Benchmark function.

The research on the value evaluation system of power-to-hydrogen (P2H) equipment configuration in integrated energy systems is of great value for optimizing resource allocation, improving energy utilization efficiency, and promoting clean energy technology development. However, there is no comprehensive evaluation system for evaluating P2H equipment configuration in integrated energy systems. Therefore, a multi-dimensional value evaluation system is proposed to realize the thorough evaluation of P2H equipment with different capacity configurations in the integrated energy system. Initially, a mathematical model considering flexibility benefit, new energy consumption benefit, economic benefit, and environmental benefit is established to maximize the comprehensive benefits brought by P2H equipment to the integrated energy system, and the model is solved using an improved backbone particle swarm optimization (IBBPSO) algorithm; subsequently, a multi-dimensional value evaluation system based on the analytic hierarchy process (AHP) -entropy weight method is constructed, and the value of P2H equipment with different capacity configurations in the integrated energy system is compared and analyzed when the comprehensive benefit is optimal. The experimental results show that the IBBPSO algorithm exhibits better performance in solving the optimization model. Compared to PSO, IBBPSO, GWO, and WOA algorithms, it improves by 9.8%, 11.09%, 33.57%, and 17.7%, respectively. The optimal solution is achieved when the P2H equipment is configured to 50 MW.