This paper presents an interconnection and damping assignment passivity-based control (IDA-PBC) applied to three-phase superconducting magnetic energy storage systems (SMES) that supports active power distribution grids with high penetration of renewable energies. The SMES is integrated to the grid using a pulse-width-modulated current source converter (PWM-CSC) which is an straightforward alternative to conventional topologies due to its intrinsic current characteristic. Dynamics of this converter is modeled by using an averaged model which considers the modulation indexes as control inputs. A hyperboloid Hamiltonian function is selected to design the closed-loop control law in the 0dq reference frame. A sensitivity analysis is performed on the proposed control. Results demonstrate the stability and efficiency of the proposed control on a medium-voltage grid under different operative conditions.