Optimal Trajectory Control for Soft Startup of Series–Parallel Resonant Repetitive-Frequency Capacitor Charging Power Supply

Series-parallel resonant converters (SPRCs) are widely adopted in high-power repetitive-frequency (RF) capacitor charging power supply (CCPS). Under RF operation, there is an interval stage between consecutive charging stages of the CCPS, leading to discrepancies between the initial voltage values of resonant components at startup charging and those at steady-state charging. This results in additional current and voltage stresses at the startup stage, which can reach up to 60% and 40% higher than normal operation levels, posing significant risks to semiconductor switches and passive components. To address these risks, a novel soft startup method based on optimal trajectory control (OTC) is proposed. The method achieves soft startup by optimizing the order of driving signals and adjusting the duty cycle of the first drive signal in the H-bridge at the startup stage. Comprehensive mathematical models are established to describe the state trajectories during steady-state charging, interval, and startup stages. Derivations of overcurrent factor, additional current, and additional voltage expressions enable precise determination of the switching duty cycle, ensuring a smooth transition from startup to steady-state charging within half a switching cycle. This approach maintains charging speed and efficiency while effectively eliminating all additional current and voltage stresses on the H-bridge and resonant tank. A hybrid control strategy for SPRC CCPSs incorporating soft startup is thus developed. Finally, both simulations and experiments are carried out to validate the proposed models and control strategy.