Stator Field-Orientation Speed Control for 3-Phase Induction Motor Under Open-Phase Fault

Mohammad Jannati*, Tole Sutikno, Nik Rumzi Nik Idris, Mohd Junaidi Abdul Aziz 1 UTM-PROTON Future Drive Laboratory, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 Skudai, Johor Bahru, Malaysia 2 Department of Electrical Engineering, Faculty of Industrial Technology, Universitas Ahmad Dahlan, Janturan, Umbulharjo 55164, Yogyakarta, Indonesia *Corresponding author, e-mail: Jannatim94@yahoo.com


Introduction
In some critical industrial applications such as aircraft and electric vehicle (EV). It is necessary to continue induction motor (IM) drive operation under fault conditions [1]. Generally, faults in IM drives can be classified as: fault in the inverter [2], fault in the sensors [1], [3] and fault in the electrical machine including stator and rotor faults [4]- [6].
Open-phase fault in stator windings of 3-phase IM is the most common type of faults in electric drives. This condition occurs because of the failure of one stator phase connection, inverter faults mitigated by using fuses [7], [8]. The conventional controller which is used for 3phase IM drives cannot be able to work during fault conditions. If a conventional controller for healthy IM is applied to the faulty machine, oscillations in the motor torque and speed can be observed [9]- [11]. For this reason, an appropriate control algorithm is needed to control faulty machine.
In all pervious works, using transformation matrices, a modified control system for faulty machine has been presented. These transformation matrices, which are used to modify the FOC algorithm leads to system complexity. The main objective of this research is to expand stator field-oriented control (SFOC) technique for 3-phase IM which can be also adopted for 3phase IM under open-phase fault. Differently from the previous papers presented in [7]- [13], the proposed control drive system in this research do not used transformation matrices. This paper is organized as follows: In part 2, d-q model of faulty machine is shown. In part 3, the proposed idea for SFOC of faulty IM is presented. The MATLAB simulation results are shown in part 4 and part 5 concludes the paper.

Machine Model
Neglecting the core saturation, the dynamic behavior of the 3-phase IM under openphase fault can be described by the following equations [9], [14]: The superscript "s" in the variables of (1)- (4) indicates that the motor variables are in the stationary reference frame. Variables v s ds , v s qs , i s ds , i s qs , i s dr , i s qr , λ s ds , λ s qs , λ s dr and λ s qr are the d-q axes voltages, currents, and fluxes of the stator and rotor. r s and r r denote the stator and rotor resistances. M d , M q and L r denote the stator, the rotor self and mutual inductances. r s and r r are stator and rotor resistance.  r is the motor speed. τ e , τ l , J and F are electromagnetic torque, load torque, inertia and viscous friction coefficient. Re-writing the model (1)-(4) by removing some asymmetries is useful for vector control applications. A transformation matrix for the stator variables is defined as: This should be applied as follows: The term (3L qs -L ds ) in equation (11) is almost zero (3L qs -L ds =3L ls +1.5L ms -L ls -1.5L ms =2L ls ≈0) and consequently, equation (11) will provide balanced stator fluxes. With respect to (10) it must be noted that besides the influence of stator flux, v ds1 and v qs1 are unbalanced due to 2r s . The influence of 2r s cannot be ignored at medium or low speed. Note that, differently from the faulty model given by (1)-(5), equations (8)- (12) are useful in deriving the vector control approaches, as shown in section 3.

Stator-Flux Control
Calculation of machine torque as a function of stator currents and stator fluxes can be achieved by using (10) and (11), and it can be written as follows: indicates that the variables are in the synchronous reference frame). Based on this assumption, the SFOC equations for faulty 3-phase IM can be represented as (14)-(16) [15], [16].  (16) in which,

Direct Stator Field-Oriented Control
Based on the vector model given by (14)- (17), Figure 1 can be proposed for direct stator field-oriented control of both healthy and faulty 3-phase IM. In Figure 1, the red arrows show the parts of the conventional vector controller that require to be modified for controlling faulty machine as shown in Table 1. In Figure 1, |λ s1 * | and τ e * represent the desired amplitude of the stator flux and electromagnetic torque, respectively. The block e jθst* , transfer motor variables from coordinate reference frame aligned along with the stator flux vector to the stationary reference frame. Furthermore, i ds s* and i qs s* represent the reference d and q currents supplied to the stator current controllers, which must be imposed on the motor windings. Block CC+VSI+IM represents the current controller, the voltage source inverter, and the induction motor.

Indirect Stator Field-Oriented Control
Based on the vector control model for healthy 3-phase IM (equations (14)- (17)), the stator d and q axis currents and electromagnetic torque of machine can be written as following equations: Using these equations, Figure 2 can be proposed for indirect stator field-oriented control of both healthy and faulty 3-phase IM.

Simulation Results
Two control strategies for healthy and faulty 3-phase IM was studied by simulations (MATLAB software). Selected results are shown in Figure 3 and Figure 4. In both cases, the 3phase IM started in the healthy condition and without load, and then at t=0.5s a step load equal to 0.5N.m is applied. After that, at t=1s, a phase cut-off fault is happened in phase "c". After that at t=3s the value of load is changed to 2N.m. In Figure 3, a conventional control system for healthy and faulty 3-phase IM has been simulated. In Figure 4, the proposed control system based on Figure 2 for healthy and faulty 3-phase IM has been simulated. These results were obtained with a machine fed by PWM-VSI. In this paper, very fast fault detection is assumed as considered in [17]. In the simulations, the reference for the motor speed and stator flux is considered 400rpm and 1wb respectively. The simulated 3-phase IM parameters are listed in Table 2. As shown in Figure 3 and Figure 4, in the healthy situation, both conventional and proposed controller show good tracking performance and fast response. Simulation results of Figure 3 show that the real IM speed cannot follow the reference speed properly in the faulty mode (see Figure 3 (e)). In this case and after open-phase fault, the electromagnetic torque waveforms have many oscillations. As shown in Figure 3  Simulation results of Figure 4 demonstrate that using proposed drive system, the real IM speed can track the reference speed even under fault and under load. In Figure 4, the stator and rotor currents waveform show that the machine currents are nearly sinusoidal in both healthy and faulty conditions. Furthermore, using proposed controller, the electromagnetic torque waveforms contain low oscillations even in the faulty mode.  In this case as shown in Figure 4 (d), using proposed controller the oscillations of electromagnetic torque in the healthy condition is about 0.02N.m and in the faulty condition and is about 0.3N.m. It is shown that the proposed ISFOC controller for vector control of healthy and faulty machine has a good speed control and sufficient vector control characteristics.