## 3 Case Study
### Optimization Results of Distributed ES  
Distributed ES plays a crucial role in promoting the local consumption of renewable energy, smoothing load peaks and filling valleys, and enhancing system stability. However, ES is divided into centralized ES and distributed ES, each with its own advantages. In order to verify the superiority of distributed ES in improving the economy, a comparison of system costs is conducted for a typical spring day under different deviation factors, as presented in Table 4.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Microgrid** & **MT Rated Power (kW)** & **ES Rated Power (kW)** & **ES Rated Capacity (kWh)** \\ \hline
1 & 800 & 350 & 800 \\
2 & 800 & 450 & 1000 \\
3 & 850 & 500 & 1200 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Industrial park parameters.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\beta\) & **0.01** & **0.02** & **0.03** & **0.04** & **0.05** \\ \hline \multirow{4}{*}{Cost(CNY)} & MT & 12,797.6756 & 12,926.5608 & 13,075.4533 & 13,200.2291 & 13,071.3108 \\  & ES & 1480.3489 & 1480.3492 & 1480.3495 & 14,918.847 & 1462.4225 \\ \cline{1-1}  & Grid & 24,842.6745 & 25,101.1227 & 25,339.5636 & 25,590.5863 & 26,136.3004 \\ \cline{1-1}  & Total & 39,120.6990 & 39,508.0327 & 39,895.3664 & 40,282.7001 & 40,670.0337 \\ \cline{1-1}  & \(a\) & 0.00884 & 0.01729 & 0.02487 & 0.03272 & 0.04283 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation results of different deviation factors of a typical spring day.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\beta\) & **0.01** & **0.02** & **0.03** & **0.04** & **0.05** \\ \hline \multirow{4}{*}{Cost(CNY)} & MT & 13,172.5418 & 13,253.6666 & 13,122.6272 & 13,297.1882 & 13,436.1970 \\  & ES & 1171.7510 & 1185.7495 & 1188.6066 & 1184.6710 & 1194.382 \\ \cline{1-1}  & Grid & 41,518.1605 & 41,976.2072 & 42,657.4839 & 43,039.9528 & 43,444.3274 \\ \cline{1-1}  & Total & 55,862.4533 & 56,415.6233 & 56,968.7177 & 57,521.8120 & 58,074.9064 \\ \cline{1-1}  & & 0.00560 & 0.01516 & 0.02455 & 0.03323 & 0.04244 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Simulation results of different deviation factors of a typical summer day.  
The results shown in Table 4 demonstrate that, for varying deviation factors, the cost of utilizing distributed ES in the industrial park is lower compared to using centralized ES. This cost advantage can be attributed to the ability of distributed ES to reduce transformer losses, thereby resulting in an overall cost reduction. Furthermore, as the deviation factor increases, the cost difference between distributed ES and centralized ES becomes more pronounced. Additionally, the centralized ES solution experiences higher transformer losses as the deviation factor increases.  
In order to further reflect the superiority of distributed ES, this paper chooses to compare the cost of centralized ES and distributed ES on typical days in summer. The simulation results are shown in Table 5. As shown in Table 5, the cost of distributed ES under five deviation factors is lower than that of centralized ES. This is because the distributed ES does not need to go through the loss of the transformer which is more conducive to the application of the microgrid.