Abstract: When different loads are connected, the traditional shunt active power filter（SAPF） has a low compensation accuracy, and its DC-side voltage cannot maintain stable operation. Based on the aforementioned problems, a new topology, the superconducting magnetic energy storage shunt active power filter（SMES-SAPF）, is adopted in this study. This topology comprises a superconducting magnetic energy storage（SMES） device and an SAPF. Based on this topology, a passive dynamic evolution control and sliding mode control strategies are proposed. First, a passive dynamic evolution controller based on the Euler–Lagrange model is established according to the mathematical model of the SMES-SAPF, thereby improving the overall robustness and anti-interference ability of the system. Second, sliding mode control is used to eliminate the voltage overshoot and fluctuation caused by different connected loads, thereby improving the voltage regulation performance of the DC-side voltage. Finally, simulation experiments are conducted under three load conditions（nonlinear, unbalanced, and pulse） and other operating conditions. Simulation experiments showed that the SMES-SAPF and its control system had strong compensation accuracy and anti-interference ability that could more effectively solve the power quality problems caused by different load accesses.