Currently, using hybrid energy storage system composed of battery and supercapacitor to stabilize DC bus power fluctuation is a hot issue. In low-pass filtering control strategy to suppress the power fluctuation of DC bus, the filtering time constant is fixed, so there are problems such as poor load power fluctuation smoothing effect and over-charge and over-discharge of the battery. In this paper, a two-stage low-pass filter control strategy with variable filter time constant is designed. Firstly, the strategy builds a multi-objective function with minimum load slow target power and DC bus power difference. Using the Improved Particle Swarm Optimisation (IPSO) with compensating coefficient of inertia weight factor to solve the optimal output power by a hybrid energy storage system, and dynamically adjust the first-level filtering time constant, in order to reduce the load power change causing the fluctuation of the DC bus power; secondly, according to the charging state of the supercapacitor and the battery, the fuzzy control method is adapted to dynamically adjust the second-order filtering time constant to optimize the power distribution of the battery and the supercapacitor. The experimental results show that the control strategy can effectively reduce the power fluctuation of DC bus by about 15%, and avoid the over limit phenomenon of the battery state of charge, which has a good prospect of engineering application.INDEX TERMS Hybrid energy storage, power fluctuation, particle swarm optimization, low pass filter, filtering time constant.

Traditional hierarchical control of the microgrid does not consider the energy storage status of a distributed hybrid energy storage system. This leads to the inconsistency of the remaining capacity of the energy storage system in the process of system operation, which is not conducive to the safe and stable operation of the system. In this paper, an improved hierarchical control strategy is proposed: the first allocation layer completes the allocation between the distribution energy storage systems considering the state of hybrid energy storage systems, and the second allocation layer realizes the allocation within the hybrid energy storage systems based on variable time constant low-pass filtering. Considering the extreme conditions of energy storage systems, the transfer current is introduced in the second allocation process. The SOC (stage of charge) of the supercapacitor is between 40% and 60%, which ensures that the supercapacitor has enough margin to respond to the power demand. An example of a 300 MW photovoltaic microgrid system in a certain area is analyzed. Compared with the traditional hierarchical control, the proposed control strategy can reduce the SOC change of a hybrid energy storage system by 9% under the same conditions, and make the supercapacitor active after power stabilization, which is helpful to the stable operation of the microgrid.

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The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic viscoelasticity. In this paper, we first develop the energy method to estimate the one-dimensional space-Riesz fractional wave equation. For two-dimensional cases with the variable coefficients, the discretized matrices are proved to be commutative, which ensures to carry out of the priori error estimates. The unconditional stability and convergence with the global truncation error O(τ 2 + h 2 ) are theoretically proved and numerically verified. In particulary, the framework of the priori error estimates and convergence analysis are still valid for the compact finite difference scheme and the nonlocal wave equation.

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