**2.1. SRM fault characteristics**

Open-circuit faults are common in SRM drives. As shown in Figure 5, there are many locations to initiate an open-circuit fault, such as power converter, motor windings, position signals, and drive circuit. However, the power converter is a crucial component in an SRM drive and is also a vulnerable part in the system [15, 16].

Figure 5. Open-circuit faults for SRM drives. **Figure 5.** Open-circuit faults for SRM drives.

the system is given by:

**2.2 Bus current detection** 

The voltage equation for phase A is given by:

The branch current of phase A is given by:

The phase current can be written as:

by:

Each bridge arm is controlled independently by two switches and each phase is independent of each other, providing good fault tolerance. The system will work in Each bridge arm is controlled independently by two switches and each phase is independent of each other, providing good fault tolerance. The system will work in the open-circuit state

the open-circuit state when an open-circuit fault occurs in upper-switch or lower-switch. The average electromagnetic torque under healthy conditions is given

> 2 / <sup>0</sup> ( , ( )) <sup>2</sup>

*mN <sup>T</sup> T id* 

where *m* is the phase number, *Nr* is the number of rotor poles, *θ* is the rotor angular position, and *Tα*(*θ,i*(*θ*)) is the instantaneous torque of one phase. When the open-circuit faults occur at *k* phases, the faulty phase windings lose excitation but other healthy phases can still operate normally. In this condition, the average torque of

> *fav av m k T T m*

( ) ( ) *a a a aa a <sup>a</sup> di dL U Ri L i*

where *Ua* is the phase voltage, *Ra* is the phase resistance, *La* is the phase inductance, *ia*

/ ( ) (1 ) ( /)

*a a U i t e R dL d*

is the phase current, *ω* is the motor angular speed, and *θ* is the rotor position.

*a*

*dt d*

*a t*

    (3)

 

(1)

(2)

(4)

*Nr <sup>r</sup> av*

when an open-circuit fault occurs in upper-switch or lower-switch. The average electromag‐ netic torque under healthy conditions is given by:

$$T\_{av} = \frac{mN\_r}{2\pi} \int\_0^{2\pi/N\_r} T\_a(\theta, i(\theta)) d\theta \tag{1}$$

where *m* is the phase number, *Nr* is the number of rotor poles, *θ* is the rotor angular position, and *Tα*(*θ,i*(*θ*)) is the instantaneous torque of one phase. When the open-circuit faults occur at *k* phases, the faulty phase windings lose excitation but other healthy phases can still operate normally. In this condition, the average torque of the system is given by:

$$T\_{fav} = \frac{m-k}{m} T\_{av} \tag{2}$$

#### **2.2. Bus current detection**

SRM still has some disadvantages due to its special structure and operation mode, such as high torque ripple and noise, and it is difficult to establish the accurate mathematical model. In order to make up for these shortcomings, a lot of technologies have been developed. The optimization of motor structure and the adoption of effective control strategies are used to suppress the torque ripple and noise. And some schemes aim at sensorless control and new

SRM drives are known to be fault-tolerant by their nature but not completely fault-free. Opencircuit faults are a common fault type of the motor drive, leading to starting difficulty, overcurrents, high torque ripples, and reduced load capacity [13, 14]. Due to the harsh condition EVs/HEVs operate at, the switching devices can easily break down. In this section, the fault characteristics of SRM under open-circuit are illustrated; and the fault diagnosis strategy is

Open-circuit faults are common in SRM drives. As shown in Figure 5, there are many locations to initiate an open-circuit fault, such as power converter, motor windings, position signals, and drive circuit. However, the power converter is a crucial component in an SRM drive and

> **Current detection**

**Controller fault**

Figure 5. Open-circuit faults for SRM drives.

Each bridge arm is controlled independently by two switches and each phase is independent of each other, providing good fault tolerance. The system will work in the open-circuit state when an open-circuit fault occurs in upper-switch or lower-switch. The average electromagnetic torque under healthy conditions is given

Each bridge arm is controlled independently by two switches and each phase is independent of each other, providing good fault tolerance. The system will work in the open-circuit state

> 2 / <sup>0</sup> ( , ( )) <sup>2</sup>

*mN <sup>T</sup> T id* 

where *m* is the phase number, *Nr* is the number of rotor poles, *θ* is the rotor angular position, and *Tα*(*θ,i*(*θ*)) is the instantaneous torque of one phase. When the open-circuit faults occur at *k* phases, the faulty phase windings lose excitation but other healthy phases can still operate normally. In this condition, the average torque of

> *fav av m k T T m*

( ) ( ) *a a a aa a <sup>a</sup> di dL U Ri L i*

where *Ua* is the phase voltage, *Ra* is the phase resistance, *La* is the phase inductance, *ia*

/ ( ) (1 ) ( /)

*a a U i t e R dL d*

is the phase current, *ω* is the motor angular speed, and *θ* is the rotor position.

*a*

*dt d*

*a t*

    (3)

 

*Nr <sup>r</sup> av*

**IGBT fault** *iph* **Windings** 

**Encoder**

**Encoder fault**

(1)

(2)

(4)

**fault**

**Protective circuit**

**Controller**

power converter topology.

62 New Applications of Electric Drives

also presented.

by:

the system is given by:

**2.2 Bus current detection** 

The voltage equation for phase A is given by:

The branch current of phase A is given by:

The phase current can be written as:

**2. Fault diagnosis methods**

**2.1. SRM fault characteristics**

is also a vulnerable part in the system [15, 16].

**Control signal**

*U***s**

*-*

**Figure 5.** Open-circuit faults for SRM drives.

*+*

The voltage equation for phase A is given by:

$$dL\_a = R\_a \dot{\mathbf{i}}\_a + L\_a(\theta) \frac{d\dot{\mathbf{i}}\_a}{dt} + \dot{\mathbf{i}}\_a a \frac{dL\_a(\theta)}{d\theta} \tag{3}$$

where *Ua* is the phase voltage, *Ra* is the phase resistance, *La* is the phase inductance, *ia* is the phase current, *ω* is the motor angular speed, and *θ* is the rotor position.

The phase current can be written as:

$$\dot{m}\_a(t) = \frac{\mathcal{U}\_a}{R\_a + o(dL\_a / d\theta)} (1 - e^{-t/\tau}) \tag{4}$$

The branch current of phase A is given by:

4

$$\begin{array}{ccccccccc}\dot{\mathbf{i}}\_{dc\\_a} = \begin{bmatrix} \dot{\mathbf{i}}\_a & & \mathbf{S}\_1 & close\\_\circ & \mathbf{S}\_2 & close\\ \mathbf{0} & & \mathbf{S}\_1 & open\\_\circ & \mathbf{S}\_2 & close\\ \dot{\mathbf{i}}\_a & & \mathbf{S}\_1 & open\\_\circ & \mathbf{S}\_2 & open\end{bmatrix} \tag{5}$$

For a four-phase motor, the bus current *idc* is the sum of four branch currents, given by:

$$\dot{i}\_{dc}(t) = \dot{i}\_{dc\_{\perp}a}(t) + \dot{i}\_{dc\_{\perp}b}(t) + \dot{i}\_{dc\_{\perp}c}(t) + \dot{i}\_{\int\_{a^\*-\frac{d}{2}}d}(t) \tag{6}$$

Three bus locations can be defined as follows: Three bus locations can be defined as follows: *1)* When each phase is in the turn-on region [*θon*-*θoff*], the phase voltage is:

**1.** When each phase is in the turn-on region [*θon*-*θoff*], the phase voltage is:

$$\text{CLI}\_{k} = \begin{cases} \text{LI}\_{s} & \text{upper} - \text{switch} \quad \text{close}, \quad \text{lower} - \text{switch} \quad \text{close} \\ 0 & \text{upper} - \text{switch} \quad \text{open}, \quad \text{lower} - \text{switch} \quad \text{close} \end{cases} \tag{7}$$

*U upper switch close lower switch close*

where *Us* is the dc voltage output of the rectifier from the ac power supply. The bus current is in the chopping control state i.e., chopping bus current, denoted by *idc*2. current is in the chopping control state i.e., chopping bus current, denoted by *idc*2. *2)* When each phase is in the turn-off region [*θoff* -*θon*+*π*/3], the upper-switch and

where *Us* is the dc voltage output of the rectifier from the ac power supply. The bus


$$
\dot{\mathbf{i}}\_{dc1} = \dot{\mathbf{i}}\_{dc2} - \dot{\mathbf{i}}\_{fc} \tag{8}
$$

, (7)

5

Based on the three bus locations, there are three current sensor placement strategies in the converter, as illustrated in Figure 6. The corresponding detected currents are the chopping bus current in Figure 6(a), the demagnetization bus current in Figure 6(b), and the excitation bus current in Figure 6(c). Based on the three bus locations, there are three current sensor placement strategies in the converter, as illustrated in Figure 6. The corresponding detected currents are the chopping bus current in Figure 6(a), the demagnetization bus current in Figure 6(b), and the excitation bus current in Figure 6(c).

(b) Demagnetization bus. (c) Excitation bus. **Figure 6.** Three bus current detection schemes. (a) Chopping bus. (b) Demagnetization bus. (c) Excitation bus.

#### **2.3 Fault diagnosis based on the FFT algorithm 2.3. Fault diagnosis based on the FFT algorithm**

accuracy [17].

The FFT algorithm with Blackman window function interpolation is employed to analyze the current spectrums due to smaller side lobe, and better harmonic amplitude The FFT algorithm with Blackman window function interpolation is employed to analyze the current spectrums due to smaller side lobe, and better harmonic amplitude accuracy [17].

The fundamental frequencies of the phase current and bus current are given by:

Figure 6. Three bus current detection schemes. (a) Chopping bus.

The fundamental frequencies of the phase current and bus current are given by:

Three bus locations can be defined as follows:

Three bus locations can be defined as follows:

 

*U <sup>s</sup>*

*s*

demagnetization bus current, denoted by *ifc*.

and the excitation bus current in Figure 6(c).

**2.3 Fault diagnosis based on the FFT algorithm** 

**2.3. Fault diagnosis based on the FFT algorithm**

*k*

64 New Applications of Electric Drives

current in Figure 6(c).

accuracy [17].

by *idc*1.

**1.** When each phase is in the turn-on region [*θon*-*θoff*], the phase voltage is:

ìï - - <sup>=</sup> <sup>í</sup>

*<sup>k</sup>* 0 ,

0 ,

in the chopping control state i.e., chopping bus current, denoted by *idc*2.

demagnetization state, i.e., demagnetization bus current, denoted by *ifc*.

,

 *upper switch open lower switch close U upper switch close lower switch close*

*upper switch open lower switch close*

where *Us* is the dc voltage output of the rectifier from the ac power supply. The bus current is

*2)* When each phase is in the turn-off region [*θoff* -*θon*+*π*/3], the upper-switch and lower-switch are both shut off, and *Uk*=-*Us*. The bus current is in the phase

where *Us* is the dc voltage output of the rectifier from the ac power supply. The bus

**2.** When each phase is in the turn-off region [*θoff*-*θon*+*π*/3], the upper-switch and lower-switch are both shut off, and *Uk*=-*Us*. The bus current is in the phase demagnetization state, i.e.,

**3.** The bus current in each phase excitation state contains both the chopping bus current and reverse demagnetization bus current, i.e., excitation bus current, denoted by *idc*1.

*3)* The bus current in each phase excitation state contains both the chopping bus current and reverse demagnetization bus current, i.e., excitation bus current, denoted

Based on the three bus locations, there are three current sensor placement strategies in the converter, as illustrated in Figure 6. The corresponding detected currents are the chopping bus current in Figure 6(a), the demagnetization bus current in Figure 6(b), and the excitation bus

(a) (b) (c)

**Figure 6.** Three bus current detection schemes. (a) Chopping bus. (b) Demagnetization bus. (c) Excitation bus.

Figure 6. Three bus current detection schemes. (a) Chopping bus. (b) Demagnetization bus. (c) Excitation bus.

The FFT algorithm with Blackman window function interpolation is employed to analyze the current spectrums due to smaller side lobe, and better harmonic amplitude

The FFT algorithm with Blackman window function interpolation is employed to analyze the current spectrums due to smaller side lobe, and better harmonic amplitude accuracy [17].

The fundamental frequencies of the phase current and bus current are given by:

Based on the three bus locations, there are three current sensor placement strategies in the converter, as illustrated in Figure 6. The corresponding detected currents are the chopping bus current in Figure 6(a), the demagnetization bus current in Figure 6(b),

<sup>ï</sup> - - <sup>î</sup> (7)

*dc dc fc* 1 2 *iii* = - (8)

*dc dc fc* 1 2 *iii* (8)

, (7)

5

*U upper switch close lower switch close <sup>U</sup>*

current is in the chopping control state i.e., chopping bus current, denoted by *idc*2.

*1)* When each phase is in the turn-on region [*θon*-*θoff*], the phase voltage is:

$$f\_1 = \text{nN}\_r / \Theta0\tag{9}$$

$$f\_{bus} = mf\_1 = mm \text{N}\_r \text{ / } \text{60} \tag{10}$$

where *f*<sup>1</sup> is the fundamental frequency of the phase current, *fbus* is the fundamental frequency of the bus current in normal conditions, *n* is the motor speed in rpm, and *Nr* is the number of the rotor poles.

The excitation bus current spectrums before and after the open-circuit faults are shown in Figure 7. There are no harmonic components at *f*1 for bus current in normal condition, as shown in Figure 7(a). The dc component *A*0 changes little after phase A open, while the phase fundamental frequency component *Af*1, double-phase fundamental frequency component *Af*2, and triple-phase fundamental frequency component *Af3* all increase, especially *Af*1, as shown in Figure 7(b). The excitation bus current spectrums before and after the open-circuit faults are shown in Figure 7. There are no harmonic components at *f*1 for bus current in normal condition, as shown in Figure 7(a). The dc component *A*0 changes little after phase A open, while the phase fundamental frequency component *Af*1, double-phase fundamental frequency component *Af*2, and triple-phase fundamental frequency component *Af3* all increase, especially *Af*1, as shown in Figure 7(b).

Figure 7. Simulation spectrums of the excitation bus current (a) Normal condition. (b) Phase A open. (c) Phases A and B open. (d) Phases A and C open. **Figure 7.** Simulation spectrums of the excitation bus current (a) Normal condition. (b) Phase A open. (c) Phases A and B open. (d) Phases A and C open.

The phase fundamental frequency component *Af*1 and double-phase fundamental frequency component *Af*2 are normalized to the dc component *A*0 of the bus current, and the equations are formalized as: The phase fundamental frequency component *Af*1 and double-phase fundamental frequency component *Af*2 are normalized to the dc component *A*0 of the bus current, and the equations are formalized as:

> *\** are defined as the normalized components of *A*1 and *A*2. The simulation results at seven different speeds are shown in Table I. The values of

fundamental component in the bus current spectrum under normal conditions; hence,

phases A and C are open. Clearly, the normalized components can be used to link with

to 1.5–1.7 when phases A and B are open. Similarly, *A*<sup>2</sup>

is zero when healthy. It increases to 0.7–0.8 when phase A is open, and increases

are stable at different speeds in the same failure mode. There is no

\*

where *A*<sup>1</sup> *\** and *A*<sup>2</sup>

open-circuit faults.

*A*1 *\** and *A*<sup>2</sup> *\**

*A*1 *\**

$$\begin{array}{c} A\_1 \stackrel{\ast}{=} A\_{f1} / A\_0 \end{array} \tag{11}$$

1 10 / *A AA <sup>f</sup>* (11)

*\**

rises to about 1.0 when

$$A\_2^\* = A\_{f2} / A\_0 \tag{12}$$

where *A*<sup>1</sup> *\** and *A*<sup>2</sup> *\** are defined as the normalized components of *A*1 and *A*2.

The simulation results at seven different speeds are shown in Table I. The values of *A*<sup>1</sup> *\** and *A*<sup>2</sup> *\** are stable at different speeds in the same failure mode. There is no fundamental component in the bus current spectrum under normal conditions; hence, *A*<sup>1</sup> *\** is zero when healthy. It increases to 0.7–0.8 when phase A is open, and increases to 1.5–1.7 when phases A and B are open. Similarly, *A*<sup>2</sup> *\** rises to about 1.0 when phases A and C are open. Clearly, the normalized components can be used to link with open-circuit faults.

Experimental tests are carried out on a 150-W four-phase 8/6-pole prototype SRM. An asymmetric half-bridge converter is employed in the system, and a DSP TMS320F28335 is used as the main control chip. A fuzzy control algorithm with PWM voltage regulation control is implemented for the closed-loop system. The turn-on angle is set to 0° and the turn-off angle to 28°. An adjustable dc power supply is employed to drive the converter with a 36-V voltage. The IGBT gate signals are controlled to emulate the open-circuit faults.


**Table 1.** Simulation results of the excitation bus current

Figure8 (a)-(d) shows the chopping bus current *idc*1, excitation bus current *idc*2, and demagnet‐ ization bus current *ifc* before and after phase A open, phases A and B open, and phases A and C open, respectively, at 600 r/min. The FFT algorithm with Blackman window interpolation is generated on the bus current before and after the fault, ranging from 400 to 1500 r/min.

The phase fundamental frequency component *Af*<sup>1</sup> is very small at normal conditions. However, *Af*1 is zero in the simulation due to an ideal condition, while a small harmonic component exists in the phase fundamental frequency because of the electromagnetic interference (EMI) and rotor eccentricity in real conditions, which does not affect the accuracy of the diagnosis. The dc component *A*0 does not change and the phase fundamental frequency component *Af*<sup>1</sup> increases obviously when faults happen. Hence, *A*<sup>1</sup> \* increases both after phase A open and after phases A and B open.

open, and phases A and C open, respectively, at 600 r/min. The FFT algorithm with Blackman window interpolation is generated on the bus current before and Fault Diagnosis of Switched Reluctance Motors in Electrified Vehicle Applications http://dx.doi.org/10.5772/61659 67

is employed to drive the converter with a 36-V voltage. The IGBT gate signals are

400 34.63 25.71 0.74 32.52 50.73 1.56 33.66 32.72 0.97 600 47.02 33.12 0.71 45.78 67.30 1.47 44.86 46.25 1.03 800 62.26 47.46 0.76 61.88 100.24 1.62 60.25 58.91 0.98 1000 73.81 56.95 0.77 70.66 122.24 1.63 71.32 68.96 0.97 1200 86.72 65.32 0.75 84.93 139.28 1.64 82.13 78.68 0.96 1400 99.86 74.11 0.74 98.32 155.35 1.58 98.18 96.21 0.98 1500 108.63 83.93 0.77 106.21 176.31 1.66 105.26 102.58 0.97

Figure 8(a)-(d) shows the chopping bus current idc<sup>1</sup>, excitation bus current idc<sup>2</sup>, and demagnetization bus current ifc before and after phase A open, phases A and B

Table I Simulation results of the excitation bus current

Phase A open Phases A and B open Phases A and C open

A<sup>1</sup>

\* A<sup>0</sup>

[mA]

Af<sup>2</sup> [mA] A<sup>2</sup> \*

Af<sup>1</sup> [mA]

controlled to emulate the open-circuit faults.

Af<sup>1</sup> [mA]

after the fault, ranging from 400 to 1500 r/min.

A<sup>1</sup>

\* A<sup>0</sup>

[mA]

Speed [r/min]

A<sup>0</sup> [mA]

\*

in the bus current spectrum under normal conditions; hence, *A*<sup>1</sup>

The IGBT gate signals are controlled to emulate the open-circuit faults.

components can be used to link with open-circuit faults.

**Table 1.** Simulation results of the excitation bus current

increases obviously when faults happen. Hence, *A*<sup>1</sup>

after phases A and B open.

are defined as the normalized components of *A*1 and *A*2.

are stable at different speeds in the same failure mode. There is no fundamental component

increases to 0.7–0.8 when phase A is open, and increases to 1.5–1.7 when phases A and B are

Experimental tests are carried out on a 150-W four-phase 8/6-pole prototype SRM. An asymmetric half-bridge converter is employed in the system, and a DSP TMS320F28335 is used as the main control chip. A fuzzy control algorithm with PWM voltage regulation control is implemented for the closed-loop system. The turn-on angle is set to 0° and the turn-off angle to 28°. An adjustable dc power supply is employed to drive the converter with a 36-V voltage.

*\** rises to about 1.0 when phases A and C are open. Clearly, the normalized

**Phase A open Phases A and B open Phases A and C open**

A0 [mA] A*f1* [mA] A1\* A0 [mA] A*f1* [mA] A1\* A0 [mA] A*f2* [mA] A2\*

 34.63 25.71 0.74 32.52 50.73 1.56 33.66 32.72 0.97 47.02 33.12 0.71 45.78 67.30 1.47 44.86 46.25 1.03 62.26 47.46 0.76 61.88 100.24 1.62 60.25 58.91 0.98 73.81 56.95 0.77 70.66 122.24 1.63 71.32 68.96 0.97 86.72 65.32 0.75 84.93 139.28 1.64 82.13 78.68 0.96 99.86 74.11 0.74 98.32 155.35 1.58 98.18 96.21 0.98 108.63 83.93 0.77 106.21 176.31 1.66 105.26 102.58 0.97

Figure8 (a)-(d) shows the chopping bus current *idc*1, excitation bus current *idc*2, and demagnet‐ ization bus current *ifc* before and after phase A open, phases A and B open, and phases A and C open, respectively, at 600 r/min. The FFT algorithm with Blackman window interpolation is generated on the bus current before and after the fault, ranging from 400 to 1500 r/min.

The phase fundamental frequency component *Af*<sup>1</sup> is very small at normal conditions. However, *Af*1 is zero in the simulation due to an ideal condition, while a small harmonic component exists in the phase fundamental frequency because of the electromagnetic interference (EMI) and rotor eccentricity in real conditions, which does not affect the accuracy of the diagnosis. The dc component *A*0 does not change and the phase fundamental frequency component *Af*<sup>1</sup>

\*

increases both after phase A open and

The simulation results at seven different speeds are shown in Table I. The values of *A*<sup>1</sup>

where *A*<sup>1</sup>

**Speed [r/min]** *\** and *A*<sup>2</sup> *\**

66 New Applications of Electric Drives

open. Similarly, *A*<sup>2</sup>

2 20 / *A AA <sup>f</sup>* = (12)

*\**

*\** and *A*<sup>2</sup> *\**

is zero when healthy. It

Figure 8. Experimental results of bus currents. (a) Healthy. (b) Phase A open. (c) Phases A and B open. (d) Phases A and C open. **Figure 8.** Experimental results of bus currents. (a) Healthy. (b) Phase A open. (c) Phases A and B open. (d) Phases A and C open.

The fault characteristics of the bus current before and after phase A open and phases A and B open are shown in Figure 9. *A*<sup>1</sup> \* of the excitation bus current, chopping bus current, and demagnetization bus current are all below 0.05 at normal conditions, while the values are stable within 1.6–1.7, 0.9–1.0, and 1.4–1.5, respectively, when phases A and B are open-circuited. Clearly, the fault characteristics confirm that the normalized phase fundamental frequency component of the bus current can be used as the open-circuit fault signature. The phase fundamental frequency component Af<sup>1</sup> is very small at normal conditions. However, Af<sup>1</sup> is zero in the simulation due to an ideal condition, while a small harmonic component exists in the phase fundamental frequency because of the

8

Under phases A and C open condition, *A*<sup>1</sup> *\** cannot be used to diagnose this fault since there is no change in *Af*<sup>1</sup> compared to the normal state, as shown in Figure 9(d). However, *Af*2 changes obviously and its normalized component *A*<sup>2</sup> *\** can thus be used for this diagnosis. Figure 9(d) shows *A*<sup>2</sup> *\** before and after phases A and C open. Curve 1, curve 2, and curve 3 represent *A*<sup>2</sup> *\** of the chopping bus current, excitation bus current, and demagnetization bus current, respectively, in normal conditions. Curve 4, curve 5, and curve 6 represent *A*<sup>2</sup> *\** of the chopping bus current, excitation bus current, and demagnetization bus current, respectively, when phases A and C are open-circuited. As illustrated in the figure, the stability for curve 6 is poor, and the value declines as the speed increases, while the fault characteristic of curve 5 is more significant and more stable compared to others, which can be used for diagnosis of this fault. this fault.

value declines as the speed increases, while the fault characteristic of curve 5 is more significant and more stable compared to others, which can be used for diagnosis of bus. (b) *A*<sup>1</sup> *\** of chopping bus. (c) *A*<sup>1</sup> *\** of demagnetization bus. (d) *A*<sup>2</sup> *\** before and after phases A and C open. **Figure 9.** Fault characteristics before and after open-circuit faults. (a) *A*<sup>1</sup> *\** of excitation bus. (b) *A*<sup>1</sup> *\** of chopping bus. (c) *A*1 *\** of demagnetization bus. (d) *A*<sup>2</sup> *\** before and after phases A and C open.

Figure 9. Fault characteristics before and after open-circuit faults. (a) *A*<sup>1</sup>

By comparing the three fault characteristics, it becomes clear that the excitation bus current shows a good correlation with the faults. Therefore, it is chosen to extract the fault character‐ istics for fault diagnosis. By comparing the three fault characteristics, it becomes clear that the excitation bus current shows a good correlation with the faults. Therefore, it is chosen to extract the fault characteristics for fault diagnosis. \* Under phases A and C open condition, *A*<sup>1</sup> *\** cannot be used to diagnose this fault since there is no change in *Af*1 compared to the normal state, as shown in Figure 9(d). However, *Af*2 changes obviously and its normalized component *A*<sup>2</sup> *\** can thus be used

The fault characteristic has good robustness, as shown in Figure 10. *A*<sup>1</sup>

The fault characteristic has good robustness, as shown in Figure 10. *A*<sup>1</sup> \* has good disturbance resistance to the changes in the load and turn-on angle. Therefore, this diagnostic method is suitable for variable load drives and variable angle control systems. It needs to point out that the sampling frequency should be greater than the PWM chopping frequency to ensure the accuracy of the current detection and harmonic analysis. disturbance resistance to the changes in the load and turn-on angle. Therefore, this diagnostic method is suitable for variable load drives and variable angle control systems. It needs to point out that the sampling frequency should be greater than the PWM chopping frequency to ensure the accuracy of the current detection and harmonic analysis. for this diagnosis. Figure 9(d) shows *A*<sup>2</sup> *\** before and after phases A and C open. Curve 1, curve 2, and curve 3 represent *A*<sup>2</sup> *\** of the chopping bus current, excitation bus current, and demagnetization bus current, respectively, in normal conditions. Curve 4, curve 5, and curve 6 represent *A*<sup>2</sup> *\** of the chopping bus current, excitation bus current, and demagnetization bus current, respectively, when phases A and C are open-circuited. As illustrated in the figure, the stability for curve 6 is poor, and the

*\** . (a) *A*<sup>1</sup>

does not change with the load variations, speed regulation,

when the system is subject to a fast transient

(b) *A*<sup>1</sup> *\** with turn-on angle. **Figure 10.** Load torque and turn-on angle in relation to *A*<sup>1</sup> *\** . (a) *A*<sup>1</sup> *\** with load torque. (b) *A*<sup>1</sup> *\** with turn-on angle.

\*

and angle modulation. Therefore, the proposed method has excellent robustness to the

Figure 10. Load torque and turn-on angle in relation to *A*<sup>1</sup>

Figure 11 shows the value of *A*<sup>1</sup>

\*

fast transients, which would not generate false alarms.

disturbance. Clearly, *A*<sup>1</sup>

8

8

*\** with load torque.

has good

*\**

of excitation

Figure 11 shows the value of *A*<sup>1</sup> \* when the system is subject to a fast transient disturbance. Clearly, *A*<sup>1</sup> \* does not change with the load variations, speed regulation, and angle modulation. Therefore, the proposed method has excellent robustness to the fast transients, which would not generate false alarms.

Figure 11. Fast transients in relation to A<sup>1</sup> \* . (a) Load variation. (b) Speed regulation. **Figure 11.** Fast transients in relation to *A*<sup>1</sup> *\** . (a) Load variation. (b) Speed regulation. (c) Angle modulation.

#### 3. Fault Tolerance Topology **3. Fault tolerant topology**

from right part.

By comparing the three fault characteristics, it becomes clear that the excitation bus current shows a good correlation with the faults. Therefore, it is chosen to extract the fault character‐

since there is no change in *Af*1 compared to the normal state, as shown in Figure 9(d).

phases A and C open.

By comparing the three fault characteristics, it becomes clear that the excitation bus current shows a good correlation with the faults. Therefore, it is chosen to extract the

since there is no change in *Af*1 compared to the normal state, as shown in Figure 9(d).

Fault characteristic A2\*

(a) (b)

0.0 0.5 1.0 1.5 2.0

Fault characteristic A1\*

current, and demagnetization bus current, respectively, in normal conditions. Curve 4,

0.0 0.5 1.0 1.5 2.0

of demagnetization bus. (d) *A*<sup>2</sup>

*\**

and demagnetization bus current, respectively, when phases A and C are open-circuited. As illustrated in the figure, the stability for curve 6 is poor, and the value declines as the speed increases, while the fault characteristic of curve 5 is more significant and more stable compared to others, which can be used for diagnosis of

 (c) (d) Figure 9. Fault characteristics before and after open-circuit faults. (a) *A*<sup>1</sup>

*\**

before and after phases A and C open.

However, *Af*2 changes obviously and its normalized component *A*<sup>2</sup>

resistance to the changes in the load and turn-on angle. Therefore, this diagnostic method is suitable for variable load drives and variable angle control systems. It needs to point out that the sampling frequency should be greater than the PWM chopping frequency to ensure the

current, and demagnetization bus current, respectively, in normal conditions. Curve 4,

and demagnetization bus current, respectively, when phases A and C are open-circuited. As illustrated in the figure, the stability for curve 6 is poor, and the value declines as the speed increases, while the fault characteristic of curve 5 is more significant and more stable compared to others, which can be used for diagnosis of

*\** . (a) *A*<sup>1</sup> *\**

(a) (b)

and angle modulation. Therefore, the proposed method has excellent robustness to the

with turn-on angle.

0

1

Fault characteristic A1\*

By comparing the three fault characteristics, it becomes clear that the excitation bus current shows a good correlation with the faults. Therefore, it is chosen to extract the

2

disturbance resistance to the changes in the load and turn-on angle. Therefore, this diagnostic method is suitable for variable load drives and variable angle control systems. It needs to point out that the sampling frequency should be greater than the PWM chopping frequency to ensure the accuracy of the current detection and

The fault characteristic has good robustness, as shown in Figure 10. *A*<sup>1</sup>

However, *Af*2 changes obviously and its normalized component *A*<sup>2</sup>

\*


Normal

Phase A open

Phases A and B open

*on*(°)

*\**

*\** with load torque.

with turn-on angle.

Turn-on angle

*\** . (a) *A*<sup>1</sup>

with load torque. (b) *A*<sup>1</sup>

does not change with the load variations, speed regulation,

when the system is subject to a fast transient

\* has good

can thus be used

*\**

**5**

400 600 800 1000 1200 1400

*\**

of excitation bus. (b) *A*<sup>1</sup>

*\** cannot be used to diagnose this fault

*\**

*\** before and after phases A and C open. Curve

*\** of the chopping bus current, excitation bus

*\** of the chopping bus current, excitation bus current,

400 600 800 1000 1200 1400

Speed n(r/min)

Normal Phase A open

Phases A and B open

*\** before and after phases A and C open. Curve

**4 1 2 3**

*\** of the chopping bus current, excitation bus

*\** of the chopping bus current, excitation bus current,

can thus be used

Speed n(r/min)

of excitation

before and after

*\**

**6**

has good disturbance

*\** of chopping bus. (c)

8

8

The fault characteristic has good robustness, as shown in Figure 10. *A*<sup>1</sup>

accuracy of the current detection and harmonic analysis.

curve 5, and curve 6 represent *A*<sup>2</sup>

0.0 0.1 0.2 0.3 0.4 0.5 0.6

Normal

fault characteristics for fault diagnosis.

Phase A open

Phases A and B open

Load torque*TN*(N·m)

Figure 11 shows the value of *A*<sup>1</sup>

\*

fast transients, which would not generate false alarms.

disturbance. Clearly, *A*<sup>1</sup>

**Figure 10.** Load torque and turn-on angle in relation to *A*<sup>1</sup>

Figure 10. Load torque and turn-on angle in relation to *A*<sup>1</sup>

(b) *A*<sup>1</sup> *\**

\*

harmonic analysis.

0

1

Fault characteristic A1\*

2

this fault.

fault characteristics for fault diagnosis.

**Figure 9.** Fault characteristics before and after open-circuit faults. (a) *A*<sup>1</sup>

*\**

for this diagnosis. Figure 9(d) shows *A*<sup>2</sup>

1, curve 2, and curve 3 represent *A*<sup>2</sup>

for this diagnosis. Figure 9(d) shows *A*<sup>2</sup>

400 600 800 1000 1200 1400

Speed n(r/min)

Normal

Phase A open

Phases A and B open

1, curve 2, and curve 3 represent *A*<sup>2</sup>

400 600 800 1000 1200 1400

Speed n(r/min)

of chopping bus. (c) *A*<sup>1</sup>

Under phases A and C open condition, *A*<sup>1</sup>

Normal

Phase A open

Phases A and B open

curve 5, and curve 6 represent *A*<sup>2</sup>

istics for fault diagnosis.

*A*1 *\**

this fault.

of demagnetization bus. (d) *A*<sup>2</sup>

bus. (b) *A*<sup>1</sup> *\**

0.0 0.5 1.0 1.5 2.0

Fault characteristic A1\*

0.0 0.5 1.0 1.5 2.0

Fault characteristic A1\*

68 New Applications of Electric Drives

Traditionally, the SRM phase windings are composed of an even number of series connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which La1, La2, La3, and La4 represent for four windings of one SRM phase; the central tapped node A of phase La is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical Traditionally, the SRM phase windings are composed of an even number of series connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connec‐ tion, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two parts: left part and right part; each part has the same compo‐

half-bridge topology and phase winding; the whole circuit can be divided into two parts: left part and right part; each part has the same components, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault

(c) Angle modulation.

from right part.

nents, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault from right part. parts**:** left part and right part; each part has the same components, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two parts**:** left part and right part; each part has the same components, including diode, connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in

switching device, and phase winding, as presented in Figure 14. The two parts have

Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical

connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings

Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two

connected windings, as shown in Figure 12. Thus, central-tapped windings are formed,

Figure 12. Basic winding structure of SRM. **Figure 12.** Basic winding structure of SRM. Figure 12. Basic winding structure of SRM.

Figure 13. Central-tapped winding of a 12/8 SRM.

Figure 12. Basic winding structure of SRM.

Figure 13. Central-tapped winding of a 12/8 SRM. **Figure 13.** Central-tapped winding of a 12/8 SRM.

Figure 14. Two parts of phase converter.

On the basis of the central tapped node and axial symmetry characteristics of the traditional drive topology, the proposed fault tolerance topology is presented in Figure15. Figure 15(a) is the main driving topology composed of main topology (traditional asymmetrical half-bridge) as Figure 15(b), and fault tolerance module as Figure 15(c). The fault tolerance module is the traditional three-phase half-bridge

On the basis of the central tapped node and axial symmetry characteristics of the traditional drive topology, the proposed fault tolerance topology is presented in Figure15. Figure 15(a) is the main driving topology composed of main topology (traditional asymmetrical half-bridge) as Figure 15(b), and fault tolerance module as Figure 15(c). The fault tolerance module is the traditional three-phase half-bridge

9

9

Figure 14. Two parts of phase converter. **Figure 14.** Two parts of phase converter.

On the basis of the central tapped node and axial symmetry characteristics of the traditional drive topology, the proposed fault tolerant topology is presented in Figure15. Figure 15(a) is the main driving topology composed of main topology (traditional asymmetrical half-bridge) as Figure 15(b), and fault tolerance module as Figure 15(c). The fault tolerance module is the traditional three-phase half-bridge modular. The half-bridge central nodes are connected with central tapped node of phase windings, which are A, B, and C, respectively. Three-phase halfbridge is employed to approach fault tolerance operation. The proposed topology has the characteristics of modular structure; on the base of traditional asymmetrical half-bridge topology, only one three-phase bridge modular is needed. The basic structure of SRM is almost not changed. In normal conditions, the proposed topology works as traditional asymmetrical half-bridge topology; the fault tolerance module is in idle condition that makes the proposed converter have the same efficiency as the traditional asymmetrical half-bridge topology. The fault tolerance module works only at fault condition. 

nents, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault from right part.

connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two parts**:** left part and right part; each part has the same components, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault

connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two parts**:** left part and right part; each part has the same components, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault

> (a) 8/6 SRM (b) 12/8 SRM Figure 12. Basic winding structure of SRM.

Figure 12. Basic winding structure of SRM.

Figure 12. Basic winding structure of SRM.

Figure 13. Central-tapped winding of a 12/8 SRM.

Figure 13. Central-tapped winding of a 12/8 SRM.

Figure 13. Central-tapped winding of a 12/8 SRM.

Figure 14. Two parts of phase converter.

Figure 14. Two parts of phase converter.

On the basis of the central tapped node and axial symmetry characteristics of the traditional drive topology, the proposed fault tolerance topology is presented in Figure15. Figure 15(a) is the main driving topology composed of main topology (traditional asymmetrical half-bridge) as Figure 15(b), and fault tolerance module as Figure 15(c). The fault tolerance module is the traditional three-phase half-bridge

On the basis of the central tapped node and axial symmetry characteristics of the traditional drive topology, the proposed fault tolerance topology is presented in Figure15. Figure 15(a) is the main driving topology composed of main topology (traditional asymmetrical half-bridge) as Figure 15(b), and fault tolerance module as Figure 15(c). The fault tolerance module is the traditional three-phase half-bridge

from right part.

70 New Applications of Electric Drives

from right part.

from right part.

**Figure 12.** Basic winding structure of SRM.

**Figure 13.** Central-tapped winding of a 12/8 SRM.

**Figure 14.** Two parts of phase converter.

connected windings, as shown in Figure 12. Thus, central-tapped windings are formed, which can be easily designed in 8/6 or 12/8 SRM. Figure13 shows the traditional 12/8 SRM winding connection, in which *La1*, *La2*, *La3*, and *La4* represent for four windings of one SRM phase; the central tapped node A of phase *La* is developed as shown in Figure 13. One phase of SRM drive circuit is composed by traditional asymmetrical half-bridge topology and phase winding; the whole circuit can be divided into two parts**:** left part and right part; each part has the same components, including diode, switching device, and phase winding, as presented in Figure 14. The two parts have the characteristics of axial symmetry that can be employed in fault tolerance operation. When the central tapped node is connected with positive node of power supply source, the left part of the converter is bypassed, which can block the left part fault. The same method, when the central tapped node A is connected with negative node of power supply source, the right part of the converter is bypassed, which can block the fault

(a) Proposed fault tolerance topology

(b) Main topology for SRM

(c) Fault tolerant module Figure 15. Proposed topology for SRM fault tolerance operation.

Switching device faults and phase winding open-circuit faults are common fault phenomena. In the traditional asymmetrical half-bridge converter, there are two switching devices for each phase; and each phase has four windings for a 12/8 SRM. When there is no current in the excitation region in phase *La*, it means that the open-circuit occurs. The diagnosis needs to locate which part is under fault condition by replacing *S0* by *SA1*, and giving the turn-off single to *S0*. In the right part of the converter, *SA1*, *SA2*, *D1*, *S1*, and *La34* compose a new asymmetrical half-bridge. In the right part asymmetrical half-bridge, if the faulty phase can work, it proves that the left part of converter is under fault condition. By the same method, replacing *S1* by *SA2*, and giving the turn-off single to *S1*; in left part of converter, *S0*, *SA1*, *SA2*, *D0,* and *La12* compose a new asymmetrical half-bridge. In the left part asymmetrical half-bridge, if the faulty phase can work, it proves that the right part of the converter is under fault condition. The diagnosis flowchart of the open-circuit fault is shown in Figure 16.

**3.1 Switching device faults and phase winding open-circuit faults** 

10

**Figure 15.** Proposed topology for SRM fault tolerance operation.

9

9
