## 1 Introduction  
In the research on configuration optimization, equipment characteristic modeling refers to the establishment of mathematical models that are related to the capacity, performance parameters, and operational output parameters of equipment. It serves as the foundation for integrated configuration models. Based on the level of detail in the equipment model within the configuration optimization model, the models can be classified into two types: steady-state nominal condition models and variable operating condition models. The steady-state nominal condition model [1, 2] primarily represents a steady-state mathematical model that characterizes the relationship between energy consumption and output under nominal conditions, which can be used to describe the energy consumption and output relationship in various operating conditions. For example, [PERSON] et al. [1] established a micro-gas turbine model using thermal efficiency, intuitively describing the relationship between fuel consumption and power output. [PERSON] et al. [2] developed a cogeneration unit model, considering multiple factors such as thermal efficiency, electrical efficiency, and heat dissipation coefficient. Recently, considering the dynamic processes of equipment in the system has become a new research focus. For instance, [PERSON] et al. [3] used a simplified first-order dynamic model to replace the steady-state model and simulated the power ramp-up state of a gas turbine, studying its impact on system configuration results. [PERSON] et al. [4] applied the node method to model the dynamics of the heat network, and, after linear simplification, proposed a day-ahead optimization scheduling method that considered the dynamic characteristics of the heat network, further concluding that the dynamic features of the heat network help improve the flexibility of unit operation. Synchronized optimization of process design and control has become a recent research hotspot in chemical engineering [5; 6; 7; 8; 9; 10], but the simultaneous optimization problem of control parameters and process design is highly complex, with long solution times, and solving such complex systems exceeds the capabilities of most algorithms and commercial solvers [6]. Therefore, optimization solving methods have not yet been fully solved or overcome. Moreover, a large number of capacity configuration studies both domestically and internationally still adopt deterministic methods, using sensitivity analysis and other techniques to represent the impact of uncertainty on configuration results. However, uncertainties in the load side often arise due to random fluctuations, which can have a significant impact on the stability and efficiency of system operations. From the perspective of considering uncertainty, stochastic programming and robust optimization are currently the two most common methods in system optimization [11]. Research on the two-stage stochastic programming method for capacity configuration optimization in integrated energy systems has achieved certain results. For example, [PERSON] et al. [12] employed the two-stage stochastic programming method to design and optimize the operation of the energy storage subsystem in a renewable integrated energy system, representing random factors in the form of equivalent scenarios and converting the optimization problem into a Mixed-Integer Linear Programming (MILP) problem for solving. [PERSON] et al. [13] proposed a linear multi-stage stochastic programming method for optimizing electricity production planning, combining scenario trees and Monte Carlo sampling methods to represent uncertainties in electricity prices, investment costs, and fuel costs. [PERSON] conducted a semi-physical flight test on a fuel cell hybrid power system for UAVs based on the Grob109 model [14]. The experimental results showed that incorporating a supercapacitor into the hybrid system helps improve the durability of the fuel cell. [PERSON] et al.