Maximum Reachable Torque, Power and Speed for Five-Phase SPM Machine With Low Armature Reaction

Abstract

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.

Five-phase SPM machine with electronic pole changing effect for marine propulsion

“…In this subsection, the torque/speed characteristic of the machine is calculated: for a given mechanical speed Ω (i.e. for a given electrical speed ), taking into account the maximum DC voltage and the maximum copper losses (driven by base current ), the goal consists in finding the MM and SM current distribution that maximizes the electromagnetic torque [17]. To solve this problem is equivalent to find the optimal d-axis and q-axis references for each virtual machine.…”

Torque Optimization of a Seven-Phase Bi-harmonic PMSM in Healthy and Degraded Mode

“…By designing the shape of the PM and the third harmonic injection of the current, the machine can achieve 30% more of the torque [2]. An optimization problem that aims to maximize the torque for given maximum peak voltage and root mean square (RMS) current is formulated [3]. In terms of control, multiphase machines can be split into several fictitious two-phase machines and zero-sequence machines, each of them is related to a series of harmonics [4].…”

Comparison of Optimized Control Strategies of a High-Speed Traction Machine with Five Phases and Bi-Harmonic Electromotive Force

“…For example, more possible winding configurations for low losses, high torque density and smooth torque ripples [13][14][15][16][17][18][19] can be analyzed. Likewise, as the freedom degrees number increases, the vector control gives more possibilities: the study of the current harmonic injection for higher torque density keeping a smooth torque [20][21][22][23][24][25][26]; the enlargement, for traction machines working in flux-weakening mode under voltage saturation [27][28][29][30][31], of the area of working.…”

“…The contribution of each harmonic is of the same order, and the choice of repartition between first and third harmonics has to be optimized regarding different objectives and constraints. To the knowledge of the authors, no multiphase machine with such a E 3 /E 1 ratio has been yet considered, except in [19,[35][36][37]. In [13,23,24], the ratio E 3 /E 1 in SPM machines was less than 33%, this value being obtained with square wave emf.…”

“…For a PM synchronous machine, the impacts of the injection of a third harmonic of current and/or voltage have been studied. In [19], for SPM five-phase machines and considering only copper losses, torque-speed characteristics are defined for different values of the ratio of E 3 /E 1 , under the constraints of peak current and the voltage that is imposed by the supply and VSI characteristics. It is shown that important modifications concerning the maximum torque and speed can be expected.…”