## 4 Case Studies
### Probabilistic Forecasting of ALSC
#### 4.2.6 The Impact of Energy Storage on Probabilistic ALSC
Accordingly, the risk index decreases, indicating that ESS plays a role in increasing the load supply capability of the power system. In addition, it can be seen that the more ESS increases the mean value of wind power output, the greater the increase on the expectation of ALSC and the smaller the risk index. This shows that ESS with larger capacity has a stronger regulation capability for integrating new energy generation and can more effectively ensure an adequate load supply capability. Moreover, as the expectation of ALSC rises, the standard deviation of ALSC also increases. This is because the larger mean value of wind power output makes more sample values nonzero, which is also reflected in the \(P_{\text{EZ}}\) index, thus resulting in a larger standard deviation of ALSC. But in fact, the ALSC in Cases 1 and 2 has a smaller degree of dispersion compared to the original case (Time 9), because they have smaller variation coefficient \(\beta_{\text{ALSC}}\). By comparing Case 3 with the original case and comparing Case 4 with Case 2, it can be found that reducing the standard deviation of wind power output with ESS decreases the degree of dispersion of ALSC; that is, a smaller standard deviation and coefficient of variation. The results of Case 5 indicate that after installing ESS on both the wind power and PV generation side, the level of ALSC will be further improved. The results of Case 6 and Case 7 indicate that installing ESS at three distant loads improves ALSC more significantly. This is probably because the three distant ESSs can cover a larger area in the grid, while the three close ESSs concentrate in one region and impose limited impact on the other buses. Therefore, in practical operation, the most suitable ESS installation location should be selected for improvement of ALSC to the greatest extent. In the end, from the results of Case 8, it can be seen that under reasonable control strategies, ESS installed on the grid side can effectively improve the expectation of ALSC and reduce the degree of dispersion of ALSC. This is because when there is power imbalance in the power system, ESS can be effective at depressing such imbalance very well, thus improving ALSC. In general, whether ESS is installed on the generation side, load side or grid side, it can always effectively improve ALSC. This is reflected from increasing the expected value of ALSC on one hand, and reducing the degree of dispersion of ALSC on the other hand. \begin{table}
\begin{tabular}{c c} \hline
**Cases** & **Description** \\ \hline Case 1 & ESS is installed at bus 34, increasing the expectation of wind power to 1.5 times. \\ \hline Case 2 & ESS is installed at bus 34, increasing the expectation of wind power to 2 times. \\ \hline Case 3 & ESS is installed at bus 34, decreasing the standard deviation of wind power to 0.5 times. \\ \hline Case 4 & ESS is installed at bus 34, increasing the expectation of wind power to 2 times and decreasing the standard deviation of wind power to 0.5 times. \\ \hline Case 5 & ESS are installed at bus 30 and 34, increasing the mean of wind power and photovoltaic  power to 2 times and decreasing the standard deviations to 0.5 times. \\ \hline Case 6 & ESS are installed at bus 1, 3, 4, decreasing the mean of load to 0.5 times and decreasing  the standard deviations to 0.5 times. \\ \hline Case 7 & ESS are installed at bus 1, 15, 28, decreasing the mean of load to 0.5 times and decreasing  the standard deviations to 0.5 times. \\ \hline Case 8 & ESS are installed at bus 5, 6, 13, 14 and 19. \\ \hline \end{tabular}
\end{table} 
Table 14: Introduction of eight different cases.