## 4 Results and Discussions
### Analysis of Intraday Optimization  
The proposed CO-CSES performs linear interpolation based on the day-ahead SOC trajectories to obtain the intraday SOC trajectory. The SOC trajectories before and after linear interpolation are shown in Figure 8.  
Table 10 demonstrates intraday operational costs and benefits under different cases. Different from the day-ahead centralized solution approach, the intraday optimal scheduling problem is solved using the ADMM distributed algorithm to coordinate the operation of subnetworks while preserving privacy, with a time scale of 15 min. Comparative analysis of Tables 8 and 10 demonstrates Case 3's economic advantages in both day-ahead and intraday stages. In the day-ahead stage, Case 3 reduces total operational cost by 9.21% and 8.81% compared to Case 1 and Case 2. In the intraday stage, Case 3 reduces total operational cost by 16.51% and 3.31% compared to Case 1 and Case 2. Cost reduction proves more significant during intraday operat \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Network**} & **Electricity** & \multirow{2}{*}{**Network**} & **ESS** & **DC Network** & **Total** \\  & & **Purchase** & **Loss Cost** & **Operat-** & **Interaction** & **Operat-** \\  & & **Cost** & **(CNY)** & **(CNY)** & **Benefit (CNY)** & **(CNY)** \\ \hline \multirow{3}{*}{Case 1} & AC1 & 21,766.04 & 992.05 & 209.54 & \multirow{3}{*}{29,860.16} & \multirow{3}{*}{60,530.71} \\  & AC2 & 38,939.16 & 749.10 & 317.37 & & \\  & AC3 & 25,532.86 & 1639.21 & 245.55 & & \\ \hline \multirow{3}{*}{Case 2} & AC1 & 19,617.78 & 962.31 & 149.13 & \multirow{3}{*}{29,846.15} & \multirow{3}{*}{52,266.82} \\  & AC2 & 33,597.38 & 741.70 & 293.22 & & \\ \cline{1-1}  & AC3 & 25,958.94 & 556.41 & 236.10 & & \\ \hline \multirow{3}{*}{Case 3} & AC1 & 19,521.93 & 716.05 & 198.49 & \multirow{3}{*}{29,859.78} & \multirow{3}{*}{50,538.56} \\ \cline{1-1}  & AC2 & 31,061.62 & 1538.19 & 366.77 & & \\ \cline{1-1} \cline{2-5}  & AC3 & 25,888.00 & 797.85 & 309.43 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Intraday operational costs and benefits under different cases. Figure 8: **A** comparison of CSES SOC before and after linear interpolation; (**a**) before; (**b**) after. coordination advantages under fine time-scale and complex source-load variation. In terms of cost components, the cost of purchased electricity is the main component, and CO-CSES achieves significant reductions in both stages. In the day-ahead stage, the cost of purchased electricity in Case 3 is 6.45% lower than in Case 1; by the intraday stage, this reduction further increases to 11.33%. Among the electricity purchase costs, the AC2 subnetwork with obvious source-load imbalance accounts for the largest proportion of the electricity purchase cost, while CL-CSES and CO-CSES both have a significant reduction in the electricity purchase cost of the AC2 subnetwork. This difference indicates that shared energy storage has higher flexibility and adaptability in coping with source-load source-loa imbalance. Network loss and ESS operational costs both increase during the intraday stage, reflecting the fact that the system faces more complex load and RES generation fluctuations in actual operation. Figure 9 illustrates the intraday power equilibrium for each AC subnetwork under CO-CSES at 15-min intervals. For the AC1 subnetwork (Figure 9a), a relatively stable power pattern can be observed with consistent CSES charging during early morning hours (0-5 h) and evening hours (19-22 h), while discharging operations primarily occur during 8-18 h when RES generation is low. In AC2 subnetwork (Figure 9b), which exhibits the most volatile RES generation profile, CSES operations demonstrate sophisticated temporal management with strategic charging during surplus periods (1-6 h) and discharging during deficit periods (9-12 h, 17-22 h), while VSC exchanges facilitate complementary energy transfer. And AC3 subnetwork (Figure 9c) shows relatively balanced operation with moderate charging/discharging cycling.