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

Multiple three-phase machines have become popular in recent due to their reliability, especially in the ship and airplane propulsions. These systems benefit greatly from the robustness and efficiency provided by such machines. However, a notable challenge presented by these machines is the growth of harmonics with an increase in the number of phases, affecting control precision and inducing torque oscillations. The phase shift angles between winding sets are one of the most important causes of harmonics in the stator currents and machine torque. Traditional approaches in the study of triple-three-phase or nine-phase machines mostly focus on specific phase shift, lacking a comprehensive analysis across a range of phase shifts. This paper discusses the current and torque harmonics of triple-three-phase permanent magnet synchronous machines (PMSM) with different phase shifts. It aims to analyze and compare the impacts of different phase shifts on harmonic levels. To verify the assumption, Model-in-the-Loop (MiL) simulation based on PLECS and MATLAB/Simulink is used to build the equivalent circuit of the machines and the field-oriented-control (FOC) strategy. The mathematical model of the machine is based on a general transformation, allowing to map machine quantities into the traditional αβ-subplane and additional subplanes. These subplanes are shown to reflect both harmonic and zero sequence components. By comparing the amplitudes of current harmonics under varying phase shifts, the paper aims to pinpoint the harmonic dependencies on phase shifts. The goal is to propose a most suitable phase shift for designing the triple-three-phase machine by a comprehensive analysis of torque harmonics and losses.