## Characteristics of Typical Intermittent Distributed Generation  
### Uncertainty Model of Wind Power Generation and Photovoltaic Power Generation  
Wind energy resources are among the most abundant and mature intermittent distributed power sources. Wind power is affected by many factors, which can be roughly divided into atmospheric characteristics, terrain characteristics, wind power, behavior index, other indexes and geographical conditions. Wind power has more influence and is greatly influenced by the change of natural environment, which leads to the obvious uncertainty of wind power output. In this paper, Weibull distribution with two parameters, which has the best application effect in engineering practice, is adopted. Its probability density function [20; 21] is:  
\[f(v)=\frac{k}{c}\bigg{(}\frac{v}{c}\bigg{)}^{k-1}exp[-\bigg{(}\frac{v}{c} \bigg{)}^{k}] \tag{1}\]  
where \(k\) is the shape parameters, \(c\) is the scale parameters, and \(v\) is the wind speed. The wind speed data used in this paper are from China National Meteorological Data Center. Scale parameter \(c\) and shape parameter \(k\) can be determined by Equation (2):  
\[k=\bigg{(}\frac{\sigma_{w}}{E_{w}}\bigg{)}^{-1.086},\ c=\frac{\overline{v}}{ \Gamma(1+k^{-1})} \tag{2}\]  
where \(\sigma_{w}\) is the variance of \(v\); \(\overline{v}\) is the average value of \(v\); \(E_{w}\) is the generation capacity; \(\Gamma\) is the gamma function. The turbine used here is a W2000-116-90 unit produced by the Shanghai Electric Group (Shanghai, China). When the cut-in wind speed is reached, the turbine starts to produce its power. As the wind speed increases, the turbine output will also increase. When the wind speed is too high, in order to protect the turbine, the turbine equipment will be automatically removed. Therefore, the output power of the turbine can generally be expressed by a piecewise function, as shown in Equation (3):  
\[P_{WTG(v)}=\left\{ \begin{array}{cc}0,&0\leq v\leq v_{ci}\\ \frac{P_{r}(v-v_{ci})}{v_{c}-v_{ci}},&v_{ci}<v\leq v_{cr}\\ P_{r},&v_{cr}<v\leq v_{co}\\ 0,&v>v_{co}\end{array} \right. \tag{3}\]  
where \(P_{WTG(v)}\) is the turbine output, \(v_{ci}\) is the cut-in wind speed, \(v_{cr}\) is the rated wind speed, \(v_{co}\) is the cut-out wind speed, and \(P_{r}\) is the rated active power. The cut-in wind speed is 3 m/s, the cut-out wind speed is 25 m/s and the rated wind speed is 6.7 m/s. Solar energy is the most abundant of all renewable energy sources. Photovoltaic power generation has remarkable flexibility, and its installation is simple and flexible. It is an important form and component of distributed power generation. At the same time, with the continuous development of photovoltaic power generation and the increase of investment, the cost of photovoltaic power generation has decreased significantly in recent years. The continuous increase of grid-connected photovoltaic power generation has also brought many impacts on the current grid scheduling and control, and this impact will continue to increase with the increase of grid-connected photovoltaic power generation. Similar to wind power, photovoltaic power generation has obvious randomness and uncertainty. In this paper, Beta distribution in probability model is used to describe the uncertainty of illumination intensity. Its probability density function [22; 23] is shown in Equation (4):\[f(S)=\frac{\Gamma(\alpha+\beta)}{\Gamma(\alpha)\Gamma(\beta)}\bigg{(}\frac{S}{S_{ max}}\bigg{)}^{\alpha-1}(1-\frac{S}{S_{max}}\bigg{)}^{\beta-1} \tag{4}\]  
where \(S\) is the illumination intensity; \(S_{max}\) is the maximum illumination intensity; \(\alpha\) and \(\beta\) is the two parameters corresponding to Beta distribution. The illumination intensity data in this paper are from China National Meteorological Data Center.