## 4 Case Studies
### Probabilistic Forecasting of ALSC
#### 4.2.6 The Impact of Energy Storage on Probabilistic ALSC  
Energy storage systems (ESS) refer to various devices or systems used for keeping the power balance. ESS in power systems can be usually divided into three types according to their installation locations: (1) installed on the generation side, (2) installed on the load side, (3) installed on the grid side. For ESS installed on the generation side, considering the smoothing effect of ESS on the uncertainty of wind turbine and photovoltaic cell outputs [46], it can be assumed that the ESS can reduce the standard deviation of the probability distribution of renewable energy generation. In addition, some energy storage elements such as superconducting magnetic energy storage can discharge instantly and increase power output [47]. Therefore, ESS can also increase the mean of the probability distribution of power output in a short period of time. Both of these effects aim at improving the ALSC. Similarly, for ESS installed on the load side, it can also reduce the expectation and standard deviation of the probability distribution of the load to enhance the ALSC. For ESS installed on the grid side, its charging and discharging characteristics are set to be determined by the power imbalance in the whole system [48]. Specifically, when the power generation is greater than the load demand in the power system, the ESS charges; when  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Time** & \multirow{2}{*}{\(\mathbf{E_{\text{ALSC}}}\)} & \multirow{2}{*}{\(\mathbf{S_{\text{ALSC}}}\)} & \multirow{2}{*}{\(\mathbf{\beta_{\text{ALSC}}}\)} & \(\mathbf{P_{\text{ET}}}\) & \(\mathbf{P_{\text{ET}}}\) & \(\mathbf{P_{\text{ET}}}\) & \(\mathbf{P_{\text{ET}  
the power generation is less than the load demand, the ESS discharges. The mathematical expression is shown in (53):  
\[P_{ESS,i}=\frac{1}{N_{ESS}}(\sum P_{Gi}-\sum P_{Di}) \tag{53}\]  
where \(P_{\text{ESS}}\) is the power of the ESS and \(N_{\text{ESS}}\) is the number of ESS. As shown in (53), each ESS shares the total power imbalance equally. When the power generation is greater than the load demand, the ESS charges and is treated as a positive load; when the power generation is less than the load demand, the ESS discharges and is treated as a negative load. In order to study the impact of different installation quantities and locations of the ESS on probabilistic ALSC, take the time 9 in Table 13 as an example; the experimental design is shown in Table 14. All cases are modified based on the base value at time 9. Cases 1-4 only study the case where ESS is installed together with wind turbines. Specifically, in Case 1 and Case 2, ESS only changes the mean of wind power output, checking the impact on ALSC of ESS with the mean changed to different extents. In Case 3, ESS only changes the standard deviation of wind power output, which can study the impact brought by ESS changing different characteristics of the probability distribution of wind power output. In Case 4, ESS changes both the mean and standard deviation, while Case 5 increases the number of ESS, with ESS installed on both wind power generators and photovoltaic power farms. Case 6 and 7 study the case where ESS is installed on the load side. Case 6 focuses on the three loads with close distances, and Case 7 covers the three loads which are far away with one another. It is worth noting that, in order to study the impact of different locations of energy storage on ALSC, the capacities of loads in Case 6 and Case 7 are close to each other, which implies that the energy storage facilities also have similar capacities. Case 8 studies the case where ESS is installed on the grid side. Figure 13: The prediction interval of ALSC at different moments. Table 15 shows the experimental results on the impact of energy storage on ALSC. Through the results of Case 1 and Case 2, it can be seen that when ESS increases the mean value of wind power output, the expectation of ALSC also becomes larger.