## 5 Case Study Analysis  
### IEEE 24-Node Case  
(1) Example Parameters and Scenario Setting  
This paper uses the IEEE RTS 24-node system [24] to validate the planning model. The 24-node case network topology is shown in Figure 2. To simplify the model, only coal-fired, wind, and photovoltaic power units are considered. The modifications are as follows: nodes 3, 10, and 19 each connect to a 200 MW wind farm, and nodes 5 and 8 each connect to a 200 MW photovoltaic plant. In the example, the total installed capacity of coal-fired power units is 3405 MW, with 1636 MW being aged units. The investment cost for coal-fired power units is considered as 3.5 million CNY/MW, for wind power units is considered as 5 million CNY/MW, for photovoltaic units is considered as 4 million CNY/MW, and for associated energy storage is considered as 4 million CNY/MW and 1.5 million CNY/MWh. The total retirement cost for aged coal-fired power units (unit capacity disposal cost-unit capacity recovery benefit) is considered as 32,000 CNY/MW, and the retrofit cost is considered as 800,000 CNY/MW. The coal cost for coal-fired power units is considered as 300 CNY/MWh, the operation and maintenance cost for hydropower is considered as 150 CNY/MWh, the operation and maintenance cost for new energy units is considered as 80 CNY/MWh, and the curtailment cost is considered as 300 CNY/MWh. \(R_{f\max}=0.24 Hz/s\). The remaining parameters are set based on studies [18; 25]. Due to the randomness, intermittency, and volatility of wind and solar power output, this paper uses the Copula function to model the correlation of output data for wind and photovoltaic units, combined with the K-means clustering method to obtain typical daily wind and solar output conditions. The normalized typical daily output and load data are shown in Table 1. The proposed optimization model can be solved using the YALMIP [26] toolbox and Gurobi solver [27], with a solution accuracy set to 0.1%. To validate the effectiveness of the model proposed in this paper, three comparison schemes are set as follows: Scheme I: a retirement and source-grid planning model that does not consider frequency security; Scheme II: a retirement and source-grid planning model that considers overall system frequency security but does not account for node inertia constraints; Scheme III: a retirement and source-grid planning model that comprehensively considers both overall system frequency security and node inertia constraints. Figure 24: Model-model case network topology. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Scenario 1**} & \multicolumn{4}{c}{**Scenario 2**} \\ \hline
**Time** & **Wind Power Output** & **Photovoltaic Power Output** & **Load** & **Time** & **Wind Power Output** & **Photovoltaic Power Output** & **Load** \\ \hline
1 & 0.59 & 0 & 0.74 & 1 & 0.23 & 0 & 0.50 \\ \hline
2 & 0.59 & 0 & 0.72 & 2 & 0.25 & 0  
2 Analysis of Planning Results  
The planning results obtained from solving the three schemes are shown in Table 2.  
From the planning results of each scheme, it can be seen that Scheme I, because it does not consider system frequency security during the retirement of coal-fired units and the construction of new energy units, has the highest retirement capacity of aged coal-fired units at 836 MW, accounting for 51% of the total capacity of aged units. Additionally, the new capacity for new energy units is 3400 MW, with wind and solar accounting for 59.4%. In Scheme II, under the premise of ensuring the overall system inertia level, the retirement of units and the expansion planning of new energy units are carried out. The capacity of retired units decreases compared to Scheme I, while the newly added renewable energy capacity reaches 3000 MW, with a wind-solar share of 51.7%. Scheme III, while considering system frequency security, further constrains the inertia levels at key nodes.