The article constructs the covariance matrix as well as the mean vector of the stochastic differential equation and tests its hypotheses using the EM algorithm estimation. The model is applied to the PV carrying capacity assessment of county distribution networks, and the method is utilized to solve for the maximum PV capacity under the constraints such as the discard rate. Meanwhile, the distribution of PV carrying capacity prediction error uncertainty is analyzed by cloud modeling, and the kernel density estimation is used to quantify the prediction error confidence interval. Combined with the collected PV historical operation and real-time observation data, the carrying capacity assessment and uncertainty analysis are carried out. When the PV abandonment rate is 3.5%, the maximum overload and maximum network loss are 6.495 MW and 0.712 MW, respectively, and the PV acceptable capacity reaches a steady state. The results of PV carrying capacity assessment of this paper’s method and Monte Carlo method in power supply station area are close to 6.73MW and 6.71MW, respectively, but the calculation time of this paper’s method is faster. The application of stochastic differential equation modeling yields high accuracy of PV carrying capacity prediction results, which fall completely inside the 85% to 95% confidence interval. The PV carrying capacity prediction result of this paper’s method for 816 households in a county is 2652 kW. This paper’s method can effectively predict the PV carrying capacity of county distribution networks and realize accurate assessment. The confidence interval of the carrying capacity is quantified by combining the nonparametric kernel density estimation method.
