## 3 Calculation of the Output Realization Probability of REG Stations  
At present, various types of renewable energy power prediction systems can provide the power prediction data of REG stations over different time scales, and the prediction errors basically conform to normal distribution [22; 23]. To ensure that each REG station can meet the maximum probability of output requirements, the allocation of the section margin should take into account the accuracy of each REG station's own power forecast in order to cope with the randomness and uncertainty of renewable energy output caused by the reduction in the output, as well as the fact that the REG station cannot meet the output requirements after the section margin allocation. Due to the different output forecasting models used by each REG station, as well as different natural conditions such as the geographical location and the meteorological  
Figure 2: Flow chart of section margin allocation for REG clusters considering the randomness of source and load power. characteristics of the construction, there are differences in the accuracy of the output forecasts of each REG station in the REG cluster [24; 25; 26; 27], which in turn leads to different probability distributions of the output forecast errors of each REG station. The historical output forecasts and the errors between the forecast and the actual values are collected for each REG station, and the probability density function of the predicted REG power error is obtained. The data required to establish the probability density function is the historical forecast error of the power output of the REG station, without regard to the type of renewable energy. Define the prediction error of the power output of the REG station \(i\) at time \(t\) as \(F_{i,t}\). The probability density function of the predicted REG power error of the REG station \(i\) at moment \(t\) is \(P_{f,i,t}(F_{i,t})\). From the historical forecasting information of the REG stations, the forecast errors of the REG station output are basically normally distributed. The probability density function of the predicted REG power error is:  
\[P_{f,i,t}(F_{i,t})=\frac{1}{\sqrt{2\pi}\sigma_{i,t}}e^{\frac{-(F_{i,t}-\mu_{i })^{2}}{2\sigma_{i,t}^{2}}} \tag{5}\]  
where \(\sigma_{i,t}\) is the standard deviation of the probability of prediction error for the REG station \(i\) at moment \(t\). \(\mu_{i,t}\) is the expectation of the prediction error of the REG station \(i\) at moment \(t\). In general, \(\mu_{i,t}\) = 0. \(P_{f,i,t}(F_{i,t})\) function image is shown in Figure 3.  
From Equation (4), the probability density function of the predicted REG power error of the REG station \(i\) at moment \(t\) is given by  
\[ \begin{array}{l}Pr_{i,t}(P_{it})=\int_{P_{i,t}}^{+\infty}P_{f,i,t}(F_{it}) \mathrm{d}F_{i,t}\\ =\int_{P_{i,t}}^{+\infty}\biggl{(}\frac{1}{\sqrt{2\pi}\sigma_{i,t}}\exp(- \frac{(F_{i,t}-\mu_{i,t})^{2}}{2\sigma_{i,t}^{2}}))\mathrm{d}F_{i,t}\end{array}  \tag{6}\]  
If \(P_{i,t}\) satisfies  
\[\frac{P_{i,t}-P_{i,t}^{pre}}{P_{i,t}^{pre}}=-\sigma_{i,t} \tag{7}\]  
The probability that the REG station \(i\) can achieve a power output of \(P_{i,t}\) at this point is shown in Figure 2.  
From Equations (5) and (6), it can be seen that the closer the predicted active power output of a REG station is to its rated active power output, the more accurate the predicted power is, and the greater the probability that the REG station can issue a more active power output, the greater the probability that it can meet the power output command after the margin allocation. Figure 3: Probability density function diagram of output prediction error of the REG station.