Distributionally Robust Optimization of Photovoltaic Power With Lifted Linear Decision Rule for Distribution System Voltage Regulation

This article proposes a lifted linear decision rule (LLDR) as a photovoltaic (PV) power control strategy for distribution system voltage regulation. First, the active-reactive power control is designed as a linear function in a lifted space of PV power, which is presented as a piecewise linear function without auxiliary integer variables for benefiting the parameter optimization of control functions. Then, a hierarchical central-local voltage regulation framework is designed. In the central control stage, the constant part of LLDR determines the reactive power of PV units, which is also coordinated with other voltage regulation devices. In the local control stage, the adjustable part of LLDR would control the PV power in real time for reducing voltage deviations. Finally, optimization problems and their solution methods are developed to obtain LLDR parameters. In particular, robust optimization (RO) and distributionally robust optimization (DRO) problems are designed to obtain the affine coefficients of LLDR considering multiple PV power uncertainty models. The tractable formula of RO is derived based on the convex hull of PV power uncertainty sets in the lifted space, and Benders decomposition is combined with a distribution separation method to solve the DRO problem. The proposed method is tested on distribution systems with actual PV power data, and the results are compared with those of other linear and piecewise-linear control methods to validate the effectiveness of the proposed method in diminishing voltage deviations caused by variable PV power.