**3.2. Fault tolerance operation under open-circuit fault conditions**

When a faulty part is identified in the faulty phase, the fault tolerance module and main topology combines new topology for faulty phase converter. If the left part of one phase converter is in fault condition, in the fault tolerant topology, the left part of one phase converter, including the switching device *S0*, diode *D0* and phase winding *La12*, is shorted by half-bridge *SA1* and *SA2* to block faulty part. Figure 17(a) is the typical example of *S0* under open-circuit condition. When open-circuit fault occurs, the half-bridge *SA1* and *SA2* is activated to combine with right part converter to form a new fault tolerant topology. In the new-formed fault tolerance operation topology, when *SA1* and *S1* conduct, the excitation circuit is shown in Figure 17(b). Figure 17(c) presents the energy-recycling mode, in which the winding voltage is –*Uin* to speed up winding demagnetization. Figure 17(d) shows the freewheeling conduction mode, in which the winding voltage is 0. The working modes of the fault tolerance converter are the same as a traditional converter, except only a half phase-winding is operating.

Figure 16. Flowchart for the diagnosis of the open circuit fault.

(a) Upper switch open circuit (b) Excitation circuit

(c) Energy recycling mode (d) Freewheeling conduction mode Figure 17. Fault tolerance operation topology under open-circuit condition. The same fault tolerance operation can be achieved, when *D0* or *La12* is faulty. When the right part of one phase converter is under open-circuit fault condition, the left part of one phase converter and fault tolerance module can combined to form a

new fault tolerance topology, using the same method as Figure 17.

*D0*

*S0*

**Open Circuit**

*Uin*

*La12*

*S***A2**

*S***A1**

*C* **A**

*D1*

*La34*

*S1*

**Figure 16.** Flowchart for the diagnosis of the open circuit fault.

Fault Diagnosis of Switched Reluctance Motors in Electrified Vehicle Applications http://dx.doi.org/10.5772/61659 73

The same fault tolerance operation can be achieved, when *D0* or *La12* is faulty. **Figure 17.** Fault tolerance operation topology under open-circuit condition.

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

72 New Applications of Electric Drives

flowchart of the open-circuit fault is shown in Figure 16.

**Figure 16.** Flowchart for the diagnosis of the open circuit fault.

**3.2. Fault tolerance operation under open-circuit fault conditions**

same as a traditional converter, except only a half phase-winding is operating.

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

When a faulty part is identified in the faulty phase, the fault tolerance module and main topology combines new topology for faulty phase converter. If the left part of one phase converter is in fault condition, in the fault tolerant topology, the left part of one phase converter, including the switching device *S0*, diode *D0* and phase winding *La12*, is shorted by half-bridge *SA1* and *SA2* to block faulty part. Figure 17(a) is the typical example of *S0* under open-circuit condition. When open-circuit fault occurs, the half-bridge *SA1* and *SA2* is activated to combine with right part converter to form a new fault tolerant topology. In the new-formed fault tolerance operation topology, when *SA1* and *S1* conduct, the excitation circuit is shown in Figure 17(b). Figure 17(c) presents the energy-recycling mode, in which the winding voltage is –*Uin* to speed up winding demagnetization. Figure 17(d) shows the freewheeling conduction mode, in which the winding voltage is 0. The working modes of the fault tolerance converter are the

Figure 16. Flowchart for the diagnosis of the open circuit fault.

(a) Upper switch open circuit (b) Excitation circuit

(c) Energy recycling mode (d) Freewheeling conduction mode Figure 17. Fault tolerance operation topology under open-circuit condition. The same fault tolerance operation can be achieved, when *D0* or *La12* is faulty. When the right part of one phase converter is under open-circuit fault condition, the left part of one phase converter and fault tolerance module can combined to form a

new fault tolerance topology, using the same method as Figure 17.

*D0*

*S0*

**Open Circuit**

*Uin*

*La12*

*S***A2**

*S***A1**

*C* **A**

*D1*

*La34*

*S1*

11

When the right part of one phase converter is under open-circuit fault condition, the left part of one phase converter and fault tolerance module can combined to form a new fault tolerance topology, using the same method as Figure 17. **3.3 Switching device and phase winding short-circuit fault diagnosis**  The same fault tolerance operation can be achieved, when *D0* or *La12* is faulty. When the right part of one phase converter is under open-circuit fault condition, the left part of one phase converter and fault tolerance module can combined to form a new fault tolerant topology, using the same method as Figure 17.

Figure 17. Fault tolerance operation topology under open-circuit condition.

#### When *S0* is short-circuited, a freewheeling loop is formed, as shown in Figure 18(a). When the short-circuit fault of switching device *S1* occurs, the only freewheeling **3.3. Switching device and phase winding short-circuit fault diagnosis**

mode is illustrated in Figure 18(b); both in Figure 18(a) and 18(b) fault condition, the corresponding phase current is always over zero, which can be employed in short-circuit fault diagnosis. When a short-circuit fault is detected, the next step is to locate which switching When *S0* is short-circuited, a freewheeling loop is formed, as shown in Figure 18(a). When the short-circuit fault of switching device *S1* occurs, the only freewheeling mode is illustrated in Figure 18(b); both in Figure 18(a) and 18(b) fault condition, the corresponding phase current is always over zero, which can be employed in short-circuit fault diagnosis.

devices is under fault condition. For example, if *S0* has a short-circuit fault, *SA1* is enabled by giving drive signals to replace *S0*. The right part of converter and half-bridge compose a new asymmetrical half-bridge. In the right-part asymmetrical half-bridge, if the freewheeling current can decrease to zero, the faulty part can be located in *S0*; the right-part converter and half-bridge can form a new converter to achieve fault tolerance operation that is the same as open-circuit. The diagnosis flowchart of the short-circuit fault is shown in Figure 18(c). When a short-circuit fault is detected, the next step is to locate which switching devices is under fault condition. For example, if *S0* has a short-circuit fault, *SA1* is enabled by giving drive signals to replace *S0*. The right part of converter and half-bridge compose a new asymmetrical halfbridge. In the right-part asymmetrical half-bridge, if the freewheeling current can decrease to zero, the faulty part can be located in *S0*; the right-part converter and half-bridge can form a new converter to achieve fault tolerance operation that is the same as open-circuit. The diagnosis flowchart of the short-circuit fault is shown in Figure 18(c).

The left part of the converter and half-bridge compose a new asymmetrical half-bridge. In the left-part asymmetrical half-bridge, if the freewheeling current can decrease to zero, the faulty part can be located in *S1*; the left-part converter and The left part of the converter and half-bridge compose a new asymmetrical half-bridge. In the left-part asymmetrical half-bridge, if the freewheeling current can decrease to zero, the faulty

half-bridge can form a new converter to achieve fault tolerance operation that is the

part can be located in *S1*; the left-part converter and half-bridge can form a new converter to achieve fault tolerance operation that is the same as open-circuit.

For instance, when the switching device *S0* is short-circuited, the half-bridge arm and rightpart converter form new topology. In order to block the faulty part, switching devices *S1* is employed as chopping devices. In excitation and freewheeling state, due to *SA1* conducting, both sides of phase winding *La12* share the same electric potential, which prevents the current forming in *La12*; in energy recycle mode, there is no current loop for *La12*. Therefore, in the three basic working states, there is no current in phase winding *La12*, as presented in Figure 19(a)- (c),which proves that left-part converter is blocked. Similarly, when switching device *S1* is in short-circuit condition, in order to block the right-part converter, *S0* is employed as chopping switch.

Inner turn short-circuit faults are also the faults to cause the decreasing of phase inductance; but the faulty phase still can operate. The proposed fault tolerance strategy also can bypass the short-circuited part to stop it from propagating.

(c) Diagnosis flowchart of the short‐circuit fault

(a) Excitation circuit (b) Freewheeling conduction mode (c) Energy recycling mode Figure 19. Fault tolerance operation under *S0* short-circuit condition.

After locating a fault part, the corresponding fault tolerance control strategy is

Figure 20 shows the relationship between phase current and phase inductance. As

12

Figure 18. Diagnosis of switching device short-circuits. **Figure 18.** Diagnosis of switching device short-circuits.

**3.4 Fault tolerance operation control strategy** 

needed to deal with the faulty condition.

Fault Diagnosis of Switched Reluctance Motors in Electrified Vehicle Applications http://dx.doi.org/10.5772/61659 75

12

Figure 19. Fault tolerance operation under *S0* short-circuit condition.

**3.4 Fault tolerance operation control strategy Figure 19.** Fault tolerance operation under *S0* short-circuit condition. illustrated in the figure, *θ*on and *θ*off are the turn-on and turn-off angles, respectively, *i*<sup>1</sup> and *L*1 are the phase current and phase inductance under the normal conditions, *i*2 and

#### After locating a fault part, the corresponding fault tolerance control strategy is needed to deal with the faulty condition. **3.4. Fault tolerance operation control strategy** *L*2 are under the fault tolerance conditions, and *i*4 and *i*5 are the phase currents when the turn-on angle is set lagging behind. Figure 20(a) shows the phase current and

part can be located in *S1*; the left-part converter and half-bridge can form a new converter to

For instance, when the switching device *S0* is short-circuited, the half-bridge arm and rightpart converter form new topology. In order to block the faulty part, switching devices *S1* is employed as chopping devices. In excitation and freewheeling state, due to *SA1* conducting, both sides of phase winding *La12* share the same electric potential, which prevents the current forming in *La12*; in energy recycle mode, there is no current loop for *La12*. Therefore, in the three basic working states, there is no current in phase winding *La12*, as presented in Figure 19(a)- (c),which proves that left-part converter is blocked. Similarly, when switching device *S1* is in short-circuit condition, in order to block the right-part converter, *S0* is employed as chopping

Inner turn short-circuit faults are also the faults to cause the decreasing of phase inductance; but the faulty phase still can operate. The proposed fault tolerance strategy also can bypass

(a) *S0* short‐circuit (b) *S1* short‐circuit

(c) Diagnosis flowchart of the short‐circuit fault Figure 18. Diagnosis of switching device short-circuits.

(a) Excitation circuit (b) Freewheeling conduction mode (c) Energy recycling mode Figure 19. Fault tolerance operation under *S0* short-circuit condition.

After locating a fault part, the corresponding fault tolerance control strategy is

Figure 20 shows the relationship between phase current and phase inductance. As

**3.4 Fault tolerance operation control strategy** 

needed to deal with the faulty condition.

**Figure 18.** Diagnosis of switching device short-circuits.

*D0*

*S0*

*Uin*

*La12*

*S***A1**

*C* **A**

*D1*

*La34*

*S1*

**Circuit**

*S***A2 Short**

12

achieve fault tolerance operation that is the same as open-circuit.

the short-circuited part to stop it from propagating.

switch.

74 New Applications of Electric Drives

Figure 20 shows the relationship between phase current and phase inductance. As illustrated in the figure, *θ*on and *θ*off are the turn-on and turn-off angles, respectively, *i*<sup>1</sup> and *L*1 are the phase current and phase inductance under the normal conditions, *i*2 and *L*2 are under the fault tolerance conditions, and *i*4 and *i*5 are the phase currents when After locating a fault part, the corresponding fault tolerance control strategy is needed to deal with the faulty condition. phase inductance in the fault tolerance operation with a half phase winding, compared to a normal operation. Figure 20(b) shows that the phase current operates in fault tolerance conditions when the turn-on angle is set lagging behind.

the turn-on angle is set lagging behind. Figure 20(a) shows the phase current and

(a) Fault tolerance operation with a half phase winding

(b) Turn-on angle lagging behind (b) Turn‐on angle lagging behind Figure 20. Relationship between the phase current and phase inductance.

Figure 20. Relationship between the phase current and phase inductance. **Figure 20.** Relationship between the phase current and phase inductance.

and *θ*3 are the corresponding rotor position.

In the region of *θ*on≤*θ*<*θ*2, the phase current is expressed as:

12 The phase inductance slope factor in the inductance ascending region is expressed as: max min 3 2 *L L L <sup>K</sup>* (13) where *L*min and *L*max are the minimum and maximum of the phase inductance, and *θ*<sup>2</sup> Figure 20 shows the relationship between phase current and phase inductance. As illustrated in the figure, *θ*on and *θ*off are the turn-on and turn-off angles, respectively, *i*1 and *L*1 are the phase current and phase inductance under the normal conditions, *i*2 and *L*<sup>2</sup> are under the fault tolerance conditions, and *i*4 and *i*<sup>5</sup> are the phase currents when the turn-on angle is set lagging

*i*

min *in on r U*

(14)

*L* 

where *Uin* is the bus voltage, and *ωr* is the angular velocity. In this region, the phase

behind. Figure 20(a) shows the phase current and phase inductance in the fault tolerance operation with a half phase winding, compared to a normal operation. Figure 20(b) shows that the phase current operates in fault tolerance conditions when the turn-on angle is set lagging behind.

The phase inductance slope factor in the inductance ascending region is expressed as:

$$K\_L = \frac{L\_{\text{max}} - L\_{\text{min}}}{\theta\_3 - \theta\_2} \tag{13}$$

where *L*min and *L*max are the minimum and maximum of the phase inductance, and *θ*2 and *θ*<sup>3</sup> are the corresponding rotor position.

In the region of *θ*on≤*θ*<*θ*2, the phase current is expressed as:

$$i\left(\theta\right) = \frac{\mathcal{U}\_{\rm in}}{o\nu\_r} \frac{\theta - \theta\_{\rm ou}}{L\_{\rm min}} \tag{14}$$

where *Uin* is the bus voltage, and *ωr* is the angular velocity. In this region, the phase current goes up quickly, following the current slope factor *Ki* , given by:

$$K\_i = \frac{d\dot{\imath}}{d\theta} = \frac{\mathcal{U}\_{\rm in}}{\alpha \rho\_r L\_{\rm min}} > 0 \tag{15}$$

In the region of *θ*2≤*θ*<*θ*off, the phase current is expressed as:

$$\mathrm{Li}\left(\theta\right) = \frac{\mathrm{II}\_{\mathrm{in}}}{\mathrm{op}\_{r}} \frac{\theta - \theta\_{\mathrm{on}}}{\mathrm{L}\_{\mathrm{min}} + \mathrm{K}\_{\mathrm{L}}\left(\theta - \theta\_{\mathrm{2}}\right)}\tag{16}$$

The peak value of the phase current is at the position *θ*=*θ*2, which is given by:

$$\dot{\sigma}\_{\text{max}} = \frac{\mathcal{U}\_{\text{in}}}{\alpha\_r} \frac{\theta\_2 - \theta\_{\text{on}}}{L\_{\text{min}}} \tag{17}$$

The average electromagnetic torque of one phase is given by:

$$T\_{av} = \frac{N\_r}{2\pi} \frac{\mathcal{U}\_{in}}{o\_r^2} \left(\theta\_{\text{off}} - \theta\_2\right) \left(\frac{\theta\_2 - \theta\_{\text{on}}}{L\_{\text{min}}} - \frac{1}{2} \frac{\theta\_{\text{off}} - \theta\_2}{L\_{\text{max}} - L\_{\text{min}}}\right) \tag{18}$$

where *N*r is the rotor poles.

If the motor system has an open-circuit or short-circuit fault in the converter, the proposed converter will operate with a half part of the fault phase winding, then

behind. Figure 20(a) shows the phase current and phase inductance in the fault tolerance operation with a half phase winding, compared to a normal operation. Figure 20(b) shows that the phase current operates in fault tolerance conditions when the turn-on angle is set lagging

The phase inductance slope factor in the inductance ascending region is expressed as:

*L L L <sup>K</sup>* q q

( )

*i*

q

*<sup>U</sup> <sup>i</sup>*

*di <sup>U</sup> <sup>K</sup> d L* q w

In the region of *θ*on≤*θ*<*θ*2, the phase current is expressed as:

goes up quickly, following the current slope factor *Ki*

In the region of *θ*2≤*θ*<*θ*off, the phase current is expressed as:

( )

The average electromagnetic torque of one phase is given by:

*av off r*

p w

*N U <sup>T</sup>*

where *N*r is the rotor poles.

q

*<sup>U</sup> <sup>i</sup>*

w

The peak value of the phase current is at the position *θ*=*θ*2, which is given by:

*<sup>U</sup> <sup>i</sup>*

*max*

2 2

q q

2 2 *off r in on*

max min 3 2

where *L*min and *L*max are the minimum and maximum of the phase inductance, and *θ*2 and *θ*<sup>3</sup>

min *in on*

*L* q q

where *Uin* is the bus voltage, and *ωr* is the angular velocity. In this region, the phase current

min 0 *in*

min ( <sup>2</sup> ) *in on r L*

> 2 min *in on*

*L* q q

( ) <sup>2</sup> <sup>2</sup> <sup>2</sup>

q q

æ ö - - =-- ç ÷ - è ø

min max min 1

q q

*L LL*

*r*

w

q q

*L K* q q

*r*

*r*

w



== > (15)



(18)

, given by:

behind.

76 New Applications of Electric Drives

are the corresponding rotor position.

$$\begin{cases} L\_{\text{max}} \, ^\circ = \frac{1}{2} L\_{\text{max}} \\ L\_{\text{min}} \, ^\circ = \frac{1}{2} L\_{\text{min}} \end{cases} \tag{19}$$

where *L*min' and *L*max' are the minimum and maximum of the faulty phase inductance.

The phase inductance slope factor in the inductance ascending region in the fault-tolerant operation is as follows:

$$K\_L \, ^\circ = \frac{1}{2} \frac{L\_{\text{max}} \, ^\circ - L\_{\text{min}} \, ^\circ}{\beta\_s} = \frac{1}{2} K\_L \tag{20}$$

In the region of *θ*on≤*θ*<*θ*2, the phase current slope in fault-tolerant operation is as follows:

$$K\_i \text{"} = (\frac{d\mathbf{i}}{d\theta}) \text{"} = \frac{\mathbf{U}\_{in}}{o\nu\_r \frac{1}{2}\mathbf{L}\_{\text{min}}} = \frac{2\mathbf{U}\_{in}}{o\nu\_r \mathbf{L}\_{\text{min}}} = 2\mathbf{K}\_i \tag{21}$$

The peak value of the phase current at the position *θ*=*θ*2, in fault-tolerant operation, is:

$$\dot{i}\_{\text{max}} = \frac{\mathbf{U}\_{in}}{o o\_r} \frac{\theta\_2 - \theta\_{on}}{\frac{1}{2}} = \frac{\mathbf{U}\_{in}}{o o\_r} \frac{\mathbf{2}(\theta\_2 - \theta\_{on})}{L\_{\text{min}}} = \mathbf{2}i\_{\text{max}} \tag{22}$$

The average electromagnetic torque of the failure phase is given by:

$$T\_{av} = \frac{N\_r}{2\pi} \frac{\mathcal{U}\_{in}}{\alpha\_r^2} \left(\theta\_{\text{off}} - \theta\_2\right) \left(\frac{\theta\_2 - \theta\_{\text{on}}}{\frac{1}{2}L\_{\text{min}}} - \frac{1}{2} \cdot \frac{\theta\_{\text{off}} - \theta\_2}{\frac{1}{2}L\_{\text{max}} - \frac{1}{2}L\_{\text{min}}}\right) = 2T\_{av} \tag{23}$$

According to Eqs. (22) and (23), the peak value of the phase current and the average electro‐ magnetic torque of the failure phase are double of the normal value when working in faulttolerant operation. However, in a closed-loop system, the total average electromagnetic torque is the same as that in the normal state, due to a constant load.

When an open-circuit fault of the drive happens, conventionally, the system still works in the phase absence operation to ensure the continued working ability in a closed-loop system. However, the currents of other normal phases will be larger than the previous one to com‐ pensate the torque output, due to the adjustment of the speed controller. The unbalanced phase current increases the torque ripple and the load capacity also is reduced considerably. When the short-circuit fault of the drive happens, the demagnetization current cannot decrease to zero due to a zero-voltage loop, which causes phase current to become more unbalanced and obviously increases the torque ripple.

Considering the proposed fault tolerance scheme in the CCC system, a half of the failure phase still can be put into use to ensure the torque output. Since the phase current is the control target, it will be regulated to the same reference compared to the normal one, even though a half of the failure phase is removed. In voltage-PWM control strategy, the phase voltage is the control target. The imposed voltage on each phase is the same, regardless of the whole or half of the phase winding works. In order to reduce the unbalanced phase current further in voltage-PWM system, the turn-on angle of the failure phase can be adjusted lagging behind to reduce the increased phase current in the failure winding, as illustrated in Figure 20(b). Hence, the proposed drive topology can be used to compensate the current and torque, and reduce the torque ripple to improve the drive performance in fault conditions.
