# Power System Reliability Assessment Considering Coal-Fired Unit Peaking Characteristics
## 1 Introduction
UGF serves as a robust mathematical tool for modeling and analyzing multi-state systems by representing system states and their corresponding probabilities in polynomial form. The fundamental principle of UGF lies in mapping discrete system states into a generating function, where each polynomial term characterizes a potential system state with its coefficient denoting the occurrence probability of that state. In the field of reliability modeling for power systems, UGF has emerged as a critical methodology that enhances model clarity and computational efficiency. A study [15] leverages the UGF model for the reliability analysis of hybrid uncertainty structures in turbine systems, demonstrating a nearly 18-time improvement in computational efficiency compared with Monte Carlo simulations. Another study [16] integrates UGF with Bayesian methods for the reliability assessment of complex multi-unit power generation systems, achieving significant efficiency optimization. Furthermore, researchers [17] have employed UGF techniques combined with Weibull distribution analysis to evaluate the operational reliability of wind turbine components, providing a probabilistic framework for failure mode assessment in wind power generation systems. Probabilistic models serve as critical tools for describing and analyzing system behaviors under uncertain operational conditions, particularly in evaluating key performance indicators such as operational reliability and risk profiles of power systems. The development of component-level state probabilistic models forms the foundation for such analyses. Researchers [18] have established a probabilistic reliability model for microgrids and develops an analytical framework for assessing the reliability of distribution systems with microgrids. The proposed microgrids probabilistic model can simplify and accelerate computational processes associated with reliability evaluation of distribution systems incorporating multiple microgrids. For coal-fired power plants, researchers [19] have developed accident probabilistic models to assess operational risks through dynamic likelihood evaluation of turbine generator contingencies. Additionally, in smart grid applications, an Electric Vehicle Virtual Energy Storage System charging/discharging power probabilistic model has been proposed to enhance the reliability assessment of distribution networks incorporating virtual energy storage technologies [20]. These implementations demonstrate the adaptability of probabilistic modeling in addressing diverse challenges across renewable energy integration, conventional power generation, and modern grid management. To fully consider the impact of coal-fired unit peak shaving characteristics on the reliability of the power system, an improved PPS method is proposed in this study, inspired by the multi-state unit model in the literature [21]. This method first rigorously considers the temporal fluctuations of load demand and renewable energy. Secondly, a multi-state model for coal-fired units is established, incorporating their life degradation and failure rates under different output states. The transition rates between unit states are dynamically adjusted based on load demand and operational status. Similarly, a multi-period equivalent multi-state model is developed for wind power generation. Finally, the UGF algorithm is employed to perform joint calculations on the probabilistic models of different units, enabling the PPS. This approach allows for the computation of system reliability indicators, dynamic costs such as unit start-up and shut-down, and the evaluation of the system's ability to accommodate wind power. This study investigates the influence of different peak shaving capabilities of units on the reliability of the power system. The proposed method is then verified through case analysis using the IEEE-RTS79 test system.