Five-phase Permanent Magnet Synchronous Machine Research Articles

Design and Optimization of a Five-Phase Permanent Magnet Synchronous Machine Exploiting the Fundamental and Third Harmonic

This paper deals with the design of five-phase permanent magnet synchronous machines (PMSMs) exploiting the third harmonic for torque generation. Through the optimization of the stator size and rotor structure, the objective functions related to mass and electric losses are minimized for a targeted electromagnetic power (10 kW and 400 rpm) and a given volume. The study takes into account saturation, thermal, electrical and mechanical constraints. On that note, a 1D analytical magnetic model, considering the existence and use of the third harmonic, is presented. The design optimization then shows how the use of harmonic 3 can improve the machine’s performance. It will be shown that, for a given electromagnetic torque, taking the third harmonic into account in the sizing process leads to a mass reduction that can reach 20% and electrical losses that can go up to 21%. A finite element analysis model of the five-phase PMSM is then established in order to verify the results of the optimization and validate them.

Effects of harmonics and voltage unbalance on the behavior of a five-phase permanent magnet synchronous machine

Effects of harmonics and voltage unbalance on the behavior of a five-phase permanent magnet synchronous machine

Model of Five-Phase Permanent Magnet Synchronous Machines Including the Third Harmonic of the Airgap Induction

Model of Five-Phase Permanent Magnet Synchronous Machines Including the Third Harmonic of the Airgap Induction

A high-fidelity model for FPMSM considering spatial harmonics, mutual inductance, and load change

In this paper, a high-fidelity and computationally efficient model for five-phase permanent magnet synchronous machines (FPMSMs) is proposed. The nonlinear machines parameters in the fundamental subspace and 3rd subspace are accurately modeled. The spatial harmonics related to rotor position, the mutual inductances between d–q axes and subspaces, and the flux saturations changing with current vector variations are considered. The proposed model is compared with finite element analysis (FEA) results and existing modeling techniques. It is shown that the proposed method can model the FPMSMs with higher accuracy compared with the state-of-the-art methods.

Decoupled Modulation Scheme for Harmonic Current Suppression in Five-Phase PMSM

Harmonic currents always exist in a five-phase permanent magnet synchronous machine due to some disturbances. This letter proposes a unique modulation scheme to synthesize the control voltage in the harmonic subspace, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> -space, to suppress harmonic currents actively. The advantage of the proposed modulation scheme is that it is decoupled from the modulation process in the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> -space, thereby not affecting the torque output or <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dq</i> -axis currents. First, according to the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">αβ</i> -space control voltage reference, the action time ranges of two large and two middle voltage vectors adjacent to the control voltage reference are determined. Second, the ranges are divided into several segments equally. Then, the best action time is selected from these segments to generate a proper control voltage in <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">xy</i> -space. Finally, the switching pattern of the inverter is designed with the selected action time. Experiments have been implemented to verify the effectiveness of the proposed modulation scheme.

Analysis and fault-tolerant control of inter-turn short-circuit fault for five-phase permanent-magnet synchronous machine

For the demand of high reliability in the aerospace field, multi-phase electric machines have become a research hotspot for the fault-tolerant ability. Inter-turn short-circuit fault is one of the main fault forms in the electric machine. The fault mechanism, diagnosis method and fault-tolerant control strategy of inter-turn short-circuit fault of the open-winding five-phase permanent-magnet synchronous machine that is used as the starter/generator system are studied in this paper. Firstly, the fault mechanism of the inter-turn short-circuit fault (ITSCF) is analyzed. The characteristics of phase voltage, inter-turn short-circuit current and torque ripple are compared using the phase winding open-circuit method and the phase winding short-circuit method. Secondly, a fault diagnosis method based on the information fusion is proposed, which determines the fault phase firstly and then identifies the inter-turn short-circuit ratio. According to the fault mechanism, a fault-tolerant control method is proposed, in which the accurate inter-turn short-circuit ratio and inter-turn short-circuit current are not required. The proposed fault-tolerant control method has similar torque ripple compared with the control method using accurate inter-turn short-circuit ratio and inter-turn short-circuit current. Finally, the effectiveness of the proposed fault-tolerant control method has been verified by experimental results.

Short-Circuit Fault-Tolerant Control Without Constraint on the D-Axis Armature Magnetomotive Force for Five-Phase PMSM

In this article, we investigate the short-circuit (SC) fault-tolerant control (FTC) method for a five-phase permanent-magnet synchronous machine (PMSM) with surface-mounted permanent magnets. By relieving the constraint of zero <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> -axis armature magnetomotive force (MMF) and restraining the backward-rotating MMF components to be zero, round-rotating armature MMF with maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</i> -axis armature MMF is achieved, which enables five-phase PMSM to output maximum smooth torque with lower losses and higher efficiency under SC fault condition. To ensure smooth postfault operation in full-speed range, the influence of winding resistance on SC current is further considered, which improves low-speed operation performance. The proposed FTC method features sinusoidal currents with equal amplitude, which ensures better control simplicity and postfault thermal uniformity between phases. The finite-element analysis and experiments are carried out to verify the proposed method.

Compensation Strategy Based on Rotating Rhombus Method for Five-Phase PMSM With One-Phase Terminal Short-Circuit Fault

Based on the rotating rhombus method (RRM), an equal-magnitude sinusoidal current compensation strategy is proposed to improve the post-fault performance of the five-phase permanent-magnet synchronous machine (PMSM) with short-circuit fault. RRM is a graphic method which is proposed to obtain optimal compensation currents, and the equal-magnitude phase currents are treated as rhombic current vectors. To maintain the same magnetomotive force (MMF) under fault condition, the geometric relations of a rhombus are used to derive phase angles of the compensation currents. The effectiveness of the proposed strategy is verified by a 10-slot/8-pole five-phase PMSM, and the torque ripple caused by short-circuit fault is significantly reduced. In addition, the proposed strategy is compared with an existing strategy from aspects of torque, torque ripple, losses, and efficiency, and the proposed strategy has advantages of balanced copper loss of the healthy phases and lower inverter cost.

High Efficiency and Quick Response of Torque Control for a Multi-Phase Machine Using Discrete/Continuous Approach: Application to Five-phase Permanent Magnet Synchronous Machine

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Fault-Tolerant Control Strategy for Five-Phase PMSM Drive System With High-Resistance Connection

High-resistance connection (HRC) fault can result in increased copper loss, thus possibly causing damage to the electric machine drive system. Therefore, a fault-tolerant control strategy is proposed for a five-phase permanent magnet synchronous machine drive system with HRC to minimize the copper loss. The fault-tolerant control strategy is realized based on the magnetomotive force invariance principle and copper loss minimization principle. The simulation and experiment are carried out to quantitatively validate the effectiveness of the proposed fault-tolerant control strategy. Both the simulation and experimental results show that the proposed strategy can effectively reduce the copper loss caused by the HRC fault.

Optimum Design of Fractional Order PIᵅ Speed Controller for Predictive Direct Torque Control of a Sensorless Five-Phase Permanent Magnet Synchronous Machine (PMSM)

In both direct torque control (DTC) and predictive direct torque control (PDTC) strategies, just single voltage vector is applied. The question arose, is this applied vector the optimumin terms of minimizing torque and stator flux ripples? In DTC, it may not be the optimum one. However, in case of PDTC, there is a possibility to evaluate the performance of different voltage vectors, where a cost function is proposed to determine the appropriate voltage vector that brings the lowest torque and stator flux ripple within one cycle. On the other hand, PI controller provides a good performance but if the parameters change, the system may lose its performance. With the aim of enhancing the robustness of the PDTC scheme, a fractional order PI controller is proposed that can be considered as a generalization of the classical PI controller, and to set its parameters, a Grey Wolf Optimization algorithm is employed. Furthermore, omitting the sensor increases reliability and decrease the size and cost of the drive system. For these reasons, an extended Kalman filter observer is adopted, where the rotor speed and rotor position as well as the load torque are estimated. In this work, a fractional order PI controller tuned by GWO for PDTC of a five-phase permanent magnet synchronous machine (PMSM) based on EKF observer is presented. Analysis of simulation results exhibit clearly the efficiency and robustness of the suggested control compared to conventional DTC based on classical PI controller.

Low-Complexity Deadbeat Model Predictive Current Control With Duty Ratio for Five-Phase PMSM Drives

Model predictive control (MPC) is considered as a promising control strategy for power electronic converters and drive systems due to its merits of simplicity, fast-dynamic response, and multi-variable control flexibility. However, the variable switching frequency and the large computational burden represent serious problems for applying MPC in high-power multi-phase converters and drive systems. This article introduces a low-complexity model predictive current control (MPCC) for five-phase permanent magnet synchronous machine (PMSM) with constant switching frequency based on the deadbeat (DB) principles. To avoid the full enumeration process, the proposed method calculates the reference voltage vector using the DB technique, considering one-step delay compensation. The information of the reference voltage is used to select the best approximation for the reference voltage from the enhanced control set with virtual voltage vectors (V3), which eliminate the third-harmonic phase voltage and phase current components. Moreover, the optimal duty ratio is calculated to fit the selected voltage vector on the reference voltage vector. The proposed control strategy is compared with three existing MPC techniques. The effectiveness of the proposed MPCC strategy is validated using MATLAB simulation and hardware-in-the-loop results.

Hybrid control of five-phase permanent magnet synchronous machine using space vector modulation

This paper aims to study the hybrid control of a five-phase permanent-magnet synchronous machine improved by the space vector modulation (SVM) technique. The torque ripples and currents will therefore be reduced. This control is based on the theory of hybrid dynamic systems (HDS), its discrete component is the voltage inverter which has a finite number of states controlling the continuous component that represents the machine. The results of the simulation made on MATLAB/Simulink are presented and discussed in order to check the performance of the strategy of the studied control. They show, in particular, the main advantages of this control manifesting the good dynamic of the electromagnetic torque and the robustness against the parametric variations.

FOC Transformation for Single Open-Phase Faults in the Five-Phase Open-End Winding Topology

Many critical five-phase permanent-magnet synchronous machine drive systems require operation after a single open-phase fault. The single dc supply open-end winding inverter topology allows for the injection of four unbalanced phase currents to better optimize the postfault machine torque after this fault. However, all previously published field-oriented control schemes send varying current references to the proportional–integral (PI) current controllers when controlling four unbalanced phase currents. This makes the design of the PI controllers considerably difficult as each machine operating point will require a different gain to accurately track the varying reference with minimum ripple. Consequently, this paper proposes a new postfault transformation matrix that obtains constant current references for any given set of four unbalanced sinusoidal phase currents. This facilitates easy design of the PI current controllers as the steady-state error can be reduced to zero in a user-defined response time for all operating points. This current control technique is the first to be designed specifically for the case of an open-phase fault to a five-phase open-end winding system.

Low-Complexity Model Predictive Torque Control Method Without Weighting Factor for Five-Phase PMSM Based on Hysteresis Comparators

An improved model predictive torque control (MPTC) method without weighting factors is proposed for five-phase permanent magnet synchronous machine (PMSM) drives, which aims to reduce heavy computation complexity, and the low-order current harmonics existing in harmonic subspace in the traditional finite-control-set (FCS) MPTC. In the proposed MPTC scheme, a modified control set consisting of virtual voltage vectors has been defined and adopted with two hysteresis comparators. Duty ratio optimization is also introduced to reduce torque ripples and eliminate weighting factors in the predefined cost function. In addition, a digital delay compensation solution of the proposed MPTC scheme is adopted to improve the control precision. Finally, a series of hardware-in-loop real-time simulation and experimental tests is achieved to compare the performances of the proposed and traditional FCS-MPTC schemes. Simulation and experimental results have verified the effectiveness of the proposed MPTC scheme.

Implementation of Postfault Decoupling Vector Control and Mitigation of Current Ripple for Five-Phase Fault-Tolerant PM Machine Under Single-Phase Open-Circuit Fault

The multiphase machine is a competitive candidate for applications where uninterrupted operation is demanded under postfault conditions. In this paper, the decoupling vector control for a surface mounted five-phase permanent-magnet synchronous machine (PMSM) under single-phase open-circuit fault is investigated. The decoupled mathematical model of the five-phase PMSM under single-phase open-circuit fault is derived. Then, two postfault control strategies are obtained, which are based on the principles of minimum copper loss and equal amplitudes of currents, respectively. The postfault control strategy based on the feed-forward compensation is proposed in order to eliminate the influences of certain factors and decrease the current ripple. The validity of the postfault control strategies is proved by experiments.

Model predictive optimal control considering current and voltage limitations: Real-time validation using OPAL-RT technologies and five-phase permanent magnet synchronous machines

Multiphase machines have recently gained interest in the research community for their use in applications where high power density, wide speed range and fault-tolerant capabilities are required. The optimal control of such drives requires the consideration of voltage and current limits imposed by the power converter and the machine. While conventional three-phase drives have been extensively analyzed taking into account such limits, the same cannot be said in the multiphase drives’ case. This paper deals with this issue, where a novel two-stage Model Predictive optimal Control (2S-MPC) technique is presented, and a five-phase permanent magnet synchronous multiphase machine (PMSM) is used as a case example. The proposed method first applies a Continuous-Control-Set Model Predictive Control (CCS-MPC) stage to obtain the optimal real-time stator current reference for given DC-link voltage and stator current limits, exploiting the maximum performance characteristics of the multiphase drive. Then, a Finite-Control-Set Model Predictive Control (FCS-MPC) stage is utilized to generate the switching state in the power converter and force the stator current tracking. An experimental validation of the proposed controller is finally provided using a real-time simulation environment based on OPAL-RT technologies.

Extended Kalman Filter Based Sliding Mode Control of Parallel-Connected Two Five-Phase PMSM Drive System

This paper presents sliding mode control of sensor-less parallel-connected two five-phase permanent magnet synchronous machines (PMSMs) fed by a single five-leg inverter. For both machines, the rotor speeds and rotor positions as well as load torques are estimated by using Extended Kalman Filter (EKF) scheme. Fully decoupled control of both machines is possible via an appropriate phase transposition while connecting the stator windings parallel and employing proposed speed sensor-less method. In the resulting parallel-connected two-machine drive, the independent control of each machine in the group is achieved by controlling the stator currents and speed of each machine under vector control consideration. The effectiveness of the proposed Extended Kalman Filter in conjunction with the sliding mode control is confirmed through application of different load torques for wide speed range operation. Comparison between sliding mode control and PI control of the proposed two-motor drive is provided. The speed response shows a short rise time, an overshoot during reverse operation and settling times is 0.075 s when PI control is used. The speed response obtained by SMC is without overshoot and follows its reference and settling time is 0.028 s. Simulation results confirm that, in transient periods, sliding mode controller remarkably outperforms its counterpart PI controller.

Experimental Investigation of Inverter Open-Circuit Fault Diagnosis for Biharmonic Five-Phase Permanent Magnet Drive

This paper proposes a procedure that is suitable for experimental investigation of real-time open-switch and open-phase faults diagnosis of a five-leg voltage source inverter feeding a five-phase biharmonic permanent magnet synchronous machine (PMSM). The algorithm is based on the specific characteristics of multiphase machines, which allows inverter fault detection with sufficient robustness of the algorithm in the presence of fundamental and third harmonic components. First, the inverter fault effects analysis is achieved in the characteristic subspaces of the five-phase PMSM. Specificities that are interesting for the elaboration of a real-time fault detection and identification (FDI) process are highlighted. Original and particular algorithms are used for an accurate 2-D normalized fault vector extraction in a defined fault reference frame. This frame is dedicated only for FDI. To ensure the high immunity of the FDI process against transient states, a particular normalization procedure is applied. The normalized diagnostic signals are formulated from the defined frame and other variables derived from the reference and measured currents. Simulation and experimental results of open-switch and open-phase faults are provided to validate the proposed algorithm.

Finite control‐set model predictive current control of five‐phase permanent‐magnet synchronous machine based on virtual voltage vectors

This study proposes a finite control-set model predictive current control (FCS-MPCC) scheme based on virtual voltage vectors for five-phase permanent magnet synchronous machines, which aims to reduce the low-order harmonic components of stator currents. In addition, comparing with traditional FCS-MPCC algorithms, the proposed algorithm retains fast control dynamic response and brings several other benefits: such as smaller burden of calculation, approximate constant switching frequency in entire speed operation range and lower current harmonics, especially for three-order harmonics. Furthermore, the one-step delay compensate solution of the proposed FCS-MPCC scheme in digital-controller implementation is presented. Finally, a series of computer simulation and hardware-in-loop (HIL) experimental tests are adopted to compare the performances of the proposed FCS-MPCC and two traditional FCS-MPCC schemes. Simulation and HIL experimental results have verified the validity and effectiveness of the proposed FCS-MPCC scheme using virtual voltage vectors.