# Synergistic Optimization of Coal Power and Renewable Energy Based on Generalized Adequacy
## 1 Introduction  
The power production landscape is undergoing profound changes. Large-scale, intermittent renewable energy is gradually replacing controllable coal-fired units, leading to significant challenges in terms of energy absorption and curtailment of wind and solar power in some regions [1; 2; 3]. This issue primarily stems from insufficient system flexibility. The uncertainty of wind and solar power, combined with load-side uncertainties, can result in inadequate flexible capacity, impacting the system's dynamic supply-demand balance [4; 5]. Ensuring this balance requires not only meeting electricity demand but also having sufficient flexibility to accommodate dynamic changes in wind, solar, and load. Additionally, the extensive integration of converter-based resources has reduced the system inertia, making it more susceptible to disturbances [6]. For instance, the significant power outage in the UK in 2019 was due to high instantaneous shares of renewable energy lacking sufficient inertia support during large disturbances [7]. Furthermore, accelerating the decarbonization of the power sector is essential to meet low-carbon goals. Policies encourage the increase of renewable energy, with global projections indicating that renewable generation will constitute 45% of the total generation by 2030 [8; 9]. China aims to establish a power system dominated by renewable energy. Ensuring an adequate and secure energy supply during this transition is crucial [10; 11]. For example, Australia experienced a blackout due to the wind power output failing to meet the surging demand, and northeastern China faced power rationing in 2021 due to the insufficient coal supply [12]. Extreme weather significantly impacts renewable energy systems, as seen in Texas in 2021, where extreme cold led to power outages, and Sichuan, China, in 2022, where extreme heat increased the load and reduced the power output, resulting in power rationing [13; 14]. Such conditions can severely affect the adequacy and safety of renewable energy-reliant power systems. To enhance the energy supply stability, many countries are exploring large-scale utilization of broader clean energy sources, such as hydrogen and methane, while also investigating their potential to reduce carbon dioxide and solid waste. For example, [PERSON] et al. [15] identified hydrogen as a promising energy option for infrastructure-limited countries like Libya, after systematically analyzing hydrogen types, characteristics, production methods, and applications. Additionally, [PERSON] et al. [16] presented a method to assess the potential of converting solid waste, such as paper cups, into methane and hydrogen. They demonstrate through practical application in Ghana that transforming solid waste into these gases could significantly reduce energy consumption and pollution. Despite the undeniable advantages, hydrogen and methane still face challenges like high costs and safety concerns compared to more mature resources like wind, solar, and hydropower. However, recent research on retrofitting coal-fired units with carbon capture, utilization, and storage (CCUS) technology shows significant potential. CCUS is increasingly viewed as an effective approach for reducing CO\({}_{2}\) emissions and converting them into valuable methane during the energy transition [17; 18]. Given these technological and policy-driven requirements, the traditional concept of capacity adequacy is insufficient for new power systems. A \"Generalized Adequacy\" concept encompassing various dimensions, including traditional capacity adequacy, flexibility for dynamic balancing, and inertia for maintaining dynamic frequency safety, is urgently needed. In 2021, the Chinese Central Economic Work Conference emphasized that the gradual phase-out of traditional energy must be based on the secure and reliable substitution of renewable energy.