Unified data-driven stochastic and robust service restoration method using non-parametric estimation in distribution networks with soft open points

The service restoration is a vital measurement to enhance the resilience of the electrical distribution network. With the integration of distributed generations (DGs) in the distribution network, the uncertainties are introduced, which have a considerable impact on service restoration. Meanwhile, the soft open points (SOPs) are electronic devices installed in the tie-line of the distribution networks. They have the ability to control the branch power flow, which can be utilised to assist the service restoration. This study proposes a data-driven stochastic and robust service restoration method to handle the uncertainties of DGs outputs, which is modelled as a two-stage conic optimisation programming problem. The non-parametric estimation method is introduced to estimate the probability density function of forecasted error based on historical data. Furthermore, the nonlinear constraints of the SOPs are reformulated into conic forms so that the proposed model could be solved efficiently. Numerical tests are carried out on the IEEE 33-bus and 123-bus distribution networks to show the effectiveness of the proposed method, and the results show the superiority of the proposed method.