## 4 Case Study
### Sensitivity Analysis
#### 4.4.3 Reserve Level of BESS  
As mentioned earlier, the forecast error of wind power can be described by a normal distribution with a certain mean and standard deviation. That is, the forecast error interval concentrates in the larger probability of the inter-range. If considering the full reserve by the costly BESS for the 100% confidence interval of wind forecast error, there may be some reserve idle with less economical. Therefore, it is necessary to analyze the influence of the reserve level of BESS on the optimal capacity. The reserve  
Figure 8: Optimal results under different investment costs of BESS. C\({}_{\rm E}\): unit capacity cost of BESS.  
Figure 9: Optimal results under different cycle life of BESS. Lcy,N: cycle life of BESS with fully charge/discharge.  
level of BESS in Case 3 and Case 5 can be regarded as 100% and 0%. Based on Case 3 with the 100% reserve level, the reserve level is shortened successively. Thus, the effect of different reserve levels on the optimization results is analyzed, as shown in Table 6.  
It is worth mentioning that, in order to ensure that the reserve capacity that is provided by conventional units and BESS meet the uncertainty of wind output, the BESS constraints and spinning reserve constraint of units can be rewritten as:  
\[\left\{\begin{array}{l}-{{{\eta}_{s}}}{{P}_{cap}}+\Delta{P}_{wind,t}^{dt} \leq{{S}_{t}}\leq{{\eta}_{s}}{{P}_{cap}}-{{\varepsilon}_{s}}\Delta{P}_{wind,t} ^{up}\\ \Delta{P}_{wind,t}^{dt}\Delta t\leq{{S}_{soc,t}}\leq{{S}_{cap}}+\ {{\varepsilon}_{s}} \Delta{P}_{wind,t}^{up}\Delta t\end{array}\right. \tag{22}\]  
\[\left\{\begin{array}{l}\sum\limits_{i=1}^{{{N}_{g}}}{{{u}_{i}}}{{P}_{g,i}^{ \max}}-\sum\limits_{i=1}^{{{N}_{g}}}{{{u}_{i}}}{{P}_{g,i}}\geq\Delta{P}_{load,t }+(1-{{\varepsilon}_{s}})\Delta{P}_{wind,t}^{up}\\ \sum\limits_{i=1}^{{{N}_{g}}}{{{u}_{i}}}{{P}_{g,i}}-\sum\limits_{i=1}^{{{N}_{g }}}{{{u}_{i}}}{{P}_{g,i}^{\min}}\geq\Delta{P}_{load,t}+(1-{{\varepsilon}_{s} })\Delta{P}_{wind,t}^{dn}\end{array}\right. \tag{23}\]  
As can be seen from Table 6, with decreasing the BESS reserve level for wind uncertainty, the net benefit of wind-energy union system returns to increase first and then decrease. This is mainly because that the investment cost of BESS is still expensive when compared to the benefit of auxiliary service compensation. If BESS provides full reserve capacity for the wind uncertainty, there will be a lot of waste for the wind uncertainty being mostly concentrated in the small confidence interval with high probability. However, with the reserve level decreasing, the net benefit of wind-energy union system decreases again limited by the equivalent cycle life and the auxiliary service compensation income.  
In addition, it can be seen from Table 6 that, when the reserve level being 60%, both the net benefit of wind-energy union system and the operation efficiency of conventional units are the maximum. The variety rates of the performance indices (_f_, \({{c}_{g}}\), and \({q}\)) are small with the reserve level between 40% and 60%. It means that the installed power of BESS being 68.75-76.8 $/MW\(\cdot\)h and the installed capacity of BESS between 30.2 and 32.8 MW can realize the operation efficiency of BESS and conventional units in this wind farm.