## 4 Case Study
### Optimization Results Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(\mathbf{a_{m}}\)/(\(\mathbf{\text{V}}\cdot\text{MW}^{-2}\)) & \(\mathbf{b_{m}}\)/(\(\mathbf{\text{V}}\cdot\text{MW}^{-1}\)) & \(\mathbf{c_{m}}\)/(\(\mathbf{\text{V}}\)) & \(\mathbf{c_{i,\text{res}}^{\text{re}}}\)/(\(\mathbf{\text{V}}\cdot\text{W}^{-1}\)) \\ \hline SG & 0.03 & 97.65 & 1229.69 & 100 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Related parameters of SG. Figure 9: The variation in the NFDC of generators in typical scenarios. the ESSs is larger than the capacity requirement of the GFM-ESS. As a result, the power system can not only ensure its own stable operation but can also save the configuration cost of the ESS. Based on the NFDC, it is known that the inertia level of G30 is relatively low, for which the GFM-ESS should be configured. G32 and G33 belong to wind power, and the configuration of the GFM-ESS is influenced by the power output of the wind power. Before configuring the ESS, the inertia levels of various nodes in the system are relatively low. As shown in the system inertia distribution in Figure 8, the G30 node exhibits the weakest inertia support capability, where its value of NFDC is 0.18. As shown in Figure 9, with changes in the active power output of RESs, the value of the NFDC at certain generators may increase to around 0.25. This will weaken the inertia support capability of RESs, making the power system more prone to instability risks. Based on the energy storage allocation scheme of Scenario 1, a GFM-ESS can be constructed, and the variation in the NFDC as shown in Figure 10 can be described. After the ESS is configured, the NFDC of all generators in 39-bus system is less than 0.1. At the same time, the inertia distribution characteristics of the power system have also been enhanced. Moreover, the distribution of the inertia resources of the power system has become more balanced. In summary, this section first validates the feasibility of the value of the NFDC in assessing the inertia distribution of the power system. Subsequently, an optimization  
Figure 10: The variation in the NFDC of generators after the configuration of ESS. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Typical Scenarios** & \begin{tabular}{c} **The Operation** \\ **Cost of SGs** \\ **(Million V)** \\ \end{tabular} & \begin{tabular}{c} **The Configuration** \\ **Cost of ESSs** \\ **(Million V)** \\ \end{tabular} & \begin{tabular}{c} **The** \\ **Configuration** \\ **Location** \\ \end{tabular} & \
\begin{tabular}{c} **The Allocated** \\ **Capacity of** \\ **GFL-ESSs (MW)** \\ \end{tabular} &
\begin{tabular}{c} **The Allocated** \\ **Capacity of** \\ **GFM-ESSs (MW)** \\ \end{tabular} \\ \hline \multirow{3}{*}{Scenario 1} & \multirow{3}{*}{486.74} & \multirow{3}{*}{6.389} & G30 & 127.182 & 68.548 \\  & & G32 & 89.527 & 71.363 \\  & & G33 & 222.899 & 63.031 \\ \hline \multirow{3}{*}{Scenario 2} & \multirow{3}{*}{378.33} & \multirow{3}{*}{1.486} & G30 & 0 & 68.548 \\  & & G33 & 62.19 & 14.801 \\ \hline \multirow{3}{*}{Scenario 3} & \multirow{3}{*}{586.9} & \multirow{3}{*}{5.896} & G30 & 230.492 & 68.548 \\  & & G32 & 169.36 & 0 \\ \cline{1-1}  & & G33 & 115.476 & 27.334 \\ \hline \multirow{3}{*}{Scenario 4} & \multirow{3}{*}{581.6} & \multirow{3}{*}{1.99} & G30 & 30.952 & 68.548 \\  & & G33 & 82.698 & 16.802 \\ \hline \end{tabular}
\end{table} 
Table 5: The configuration locations and operation costs of ESSs under various scenarios. configuration method for the GFL-ESS and GFM-ESS is devised by integrating typical wind-load operation scenarios. Finally, the effectiveness of the proposed configuration method is verified through the improved IEEE 39-bus system. These findings can be used by stakeholders and policy makers to promote the full exploitation of the GFM-ESS in renewable energy power systems.