Damping of low-frequency oscillations (LFOs) has become a critical challenge in modern power system. Since interarea LFO modes are associated with power oscillation, therefore, proper modulation of power through energy capacitor system (ECS) can be a competent way to conserve system stability. In this article, modeling of grid-connected ECS unit is explained thoroughly. Further to provide adequate damping to critical LFO modes, a linear quadratic Gaussian (LQG) based optimal <inline-formula><tex-math notation="LaTeX"> H_{2}</tex-math></inline-formula> wide-area damping controller (WADC) is proposed for ECS integrated power grid. The parameters of the proposed WADC are tuned by accelerated particle swarm optimization (APSO) technique. Furthermore, to select the proper wide-area signals for controller design, geometric approach is adopted. The efficacy of proposed methodology has been tested on large power systems containing multiple interarea modes viz. 10-machine, 39-bus system and 16-machine, 68-bus system. Simulation studies demonstrated the capability of proposed WADC to adequately damp the multiple interarea modes simultaneously. Moreover, it also provides robust performance for operating point uncertainties (load variation, permanent outage of transmission lines, etc.) and variable time delays in feedback signals.