Study on the thermodynamic-dynamic-electrical coupling model of free-piston Stirling generator and the impact of load on its characteristics

The Free-Piston Stirling Generator (FPSG) — an external combustion generator — plays a key role in aerospace and military applications and in the utilization of low-grade heat, attracting growing research interest. For FPSG parameter design, optimization, and thermodynamic analysis, the second-order mathematical model is preferred for its cost-effectiveness, reliability, and ease of further development. A comprehensive thermodynamic-dynamic-electrical coupling (TDEC) model is developed for Free-Piston Stirling Generators (FPSGs). Its innovation lies in the integrated simulation of key physical processes, including a calibrated load model for realistic motor operation. The model's predictions show good agreement with experimental benchmarks from the literature, the average relative error of |Xp| is 14.25%, f is 1.35%, We is 13.62% and V is 11.02% and ηte is 13.71%, respectively. Besides, this study examines how the FPSG's characteristics change with average operating pressure (Pm) for different load characteristics. Interestingly, for characteristics such as ηt, Qr and Whys, there exists a specific value of Pm at which the influence of load on these characteristics becomes diametrically opposed. This finding provides a critical theoretical basis for the optimal design of FPSG systems.