An FPGA-Based Real-Time Spatial Harmonics Model of a PMSM Considering Iron Losses and the Thermal Impact

This article presents a spatial harmonics model of a permanent magnet synchronous machine implemented on a field-programmable gate array (FPGA). The real-time model is parameterized by finite element analysis (FEA) and is suitable for model-based development and hardware-in-the-loop (HIL) applications. Since the quality of the real-time model depends on the parameterization, the accuracy of three FE models of different fidelity levels is evaluated by test bench measurements. It was found that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> assessment can be realized with good precision by virtual prototypes. In addition to the selection of a suitable FE model for parameterization, a surrogate model to describe the machine effects is mandatory to achieve real-time capability. Using an inverse current-flux correlation in the dq reference frame and a parallel resistor in the equivalent circuit for iron loss consideration, a high-fidelity model is developed. Moreover, the temperature effect is solved by a highly sophisticated shifting strategy of the reference currents to affect the nonlinearity and harmonics of the electromagnetic behavior. The temperature correction approach yields a maximum deviation of 0.3 Nm. This corresponds to a percentage error of less than 1%.