This paper presents an integration of three-phase supercapacitor energy storage (SCES) in power grids via passivity-based control (PBC) theory under different reference frames. The SCES systems have the possibility to interchange active and reactive power between the supercapacitor and converter to the electrical power network. The active power is directly related to the energy stored on the supercapacitor, while the reactive power is redistributed by the forced commutated switches present in the voltage source converter (VSC) used to integrate the SCES system to the power grid. PBC theory allows designing Lyapunov stable controllers for autonomous and non-Autonomous dynamical sys-Tems via port-Hamiltonian (pH) representations. The averaging modeling theory employs to develop the controllers under abc, alpha\beta and dq reference frames. Simulation results show the possibility of using the SCES devices to compensate active and reactive power in power grids dynamically in all operating quadrants. All simulations are conducted via MATLAB/SIMULINK software. © 2018 IEEE.