:This paper presents the criteria in selecting the size of the tuning capacitor, and the cost tradeoff between magnet volume and tuning capacitor in a free piston Stirling engine power generation system. The permissible range of capacitor size corresponding to different magnet volume, in order to prevent magnet demagnetization and stabilize the operation of the system, is determined. Within the permissible range suitable capacitor size may be selected to compensate the inductive load of the system to improve the overall power factor. If the capacitor size is not in the permissible range, there would exists a danger of losing magnet strength, or unstable operation of the engine that would destroy the engine due to unbounded amplitude of piston oscillations. The theory developed is then applied to a practical system, and the cost tradeoff between magnet volume and capacitor is studied.