# Synergistic Optimization of Coal Power and Renewable Energy Based on Generalized Adequacy
## 4 Results--Case Study
### Impact of Considering General Adequacy Constraints on Planning  
During power system planning and construction, adequacy has reached a new level of importance. To ensure flexibility and inertia adequacy in low-carbon transitions, the combined optimization planning model includes flexibility and inertia adequacy constraints. Table 2 sets out four cases, including normal and extreme weather conditions, to compare the impact of considering general adequacy constraints on coal and renewable energy planning. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Share of Electricity from** & **0.3** & **0.325** & **0.35** & **0.375** & **0.4** \\
**Renewable Sources** & **0.4** & **0.325** & **0.35** & **0.375** & **0.4** \\ \hline Energy storage capacity (MWh) & 15,996 & 35,891 & 35,699 & 38,211 & 40,048 \\ Energy storage power (MW) & 7522 & 16,878 & 16,787 & 17,966 & 18,832 \\ Carnot battery scale (MW) & 2873 & 3354 & 1695 & 1833 & 2225 \\ Coal-fired units scale (MW) & 61,452 & 60,130 & 60,482 & 61,248 & 60,978 \\ Wind power scale (MW) & 23,505 & 29,381 & 27,924 & 35,237 & 47,086 \\ Photovoltaic scale (MW) & 12,565 & 11,535 & 20,783 & 17,797 & 8491 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Installed capacity of various sources under different shares of electricity from renewable sources. Figure 6: Change in cost and CCUS installed capacity under different renewable energy penetrations. Figure 7 illustrates that when the flexibility and inertia adequacy constraints are not taken into account, the capacity of retiring coal units increases, leading to their accelerated retirement. This helps balance the need to avoid excessive carbon emissions while keeping more coal units online. In Case 2, wind power installation increases while solar power installation decreases, necessitating more storage capacity to manage wind power fluctuations. Considering the flexibility and inertia constraints raises the system's total cost by 0.0105% due to the need for increased investment in renewable installations and retaining more coal units for flexibility support. Comparing Case 1 with Case 4, the system's demand for flexibility and inertia support during extreme weather conditions requires higher output from coal-fired units. This results in increased carbon emissions, necessitating the installation of carbon capture units on a greater proportion of coal-fired plants to stay within the system's carbon emission limits. Overall, the total installed capacity in the system increases under extreme scenarios, whether or not flexibility reserves and inertia constraints of generalized adequacy are considered. From Figure 8, it is evident that in Case 1 and Case 2, the system's inertia supply capability remains high due to the significant installed capacity of energy storage systems. Both energy storage and coal-fired units contribute to the inertia support, thereby maintaining high levels of inertia supply for the dynamic frequency support. \begin{table}
\begin{tabular}{c c c} \hline \multirow{2}{*}{**Case Number**} & \multicolumn{3}{c}{**Considering Factors**} \\ \cline{2-3}  & **Extreme Weather** & **Flexibility and Inertia Adequacy Constraints** \\ \hline
1 & \(\times\) & \(\surd\) \\
2 & \(\times\) & \(\times\) \\
3 & \(\surd\) & \(\times\) \\
4 & \(\surd\) & \(\surd\) \\ \hline \end{tabular}
\end{table} 
Table 2: Case setting. Figure 7: Installed capacity of various sources in different cases. Comparing Case 1 with Case 2, considering the flexibility and inertia adequacy constraints shows a relative decline in the system's inertia supply capability. This is due to a reduction in the energy storage capacity and the constraints preventing excessive online unit reserves, which avoids cost escalation and resource wastage. In Case 3 and Case 4, neglecting the constraints results in long-term inertia supply levels below the system's requirements for dynamic frequency support, especially during extreme weather conditions. This makes it difficult to maintain frequency stability at the required inertia levels.