Optimal magnet shaping with third order harmonic for maximum torque in brushless AC machines

Abstract

This paper describes the optimal magnet shaping techniques to increase the torque capability in brushless AC machines by utilising the 3 rd order harmonic in inverse cosine shape airgap and sinusoidal shape magnet. It is analytically found that for different types of magnet shaping methods, the optimal magnitude of the 3 rd order harmonic is always 1/6 of that of the fundamental, which is validated by the finite element analysis. By utilising the optimal 3 rd order harmonic, the average torque of two 10-pole/12-slot machine can be increased by ~11%, while their torque ripple is only slightly increased by less than 1.5%, compared to machines employing magnet shaping techniques without the 3 rd order harmonic.

Torque Capability Enhancement of Dual Three-Phase PMSM Drive With Fifth and Seventh Current Harmonics Injection

“…To maximize the magnitude of fundamental current for a given allowed current peak value, the optimal magnitude of the third harmonic is 1/6 of the fundamental component [9][10][11], then the magnitude of fundamental can be increased up to 1.15 times. In the same way, the amplitudes and phase angles of the fifth and seventh harmonics can be optimized aiming for the maximum fundamental component for the defined stator current peak value.…”

“…11. As the optimal magnitude of the third harmonic is 1/6 of the fundamental component [9][10][11], the magnitude of fundamental can be increased up to 1.15 times of 1.5A, that is 1.5A*1.15 = 1.725A [ Fig. 12(e)].…”

“…As proposed in [9][10][11], one typical approach to increase the torque of PMSMs is to employ the optimal third-harmonic magnet shaping to obtain maximum fundamental flux within the flux limitation. In the same way, the current harmonics can also be injected to current to obtain the maximum fundamental current within allowed current limit.…”

Optimal Third-Harmonic Current Injection for Asymmetrical Multiphase Permanent Magnet Synchronous Machines

“…In the case of machines characterized by an odd number of phases and a symmetrical winding configuration, it has been verified that, based on the stator winding loss minimization criterion, the optimal injection ratio coincides with the one between the corresponding magnets' induced back-EMFs [4][5][6][7][8][9][10][11][12][13]. Several applications of these strategies can be found, especially for five-phase machines [9][10][11][12][13][14][15][16][17].…”

Torque ripple suppression of permanent magnet synchronous motors considering total loss reduction

“…Moreover, in machine design strategies, there is a tradeoff between their torque ripple suppression effect and mean torque attenuation. In [3] and [4], to prevent a reduction in the mean torque produced by PMSMs, optimal rotor shaping techniques for increasing the fundamental component of the flux linkage due to the rotor magnets has been proposed. However, the manufacturing cost is expensive due to the complicated shaping.…”