The resulting state graph H n and optimal sequence of (triples of) moves lead to surprising connections to other mathematical objects when n tends to infinity, in the latter case to square-free sequences, in the former case to the fractal structure of the Sierpiński gasket (SG) and Pascal’s arithmetrical triangle (AT). The problem consists in transferring n discs of mutually different diameter, originally stacked in natural order on one or more three pegs, to a designated final position, usually a “tower” on one of the pegs, subject to the divine rule never to place a larger disc on a smaller one. This revived interest resulted in a number of new discoveries about its rich mathematical structure. Invented more than a hundred years ago by the French number theorist Édouard Lucas as a mathematical puzzle, the Tower of Hanoi (TH) has recently attracted computer scientists in connection with recursion and complexity of algorithms. The future trends for REPS with HESS combination and control strategies are also discussed. A detailed review of the state-of-the-art control strategies such as classical control strategies and intelligent control strategies for REPS with HESS are highlighted. As there are a variety of energy storage technologies available in the market, decision matrixes are introduced in this paper to evaluate the technical and economic characteristics of the energy storage technologies based on the requirements of stand-alone REPS. This paper presents different structures of stand-alone REPS with HESS such as passive, semi-active, and active HESS. The structure and the common issues of stand-alone REPS with ESS are discussed in this paper. A hybrid energy storage system (HESS) is a better solution in terms of durability, practicality and cost-effectiveness for the overall system implementation. In certain systems, the ESS is oversized to reduce the stress level and to meet the intermittent peak power demand. The energy storage system (ESS) in a conventional stand-alone renewable energy power system (REPS) usually has a short lifespan mainly due to irregular output of renewable energy sources. Moreover, he proposed system increases the level of supercapacitor utilization up to 687.122% in comparison to the conventional control strategies. The proposed system reduces the battery peak current, battery peak power, maximum absolute value of the rate of change of power and average absolute value of the rate of change of power by 16.05%, 15.19%, 77.01%, and 95.59%, respectively as compared to the conventional system with battery-only storage.
The proposed system is compared to the conventional system with battery-only storage and the systems with conventional control strategies (Rule Based Controller and FBC). Particle swarm optimization (PSO) algorithm optimizes the membership functions of the FLC to achieve optimal battery peak current reduction. FLC minimizes the battery peak current demand while constantly considering the state-of-charge of the supercapacitor. Firstly, LPF removes the high dynamic components from the battery demand.
Unlike the conventional methods which only use either filtration based controller (FBC) or fuzzy logic controller (FLC), the proposed control strategy comprises of a low-pass filter (LPF) and FLC. This paper proposes an optimal control strategy for a standalone PV system with Battery-Supercapacitor Hybrid Energy Storage System to prolong battery lifespan by reducing the dynamic stress and peak current demand of the battery.
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