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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. NOMENCLATUREA.

This paper presents a method to find the optimal size and place of the switched capacitors using a hybrid optimization algorithm. The objective function includes the active and reactive power of power plants, the capital and maintenance costs of capacitor banks, and the cost of active and reactive power losses in distribution lines and transformers. The impact of the load model on the optimal sizing and placement of switched capacitors is studied using three different scenarios: In the first scenario, all loads are voltage-dependent; in the second scenario, only a portion of loads are voltage-dependent; in the third scenario, all loads are voltage-independent. The proposed hybrid algorithm incorporates an outer and two inner optimization layers. The outer layer is executed by a genetic algorithm (GA), while the inner layer is performed by a GA, an exchange market algorithm (EMA), or a particle swarm optimization (PSO). The performance of GA-GA, GA-EMA, and GA-PSO hybrid schemes are compared on an IEEE 33-bus test system. Moreover, IEEE 33-bus and 69-bus networks are used to verify the effectiveness of proposed hybrid scheme against the gravitational search algorithm (GSA), a combination of PSO and GSA (PSOGSA), cuckoo search algorithm (CSA), teaching learning-based optimization (TLBO), and flower pollination algorithm (FPA). The results highlight the advantage of the proposed hybrid optimization scheme over the other optimization algorithms. INDEX TERMS Exchange market algorithm (EMA), genetic algorithm (GA), particle swarm optimization (PSO), radial distribution system (RDS), switched capacitors.