Filtration-based (FB) power/current allocation of battery-supercapacitor (SC) hybrid energy storage systems (HESSs) is the most common approach in DC microgrid (MG) applications. In this approach, a low-pass or a high-pass filter is utilized to decompose the input power/current of HESS into high-frequency and low-frequency components and then assign the high-frequency parts to SC. Moreover, to avoid the state of charge violation (SoC) of SC, this approach requires a rulebased supervisory controller which may result in the discontinuous operation of SC. This paper first provides a small-signal stability analysis to investigate the impact of an FB current allocation system on the dynamic stability of an islanded DC MG in which a grid-forming HESS supplies a constant power load (CPL). Then, it shows that the continuous operation of SC is essential if the grid-forming HESS is loaded by large CPLs. To address this issue, this paper proposes a model predictive control (MPC) strategy that works in tandem with a high-pass filter to perform the current assignment between the battery and SC. This approach automatically restores the SoC of SC after sudden load changes and limits its SoC variation in a predefined range, so that ensure the continuous operation of SC. As a result, the proposed FB-MPC method indirectly enables the MG's proportional-integral (PI) voltage controller to operate with higher gain values leading to better transient response and voltage quality. The performance of the proposed approach is then validated by simulating the system in MATLAB/Simulink. INDEX TERMS Filtration-based power/current allocation systems, battery/supercapacitor hybrid energy storage systems, model predictive control, stability analysis, state of charge recovery.
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