Two-stage robust optimization for practical reactive power in distribution network based on multiple constraint convex approximation.

• A data-based method of modeling multiple uncertainty is proposed and the proposed uncertainty set contains the interval constraint and convex hull of an ellipsoid constraint. • A pseudo-decoupling PV dispatch strategy is proposed to approximate the separation of reactive power and uncertainty through convex optimization. • A two-stage robust optimization at the hourly level is proposed based on an SOCP relaxation-based model, the aforementioned multiple uncertainty set, and the pseudo-decoupling PV dispatch strategy. • A dispatch method is proposed to minimize the network loss without the short-time optimization in the centralized optimization framework. In multi-time-scale optimization frameworks of daily, hourly, and minute levels, centralized optimization has a demand for real-time communication and prediction technology. In the distribution network of an undeveloped area, the minute level optimization does not work because of the lack of accurate prediction and real-time communication. The practical reactive power originally obtained from the minute-level optimization does not exist, and the uncertainty should be considered in hourly level optimization. In this study, a two-stage robust optimization at the hourly level is proposed to minimize the network loss without the minute level optimization. A simple data-based method of modeling multiple uncertainty is proposed, which directly uses historical data with minimal mathematical knowledge. The multiple uncertainty set contains the interval constraint and convex hull of an ellipsoid constraint. The convex hull of the ellipsoid constraint is formed by ellipse tangents. In addition, the practical reactive power cannot be obtained through the common robust inverter dispatch strategy, which sets the maximum available active power as an uncertain variable. A pseudo-decoupling dispatch strategy is proposed to approximate the separation of reactive power and uncertainty and obtain the practical reactive power. The Benders decomposition framework is used to solve the two-stage robust optimization, and a feasible linear constraint generated from the subproblem is added to the master problem. The simulation results demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]