This paper presents a generalized interconnection and damping assignment passivity-based control (IDA-PBC) for electric energy storage systems (EESS) such as: superconducting magnetic energy storage (SMES) and supercapacitor energy storage (SCES). A general framework is proposed to represent the dynamical behavior of EESS interconnected to the electrical distribution system through forced commutated power electronic converters. A voltage source converter (VSC) and a pulse-width modulated current source converter (PWM-CSC) are used to integrate SCES and SMES systems to the electrical power systems respectively. The proposed control strategy allows active and reactive power interchange between the EESS and electric distribution grids independently, guaranteeing globally asymptotically convergence in the sense of Lyapunov via Hamiltonian formulation. Simulation results show the effectiveness and robustness of the generalized IDA-PBC to operate EESS as active and reactive power compensator in order to improve operative conditions in power distribution grids under balanced and unbalanced conditions. © 2018 Elsevier Ltd