Sensorless control of Fault Tolerant PMSM drives in case of single-phase open circuit fault

This paper introduces a new method to track the saliency of a PMSM motor fed by a four-leg inverter in case of a single phase open circuit fault through measuring the dynamic current response of the motor line currents due the IGBT switching actions. In the case of a single phase open circuit fault, a fault-tolerant control strategy that includes taking appropriate actions to control the two remaining healthy currents, resulting in minor system performance degradation. The new strategy introduced in this paper includes software modifications only to the saliency tracking algorithm used in healthy mode to make it applicable to the reconfigured converter in the presence of a fault. The new method uses only the fundamental PWM waveform (i.e there is no modification to the operation of the four-leg inverter) similar to the fundamental PWM method proposed for a three-leg inverter. Simulation results are provided to verify effectiveness of the proposed strategy of saliency tracking of a PMSM motor driven by fault tolerant four-phase inverter over a wide speed ranges under the case of a single phase open circuit fault.


I. INTRODUCTION (HEADING 1)
Tracking the saliency of ac motors fed by two level three-leg inverters has been widely researched for healthy mode systems. At low and zero speed, some form of additional excitation has been proposed, such as the injection of a high frequency (HF) voltage or current [1][2][3] or the injection of test pulses [4][5][6].
In some applications such that in the coiling and spooling textile machines and that of the aerospace and automotive (electric cars) industry, the safety procedures extremely demands a continued operation of the motor drive system after a fault has occurred to reduce the impact of the fault on the system operation. And hence, number of fault tolerant strategies for sensored ac motor drives have been used to enhance the system operation under open phase faults. The fault tolerant strategies proposed [7 ] are based on the connection of either the stator winding neutral point or the motor phase to the dc link middle point of the two level three -leg inverter through a triac . [8] proposed a two level four-leg inverter where the fourth leg is connected to the neutral point of the motor in the case of open circuit phase fault. In [9] the fourth leg is connected to the neutral point in healthy and faulty cases and so 3D space vector modulation is introduced. [10] proposed the switch function algorithm for a four-leg converter to synthesize redefined output waveforms under fault conditions. However, the approaches to track the saliency in the fault-tolerant inverters have received little attention in the literature. This paper proposes a fault tolerant, four-phase inverter PMSM drive topology which can be used to track the saturation saliency in PM motors and rotor slotting saliency in induction motors in the case of single phase open circuit faults in order to maintain a continues system operation with a satisfactory performance to meet the safety procedure for the whole system and increase the reliability of the system. Fig 1 shows the proposed fault tolerant two level four-leg converter drive topology [11]. In this topology, a fourth-leg is added to the conventional three-leg inverter and the redundant leg is permanently connected the motor neutral point to provide the fault tolerant capability in case of an open phase fault. Under healthy operating conditions, the fourth-leg will be redundant which means that the two switches in this leg will be inactivated resulting in no connection between the supply and the motor neutral point. Therefore, the proposed converter normally operates as a conventional two level three-leg inverter. Under faulted operating conditions, the switches on the faulty phase are disabled and the switches in the fourth phase are immediately activated in order to control the voltage at the neutral point of motor. Indirect vector control is employed to control the speed of the motor speed in both normal and faulted operating conditions. Figure 2 shows the vector control structure used for the two level four-leg inverter motor drive under normal operation in sensored mode. The three phase motor currents are transformed to the d-q synchronous rotating frame, id and iq, as given in (1) to compare to the reference values. The reference voltages (vd and Vq) generated from the controller are transformed back using eq 2 to a three phase quantities which then delivered to the space vector modulator to generate the appropriate switching signals for the fault tolerant inverter switches.

A. Normal operating condition in sensored mode
where θ is the rotor angle of the reference frame. I0 is the zero sequence current while In is the motor neutral current as expressed in (1) and (2), respectively. Under normal operation the neutral current is always zero.

B. Open phase fault operation
The modification introduced to the control strategy of the system under open phase fault condition is illustrated in Figure  3 [12]. Firstly, In order to disable the switches in the faulty phase, the reference voltage of the faulty phase is set to zero. In this structure, it is assumed that phase 'b' is opened so the motor current in phase 'b' drops to zero and Vb_ref is set to zero whereas the motor neutral current, which is the sum of the two remaining output currents(Ia and Ic), can circulate through the fourth phase of the inverter. Secondly, by adopting Ib = 0 in (1), it can be seen that in order to keep the motor performance under faulty operation, the rotating MMF obtained from the armature currents(Ia,Ib,Ib) in healthy condition, should be maintained by the two remaining motor currents (Ia,Ic) in the case of open circuit fault that demands an increasing by as well as phase shifting 30 degrees away from the faulted phase compared to the currents generated under normal operation as given in equation 3. (3)

C. Simulation Results
The simulation of four-leg converter PMSM drive has been carried out using SABER. A 5 Nm load torque and a 500 rpm speed command are applied to the system. Figure 4 shows the simulation results of the four-leg converter PMSM drive system under healthy and faulted conditions. It is clear that the controller could regulate the motor speed to follow the reference speed properly under normal operating condition. The controlled currents id and iq are stable at the reference levels while the motor currents are balanced three-phase sinusoidal. The phase 'b' open circuit fault is introduced at the time of 2.5s. As the switches in the fourth leg of the inverter are not activated yet then In=0, and I0=0, and as the sum of three current equals to zero then Ia and Ic currents increase in magnitude with phase shifting 180 degrees with respect to each other . It can be seen in this period significant ripple in Id and Iq in this period which leads to significant ripple in torque and speed. At 3.0s, the switch of the fourth leg are activated which means that the neutral is connected to the supply. The simulation results show that ripple in the torque is significantly reduced and almost the same as under normal operating condition. The currents id and iq are now controlled Properly Where is the average inductance and is the variation of leakage inductance due to the rotor anisotropy ( =2 for saturation anisotropy ) This modulation of the stator leakage inductances will be reflected in the transient response of the motor line current to the test vector imposed by the inverter. So by using the fundamental PWM wave form and by measuring the transient current response to the active vectors it is possible to detect the inductance variation and track the rotor position as shown in [6] for three-leg inverter.
Fig5 SVPWM modulation technique of 3-leg inverter in healthy mode Table 1 Selection of pa, pb and pc in six sectors for a starconnected machine using fundamental PWM method After obtaing the scalar quantities pa , pb and pc then the position of the saliency can be constructed as shown in the equation below:-(7) For four leg-inverter, under the healthy operation, the switches in the fourth leg will not be activated under healthy mode so the algorithm proposed in [6] to track the saliency for three-leg inverter PMSM drive system can be applied for the four-leg inverter PMSM drive system as shown if Fig 6. In open phase fault case, the measurement of the current response (di/dt) associated with the faulty phase will become zero i.e

Pa
Pb Pc

Healthy mode
No neutral connection Neutral connection become zeros as ib=0. Table 1 shows that Pa is obtained using in sector 2 and 5 , Pb is obtained using in sectors 3 and 6 and Pc is obtained using in sectors 1 and 4, which means that these position scalars will be zero in these sectors as seen in fig 6. More over the active vectors V1,V2, and V0 in each sector won't be obtained by applying specific switching actions in phase a,b and c as in healthy case as there won't be any switching action in phase b due to the fault. Hence the tracking saliency algorithm will be incorrect as shown if in Fig 6.

Fig7 SVPWM modulation technique in phase b open circuit fault case
The stator circuit when the vectors V1, V2 and V0 are applied are shown in Fig 8.a, 8.b and 8.c respectively.
Finally when V0 is applied as shown in Fig 8.c, the following equations hold true:- Assuming that the voltage drop across the stator resistances are small and can be neglected and the back emf can be cancelled if the time separation between the vectors is small. Subtracting (10,13) from (11,9)    The estimated position signals Pαβ from the equations selected, are used as the input to a mechanical observer [13] to obtain the speed and a "cleaned" position . Note the simulation includes a minimum pulsewidth of 10us when di/dt measurements are made -a realistic values seen from experimental results of [6]. This estimated speed and position are used to obtain a fully sensorless speed control as shown in   Figure 11 shows the results of a fully sensorless speed control of a PMSM motor driven by a four-leg inverter at loaded conditions using the algorithm proposed in [6] for the healthy  Fig 11 shows that performance of the whole system under faulty condition is in the same level of the performance in healthy mode. Moreover the motor responded to a speed step from 0 to 0.5 Hz at t=10.5 with acceptable transient and steady state performance.