Online Minimum-Copper-Loss Control of an Interior Permanent-Magnet Synchronous Machine for Automotive Applications

This paper presents an algorithm to calculate the current references on line, considering the inherent nonlinear nature of the saturation effect in an interior permanent-magnet synchronous machine for the minimum-copper-loss control under the current and voltage limit of the drive system. This paper basically approaches this issue as a nonlinearly constrained optimization problem where the torque command imposes the nonlinear equality constraint and the voltage limit imposes the nonlinear inequality constraint. Depending on the operating region, it solves the corresponding set of nonlinear equations in real time derived from the Lagrange multiplier method. Newton's method among various techniques is adopted to implement the numerical solution. This scheme gives accurate results not only in motoring but also in generating operation of the machine, since the voltage drop of the stator resistance is taken into account, which is hardly applicable to a two-dimensional lookup table where the inputs are the torque command and the maximum flux amplitude, and the output is each axis current reference in the rotor reference frame. The simulation and experimental results show the feasibility and performance of the proposed technique.