Relaxation Parameter Optimization in Electrical-to-Mechanical Co-Simulation Based on Time Windowing WR Technique

This paper presents an innovative approach to enhancing the time windowing waveform relaxation (WR) technique in electrical-to-mechanical co-simulation by optimizing relaxation parameters for improved performance. An analytical model is introduced to determine the optimal number of time windows, considering the circuit’s dynamic characteristics. Additionally, a genetic algorithm (GA) is applied to refine relaxation parameters (e.g., impedance values), effectively addressing challenges posed by nonlinear device behaviors and improving the accuracy of co-simulation results. In the case study, it is crucial to emphasize that the full system simulation is used exclusively for retrospective validation of the co-simulation, without incorporating its results as inputs or convergence criteria. The proposed method significantly reduces the average error between co-simulation results and the full system output voltage, decreasing it from -2.8 dB to less than −26.2 dB. This demonstrates improved alignment and faster convergence compared to using the WR method. The validation of GA method is then applied to the co-simulation of an electrical (buck converter) and mechanical (DC motor) system, with results compared against the full system. The WR method exhibited significantly lower power efficiency (57.4%) compared to the full system (81.4%), rendering it insufficient. Time windowing WR enhanced power efficiency through simulation segmentation, reaching 74.6%, though it still fell short of the full system. The most advanced approach, time windowing WR with GA optimization, dynamically adjusted relaxation parameters, resulting in a power efficiency of 80.8%, nearly matching the 81.4% recorded in the single-kernel simulation. These findings underscore the effectiveness of integrating time segmentation with adaptive optimization to enhance simulation performance.