# Capacity-Operation Collaborative Optimization for Wind-Solar-Hydrogen Multi-Energy Supply System
## 1 Introduction
Optimizing and efficiently operating systems can significantly enhance their performance [24; 25; 26]. Extensive research has been conducted on the optimization of multi-energy systems (MES), focusing on objectives like energy, economy, and the environment. The primary decision variable is often the equipment capacity. While the majority of studies prioritize single-objective optimization centering on economic feasibility, other factors such as efficiency, reliability, and environmental protection are equally vital in determining system operability [27]. Multi-objective programming addresses these considerations, especially in MES, where reducing pollution and improving reliability might mean compromising on economic feasibility to some extent [28]. [PERSON] et al. [29] used the genetic-algorithm-particle-swarm optimization to optimize the nominal PV, system power output point, and thermal energy storage capacity of a thermal-storage PV-CSP system for various scheduling strategies, aiming to achieve the most cost-effective electricity level. [PERSON] [30] developed an integrated energy system incorporating hydrogen storage and performed a multi-objective optimization focusing on carbon emissions and operational costs. This study revealed that multi-objective optimization outperformed its single-objective counterpart. The system's operating strategy also plays a pivotal role in the performance of MES [31]. [PERSON] et al. [32] introduced an enhanced operating strategy rooted in an electric heating load following and optimized the system using the Artificial Bee Colony Algorithm. They then compared optimization results across four variable operating strategies to identify the most effective one. Meanwhile, [PERSON] et al. [33] incorporated load scheduling into the multi-objective capacity optimization process, executing a capacity operation collaborative optimization for a solar-assisted coal-fired cogeneration system. Their aim was to strike the right balance between economic considerations and carbon emissions. Their method provided insights into the primary capacity and the system's annual load scheduling. A comparative analysis between this study and the referenced research can be found in Table 1.  
From a literature review perspective, a limited number of researchers have delved into the energy supply constraints of multi-source energy systems powered exclusively with renewable energy. Notably, few proposed systems have been designed to use CSP-wind-PV-PEMFC collectively for energy supply, while concurrently harnessing surplus energy for green hydrogen production, ensuring a consistent electrical output. Existing research primarily emphasizes integration methods and performance evaluations, often sidelining capacity and operational optimization. Furthermore, previous endeavors typically focused on the individual optimization of capacity and load scheduling for major components in systems connected to renewable energy sources. However, for determining the optimal capacity configuration, a combined approach to capacity operation is imperative. This is because load scheduling and capacity configuration are closely inter-related, influencing one another. Additionally, the wind-solar-hydrogen multi-energy supply (WSH-MES) system exhibits a sophisticated architecture. It encompasses diverse energy conversion pathways and mechanisms within its core processes, encompassing both photovoltaic-thermal and established thermal cycle energy conversion methods. Notably, the system is subject to the influence of meteorological conditions and user load requirements [24; 33; 34]. Remarkably, the factor of uncertainty stemming from this intricate interplay between energy source and load demand has been notably absent in prior system optimization investigations. This is particularly relevant for systems that are exclusively reliant on renewable energy sources. To fill the gaps in the previous studies, a capacity-operating co-optimization model that considers source-load uncertainty in the optimization process is proposed.