## 4 Case Studies
### Probabilistic Forecasting of ALSC
#### 4.2.5 The Probabilistic Forecasting Results of ALSC and Risk Analysis  
Using the probabilistic forecasting data of wind power, photovoltaic power and load power can predict the probabilistic ALSC results at future moments. Therefore, we can have an understanding of the load supply capability of the power grid at future moments. More importantly, based on such probabilistic information, we can determine the risk of ALSC threshold overlimit \(P_{\text{ET}}\) and the probability that ALSC is equal to 0 \(P_{\text{EZ}}\), and, based on these indices, an early warning on the operation of power grid in the future can be hence achieved. Twenty-four time points (one day) are selected herein to present the probabilistic forecasting results of ALSC, as shown in Table 13.  
Table 13 provides the probabilistic forecasting results of ALSC: expectation of ALSC \(E_{\text{ALSC}}\); standard deviation of ALSC \(S_{\text{ALSC}}\); variation coefficient of \(\beta_{\text{ALSC}}\); the results of risk: probability of exceeding threshold for ALSC \(P_{\text{ET}}\) under different thresholds (0.05, 0.10, 0.15, 0.20, 0.25, 0.30); and the probability of ALSC equal to zero \(P_{\text{EZ}}\). It can be seen that the fluctuation of renewable energy generation and load over time poses a significant influence on the ALSC. As the forecasting values of wind power \(P_{\text{wind}}\), photovoltaic power \(P_{\text{pv}}\) and load power \(P_{\text{load}}\) change, the results of probabilistic ALSC evaluation are different for each moment. According to the forecasting results, we can estimate and warn the load supply capacity of the power grid at future moments. For example, from the 1 st time point to the 6 th time point, the \(E_{\text{ALSC}}\) is relatively high, the \(P_{\text{ET}}\) with threshold less than 0.2 equal to 0, and even the \(P_{\text{ET}}\) with threshold higher than 0.2 are relatively low and the \(P_{\text{EZ}}\) all equal to 0, illustrating that in this period, the load power supply capacity of the power system is sufficient. But from the 13 th to the 18 th time point, the \(E_{\text{ALSC}}\) is low, the \(P_{\text{ET}}\) almost equal to 1 and the \(P_{\text{EZ}}\) is high, illustrating that in this period, the load power supply capacity of the power system is seriously inadequate. Therefore, during this period, corresponding measures should be taken to increase the load supply capacity of power system to enhance the security and stability of the power grid. For example, the energy storage facilities such as pumped storage and large-scale battery energy storage systems are influential, and can change the probabilistic distribution of the generation and load power through their charging/discharging characteristics and can also provide power when generation is insufficient, so as to increase ALSC. Specifically, the impact of energy storage facilities on the probabilistic ALSC will be discussed in the next subsection.  
Figure 12: Comparisons on PDF of the ALSC with different forecasting models: (**a**) Comparisons amongst LGBM, XGB, RR and Stacking; (**b**) Comparisons amongst SVR, KNN, LR, LSTM and Stacking.  
To illustrate the results of probabilistic ALSC forecasting more intuitively, Figure 13 provides the prediction intervals (PIs) of ALSC at different confidence levels (10%, 20%, \(\ldots\), 90%). The PI is an interval range constructed around the predicted value of the model given a confidence level, used to indicate the probability that the true target value of a new sample will fall within this interval. The upper and lower bounds of the PIs are obtained through two quantiles. For example, the upper bound of the PI with 90% confidence level is the 0.95 quantile, and the lower bound is the 0.05 quantile. From Figure 13, it can be seen that as the confidence level increases, the PI gradually becomes narrow. In practical applications, the appropriate confidence level should be chosen according to the requirements to guide the operation of power systems.