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

Abstract

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.

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

“…The slotted stator structure is comprised of 7-phase concentrated winding which allows adding the 3rd rotor with PMs radially magnetized in order to reinforce the torque density. Thanks to the extra degrees of freedom the 7-phase bi-harmonic machines, more possibilities for the control of the torque and current supply can be applied [12].and the bi-harmonic machine has properties that are interesting for machine payload [13]. Moreover, the winding factor for both the fundamental harmonic and the 3rd harmonic are of high values.…”

Five-phase Bi-harmonic PMSM control under voltage and currents limits

“…This approach is different from the one used in classical three phase machines, in which flux-weakening appears as the only possible solution to increase speed when the voltage limit is reached. For the bi-harmonic machine, the determination of the current references in high speed zone requires the resolution of four variables non-linear optimization problem [8].…”

“…This machine allows creating torque from both 1 st and 3 rd harmonic components [6]. The contribution of each harmonic component depends mainly on the amplitude of the harmonic content of the back-EMF [7]- [8]. Generally, the 3 rd harmonic is used to improve the torque, which comes essentially from the fundamental harmonic.…”

“…Therefore, the fractional slot concentrated winding with a number of slots per pole and per phase equal to 0.5 is used 0- [15]. The control strategies applied to multiphase machines are based on the Maximum Torque Per ampere MTPA [8]-0. Consequently, a ratio ρ between 1 st and 3 rd current harmonic components must be fixed to have collinear current and back-EMF (these assertions are detailed in section III).…”

“…The total torque/speed characteristic is the sum of the characteristic associated to each harmonic component [8][13]. 3) Low losses associated to eddy currents when high frequency is required at high speed: the winding configuration is selected so that the harmonic content of the MMF is low.…”