Several researchers have investigated the fault-tolerant PMSM drive systems. For example, Jlassi et al. proposed a robust control for a Hall sensor fault and an IGBT fault (Jlassi et al., 2017). Eickhoff et al. (2018) investigated a PWM switching algorithm to reduce torque pulsations when one power device is opened. An et al. (2015) studied the current residual vector to diagnose an open circuit of power switches and then executed fault-tolerant control to keep the motor rotating at the same speed. Zeng et al. used a three-leg four-switch inverter to drive a three-phase permanent magnet synchronous motor. The cost of the whole drive system was reduced; however, the torque ripple was increased (Zeng et al., 2017).

AC motors have replaced DC motors for more than 4 decades because the DC motor uses the brush and commutator, which requires maintenance and may cause arc when the brush touches the commutator. The AC motor includes induction motors and PMSMs. PMSMs have higher efficiency, high power density, and easier control characteristics than induction motors. As a result, most of electric vehicles and elevators use PMSMs as the drive systems. The details are discussed as follows. Figure 1 shows the fault-tolerant permanent-magnet synchronous motor fed by a single-phase full-bridge rectifier. To improve the reliability of the drive system, several fault-tolerant parts need to be investigated including one power switch of the inverter is opened or short-circuited (Liu et al., 1993; Liu et al., 2021). One phase of the motor is opened or partially short circuited (Akin et al., 2008). Some researchers proposed using different sensorless techniques to replace the encoder signal when it was faulty (Vas, 1993). In addition, the DC-link capacitor could be deteriorated after the PMSM drive system is operated 4–5 years. Furthermore, the rectifier diode also could be opened or short-circuited. To narrow down the research topic, in this paper, the fault-tolerant cases of the DC-link capacitor fail and the rectifying diode fail are investigated. Figure 1 shows the proposed fault-tolerant surface-mounted PMSM drive system with a single-phase full-bridge rectifier. The single-phase full-bridge rectifier includes four diodes, D ₁, D ₁, D ₂, and D ₂. Because the diodes are quite cheap, in this paper, when any diode is opened or short-circuited, the DSP uses a back-up full-bridge rectifier to replace the faulty full-bridge rectifier via a single-pole double-throw mechanical switch. The high speed fuses, the F _a and F _b are used to transfer the diode from a short circuited into an open circuited. The resistances, R ₁ and R ₂, are used to limit the surge current when the capacitors C ₁ and C ₁ are immediately connected into the DC-link. The DC switches S ₄ and S ₅ are used to short circuit the resistor and then reduce the power consumption. In this paper, the resistances R ₁ and R ₂ are both 50 Ω , and then the surge current of the capacitor can be limited to 7 A.

Figure 1 includes an AC source, AC/DC converters, DC-link capacitors, an inverter, and a surface-mount PMSM (SPMSM). In the real world, each part of the SPMSM drive system could be faulty. To improve the reliability of the whole system, a fault-tolerant configuration of the SPMSM drive system is required. Several researchers have investigated this issue. For example, Chai et al. studied the fault-tolerant control method when the SPMSM is faulty (Chai et al., 2019). Liu et al. used periodic control algorithms to improve the dynamic responses when the inverter has one IGBT open circuited or short circuited (Liu et al., 2019). In addition, Liu et al. also proposed a predictive controller and a sliding-mode estimator to improve the reliability of the SPMSM drive system when one Hall-effect sensor or the encoder is faulty (Liu and Chang, 2019). Several researchers focused on a novel fault-tolerant inverter (Li et al., 2017), stator turn fault tolerant method (Hadef et al., 2010), and Hall sensor fault tolerant method (Mehta et al., 2015). For AC/DC converter fault tolerant method, Lee et al. proposed a DC-link capacitor estimation when the motor was stopped (Lee et al., 2008).

In this paper, the authors focus on the fault-tolerant control of the AC/DC converter. The faulty cases include: one diode opened, one diode short-circuited, and a degradation of the DC-link capacitor. The fault-tolerant control of AC/DC converter for an SPMSM drive system has not been investigated by previous papers (Jlassi et al., 2017; Eickhoff et al., 2018; An et al., 2015; Zeng et al., 2017; Liu and Chang, 2019; Liu et al., 2021; Akin et al., 2008; Vas, 1993; Chai et al., 2019; Liu et al., 1993; Liu and Chang, 2019; Li et al., 2017; Hadef et al., 2010; Mehta et al., 2015). The paper first time proposes to measure the input AC side currents to diagnosis the open circuit or short-circuited for a full-bridge rectifier, and then to execute its fault-tolerant control. In addition, the paper first time proposed the estimation the DC-link capacitor when the motor is operated at different speeds. In previously published paper, the DC-link capacitor was estimated when the motor was stopped (Lee et al., 2008). Although the proposed methods are straight forward, they are original ideas and have not been investigated in the previous papers. In addition, the proposed methods are practical and useful. The details are as follows.

The block diagram of the implemented fault-tolerant surface-mounted PMSM drive is shown in Figure 7A. The block diagram was discussed in references (Liu et al., 1993; Liu et al., 2021; Liu et al., 2019; Liu and Chang, 2019) by one of the authors in this paper. This author investigated the faulty of one power switch, which includes one power switch is opened or short-circuited, of the inverter in references (Liu et al., 1993; Liu et al., 2021; Liu et al., 2019; Liu and Chang, 2019). Then, a new switching patterns of the inverter were proposed to maintain the motor’s speed and torque as a constant. In this paper, the authors assume the inverter is normally operated and the single–phase AC/DC rectifier or the three-phase AC/DC rectifier is faulty, including one diode is opened, or short-circuited or the DC-link capacitor is faulty. First, the speed command ω m ∗ is compared to the feedback speed ω _m . Then, the speed error Δ ω m is obtained. By using a speed-loop PI controller, the q-axis current command i q ∗ is obtained, and the d-axis current command i d ∗ is set as zero. After that, the d-q axis current commands are compared to the d-q axis currents. Then, the d-q axis current errors Δ i d and Δ i q are computed. Next, the current controller determines the d-q axis voltage commands, v d ∗ and v q ∗ . The d-q axis voltage commands are transferred to the a-b-c axis voltage commands, v a ∗ , v b ∗ , and v c ∗ . In addition, a space vector pulse-width modulation is executed. Finally, the triggering signals determine the switching states of the inverter and then the surface-mounted PMSM rotates. A closed-loop motor drive system, is thus achieved. Figure 7B shows the photography of the implemented AC/DC converter, which includes a full-bridge rectifier, a relay, a single-phase AC voltage source or a three-phase AC voltage source, a DC-link capacitor, and a fault-tolerant control circuit. Figure 7C shows the photograph of the implemented surface-mounted PMSM drive system, which includes a DSP, an inverter, and some sensors. The PMSM drive system provides the 10 kHz, variable voltage, variable frequency, 3-phase AC voltage to the surface-mounted PMSM to adjust its speed.

Several experimental results are shown here to validate the theoretical analysis. Figure 8 shows the photograph of the SPMSM drive system and its dynamometer. Table 1 shows the specification of the SPMSM that used in this paper.

Figures 9A,B show the waveforms when using the fault-tolerant algorithms of a diode opened for a single-phase full-bridge rectifier. Figure 9A demonstrates the DC-link voltage. When a diode opened, the voltage ripples increase to ± 5 V. After that, the DSP executed the fault-tolerant control and then isolates the faulty single-phase full-bridge rectifier and connects the motor drive system to a back-up single-phase full-bridge rectifier. A huge voltage is produced. Finally, the fault-tolerant algorithms are finished and the voltage ripples of the capacitor are abruptly reduced and returned to the original value. Figure 9B demonstrates the measured current of the capacitor current, which is discontinuous. Figures 10A,B show the measured waveforms when using the fault-tolerant algorithms of a diode opened for a three-phase full-bridge rectifier. Figure 10A demonstrates the measured DC-link voltage. When a diode opened, the voltage drop is near 8 V. After that, the DSP executes fault-tolerant control, isolates the fault three-phase full-bridge rectifier, and then connects the SPMSM drive to a back-up three-phase full-bridge rectifier. A huge voltage spike, which is near a 50 V drop, is produced. Finally, the fault-tolerant algorithms are finished and the voltage ripples are obviously reduced to their original values. Figure 10B demonstrates the measured capacitor current, which is also discontinuous but has a higher frequency than the capacitor current of the single-phase full-bridge rectifier.

Figures 11A,B show the measured waveforms of the DC-link capacitor fault for a single-phase full-bridge rectifier. Figure 11A demonstrates the measured DC-link voltage, and Figure 11B demonstrates the estimated capacitor. When the DSP detects the capacitor becomes 720 µF, the fault-tolerant algorithms are executed to connect another back-up capacitor, which is 720 µF. The total value of the capacitor returns to the original value. Figures 12A,B show the measured waveforms of the DC-link capacitor fault for a three-phase full-bridge rectifier. Figure 12A demonstrates the DC-voltage, which provides a DC average voltage near 308.5 V. Figure 12B demonstrates the estimated capacitor, which is 1,440 µF in normal. When the DC-link capacitor is faulty, the capacitance value reduces to 720 µF; however, it returns to its original capacitance 1,440 µF after the fault tolerant algorithms are executed.

Figures 13A,B show the measured waveforms at 300 r/min and 2 N m by using a single-phase full-bridge rectifier. Figure 13A demonstrates the a-phase measured current, which is near a sinusoidal waveform. Figure 13B shows the line-line voltage at the same case. Figure 13C shows the DC-link current at the same case. Figure 13D shows the input ac current by using a single-phase full-bridge rectifier, which is obviously a discontinuous current. Figure 13E shows the input ac current by using a three-phase full-bridge rectifier, as you can observe, the frequency of the current pulsations become triple when it is compared to a single-phase full-bridge rectifier.

Comparing with the previously proposed method (Isermann, 2006), which only needed one voltage sensor, the proposed method in our paper requires one voltage sensor and one current sensor to measure the voltage and current of the DC-link capacitor. However, the proposed method in our paper provides a better accurate of the diagnosis results than the previously published paper (Isermann, 2006). In addition, comparing with reference (Lee et al., 2008), which estimated the DC-link capacitor when the motor was stopped, our paper can compute the DC-link capacitor when rotor is operated at different speeds.

In this paper, one diode opened for a single-phase full-bridge rectifier and a three-phase full-bridge rectifier, and a DC-link capacitor degraded fault for a single-phase full-bridge rectifier and a three-phase full-bridge rectifier are investigated. Experimental results verify the proposed method which uses real-time detection and diagnosis of the faults and then executing the fault-tolerant control algorithms. The surface-mounted PMSM drive system can be operated normally after the fault-tolerant control is executed. The proposed method can be used in industry to improve the reliability of the motor drive system due to its simplicity.