## 4 Case Study
### Optimization Results Analysis  
RESs and loads have different power curves in different seasons. In order to explore the inertia distribution characteristics of a power system during different time periods, this study considers four normalized power scenarios of wind and load, as shown in Figure 8, aiming to configure the GFM-ESS and GFL-ESS in the most economical way. This will help improve the utilization efficiency of RESs in the power system and enhance the inertia distribution characteristics of the power system. G32 to G34 in the 39-bus system are designated as wind power. The predicted power output of the wind power and the power consumption of the load nodes are constrained in accordance with the power curves depicted in Figure 8.  
The four typical power scenarios in Figure 8 include the power characteristics of summer, winter, and transitional seasons. In winter, the wind power output is generally higher throughout the day, while in summer, it is relatively lower. In transitional seasons, wind power exhibits higher levels in the early morning and evening, with lower output during midday. Regarding load characteristics, winter shows higher power consumption in the early morning and evening, while the peak load consumption in summer occurs around midday. Figure 8: Typical normalized power scenarios of wind and load. Figure 7: The inertia distribution characteristics of the IEEE 39-bus system. The value of the NFDC can represent the strength of the inertia support capability of each node in the power system. The variation in the NFDC of each generator in scenario 1 is shown in Figure 9.  
Based on the simulation results, it can be observed that as the active power output changes, the inertia level of wind power will change significantly. At the same time, the inertia support capability of SGs is hardly affected by their active power output. This is because the inertia response characteristics of SGs primarily rely on their rotational inertia. In contrast, wind power is limited by its control strategy and the characteristics of power electronic devices, which makes it difficult for its active power to be fully released. The relevant parameters of the generator and ESS are presented in Tables 3 and 4, including the power generation cost coefficient, RES penalty coefficient, and cost coefficient of the ESS. By outputting active power, the GFM-ESS can provide inertia support capability, which is represented by the equivalent inertia constant (EIC). The optimization configuration results of ESS, calculated under various scenarios, are presented in Table 5. The system inertia demand, the installation locations of the ESSs, and the operating costs of the generators are solved based on the CPLEX solver (version 12.10.0.0). The optimization model aims to minimize the total system operating cost while ensuring that the inertia levels at each node meet the standards, and solves for the configuration, location, capacity, and type of ESS. The capacity demand of the GFM-ESS is quantified according to the value of the NFDC, and the total configured capacity of ESSs can be calculated based on the optimization configuration method. When the total configuration capacity of ESSs is less than the required capacity of the GFM-ESS, all available resources of the ESSs will be prioritized for the construction of the GFM-ESS. Since the configuration cost of the GFM-ESS is relatively high, the GFL-ESS will be additionally configured when the total configured capacity of \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{k_{\text{GFL}}^{\text{P}}}\)/(\(\mathbf{\text{V}}\cdot\text{MW}^{-1}\)) & \(\mathbf{k_{\text{GFM}}^{\text{P}}}\)/(\(\mathbf{\text{V}}\cdot\text{MW}^{-1}\)) & \(\mathbf{r/\%}\) & **EIC/(s\(\mathbf{\text{-}}\cdot\text{MW}^{-1}\))** & \(\mathbf{L/\text{Year}}\) \\ \hline ESS & 250 & 300 & 6 & 0.2 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Related parameters of ESS.