Distributionally robust optimization model of active distribution network considering uncertainties of source and load

Abstract

To ensure the safety and reliability of the distribution network and adapt to the uncertain development of renewable energy sources and loads, a two-stage distributionally robust optimization model is proposed for the active distribution network (ADN) optimization problem considering the uncertainties of the source and load in this paper. By establishing an ambiguity set to capture the uncertainties of the photovoltaic (PV) power, wind power and load, the piecewise-linear function and auxiliary parameters are introduced to help characterize the probability distribution of uncertain variables. The optimization goal of the model is to minimize the total expected cost under the worst-case distribution in the ambiguity set. The first-stage expected cost is obtained based on the predicted value of the uncertainty variable. The second-stage expected cost is based on the actual value of the uncertainty variable to solve the first-stage decision. The generalized linear decision rule approximates the two-stage optimization model, and the affine function is introduced to provide a closer approximation to the second-stage optimization model. Finally, the improved IEEE 33-node and IEEE 118-node systems are simulated and analyzed with deterministic methods, stochastic programming, and robust optimization methods to verify the feasibility and superiority of the proposed model and algorithm.

Keywords

• Active distribution network (ADN)
• Source–load uncertainty
• Two-stage distributionally robust optimization
• Ambiguity set
• Generalized linear decision rule