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In this paper first we prove common fixed point theorems for compatible and weakly compatible maps. Secondly, we prove common fixed point theorems for weakly compatible maps along with property (E.A.) and (CLRg) property respectively.
The smart grid’s structure is distinctive because it incorporates numerous cutting-edge communication and sensor technologies. It is challenging to manage smart grids using conventional power grids’ unified optimum delivery strategy effectively. This work offers a smart grid power production and maintenance collaborative optimization framework with renewable energy based on power generation and maintenance analysis. The operating costs of conventional units, the price of generating solar or wind power, and the cost of maintaining units are the problems of objective functions; the constraints taken into account are primarily system constraints. The genetic algorithm (GA) is used in this research to examine the optimization solution strategy. Depending on the properties of the system, various loads, power sources, and constraints are considered. The difficulty of adjusting load scheduling is transformed into a control problem by developing an efficient objective function. When uncertain system components are considered, the real-time control system can dynamically alter load scheduling to meet the needs of the actual system. In this study, the real-time algorithm put forward in this research is based on a strategy that satisfies the load optimization requirement and achieves dynamic compensation for unpredictable changes in renewable energy power generation. Moreover, the simulation compares the proposed algorithm capabilities with the existing algorithms/study, demonstrating the effectiveness of the suggested approach.
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