FPGA-Based Real-Time Simulation of Externally Excited Synchronous Machines

Externally excited synchronous machines (EESMs) are a rare-earth-free solution for traction applications. However, variable field excitation and magnetic coupling increase control complexity. Efficient validation of the resulting control functionalities can be carried out using hardware-in-the-loop (HIL) testing, which requires high-fidelity real-time simulation models. This paper presents a semi-analytical, discrete-time EESM model tailored for HIL applications. Nonlinear magnetic saturation and magnetic coupling are captured using an inverted flux–current characteristic combined with a rotating coordinate transformation, which improves resource utilization. Spatial harmonics are included through a Fourier decomposition of the angle-dependent inverse characteristics. Additionally, different loss mechanisms are considered to accurately represent the physical behavior of the machine. The model is parameterized using finite element analysis (FEA) results from a 100kW salient-pole EESM. It is implemented on a field-programmable gate array to achieve real-time capability at a simulation frequency of 2.5MHz. Validation results for the typical operating range show deviations below 0.1% compared to detailed FEA results, demonstrating accurate real-time simulation of the electromagnetic behavior.