## 4 Case Study
### Operation Results with BESS  
Based on the proposed optimization model (Case 3), the effect of auxiliary service compensation benefit and BESS reserve wind uncertainty on optimal capacity are analyzed, as below in Table 4. The charge/discharge power and SOC of BESS under different cases over a scheduling period are described in Figure 7.  
* Case 3: both the auxiliary service compensation and BESS reserve wind forecast error are considered, that is, the proposed model;
* Case 4: without auxiliary service compensation and with BESS reserve wind uncertainty;
* Case 5: with auxiliary service compensation, and without BESS reserve wind uncertainty; and,
* Case 6: neither auxiliary service compensation nor BESS reserve wind uncertainty is considered. Figure 6: Scheduling results of systems without BESS; (**a**) Case1 results without wind power integration; and, (**b**) Case 2 results with wind power integration. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & \(\mathbf{c_{g}}\) **(5/MW\(\cdot\)h)** & \(\mathbf{q}\) **(\%)** & \(\sum\
olimits_{g^{\text{N}}}^{\text{N}}\) **(MW)** \\ \hline
1 & 21.201 & - & 382 \\
2 & 21.579 & 6.09\% & 437 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Scheduling results of systems with and without wind power integration. It should be noted that, the objective functions of Case 4 and Case 6 without considering the auxiliary service compensation will be rewritten as:  
\[\text{max}f=S_{ave}-C_{cap} \tag{21}\]  
(1) Table 4 shows that with configuring BESS, \(c_{g}\) of Case 3-Case 6 with BESS is significantly smaller than that of case2 without BESS (21.534 $/MW.h). It is reasonable that BESS mitigate the operational cost of conventional units caused by the wind anti-peaking characteristics through transferring the wind power in the time and space. \(c_{g}\) of the proposed model Case 3 (\(c_{g}=\) 21.236 $/MW.h) is close to the results of Case 1 without wind power integration. It means that with taking both the ancillary services compensation and BESS reserve wind uncertainty into account, wind-energy union system can achieve the \"wind power friendly integration\" and the economy operation of systems. (2) Comprising \(c_{g}\) of Case 3 with Case 4 in Table 4, it can be seen that the economical operation of conventional units is further improved with BESS keeping reserve capacity for the wind uncertainty. From the benefits \(f\) of the wind energy union system in the Case 4, it can be seen that even if the unit investment cost of BESS is assumed as 250 $/kWh, the positive income will not be realized without considering the ancillary services compensation for BESS. That is, ignoring this part benefit of the BESS adapting to scheduling will seriously hinder the enthusiasm of wind farm configuring BESS and further harmful to the large-scale wind power integration. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Case** & \(c_{g}\) **(\$/MW-h)** & \(f\) **(\$)** & \(q\) **(\%)** & \(P_{cap}\) **(MW)** & \(S_{cap}\) **(MW-h)** & \(N_{eye}\) **(time)** \\ \hline Case 3 & 21.238 & 2990 & 0.0\% & 58 & 122.4 & 1.73 \\ Case 4 & 21.305 & \(-\)1540 & 0.64\% & 55 & 88.9 & 1.71 \\ Case 5 & 21.290 & 1790 & 3.61\% & 27.75 & 60.25 & 1.85 \\ Case 6 & 21.544 & 1050 & 4.32\% & 7.15 & 35.75 & 1.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal results with BESS for different cases. Figure 7: Charge/discharge process of BESS under different cases. SOC: state of charge. (3) As the optimal results in Case 5 shows, the total benefit of wind-energy union system is less than the proposed model of Case 3. It is mainly due to the equivalent cycle number over a scheduling period is increased without considering BESS reserve wind uncertainty, which shortens the equivalent cycle life of BESS and equivalent increases the unit investment cost of BESS to some extent.