In this paper an indirect interconnection and damping assignment passivity-based control (IDA-PBC) applied to the three-phase superconducting magnetic energy storage systems (SMES) is proposed to support active and reactive power in distribution systems. The SMES is connected to the distribution network using a pulse-width-modulated current source converter (PWM-CSC), due to its intrinsic current features that are more natural for controlling the current of a superconducting coil. A Hamiltonian function is selected as an hyperboloid representation taking into account the open loop dynamics of the system. The indirect control strategy is used to decouple the dynamical behavior between ac and dc side of the system, which allows to control active and reactive power independently in the ac side, while the dc side of the converter is employed as a supervisor controller for active power interchange. Simulation results demonstrate the efficiency and robustness of the proposed control methodology applied on a low-voltage distribution network under different operative conditions where the tracking errors were less than 6.2%. © 2018 Elsevier Ltd