## 4 Case Study
### Analysis of the Thermal Energy Storage System in Power Units
Dispatch demand exhibits greater fluctuations at 20:00 and 22:00 in winter, leading to higher net load requirements for thermal power units. Consequently, the MSTS system is discharging at this time, which increases thermal power output. However, between 00:00 and 08:00, the net load on thermal power units is relatively low due to elevated wind power output, providingmore opportunities for participation in DPR. During this period, the MSTS system engages in charging, further enhancing the DPR revenue for thermal power units. Moreover, due to the influence of varying time periods and the stepped load rate adjustments on corrected output, the value of \(k_{\text{m}}^{\text{TPU}}\) is higher in winter. As a result, the revenue obtainable from DPR participation by thermal power units increases, ultimately incentivizing their involvement in PR. Consequently, the associated CA is relatively higher. Figure 9: Outputs at each time on two typical days obtained using the three-stage optimization method. Table 4 presents the total PR revenue and CA for each CS on a typical winter day, thereby quantifying the impact of CA on benefit distribution. Specifically, CSs 3 and 4 achieve higher PR revenue and exhibit a lower ratio of CA to revenue, whereas CSs 1 and 2 show the opposite trend. This disparity is attributed to the fact that CSs 3 and 4 are equipped with TPUMSTSR that possesses RLV capability and a wider adjustable output range. Observations indicate that CS 3 maintains a lower net load throughout the day and, consequently, attains the highest PR revenue. In contrast, although CS 4 records higher PR revenue than CSs 1 and 2 due to its higher net load, its participation in PR is limited to fewer time periods, leading to a relatively higher CA. Under scenarios of low net load, however, CS 4 demonstrates the potential to achieve both higher PR revenue and lower CA. Furthermore, CSs 2, 3, and 4 all realize PR revenue that exceeds their CA, thus enhancing overall profitability. Conversely, CS 1's PR revenue falls below its CA, resulting in a reduction in total profit. These results confirm that the CA method proposed herein can accurately quantify and distribute costs according to the number of DPR-participating units and the duration of their participation, thereby promoting a fair distribution of overall benefits among the CSs and IPPs. Moreover, incorporating CA into the CS dispatch process highlights the imperative for expediting flexibility retrofits of internal thermal power units to achieve a higher overall profit potential. To better compare the benefits brought by the three-stage optimization model, an independent optimization method is introduced as a benchmark. The differences between the two schemes are summarized in Table 5:  
**Scheme 1:** Multi-stage economic dispatch optimization with CA for MCSs. The optimal power flow model of the main grid determines the active/reactive power dispatch demands at each time period, with the objective function maximizing the overall weighted revenue of the MCS. The optimization process considers CA and adjusted power output following the proposed operation model. **Scheme 2:** Independent optimization for each CS without CA. The CA is calculated separately after sequentially optimizing each individual CS. In this scheme, the internal optimization of each CS aims to maximize its own intraday revenue based on known day-ahead active/reactive dispatch demands. The optimal dispatch results for these two schemes are shown in Table 6:  
The three-stage optimization model yields higher profits for all CSs compared to independent optimization. The revenue increase is most significant for CS 3, with an improvement of over 3%. The revenue differences for CSs 1 and 2 are smaller compared to CSs 3 and 4. This discrepancy arises because CSs 3 and 4 are equipped with 600 MW units retrofitted with TPUMSTSR under RLVs, whereas CSs 1 and 2 only have 200 MW/300 MW conventional units, which rarely participate in DPR.