Control of a super-capacitor energy storage system to mimic inertia and transient response improvement of a direct current micro-grid

•A virtual inertia control strategy is proposed to achieve an increased inertia from an energy storage system based on supercapacitor (SC) in the context of dc MG applications.•Virtual inertia loop is implemented in inner current control loop. It proposes a derivative term which is fast enough to decrease rate of change of dc bus voltage (RoCoV) by using virtual capacitance. This emulates the virtual inertia concept.•The proposed proportional term in the virtual inertia loop increases damping of dc bus voltage by using virtual conductance that emulates damping coefficient concept.•The SC's voltage is regulated by a PI compensator which is implemented in outer voltage loop.•The small-signal stability is considered to study the system behavior under small disturbances or load perturbations at some steady-state operational points. The analysis is validated by using the eigenvalue analysis and time-domain simulation.