Very low frequency technology is nowadays adopted in high voltage generators for testing the high voltage cables with minimized reactive power. This dissertation deals with modeling, optimization and control design of a zero-voltage switching series-parallel resonant converter (LCC resonant converter) with high voltage transformer and Cockcroft-Walton voltage multiplier, which is applied in a novel high voltage generator. Such generator is capable of generating a true sinusoidal test voltage of 0.1 Hz at some tens to hundreds kV. By applying a suitable generalized averaging method in combination with extended describing functions, the large-signal model and small-signal model of the LCC resonant converter are derived. The predicted steady-state and dynamic characteristics agree well with the experimental results. On basis of the LCC resonant converter large-signal model and loss model, a computer-aided design and multi-objective optimization environment is developed, which realizes the minimal electric stress of components and maximal efficiency of the high voltage generator. Various current mode control schemes, such as conventional PI control, fuzzy PD control and model-based Takagi-Sugeno fuzzy control, are developed and compared. The simulated and experimental results demonstrate the obvious superiority of the model-based Takagi-Sugeno fuzzy control, whose design process and the corresponding results are the significant content of this work.