# Period Cycle Optimization of Integrated Energy Systems with Long-Term Scheduling Consideration
## 1 Introduction  
The current global energy consumption pattern is gradually becoming diversified and automated [1]. A single energy source is no longer able to meet users' demands [2]. Traditional energy sources have also formed their own systems and independently carried out production and supply [3], leading to a series of issues such as high energy consumption and low efficiency, as well as security concerns. With the changing global energy landscape and scientific and technological innovation [4], there is an increasing proposal to establish an interconnected energy system that integrates traditional and new energy sources to achieve integrated production, transportation, consumption, and storage of various types of energy [5]. The latest energy system designs are increasingly aimed at integrating renewable or low-carbon energy sources to reduce costs and decrease greenhouse gas emissions [6]. [PERSON] et al. [7] designed a home power energy management system using solar renewable energy, which effectively reduces the cost of energy usage in smart homes. [PERSON] et al. [8] utilized energy efficiency measures (EEMs) and photovoltaic (PV) cells to reduce energy consumption and carbon emissions for all types of buildings, alleviating the community's peak electricity load. [PERSON] et al. [9] proposed a hydrogen-based integrated energy system as the primary clean energy source, significantly reducing operational costs and carbon emissions. [PERSON] et al. [10] utilized solar-assisted ground source heat pump systems to enhance the performance of energy systems. Over the past decade, energy systems have evolved from initially being based on electricity and heat to focusing on thermal balance, integrating various types of energy sources and employing techniques such as energystorage and intelligent control to achieve the integrated intelligent control of energy [11]. [PERSON] introduced the concept of energy hubs [12] early on, which are multi-energy systems that connect different types of energy producers and consumers, leveraging energy conversion technology and storage to facilitate energy supply planning. [PERSON] [13] further investigated this concept by establishing modeling and optimization methods and studying the interconnection of multiple energy sources in a network. Renewable energy sources, in comparison to fossil fuels, are less amenable to storage and exhibit an uneven temporal distribution with a high degree of randomness. Within integrated energy systems, various energy flows are interconnected, presenting considerable uncertainty in their utilization. As the proportion and diversity of renewable energy sources continue to grow, energy system operation scenarios encounter uncertainty stemming from both consumer behavior and energy source variability [14; 15]. Consequently, to enhance the design of integrated energy systems, it becomes imperative to develop an optimization methodology capable of accommodating the diversity of operational scenarios and optimizing operational continuity [16]. In addition to considering the instability of renewable energy and the interactions between different energy sources, various issues need to be taken into account, such as the environment and the power of energy equipment. This will also result in a highly complex system. Therefore, various optimization methods can be employed in the design of integrated energy systems to enhance system complexity, reduce modeling efforts, and improve reusability [6; 17; 18]. [PERSON] et al. [19] developed an integrated optimization approach based on MILP (Mixed-Integer Linear Programming) to optimize various energy systems, aiming to minimize overall costs and enhance efficiency. [PERSON] et al. [20] utilized a dual-layer integrated optimization method based on a GA (genetic algorithm) and MILP to optimize a comprehensive energy system consisting of ground source heat pumps and solar collectors, with the objective of reducing the total costs and carbon emissions. [PERSON] et al.