Current and Torque Harmonics Analysis of Triple Three-Phase Permanent-Magnet Synchronous Machines with Arbitrary Phase Shift Based on Model-in-the-Loop

In recent years, multiple three-phase machines have become increasingly popular due to their reliability and fault tolerance, especially in the propulsion systems of ships, aircraft and vehicles. These systems greatly benefit from the robustness and efficiency offered by such machines. However, a notable challenge for these machines is that harmonics increase with the number of phases, which affects control accuracy and triggers torque oscillations. The phase shift angles between winding sets are one of the most important causes of stator current and torque harmonics. Most of conventional approaches for studying triple-three-phase or nine-phase machines focus on specific phase shifts and lack a comprehensive analysis over a range of phase shifts. This paper discusses the current and torque harmonics of triple three-phase permanent magnet synchronous machines (TTP-PMSM) with different phase shifts. The aim of this paper is to analyse and compare the effect of different phase shifts on harmonic levels. To verify the hypotheses, a Model-in-the-Loop (MiL) simulation environment based on PLECS and MATLAB/Simulink is used to construct the equivalent circuits of the machines and the Field-Oriented Control (FOC) strategy. The mathematical model of the machine is based on a unified transformation that maps the machine quantities into the fundamental αβ-subplane and other subplans, which are shown to reflect both harmonic and zero sequence components. By comparing the amplitudes of current harmonics at different phase shifts, this paper analyses the harmonic dependencies on phase shifts. By making a trade-off between torque harmonics and copper losses caused by current harmonics, the best phase shifts for the design of a triple three-phase PMSM is proposed as (10°, 20°).