## 5 Case Study Analysis
### IEEE 24-Node Case
The planning results show a retirement capacity of 672 MW for retired units, with only 2600 MW of new energy units added, and wind and solar accounting for 48.2%. Comparing the investment cost, operation cost, and total cost of the three schemes, it can be seen that Scheme I only needs to meet the load growth and power transmission needs, so it requires the least investment cost and operating cost. Scheme II increases the commissioning and start-up of coal-fired power units in order to ensure the overall inertia level of the system, which mainly leads to an increase in operation costs. On the basis of Scheme II, Scheme III refines the inertia level at each node, which requires further control of the coal-fired unit operating status, thus again increasing the operation cost. The selection of key nodes can be adjusted based on actual conditions. In this analysis, several power source nodes are selected as key nodes, and the normalized inertia levels of the key nodes for each scheme are shown in Figure 3. In the figure, the horizontal coordinates are for Scheme I, Scheme II, and Scheme III, the vertical coordinates on the left side denote the key node numbers, and the vertical coordinates on the right side denote the normalized inertia levels of the nodes. The numbers in the squares indicate the specific normalized inertia level of each node in the corresponding scheme. As shown in Figure 3, Scheme I does not consider frequency security, resulting in lower calculated inertia levels at key nodes. The retirement of units can have a significant impact on the system, making it prone to security and stability issues. Scheme II only considers system frequency security; although the overall system meets frequency security constraints, \begin{table}
\begin{tabular}{c c c c} \hline  & **Scheme I** & **Scheme II** & **Scheme III** \\ \hline Unit retirement capacity/MW & 836 & 824 & 672 \\ \hline Unit retrofit capacity/MW & 800 & 812 & 964 \\ \hline New capacity of coal-fired power unit/MW & 440 & 1150 & 1650 \\ \hline New capacity of wind turbine/MW & 2200 & 1800 & 1600 \\ \hline New capacity of photovoltaic unit/MW & 1200 & 1200 & 1000 \\ \hline Renewable penetration/\% & 59.4 & 51.7 & 48.2 \\ \hline Renewable energy accommodation/\% & 97.1 & 98.6 & 98.2 \\ \hline New lines & (3–24) & (3–24) & (9–12) \\ (starting point-end point) & (9–12) & (10–12) & (14–16) \\ \hline Investment cost/billion & 18 & 19 & 19 \\ \hline Operation cost/billion & 57 & 66 & 70 \\ \hline Total cost/billion & 75 & 85 & 89 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of various planning results of 24-node case. the distribution of system inertia levels is uneven. Nodes with lower calculated inertia levels are prone to big frequency fluctuations following power disturbances. Scheme III takes into account the inertia level constraints of each node, resulting in improved inertia levels across all nodes in the system. The frequency variations in each scheme after adding power disturbances are shown in Figure 4. In the figure, the horizontal coordinate is the simulation time and the vertical coordinate is the frequency value. The yellow curve, the red curve, and the blue curve indicate the frequency response of Scheme I, Scheme II, and Scheme III, respectively. In each scheme, the initial value of the frequency is 50 Hz, the disturbance power is set at 0.5 s, and the lower limit of the frequency drop is 49.5 Hz. As shown in Figure 4, Scheme I, which does not consider frequency security, exhibits a large rate of frequency change and a significant frequency drop after power disturbances, resulting in poor frequency response characteristics. After considering frequency security, Schemes II and III show significant improvements in the system's RoCoF compared to Scheme I. Scheme III, which considers both system frequency security and node inertia constraints, exhibits the smallest frequency fluctuations and the best frequency response characteristics after power disturbances. Figure 4: Frequency curve after power disturbance of each scheme.