$$

(11)

The inverse transfer matrix is defined as follow Equation (12):

$$T{(\mathsf{\theta })}^{-1}=\left[\begin{array}{ccccc}\cos \mathsf{\theta }& \sin \mathsf{\theta }& \cos 3\mathsf{\theta }& \sin 3\mathsf{\theta }& \frac{1}{\sqrt{2}}\\ \cos (\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \sin (\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }-\frac{2\mathsf{\pi }}{5})& \frac{1}{\sqrt{2}}\\ \cos (\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \sin (\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }-\frac{4\mathsf{\pi }}{5})& \frac{1}{\sqrt{2}}\\ \cos (\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \sin (\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }+\frac{4\mathsf{\pi }}{5})& \frac{1}{\sqrt{2}}\\ \cos (\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})& \sin (\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})& \cos 3(\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})& \sin 3(\mathsf{\theta }+\frac{2\mathsf{\pi }}{5})& \frac{1}{\sqrt{2}}\end{array}\right]$$

(12)

In order to perform the vector control in the normal mode, the orthogonal matrix T(0) and its transpose T(0)⁻¹ are used to transform stator quantities between the phase A-B-C-D-E natural reference frame and the d₁-q₁-d₃-q₃-n arbitrary reference frame in the five-phase IM.

From Equations (8) and (9), synchronous frame of space vectors in the d₁-q₁ and d₃-q₃ can be defined as follows:

$$f_{d1q1r}=f_{d1q1s}{e}^{-j\mathsf{\theta }}=f_{d1r}+j{f}_{q1r}$$

(13)

$$f_{d3q3r}=f_{d3qs}{e}^{-j3\mathsf{\theta }}=f_{d3r}+j{f}_{q3r}$$

(14)

where θ ($={\displaystyle \int wdt}$) and 3θ are the angular velocity of fundamental and third harmonic frequency. From Equations (13) and (14), Figure 4 shows the relationship between stationary reference frame and synchronous frame of the two space vector d₁-q₁ axis and d₃-q₃ axis. Two orthogonal and two-dimensional spaces are rotating with the frequency of w and 3w, respectively.

In order to perform the vector control in the normal mode, the orthogonal matrix and its transpose are used to transform stator quantities between the A-B-C-D-E natural reference frame and the d₁-q₁-d₃-q₃-n arbitrary reference frame in the five-phase IM. The pseudo-orthogonal matrix can be expressed as:

$$T(0)=\frac{2}{5}\left[\begin{array}{ccccc}1& \cos \mathsf{\alpha }& \cos 2\mathsf{\alpha }& \cos 2\mathsf{\alpha }& \cos \mathsf{\alpha }\\ 0& \sin \mathsf{\alpha }& \sin 2\mathsf{\alpha }& -\sin 2\mathsf{\alpha }& -\sin \mathsf{\alpha }\\ 1& \cos 2\mathsf{\alpha }& \cos \mathsf{\alpha }& \cos \mathsf{\alpha }& \cos 2\mathsf{\alpha }\\ 0& -\sin 2\mathsf{\alpha }& \sin \mathsf{\alpha }& -\sin \mathsf{\alpha }& \sin 2\mathsf{\alpha }\\ \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}& \frac{1}{\sqrt{2}}\end{array}\right],\mathsf{\alpha }=\frac{2\mathsf{\pi }}{5}$$

(15)

The equivalent transformation matrix from the B, C, D, and phase E variables to the stationary d₁-q₁-q₃-n axis variables can be expressed as:

$$T(0)=\frac{2}{5}\left[\begin{array}{cccc}\cos \mathsf{\alpha }+0.25& \cos 2\mathsf{\alpha }+0.25& \cos 2\mathsf{\alpha }+0.25& \cos \mathsf{\alpha }+0.25\\ \sin \mathsf{\alpha }& \sin 2\mathsf{\alpha }& -\sin 2\mathsf{\alpha }& -\sin \mathsf{\alpha }\\ -\sin 2\mathsf{\alpha }& \sin \mathsf{\alpha }& -\sin 2\mathsf{\alpha }& \sin 2\mathsf{\alpha }\\ 1& 1& 1& 1\end{array}\right]$$

(16)

This fault-tolerant control uses five-phase transformation matrix under the open fault condition of phase A [24]. However, the five-phase drive system has same open fault probabilities in each phase in applications. If the open fault occurs in the five-phase inverter except for phase A, it is difficult to directly use the equivalent transformation matrix of Equation (16). When the open fault occurs in the power switch of the phase B, the proposed fault-tolerant control can be used in this system.

To solve this problem of any switch fault rather than phase A, this paper proposes an algorithm that can be applied the open fault of any other fault-tolerant control of five-phase AC motor drive phases as shown in Figure 5. For example, if the open fault occurs in the phase B of the five-phase inverter, the faulted phase B is changed to phase A. After that, Equation (16) can be applied to perform the fault-tolerant control. Finally, the phase A changes to phase E and phase B changes to phase A such as the right side of Figure 5. In the same manner, entire phases can be changed using the proposed algorithm.

Figure 6 shows the flow chart for fault detection and fault-tolerant control. The proposed fault detection method and fault-tolerant control are performed as shown in Figure 6. Aforementioned, when the five-phase IM is operated in normal mode, the vector control is used in the five-phase inverter. At that time, when the open fault occurs in the switch of the phase B, the position of the faulted switch can be detected as shown in Figure 6. In addition, in order to perform the proposed fault-tolerant control, the phase B changes to phase A due to faulted phase B. After that, equivalent transformation matrix Equation (16) is applied to the open fault-tolerant control.

In this paper, the fault-tolerant control is used to minimize copper loss under the one fault condition [24]. From the voltage equation of the five-phase IM, the torque equation can be expressed as Equation (17) in a synchronous frame:

$$T_e=\frac{P}{2}[L_{m1}(i_{q1s}{i}_{d1r}-i_{d1s}{i}_{q1r})+3L_{m3}(i_{q3s}{i}_{d3r}-i_{d3s}{i}_{q3r})]$$

(17)

Under the open fault-tolerant control, the equivalent transformation matrix does not consider i_d3s axis current from Equation (16). In addition, Equation (17) can be re-written in the following torque equation:

$$T_e=\frac{P}{2}[L_{m1}(i_{q1s}{i}_{d1r}-i_{d1s}{i}_{q1r})+3L_{m3}{i}_{q3s}{i}_{d3r}]$$

(18)

From Equation (18), torque value is positively influenced with synchronous frame current i_q3s, however i_q3s is negatively influenced with its copper loss.

4. Simulation and Experiment Result

4.1. The Proposed Fault Detection Result

Simulation and experiment results have been carried out for the open fault detection and fault- tolerant control algorithm. Simulation results are obtained using PSIM software tool. Specification of the five-phase IM for the simulation and experiment is listed in

Table 2. Induction Machine Specification.

Induction Machine Specification
Output Power	1.5 kW
Rated Voltage	220 V
Rated Frequency	60 Hz
Rated Current	4.9 A
Rated Speed	1684 rpm

.

Figure 7 shows the experiment set-up of the five-phase IM. Figure 7a shows the MG-set with the five-phase IM. The MG-set consists of a load motor (3.75 kW), inverter, and the five-phase IM. DSP controller TMS320F 28335 from Texas Instruments is used for digital implementation of the proposed techniques. The sampling time of the digital controller in the experimental setup is set to 100 μs.

Figure 8 shows the experimental result of the proposed fault detection method under top switch of the open fault in the phase B and phase C. When the IM is operating in normal mode, the fault_mag is zero in accordance with Equation (5), because the stationary d₁-q₁ axis current is constant in the steady state condition. In addition, the stationary d₁-q₁ axis current is used for the fault patterns of each switches. The patterns of the switch can be compared with the patterns of Figure 3 in the trajectory of stationary frame. At that time, when the open fault occurs in the top switch of the phase B, the current of d₁-q₁ axis changes as shown in Figure 8a. Because the fault_mag is produced by the change of d₁-q₁ axis under the open fault condition, the fault magnitude exceeds the threshold which can be set in accordance with the applications of the IM. In addition, the patterns of the faulted switch can be verified in comparison with the Figure 3 in the trajectory of the stationary frame. If the proposed fault detection method is applied to other applications of the IM, the threshold can be changed depending upon their situation.

Figure 9 shows the experimental result of fault detection method about fault_θ. When the IM operates in the normal mode, fault_θ of the IM is linear as shown in Figure 9a. As mentioned above, each pattern appeared in the trajectory of the stationary frame. Therefore, the analyzed fault patterns can be used for a fault diagnosis. At that time, when the open fault occurs in the top switch of the phase B, fault_θ changes rapidly in accordance with Equation (6) under the open fault condition, because the i_d1ss and i_q1ss are changed by the top switch of the fault. In addition, each flag is produced by the position information of Table 1. If these two conditions of the angle and magnitude are satisfied, the open fault switch is recognized.

4.2. The Proposed Fault-Tolerant Control Result

Figure 10 shows the simulation result of the fault-tolerant control method under the open fault condition of phase B. Synchronous frame q₁ axis current and motor speed are commanded to be 1 A and 300 rpm respectively. Figure 10a does not use fault-tolerant control. In addition, Figure 10a has a ripple about the q₁ axis current and the torque in accordance with frequency of speed. However, Figure 10b is applied proposed fault-tolerant control algorithm in accordance with Equation (16) and Figure 5. The synchronous frame q₁ axis is current and the torque is regulated without steady state error as shown in Figure 10b.

In order to verify the fault-tolerant control under the other condition, Figure 11 shows the simulation result in the i_q1s = 4 A of the synchronous frame. Because of the increase of i_q1s, the torque is changed to 4.4 Nm. When the Figure 11a is compared with Figure 11b, the torque ripple of Figure 11a is increased more than Figure 11b.

When the current reference is same as 1 A, the fault-tolerant control is performed to the high speed as shown in Figure 12. Simulation result of the fault-tolerant control has good performance compared with no fault-tolerant control. The torque ripple of Figure 12b is not almost influenced with IM speed changes under the open fault of phase B.

Figure 13 shows the simulation result of the fault-tolerant control at high torque and high speed. The difference of no fault-tolerant control and fault-tolerant control is obvious from Figure 13a. The proposed fault-tolerant algorithm of Figure 13b shows good performance compared with Figure 13a. Specially, the torque ripple is reduced over 50% compared with no fault-tolerant control.

The left side of Figure 14 shows the open fault condition when the open fault occurs in the switch of phase B. Synchronous frame q₁ axis current and motor speed are commanded to be 3 A and 300 rpm respectively. There are torque ripples due to no fault-tolerant control. After one second, the proposed fault-tolerant control is applied. Then the fault phase B is replaced with phase A as shown in Figure 14. The torque and current ripple are decreased, when the proposed fault-tolerant algorithm is applied.

Figure 15 shows result of operation sequence of the fault-tolerant control under the open fault of phase B. When the five-phase IM is operated in normal mode, the current is controlled in accordance with the current reference. At that time, if the open fault occurs in phase B, the current and torque ripple are produced by the open fault. However, after the fault-tolerant control is applied, phase A and phase B changed well without decreasing the IM speed. In addition, the current and torque ripple are regulated well. It is obvious that the fault-tolerant algorithm has good performance under one phase fault conditions. The proposed algorithm has almost the same current and torque ripple compared with normal operation conditions. To verify the feasibility of the fault-tolerant control, Figure 16 shows difference under the open fault condition of phase B in i_q1s = 1 A and 300 rpm. Figure 16a has the current at the q₁ axis current and the torque in accordance with frequency of speed. However, Figure 16b is applied to the proposed fault-tolerant control algorithm in accordance with Equation (16).

In Figure 17, the synchronous frame q₁ axis current and motor speed are commanded to be 4 A and 300 rpm, respectively. According to the increase of the q₁ axis current, the torque is changed to 5 Nm. When the fault-tolerant algorithm is not used, the torque ripple fluctuates to 5 Nm. However, when the fault-tolerant algorithm is used, torque ripple reduces to 1.5 Nm. From Figure 16 to Figure 17, it is obvious that the proposed algorithm can regulate the ripple of the q₁ axis current and torque.

To verify the ripple of the current and torque at the high speed, the fault-tolerant control is performed at 1000 rpm as shown in Figure 18. When the fault-tolerant control is not used, the torque ripple is similar with the result of the low speed operation. Because the reference of the q₁ axis current is 1 A, the torque has a low torque ripple. However, when the fault-tolerant control is used, the ripple of the current and torque no longer exists.

In Figure 19, the synchronous frame q₁ axis current and motor speed are controlled to high torque and high speed. The ripple of the current and torque is not varied depending on the speed. It is obvious that the torque ripple magnitude has been mainly influenced with magnitude of q₁ axis current.

Figure 20 shows the open fault of the phase B and the proposed fault-tolerant control. The synchronous frame q₁ axis current and motor speed are commanded to be 3 A and 300 rpm respectively. After four healthy phases operate under the open fault of phase B, the proposed fault-tolerant control is applied. Then the fault phase B is replaced with phase A as shown in Figure 20. At that time, the ripple of the current and torque is decreased.

Figure 21 shows operation sequences that are normal operations, open fault of phase B and tolerant control from left side. When the open fault occurs in phase B, the current magnitude of phase A is increased and the torque ripple is produced by the open fault. However, during the fault-tolerant control application, phase A and phase B changed well without IM speed decreasing. In addition, the current and torque ripple are regulated well, similar to the simulation result. It is obvious that the fault-tolerance algorithm has good performance under one phase fault condition.

5. Conclusions

This paper deals with the fault detection method and fault-tolerant control scheme for five-phase IM. The fault patterns are analyzed for the position information of each switch in the five-phase inverter. The fault detection method is proposed in accordance with the analyzed fault patterns of the switch position. In addition, this method can verify the information in both the faulted phase and switch position during the one cycle. The fault-tolerant control is performed by all phases. The proposed fault-tolerant algorithm contributes to reducing the torque and current ripple at any phase open fault condition. In addition, this algorithm is verified using four healthy phase currents in the open fault condition. The proposed algorithm has been described by using a five-phase IM with one open phase as a practical example and its validity has been proven through the experiments using an 1.5 kW five-phase IM.