# Synergistic Optimization of Coal Power and Renewable Energy Based on Generalized Adequacy
## 2 Generalized Adequacy Theory and Coal Power Transition Modeling  
### Expansion from Traditional Adequacy to Generalized Adequacy  
Traditional power systems have numerous controllable power sources, with strong controllability on the supply side and high predictability on the demand side. Therefore, the focus has been primarily on generation capacity adequacy to meet users' power and energy demands [29]. Ensuring sufficient generation capacity was typically sufficient to guarantee the power system's supply capability. However, the rising proportion of renewable energy generation has altered some characteristics of the power system. Firstly, renewable energy generation is highly influenced by natural conditions, increasing the uncertainty and uncontrollability on the supply side. Secondly, the intermittency of renewable energy means it cannot provide the same load-bearing capacity as conventional coal-fired generation. Thirdly, the rapid fluctuations in renewable energy generation require other controllable units to quickly respond to meet load demands. Lastly, many renewable energy sources are inverter-based resources, which cannot provide the same rotational inertia as traditional synchronous units. The concept of traditional generation capacity adequacy, established under a framework of very low renewable energy penetration, does not adequately reflect the needs of modern power systems. This necessitates the use of \"generalized adequacy\" to describe the new requirements. The term \"generalized\" reflects an expansion when describing the adequacy needs of modern power systems, also indicating the balance of energy within these systems. Combining traditional adequacy with current conditions, this paper defines \"generalized adequacy\" on the supply side as the effective capacity, inertia, and ramping capabilities of various generation resources meeting the system's needs, including power and energy, dynamic frequency security, and flexible resource ramping capability, over a given time period. According to the concept defined in this paper, generalized adequacy includes three dimensions:  
1. Traditional capacity adequacy, representing the ability to balance power and energy. 2. Flexibility adequacy, reflecting the flexible adjustment capabilities of different types of power sources and the system's supply-demand flexibility. 3. Inertia adequacy, representing the ability of different power sources to support system inertia. From the perspective of the energy balance, capacity adequacy ensures that the quantity of electrical energy is sufficient to meet user demands. Flexibility adequacy ensures timely responses to changes in energy. Inertia adequacy ensures the system's ability to maintain its state during large disturbances and to resist rapid changes in energy, allowing enough time for the system to return to a normal state. Building on the concept of 'Generalized Adequacy', a key challenge lies in achieving coordinated resource planning that incorporates this expanded adequacy framework. Figure 1 highlights the main differences between traditional coal and renewable energy (RE) planning frameworks and those that account for \"Generalized Adequacy\". The traditional approach primarily bases resource needs on load growth, focusing on the supply-demand balance without fully considering the impacts of energy transition, carbon emissions, or coal power retirement and transformation. In contrast, the \"Generalized Adequacy\" framework integrates the seasonal distribution characteristics of renewable energy (RE), the synergistic properties of diverse resources, and the diversification of thermal power transition, including technologies such as CCUS and Carnot batteries. The planning model under this framework considers the investment, retirement, and transformation costs of various resources, alongside the constraints related to \"Generalized Adequacy\".