## 1 Introduction  
Along with the rapid development of the globalization trend in the world economy, the supply of energy cannot meet the growing production and living needs of people, and the situation of energy shortages and waste has become more and more serious in recent years. As the lifeblood of the national economy, energy is fundamental to national development, so a series of problems such as the excessive use of energy will be a common challenge for human beings [1; 2; 3]. An integrated energy system covers several energy subsystems, which can realize the complementary advantages of different energy sources in operation [4] and help improve energy utilization efficiency. They are widely valued, especially the increasing maturity of electricity to gas technology has further strengthened the coupling between energy sources, while gas turbines, heat exchangers, electric chillers, energy storage, and other technologies have been more widely used as important components in integrated energy systems [5; 6]. At the same time, renewable energy is clean, environmentally friendly, and inexpensive, which makes the whole system more efficient and cleaner. However, solar, wind, and other renewable energy sources are susceptible to natural environmental factors, resulting in randomness, volatility, and uncertainty in the output of photovoltaic wind turbines [7; 8]. As one of the most important parts of an integrated energy system, energy storage plays a big role in increasing grid flexibility, improving power quality, and promoting new energy consumption [9; 10]. However, during the operation of the system, the life of energy storage is affected by the number of times of charging and discharging, the depth of discharge, temperature, etc. The capacity of energy storage, the number of cycles, etc., will change, as will the operating efficiency and life decay characteristics of energy storage. The impact of the reliability and the economy of power system operations is increasing [11]. Therefore, the impact due to the decay of the energy storage life must be considered in the process of the study of the economic optimal dispatch of the integrated energy system. A lot of research has been carried out at home and abroad on integrated energy optimization scheduling that has included energy storage lifetime decay. In the literature [12; 13; 14] studies have been carried out on the economic dispatch of integrated energy systems, but they have not considered the impact of energy storage lifetime decay. The literature [15] proposes to use a large amount of experimental data to estimate the remaining capacity of the battery and thus characterize its health status. The literature [5] uses a rainflow-like counting method to simulate the energy operation state and calculate the lifetime of the energy storage. The literature [16] uses the rainflow-like counting method to analyze battery performance and calculate the battery aging cost. The literature [17] considered the full cell capacity life decay with instability on the surface of the silicon component. Among the existing studies conducted to study battery capacity decay, one model is based on physical and data-driven models, and the literature [18; 19] uses raw input signals (current, voltage, and temperature) to train machine learning models. The literature [20; 21; 22; 23; 24] uses preprocessed features from voltage, current, temperature, impedance, or power curves as input to the machine learning model. Still, another model is a continuum approach using porous electrode theory, where the model can be extended to capture potential degradation mechanisms leading to capacity decay, including differential voltage analysis models [25] and first-principles degradation models based on porous electrode theory [26]. The literature [27] selected a commutation factor to measure energy storage life decay in terms of exchange power, but the fixed commutation ratio makes it difficult to measure the dynamic change process of the battery during the actual operation.