Two-Stage Distributionally Robust Optimization Dispatch for Power Systems with Uncertain Small-Sample Wind and Photovoltaic Data

Extreme meteorological phenomena (e.g., cold waves) are low-probability, high-impact events that present significant operational and dispatch challenges for new-energy power systems. (1) Insufficient data on wind and photovoltaic power generation hinder data-driven modelling. (2) The uncertainty of small-sample wind and photovoltaic data is difficult to characterize. Therefore, a two-stage distributionally robust optimization dispatch strategy for a power system based on small-sample wind and solar data with uncertainty is developed. First, a generalized modelling method for a conditional generative adversarial network (CGAN) is proposed, which increases the generation of hourly output data for wind and photovoltaic power. Considering the drawback of large prediction errors for wind power and photovoltaic power in small-sample cases, a two-stage distributionally robust optimization model based on the Wasserstein metric is constructed, which embeds hard constraints (e.g., the capacity constraint of wind and solar transmission lines) and soft constraints (e.g., prediction errors). This model is nonconvex, and exactly solving it incurs a heavy computational burden. Duality theory and relaxation approximation are adopted here; the robust two-stage-distribution model is transformed into a mixed-integer linear programming model, and the iterative Taylor formula algorithm is used to linearize the constraint conditions. A numerical example is provided to demonstrate that the proposed model and solution algorithm can not only address the uncertainty of small-sample wind and photovoltaic data but also reduce the system operating costs and increase the model-solving efficiency.