Sensorless Control of a Fault Tolerant Multi-level Inverter PMSM Drives in Case of an Open Circuit Fault

This paper introduces a fault tolerant multi-level inverter PMSM Drive that is capable to work in case of a single phase open circuit fault without degrading the system performance. Moreover, it can work in sensorless mode in case of an open circuit fault with the same performance as in sensor mode. The permanent magnet synchronous motor (PMSM) is fed by a 4-leg asymmetric cascaded H-Bridges multi-level inverter. The fourth leg is activated in case of an open circuit only to maintain the system performance. The reliability of the system is additionally enhanced by adopting a new method to track saliency position in case of an open circuit fault to make the system work in sensorless mode. The saliency position is obtained through measuring the dynamic current response of the healthy motor line currents due to the insulated-gate bipolar transistor (IGBT) switching actions. The new strategy includes software modifications only to the saliency tracking algorithm used in healthy mode in order to make it applicable to the reconfigured multi-level inverter in the presence of a fault. It uses only the fundamental pulse width modulation (PWM) waveform (i.e. there is no modification to the operation of the 4-leg multi-level inverter), similar to the fundamental PWM method proposed for a 3-leg multi-level inverter. Simulation results are provided to verify the effectiveness of the proposed strategy over a wide range of speeds in the case of a single-phase open circuit fault.


I. INTRODUCTION
Sensorless control of motor drives using 2-level converters has been widely researched for systems employing standard two-level converters [1][2][3][4][5][6]. These techniques introduce a significant additional current distortion which causes audible noise, torque pulsations and increases the system losses. In the other hand, a Multi-level converter can achieve a higher voltage and power capability with conventional switching devices compared to 2-level converter and is now used for high power drives [7,8,9]. The particular structure of some of these converters offers significant potential for improving sensorless control of motors, as they employ H-bridge circuits with a relatively low DC link voltage. [10][11][12] are introducing different techniques to achieve sensorless control of multi-level inverter drives in healthy mode i.e no open circuit fault. Under faulty conditions, a number of fault-tolerant strategies to control 2level motor drives [13][14][15][16][17][18] and multi-level motor drives [19][20][21][22] have been used to enhance system operation under open circuit phase faults in sensor mode. [23,24] introduced a 4-leg 2-level (PMSM) drive to track the saturation saliency in the case of single-phase open circuit faults. This paper is introducing a new method to track the saturation saliency in a surface mounted permanent magnet motor in case of an open circuit fault. This motor is driven by a 4-leg multi-level inverter. The objective is to maintain continuous system operation with a satisfactory performance to meet the safety procedure for the whole system and increase the reliability of the system.

II. RESEARCH METHOD
A. Fault tolerant multi-level four-leg converter drive topology Fig 1 shows the proposed fault tolerant multi-level 4-leg converter drive topology. In this topology, a fourth leg is added to the conventional 3-leg multi-level inverter. 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 multi-level three-leg inverter as shown in fig 2. Under faulted operating conditions, the switches on the faulty phase are disabled and the switches in the fourth leg are immediately activated in order to control the voltage at the neutral point of the motor.

B. Healthy operation of the multi-level inverter
The control strategy of the system in sensored healthy mode is illustrated in Figure 2. The reference voltages that are calculated from the controllers are used to generate pulses to control the multi-level inverter through Space Vector Pules Width Modulation Technique (SVPWM).
The multi-level SVPWM technique that is adopted in this paper is given in [8]. According to this technique the switching sequence will be one of four types as illustrated in Fig 3 ( Figure  7 in the case that an open circuit occurs in phase be as an example [18,23]. Firstly, in order to disable the switches in the phase b, the reference voltage of the faulty phase Vb_ref is set to zero whereas the motor neutral current, which is the sum of the two remaining output currents can circulate through the fourth phase of the multi-level inverter. Secondly, as the current in the faulty phase becomes zero (Ib=0), and in order to maintain the motor performance under faulty operation, the rotating magnetomotive force obtained from the armature currents (Ia, Ib, Ib) in the healthy condition should be maintained by the two remaining motor currents (Ia and Ic) in the case of an open circuit fault that demands an increase of √3 as well as phase shifting 30 degrees away from the faulted phase compared to the currents generated under normal operation, as given in Eq. (1). If the fault is occurred in other phase, the same algorithm will be applied. [ 0] = [ √3cos(θ + 30) √3sin(θ + 30) −cos(θ − 120) −sin(θ − 120) √3 cos(θ + 90) √3 sin(θ + 90) ] [ ] (1) The simulation of a 4-leg multi-level converter PMSM drive was carried out using SABER. Figure 8 shows the simulation results of a 4-leg multi-level inverter PMSM drive system under healthy and faulted conditions. The motor was driving a 30 Nm load torque at 300rpm speed. Then speed step commands from 300 rpm to 1100 rpm back to 300 rpm were applied at times 2s, 3s, 4s, 6s, 7s, and 8s to the motor. In time intervals between 2.5s to 3.5s an open circuit phase fault was introduced to phase 'a' while an open circuit in phase 'b' was introduced in time interval between 4.5s to 5.5s. Finally, in time interval between 6.5s and 7.5s the open circuit fault was introduced to phase 'c'.. It is clear that the controller could regulate the motor speed to follow the reference speed properly under faulted conditions as well as under normal operation. The controlled currents id and iq were stable at the reference level. Under faulted conditions, the amplitude of the motor currents was multiplied by √3 and the two remaining healthy currents became phase shifted by 60 o while the neutral currents was no longer zero as given in eq (1). For the rest of the test, i.e under healthy condition, The motor currents are balanced 3-phase sinusoidal and the neutral current is zero.. The simulation results show that ripple in the torque is almost the same as that exist under normal operating conditions.
Where 0 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 waveform and by measuring the transient current response to the active vectors it is possible to detect the inductance variation and track the rotor position for three-leg multilevel inverter. After obtaing the scalar quantities pa, pb and pc then the position of the saliency can be constructed as shown in the equation below:p ⃗ = p α + β = p a + b + a 2 p c (5) Fig 9 shows simulation results for tracking the saturation saliency (2fe) in a SMPM under faulted condition as well as under healthy condition. The motor is driven by a four-leg multi-level inverter. The algorithm that is used in this test track the saliency is proposed in [12] where it is used track the saliency of the SMPM motor driven by a three-leg multilevel inverter under healthy operation. The results shows that under health operating conditions, the algorithm that is used in [12] for three-leg multi-level inverter drive could track the saturation saliency efficiently at different speeds while it couldn't track the saturation saliency under faulted operating conditions i.e in time intervals (2.5s to 3.5s), (4.5s to 5.5s) and (6.5s to 7.5s). This results can be explained as follows: under healthy operating conditions, the switches in the fourth leg will not be activated and hence the four-leg multi-level inverter will operate as a three-leg multi-level inverter so the algorithm proposed in [12] could track the saliency. In time interval (2.5s to 3.5s) i.e open phase fault in phase a, the measurement of the current response (dia/dt) will become zero as ia = 0. And so the position estimation algorithm couldn't track the saliency in this time interval. Also between 4.5s and 5.5s i.e open phase fault in phase b and between 6.5s to 7.5s i.e open phase fault in phase c, the measurements of the current responses (dib/dt) and (dic/dt) will become zeros and hence the algorithm couldn't track the saliency in those time intervals as shown in Figure 9.

E. Tracking Tracking the Saliency in Multilevel Inverter under unhealthy condition
As seen in previous section, the algorithm presented in [12] couldn't track the saliency under the case of an open circuit fault. In this section a modified algorithm is introduced to track the saliency in case of an open circuit fault. This algorithm is making use of the switching action of the IGBTs in the fourth leg of the multi-level inverter under faulted conditions. It uses the current response of application of fundamental PWM waveform (no modification applied to the PWM waveform). The new algorithm uses only the current response of healthy phases to track the saliency and doesn't use the current response of the open circuit phase as it will be zero. After measuring the current response of the two healthy phases and according to the sector number and the type of the space vector modulation state diagram that the reference voltage exist in, the three position scalars quantities can be deduce and hence the saliency position can be obtained.  The stator circuit when the vectors V1, V2 and V0 are applied are shown in Fig 11.a, 11.b and 11.c respectively.
The following equations are obtained using Fig 11.b:-0 = * ( 2) + * ( 2) Finally when V0 is applied as shown in Fig 11.c, the following equations hold true:-0 = * ( 0) + * 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 equation (8) from equations (6) and equation (11) from equation (9) respectively yields:- − ( 1) ) (12) , V DC = * (

F. Fully sensorless speed control of 4-leg multilevel inverter under unhealthy condition
The speed control for a PM machine have been implemented in simulation in the SABER modeling environment. The estimated position signals Pαβ from the equations selected are used as the input to a mechanical observer [25] to obtain the speed ω^ and a cleaned position θ^. Note that the simulation includes a minimum pulse width of 10 mu s when di/dt measurements are made, similar to the experimental results of [6]. This estimated speed ω^ and position θ^ are used to obtain a fully sensorless speed control as shown in Figure 13.

Fig 12
The algorithm to track the saliency in of multilevel inverter using the fundamental PWM algorithm given in [12] for helathy mode and the algorithm presented above for unhealthy condition.  Figure 14 shows the results of a fully sensorless speed control of a PMSM motor driven by a 4-leg multi-level inverter at loaded condition using the algorithm proposed in [12 ] for the healthy case and the method proposed above in the case of an open circuit fault. The motor was working in sensorless healthy mode at speed=0.5 Hz then at time t=4 s an open circuit fault in phase 'a' is introduced to the system. The motor maintained its performance after the fault. At t=6s a speed step change from 0.5 Hz to 0 Hz is applied to the system while the motor was under open circuit fault in phase 'a'. Figure 14 shows that the motor responded to the speed step with a good transient and steady state response. When t=8s, the fault in phase 'a' is removed and introduced to phase 'b', Figure 14 shows the motor was tracking the zero reference speed during this time. At t=12s, the fault is removed from phase 'b' and introduced to phase 'c'. After that, when t=14s, a speed step change from 0 rpm to -0.5 Hz is applied to the system while the motor was working under open circuit fault in phase 'c'. Figure 14 shows that the motor responded to the speed step with good transient and steady state response. Finally, at t=16s, all the faults are removed and the motor returns to healthy condition. Figure 15 shows similar results to those shown in Figure 14 of but at higher speed steps (16. Figure 15 shows that the motor responded to the speed step with a good transient and steady state response. When t=8s, the fault in phase 'a' is removed and introduced to phase 'b', Figure 15 shows the motor was tracking the zero reference speed during this time. At t=12s, the fault is removed from phase 'b' and introduced to phase 'c'. After that, when t=14s, a speed step change from 0 rpm to -16.67 Hz is applied to the system while the motor was working under open circuit fault in phase 'c'. Figure 15 shows that the motor responded to the speed step with good transient and steady state response. Finally, at t=16s, all the faults are removed and the motor returns to healthy condition. III. CONCLUSION This paper has outlined a new scheme for tracking the saliency of a motor fed by a 4-leg multi-level inverter in the case of a single phase open circuit fault through measuring the dynamic current response of the motor line currents due to the IGBT switching actions. The proposed method includes software modification to the method proposed in [12] to track the saliency of the motor under healthy conditions to make it applicable in the cases of open circuit phase condition. The new strategy can be used to track the saturation saliency in PM motors (2 fe) and the rotor slotting saliency in IMs (14*fr) similar to the method used in a healthy motor drive and the only difference between the PM and IM will be the tracked harmonic number. The results have shown the effectiveness of the new method in increasing the safety measures in critical systems that need continuous operation. The drawbacks of this method are increasing the total harmonic distortion of the motor's current, specially at a very low speed, due to the minimum pulse width in addition to the need for 3 di/dt sensors.