Contactless power transmission system is an important part of rotary ultrasonic processing system. The widely used fully coupled power transmission system obstructs automatic tool changing because of the interference of the structure. To solve this problem, a partially coupled contactless power transmission system was developed. Firstly, a partially coupled contactless power transmission model was established, which facilitates the design of the primary and secondary coil and their coil parameters. The electrical compensation of partially coupled contactless power transmission was studied in order to improve the efficiency of power transmission. Circuit compensation topology was designed based on a rotary ultrasonic machining system using giant magnetostrictive material. The effectiveness of partially coupled power transmission and its compensation was verified by experiments. The research shows that there is more magnetic leakage between the primary and secondary core for partially coupled system, and its power transmission efficiency and the vibration amplitude are slightly lower than that of the fully coupled power transmission system. With proper electrical compensation, the partially coupled power transmission can fully meet the requirements of the ultrasonic machining. For the GMM rotary ultrasonic machining system, the single-sided series compensation method can simplify the design of the system and ensure high power transmission capacity.