Analysis and Compensation of Rounding Error in Virtual-Winding-based Harmonic Current Controller for Permanent Magnet Synchronous Machines

Harmonic current control is a key research area in permanent magnet synchronous machines (PMSMs). The virtual winding-based harmonic current controller, as a novel approach, exhibits outstanding dynamic characteristics. To construct the virtual windings, this method requires delaying the currents by a fixed angle. However, since the actual delay angle must be an integer multiple of the switching period, rounding operation is required. This paper reveals that this rounding error can result in incomplete decoupling between the fundamental and harmonic current components, which deteriorates the harmonic current control performance. It is found that lower switching frequencies, higher electrical frequencies, and smaller delay angles lead to larger rounding errors. Moreover, a modified vector space decoupling (VSD) transformation that accounts for rounding errors is derived. The Taylor series approximation is employed to simplify the matrix into the original VSD matrix and an additional compensation matrix to avoid additional real-time trigonometric calculations. Finally, simulations and experimental results confirm that the proposed algorithm significantly mitigates the incomplete harmonic decoupling caused by rounding errors.