Robust economic dispatch for distribution network with nonparametric probabilistic characteristics of centralized/distributed photovoltaics

The uncertainties of centralized and distributed photovoltaics have changed the traditional operation mode of the distribution network. In this study, a robust economic dispatch method is proposed to deal with the uncertainty of centralized and distributed photovoltaics. Firstly, distributed photovoltaics is integrated into virtual power plants. The analytical mapping relationship between the boundary interactive power of virtual power plants and high-dimensional input variables of distributed photovoltaic power is established based on the KKT condition. The Gaussian mixture model is then combined with the analytical relationship to derive the probability distributions of the maximum and minimum boundary interactive power. Secondly, a robust dispatch model considering the uncertainty of the boundary interactive power and centralized photovoltaics is established for the distribution network, which quantifies the admissible region of centralized photovoltaics power and optimizes the unit output and reserve plan. Finally, numerical experiments on the IEEE 6-bus and IEEE 33-bus systems are conducted to verify the availability of the robust economic dispatch method.