Machine variables.
Abstract
The fault-tolerant capability of multiphase induction motor (IM) drives without adding extra hardware has been an interesting research subject in recent times. Regardless of the application and reliability requirements, fault tolerance is obtained by the software. Although different types of faults may occur, the most considered is the open-phase one which leads to a reduction in the number of active phases in the multiphase drive. Predictive current control (PCC) was recently proposed in the literature for managing the post-fault operation of the drives when an open-phase fault is considered. In PCC, the motor torque is controlled indirectly by controlling the motor current. Predictive torque control (PTC) can control the motor torque directly. However, PTC-based fault tolerant control of a five-phase IM (FPIM) drive has not been published in the literature. Hence, this fault-tolerant capability using the PTC method for an FPIM has been discussed in this chapter. Detail about the modeling of an FPIM, fault detection, and controller for both healthy and faulty conditions of IM has been discussed. The same model of the drive under both healthy and faulty conditions is considered. But the applied cost function is changed in a faulty condition.
Keywords
- five-phase induction motor
- open-phase fault
- fault detection
- fault tolerant control
- predictive torque control
1. Introduction
Since the late 1990s, Multiphase motors are getting gradual popularity over their counterpart three-phase motors in various application fields, especially where critical safety is required, for example, propulsion applications, electric aircraft, electric vehicles, etc. [1]. Multiphase motors can drive the load smoothly, even if one or more phases of the motors are damaged. Among the multiphase motors, the five-phase induction motors (FPIMs) are widely used [2]. They have become a useful replacement for the three-phase motors because of higher reliability, higher power handling capacity without exceeding the current handling capacity of semiconductor switches and insulations, and better torque performance. Although multiphase drives are generally claimed to be ‘fault-tolerant’, this term is somewhat broad since many different types of faults may appear in an electrical drive, including both inverter and machine faults that may lead to short-circuit (phase, inverter switch, inter-turn) or open-circuit (inverter switch, phase or line) faults. Among the aforementioned possible faults, the probability of open-phase fault (OPF) in a drive system is high [2].
Due to the advancement of faster microprocessors, model predictive control (MPC) has received wide attention over existing control algorithms for industrial drives such as field-orientation control (FOC), direct torque control (DTC), and proportional-resonant (PR) control. MPC uses plant models and digital control platforms and allows system constraints and restrictions in a very intuitive way. In different applications of motor drives, MPC is found superior to DTC, FOC, and PR controllers for its increased flexibility and faster torque response [2, 3]. The MPC for FPIM drives has two variants: one is predictive torque control (PTC) and another one is predictive current control (PCC). Both types of MPC can effectively control the torque, flux, and thus speed of the induction motors. In PCC, the motor torque and flux are controlled indirectly by controlling the motor current. On the other hand, in PTC, the motor torque and flux are controlled directly and thus comparatively faster torque response is achieved [3]. A PCC has been recently proposed for managing the post-fault operation of the drives when an OPF is considered [4]. The faulty situation assumes zero stator current while freewheeling diodes can continue conducting in a non-controlled mode. An analysis is presented on the post-fault operation of the five-phase drive when the freewheeling diodes of the faulty phase are still conducting. Another PCC is presented in [5] for a six-phase IM drive and it is reported that PCC misbehaves in a post-fault situation if there is a significant delay in fault detection. The aforementioned PCC approaches need to be reconfigured when a fault occurs. A universal reconfiguration-less PCC approach is presented in [6] and it is shown that the system is naturally fault-tolerant. However, the fault-tolerant capability of an FPIM using PTC has not been stated yet in the literature. In this chapter, the performance of a PTC-based FPIM drive in both healthy and faulty conditions has been discussed.
2. System modeling
The block diagram of the proposed PTC for the FPIM is shown in Figure 1. The motor is fed by a two-level five-phase (2L–5Ф) voltage source inverter (VSI). The inverter is driven by the control signals which are generated by the PTC controller (a variant of MPC). The control system has four sub-sections: FPIM, 2L–5Ф inverter, PTC controller, and fault identification. The reference torque is generated by an outer speed loop and PI controller. PTC uses the measured stator current and dc-link voltage, and also receives the status of the machine whether it is healthy or faulty from the fault identification sub-section to predict the control objectives such as stator current (
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F1.png)
Figure 1.
Block diagram of the proposed fault-tolerant PTC of a five-phase induction motor drive.
2.1 Five-phase induction motor modeling
The FPIM with a squirrel cage rotor has distributed windings that are symmetrically displaced by
Here,
Applying the current-invariant decoupling of Clarke’s transformation, Eq. (2) can be mapped into two orthogonal stationary subspaces,
Considering a sinusoidally distributed magnetomotive force (MMF), uniform air gap, symmetrically distributed windings, minimal magnetic saturation, and core losses, and with the application of a series of voltage equilibrium equations derived from the stator and rotor electromagnetic circuits, the five-phase IM may be represented in a stationary reference frame. Given this information, the functioning of the multiphase machine is defined by Eqs. (4)–(12).
The symbols or variables in Eqs. (4)–(12) have their usual meanings, as shown in Table 1 given in Appendix. Integrating Eq. (9) with respect to time, the rotor angular speed
2.2 FPIM modeling under faulty condition
If a fault occurs in the machine, the controller detects the fault first. Then, the controller reconfigures itself to accommodate the fault and continues to operate the drive under faulty condition. Eq. (13) is verified when the motor drive is in healthy operation. But when an OPF occurs (assume the faulty phase is ‘
Where, [
The new reduced-order Clarke transformation matrix permits the same set of
Several pieces of literature have been published, focusing on different fault-tolerant techniques based on VSD variables (named VSDFD) [4, 8] and observing the phase currents [9]. Reference [8] analyzes the fault occurrence using fault indices that are directly dependent on
Here,
The ratios
When any OPF occurs, the subspace orthogonal voltage components,
2.3 Two-level five-phase inverter
The 2L–5Ф VSI has ten switches (two switches per leg), as shown in Figure 2. The number of total states is 25 = 32 with which two zero vectors and thirty active vectors. The voltage vector expressions in
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F2.png)
Figure 2.
FPIM drive schematic diagram.
where,
The relation between phase voltage
where the switching states of phase
The subspace voltage components produced by a 2L–5Ф VSI are plotted in
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F3.png)
Figure 3.
Voltage vectors (a)
The controller generates the optimum switching signal for the inverter as per the minimization of an objective function. The selected switching signal is then applied to the inverter. The inverter then supplies the required voltage to the induction motor.
2.4 PTC algorithm
The PTC works in three steps: the generation of the available voltage vectors for the inverter, the prediction of control objectives, and the selection of an optimal voltage vector by minimizing a predefined cost function. The number of available voltage vectors for 2L–5Ф inverter is 32 which are 16 if an OPF occurs in any one of the phases. The controller selects an optimum voltage vector by using the discrete mathematical models of the FPIM and inverter. The control objectives such as stator currents (
where
Where,
3. Mode of operation
An FPIM fed by a 2L–5Φ is controlled by the PTC algorithm, and the motor is operated under both healthy and faulty conditions. The parameters of the motor and controller are given in Appendix (Table 3). The performance of the PTC for both healthy and faulty conditions of the motor has been illustrated in the following sub-section.
3.1 Healthy mode
3.1.1 No-load operation
The no-load speed, torque, stator current, stator flux, and fault indices responses under healthy condition are shown in Figure 4. The motor is driven at 500 rpm with no load. The stator flux vector is maintained constant at 0.55 wb. It can be seen that the motor behavior is good. The machine takes only 0.4
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F4.png)
Figure 4.
(a) No-load speed, (b) torque, (c) stator current, (d) stator flux, and (e) fault indices response at no-load under healthy conditions.
3.1.2 Loaded operation
The loading behavior of the drive system is shown in Figure 5. A load of 56% of the nominal load (4.7 N-m) is suddenly applied to the motor at
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F5.png)
Figure 5.
(a) Speed, (b) torque, (c) stator current, (d) stator flux, and (e) fault indices response at 56% of nominal load under healthy conditions.
3.1.3 Speed reversal operation
The speed transient behavior of the motor drive is shown in Figure 6. The motor is driven at 500 rpm, and a reverse speed of −500 rpm is commanded at
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F6.png)
Figure 6.
Speed reversal test (a) speed, (b) torque, (c) current, (d) fault indices response at 56% of nominal load under healthy condition.
3.2 Faulty mode
3.2.1 Fault detection
The behavior of the PTC-based FPIM drive is tested in a faulty condition. Only OPF behavior is considered, and the fault is detected using the VSDFD technique. The machine is driven at 500 rpm with 56% of the nominal load, and the VSDFD algorithm is executed from the beginning when the motor was running in healthy condition. When the machine reaches the steady state, phase ‘
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F7.png)
Figure 7.
Open switch fault detection (a) relation between
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F8.png)
Figure 8.
Zoom-in figure of the fault indices of the marked portion in
3.2.2 Loaded operation
There is a smooth transition from the pre-fault to the post-fault situation of the motor drive, as shown in Figure 9. As the fault is injected in phase ‘
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F9.png)
Figure 9.
(a) Speed, (b) torque, (c) current, (d) fault indices response at 56% of nominal load torque in OPF condition.
However, the
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F10.png)
Figure 10.
(a) Speed, (b) torque, (c) current, (d) fault indices response at 28% of nominal load torque in OPF condition.
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F11.png)
Figure 11.
(a) Speed, (b) torque, (c) current, (d) fault indices response at 70% of nominal load torque in OPF condition.
3.2.3 Speed reversal operation
Figure 12 demonstrates the rated-speed transient behavior of the machine under OPF situation while the machine carries 56% of the nominal load. Figure 12(b) shows that electrical torque is satisfactorily following the reference torque with less ripple. It can also be seen that the stator ‘
![](/media/chapter/a043Y00000vBvn4QAC/a093Y00001eIqF9QAK/media/F12.png)
Figure 12.
(a) Speed, (b) torque, (c) stator current and (d) fault indices response at faulty condition under speed reversal with 56% of nominal load.
4. Conclusions
Predictive torque control (PTC) of a five-phase induction motor (FPIM) with fault-tolerant capability is discussed in this chapter. Both healthy and faulty conditions (i.e. OPF) of the motor drive have been analyzed. The vector space decomposition fault detection (VSDFD) technique is used in PTC to detect the fault. Based on the detected fault, PTC reconfigures its control structure so that it can control the motor in a faulty situation. Basically, the controller sets a new harmonic current reference in the cost function for handling the post-fault situation. The VSDFD algorithm is executed in both healthy and faulty conditions. If there is no fault occurs, the VSDFD algorithm generates an output of zero for each phase, otherwise one. Based on this zero or one output, the controller determines whether it needs to reconfigure itself or not. There are two challenges of a fault detection algorithm that is applicable for multiphase drive: one is fault detection speed and another one is a smooth transition from pre-fault to the post-fault situation. It is shown that the controller can detect the fault within 17 ms which is fast, and this detection time is a fraction of the fundamental current cycle. The proposed PTC can control the motor in both healthy and faulty conditions effectively. Moreover, a smooth transition is maintained from pre-fault to post-fault situations. The controller yields similar speed, torque, stator flux, and stator current responses at any load torque within the rating of the machine in both healthy and faulty conditions. Hence, the proposed PTC for the FPIM drive is fault-tolerant and robust against load disturbance.
Acknowledgments
This research is funded by University Grant Commission (UGC), Bangladesh. I also thank Khulna University of Engineering & Technology (KUET), Khulna, Bangladesh for allowing me to conduct this research.
Appendix
Symbols | Variables |
---|---|
Stator voltage | |
Stator current | |
Rotor current | |
Stator flux | |
Rotor flux | |
Electromagnetic torque | |
Load torque | |
Rotor angular speed | |
Rotor angular frequency | |
Pole pairs |
Table 1.
Factor | Symbols | Expression |
---|---|---|
Total leakage factor | σ | |
Rotor coupling factor | ||
Equivalent resistance ref. to the stator | ||
Transient stator time constant | ||
Leakage inductance | ||
Rotor time constant |
Table 2.
Compact factors used in machine modeling.
Parameter | Value | Parameter | Value | Parameter | Value |
---|---|---|---|---|---|
50 μs | 3 | 300 V | |||
1.09, 38.48 | 681.7 mH | 0.02 kg m2 | |||
15 | 761.63 mH | 0.55 Wb | |||
0.7 | 12.85 Ω | 4.7 N-m |
Table 3.
Controller and machine parameters used in the simulation.
Nomenclature
phase displacement angle
switching state of each inverter leg
DC link voltage
phase voltages
stator and rotor currents
stator and rotor flux
electromagnetic torque
total leakage factor
rotor coupling factor
equivalent resistance ref. to the stator
transient stator time constant
leakage inductance
rotor time constant
rotor angular speed
rotor angular frequency
fault indices
References
- 1.
Riveros JA, Barrero F, Levi E, Duran MJ, Toral S, Jones M. Variable-speed five-phase induction motor drive based on predictive torque control. IEEE Transactions on Industrial Electronics. 2013; 60 (8):2957-2968. DOI: 10.1109/TIE.2012.2198034 - 2.
Bermudez M, Gonzalez-Prieto I, Barrero F, Guzman H, Duran MJ, Kestelyn X. Open-phase fault-tolerant direct torque control technique for five-phase induction motor drives. IEEE Transactions on Industrial Electronics. 2017; 64 (2):902-911. DOI: 10.1109/TIE.2016.2610941 - 3.
Guzman H, et al. Comparative study of predictive and resonant controllers in fault-tolerant five-phase induction motor drives. IEEE Transactions on Industrial Electronics. 2016; 63 (1):606-617. DOI: 10.1109/TIE.2015.2418732 - 4.
Guzman H, Duran MJ, Barrero F, Bogado B, Toral S. Speed control of five-phase induction motors with integrated open-phase fault operation using model-based predictive current control techniques. IEEE Transactions on Industrial Electronics. 2014; 61 (9):4474-4484. DOI: 10.1109/TIE.2013.2289882 - 5.
González-Prieto I, Duran MJ, Rios-Garcia N, Barrero F, Martín C. Open-switch fault detection in five-phase induction motor drives using model predictive control. IEEE Transactions on Industrial Electronics. 2018; 65 (4):3045-3055. DOI: 10.1109/TIE.2017.2748052 - 6.
Barrero F, Bermudez M, Duran MJ, Salas P, Gonzalez-Prieto I. Assessment of a Universal Reconfiguration-less Control Approach in Open-Phase Fault Operation for Multiphase Drives. Energies 2019; 12 :4698. DOI: 10.3390/en12244698 - 7.
Zhao Y, Lipo TA. Modeling and control of a multi-phase induction machine with structural unbalance. IEEE Transactions on Energy Conversion. 1996; 11 (3):578-584. DOI: 10.1109/60.537028 - 8.
Duran MJ, Gonzalez-Prieto I, Rios-Garcia N, Barrero F. A simple, fast, and robust open-phase fault detection technique for six-phase induction motor drives. IEEE Transactions on Power Electronics. 2018; 33 (1):547-557. DOI: 10.1109/TPEL.2017.2670924 - 9.
Chikondra B, Muduli UR, Behera RK. An improved open-phase fault-tolerant DTC technique for five-phase induction motor drive based on virtual vectors assessment. IEEE Transactions on Industrial Electronics. 2021; 68 (6):4598-4609. DOI: 10.1109/TIE.2020.2992018 - 10.
Cortes P, Rodriguez J, Silva C, Flores A. Delay compensation in model predictive current control of a three-phase inverter. IEEE Transactions on Industrial Electronics. 2012; 59 (2):1323-1325. DOI: 10.1109/TIE.2011.2157284