In this paper, the study of the torque and power versus speed characteristics for a family of five-phase Surfacemounted Permanent Magnet (SPM) machine is carried out. With considering hypotheses (linear magnetic modeling, only first and third harmonic terms in the back-emf and current spectrums), an optimization problem that aims to maximize the torque for given maximum peak voltage and RMS current is formulated: the optimal torque sharing among the two virtual machines (the two dq-axis subspaces) that represent the real five-phase machine is thus calculated for any mechanical speed. For an inverter and a DC voltage sized with only considering the first harmonic of backemf and current, the problem is solved with changing the virtual machine back-emfs and inductances ratios. With the introduction of the maximum torque/speed point, maximum power/speed point and maximum reachable speed, it can be shown that, if the inductance ratio is large enough, for given Volt-Ampere rating, the machine can produce higher torque without reducing its speed range thus meaning that the capability of the inverter to work is improved with the use of the third harmonic. This property is all the truer as the base armature reaction is large. A particular five-phase machine is sized and numerically analyzed to check this property.

His current research interest includes design, modeling, and control of multiphase machines.

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Abstract:The purpose of the paper is to present the potentialities in terms of the control of a new kind of PM synchronous machine. With five phases and electromotive forces whose first (E 1 ) and third (E 3 ) harmonics are of similar amplitude, the studied machine, so-called bi-harmonic, has properties that are interesting for traction machine payload. With three-phase machines, supplied by a mono-harmonic sinusoidal current, the weak number of freedom degrees limits the strategy of control for traction machines especially when voltage saturation occurs at high speeds. As the torque is managed for three-phase machines by a current with only one harmonic, flux weakening is necessary to increase speed when the voltage limitation is reached. The studied five-phase machine, thanks to the increase in the number of freedom degrees for control, aims to alleviate this fact. In this paper, three optimized control strategies are compared in terms of efficiency and associated torque/speed characteristics. These strategies take into account numerous constraints either from the supply (with limited voltage) or from the machine (with limited current densities and maximum acceptable copper, iron and permanent magnet losses). The obtained results prove the wide potentialities of such a kind of five-phase bi-harmonic machine in terms of control under constraints. It is thus shown that the classical Maximum Torque Per Ampere (MTPA) strategy developed for the three-phase machine is clearly not satisfying on the whole range of speed because of the presence of iron losses whose values can no more be neglected at high speeds. Two other strategies have been then proposed to be able to manage the compromises, at high speeds, between the high values of torque and efficiency under the constraints of admissible total losses either in the rotor or in the stator.

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This paper addresses the design of a bi-harmonic five-phase Surface-mounted Permanent Magnet (SPM) machine for marine propulsion. The bi-harmonic characteristic results from the particular 20 slots-8 poles configuration that makes possible high value of third harmonic current injection. Thus the machine performance can be improved in terms of average torque, speed range, losses control and torque quality, this last feature being the scope of the paper. As low ripple torques are wanted at low speed, the magnet layer is defined to reduce the cogging torque and to make third harmonic current injection increasing average torque and reducing pulsating torque in the same time. According to a selection procedure based on the numerical simulations of a high number of machines, it appears that designing the rotor with two identical radially magnetized magnet that cover two-third the pole arc allows to reach this goal. Referring to an equivalent three-phase machine, the torque ripple level of the bi-harmonic five-phase machine is more than three times lower, thus being obtained with a simple control strategy that aims at achieving constant currents in the rotating frames. The time simulations of the drive confirm the significant reduction of the speed oscillation, especially at low speed.

The paper studies the impact of first and third current-harmonic repartition in a five-phase Permanent Magnet machine whose Electromotive Forces (emfs) have first and third harmonics of the same amplitude. With a five-phase machine, it is possible for the torque production to achieve independent controls of the first and third harmonics of currents by using a vector control in each one of the two characteristic orthogonal sub-spaces of the machine. The same torque quality as obtained with a three-phase machine with sinusoidal emf can be thus obtained with a non-sinusoidal emf and with one more supplementary degree of freedom for the control. Based on the Maximum Torque Per Ampere (MTPA) strategy used for threephase machines, a comparison of the obtained torque/speed characteristics of the machine is achieved using either one or two harmonics. The voltage limits imposed by the Voltage Source Inverter and two different values of the maximum allowed current densities are taken into account for obtaining the optimum repartition between first and third harmonics of currents: it appears that at first, from the point of view of efficiency, the MTPA is not optimal except for low speeds and secondly that the repartition of currents is not trivial and depends for example on the considered maximum current densities.

If multi-phase machines equipped with toothconcentrated winding with half a slot per pole and per phase offer interesting characteristics (simplified manufacturing, no space subharmonic, fault-tolerant ability), their low fundamental winding factors make their designs and controls challenging. The paper addresses the case of a seven-phase Surface-mounted Permanent Magnet (SPM) machine which has a fundamental winding factor lower than the third. This so-called bi-harmonic specificity is considered in order to achieve good torque quality (average value and ripples). Regarding the design, the magnet layer is segmented into two identical radially magnetized tiles that cover about three-quarters the pole arc. Regarding the control, the rated Maximum Torque Per Ampere (MTPA) supply strategy (h1h3 control) aims at generating a third harmonic current component greater than the fundamental. A prototype has been manufactured: the ability of the machine to provide smooth torque is experimentally confirmed through the implementation of a simple MTPA control which copes with high distortion in no-load voltage.