Sensorless Speed Control of a Fault-tolerant Five-phase PMSM Drives

This paper introduces a novel method to achieve sensorless speed control of a Five-phase Permanent Magnet Synchronous Motor (PMSM) drive in case of a single-phase open-circuit fault regardless which phase is open. The motor performance when an open circuit fault occurs is as good as it is before the fault. The degradation in motor performance, when an open circuit fault occurs, is minimized due to implementing a novel control technique that is using the four remaining healthy currents. This strategy includes introducing two software modifications to the operation of the five motor post the fault. Firstly, an asymmetric SVPWM is used post the fault instead of multi-dimension SVPWM that is used before the fault. Secondly, a new algorithm is introduced to track the saliency post the fault. The new algorithm is considering the application of the new modulation technique. Moreover, it uses only the excitation in the healthy currents of the motor due to the IGBT switching actions. Simulation results presented in this paper shows that the performance of the motor over a wide speed range and at different load conditions is maintained post the fault.


Introduction
Multi-phase motor drives are witnessing an increasing interest in research and in the industry in recent years. The multi-phase motors have higher reliability, better efficiency, higher torque density, and lower torque pulsation compared to classical three-phase machines s [1,2]. Due to previous features, multi-phase motor drives are starting replacing three motor drives in the applications such as electrical vehicles, electric craft, electrical ships and high power applications. There are many techniques that are proposed to control five-phase under healthy operating conditions such as scalar control [3], vector control [4], direct torque control [5], model predictive control [6]. And sensorless control [7][8] and multi-dimension SVPWM [9][10][11][12].
To maintain the performance of the five-phase motor drive post the fault, optimal current control is usually employed to control the current in the healthy phases to ensure certain optimization criteria including minimum torque ripples, equal phase currents, and minimum copper losses [13][14][15]. This can be achieved by implementing a fault-tolerant technique post the fault. Fault tolerant techniques can be divided into two primary groups: 1) control system based [16][17][18][19][20] and 2) inverter configuration based [21][22][23][24][25]. Sensorless control of a multi-phase motor drive post an open circuit fault is introduced in [26] only. The novelty in this paper is that it proposes a sensorless-fault-tolerant control technique of a five-phase PMSM drive that enables the five-phase motor to continue operating in the case of single-phase open-circuit fault without introducing and hardware modification. The performance of this drive under an open-circuit fault is at the same quality as the performance under healthy operating condition. This will increase the reliability of the system. Figure 1 shows the topology of the five-phase motor drive used in this work [12]. The five-phase motor can be modeled according to the equations below.
Where represents the fluctuation of the stator inductance and represents the average mutual inductance. The term (2 ) in the above equations represents the saturation saliency. Finally, the flux linking the stator coils due to the rotor magnets are:

Normal operation of a five-phase drive
The classical space vector pulse width modulation technique that is used in a three-phase motor drive can't be applied in five-phase motor drive. This is due to the fact that this modulation technique will generate voltages at the output of the five-phase inverter that has a third harmonic component. This third harmonic voltage component will generate a third harmonic current component that does not produce any rotating MMF (not electro-mechanical energy conversion related). And so, even the inverter generates a very small third harmonic voltage, a large third harmonic component will be circulating in the motor stator windings. It is, therefore, important that the five-phase inverter output is kept as close as possible to sinusoidal i.e the third harmonic component in the output voltage of the inverter should be controlled to zero. This can be done by mapping the reference voltage into two orthogonal planes either stationary (α1-β1 and α3-β3) or rotating at synchronous speed and 3 times the synchronous speed (d1-q1 and d3-q3) respectively [9][10][11][12].
This allow controlling the fundamental and the third harmonic components of the voltage generated by the inverter independently as shown in Figure 2. Figure 3 illustrates the multi-dimension SVPWM modulation technique. In this example, the reference voltage V_ref exists in the third sector. The mapping of V_ref into the α1-β1 plane and into the α3-β3 is illustrated. Then the adjacent vectors (00000, 01000, 01100, 11100,11110, 11111) are used to generate the fundamental and the third component of the reference voltage.

Post-fault operation of a five-phase drive
Vector control of five-phase motor drive under healthy condition guarantees equal magnitudes of the stator currents and equal phase shifts of 2 5 between them. If an open-circuit fault is introduced to one phase of the five-phase motor then the remaining healthy phases are usually controlled to ensure equal stator phase currents, minimum machine torque ripples and maximum torque production and nullifying the fundamental negative sequence [24,25]. This done by shifting the two healthy stator currents adjacent to the faulted current by 5 and making the amplitudes of all healthy currents to equal `138.2% as shown in Figure 4. Asymmetric SVPWM To maintain the operation of a five-phase motor drive post the fault, the asymmetric SVPWM method is used [18]. This method is based on obtaining a new space vector diagrams that consider the change in amplitude and phase angle of the remaining healthy currents post the fault as shown in figure 5.a, figure  5 Figure 6 shows the reference voltage (Vref_ α-β) that exists in the second sector in space vector diagram 5.c. All the adjacent vectors (V3=0010, V12= 0011, V7=0111 , V0=1111) are used to generate the reference voltage (V_ref) as shown in figure 6. The dwell times can be obtained as follows:-= * cos ( ) (7) , = * sin ( ) (8) , 1 = * sin (   If an open-circuit fault is introduced to any phase of the motor, the asymmetric SVPWM is applied using a switch. The results from the above test are shown in figure 8. The motor was loaded by 50% and running at 100 rpm in the healthy condition. In time interval (2s-3s) an open circuit fault is introduced to phase 'a' and at the same time, an asymmetric SVPWM was applied. Figure 8 shows that the stator current in phase 'a' became zero. In addition to that, the magnitudes of the currents in phases 'b','c','d', and 'e' were increased by 38.2% and the phase currents in phases 'b' and 'e' are shifted by 36 0 towards phase 'a'. these results are identical to those shown in figure 4. Similar results can be obtained in intervals (4s-5s),(6s-7s),(8s-9s) and (10s to 11s) where an open-circuit faults in phases 'b', 'c', 'd'and 'e' were introduced to the operation of the motor respectively and at the same time an asymmetric SVPWM were applied. Outside these intervals, the fault was removed and the motor returned to run in healthy operating conditions using multi-dimension SVPWM. The results show that the quality of the performance of the system is maintained during the faults.

Post-fault algorithm for tracking the saliency
The algorithm that is proposed in [7,8] to track the saturation saliency of a five-phase motor drive running under healthy operating conditions is no longer valid to be applied in case of an open-circuit fault as shown in figure 9 . In time intervals when the motor was running in normal operating conditions, the algorithm proposed in [7,8] worked fine and the saturation saliency could be tracked. Unfortunately, this was not the case post the fault as shown in time intervals (2s-3s),(4s-5s),(6s-7s),(8s-9s) and (10s-11s). In these time intervals the position scalars pa,pb,pc,pd and pe were corrupted and the saliency position couldn't be obtained from them anyway.
To illustrate the above results an example is considered in which the motor running is running under the condition where phase 'a' is lost and the reference voltage exists in sector four as an example. According to [7,8]  . From these equations, it is clear that in order to obtain p , the dynamic responses of phase'a' due to applying V4 and V0 should be used while these values are zero since an open-circuit fault is introduced to phase 'a'. And Hence p will be zero. Similar results will be obtained in different sectors and different faulted phases because this method is proposed to work in healthy mode when all the currents are healthy. To obtain the saliency position in a five-phase PMSM drive post the fault, a new equivalent circuit for the motor should be considered that reflects the loss of one phase of the five motor in addition to use Asymmetric SVPWM . Figure 10 shows the Asymmetric SVPWM for a five-phase inverter post a fault in phase 'a' and when V_ref exists in the fourth sector. The PWM waveforms are shown in Figure 10.   Using the circuit in Figure 11.a and 11.b, the following equations hold true. [ − ( 0) ) * ( ( 2) − ( 0) ) * ( ( 2) − ( 0) ) * ( Where , , , are the stator leakage inductances and , , , are the back emf. The following equations are obtained using Figure 11.b and Figure 11.c:- − ( 11) ) * ( ( 6) − ( 11) ) * ( ( 6) − ( 11) ) * ( The following equations are obtained using Figure 13.b and Figure 13.c:- − ( 12) ) * ( ( 7) − ( 12) ) * ( ( 7) − ( 12) ) * ( − ( 12) ) ] + [ ( 7) − ( 12) ( 7) − ( 12) ( 7) − ( 12) ( 7) − ( 12) ] (21) Assuming that the voltage drop across the stator resistances are small and the back emf can be neglected providing the time separation between the vectors is small, the following equations can be obtained using vector V0, V3,V12 and V7: -  [7,8] is used to track the saliency under healthy conditions while the technique proposed in this paper is used to track the saliency in five-phase PMSM motor post the fault. Figure 14 shows that the saliency of the PMSM motor pre and post the fault can be tracked with a good in both conditions.

Sensorless Speed Control
The control scheme to achieve a fully sensorless control of a five-phase PMSM is shown in figure 15. In this control scheme, the algorithm proposed in [7,8] was used to track the saliency during normal operation ( position estimator under healthy condition block) while the algorithm proposed in this paper was used to track it post the fault (position estimator under faulty condition block). These two algorithms generated position signal scalars of the saliency (Pαβ) that were noisy and hence a mechanical observer [27] was used to obtain a filtered speed signal ^ and a filtered position ^. And to make the simulation realistic, a minimum pulse width of 10us when di/dt measurements were made. The outputs of the mechanical observer were then used to obtain in sensorless vector control as shown in figure 15. Figure 16, figure 17 and figure 18 show results of a different tests done on the five-phase PMSM motor at different conditions pre and post the fault. In figure 16, the motor was working in normal operating conditions and in sensorless mode at 30 rpm. A time t=3s, an open-circuit fault was introduced to phase 'a'. Then a speed step command from 30 rpm to 0 at time 4s was applied to the motor while phase 'a' was opened. The motors responded to this step command. While the motor was running at zero speed and at time t=5s, the fault was removed from phase'a' and the motor returned to works in healthy operating conditions. At time t=7s, a singlephase open-circuit fault was introduced to phase'b'. After that, at time t=8s a speed command from 0 to -30 rpm was applied to the motor. Figure 16 shows that the performance of the whole system pre and past the fault was the same. Figure 17 demonstrates the ability of the motor to response to high speed command steps (from 0 to 300rpm and from 300 rpm to -300 rpm) post the fault with performance quality equals to that in healthy condition.