A robust restoration decision-making strategy for unbalanced distribution networks considering the uncertainty of photovoltage generators

Abstract

The intermittent and stochastic power injections of the penetration of photovoltaic (PV) generators make the processing of fault restoration in the distribution network need to consider more uncertainties. A new scheme of robust fault restoration methods, aiming to maximize the recovery of outage power, is proposed for unbalanced distribution networks utilizing affine numbers to describe the uncertainty of PV outputs. Besides, the safe operation of the network is taken into account as its constraint condition. This restoration method is presented in two subsequent steps. The first step is the restoration of the island power outage, with the objective to reasonably isolate the power outage area containing the black-start PV to achieve island power supply recovery. Then the second step is to maximize the use of the remaining capacity of the main network and restore the power outage to ensure the power supply of the entire network. To solve the mathematical restoration model accurately, the piecewise linear approximation method based on the best isometric idea is introduced to relax the original objective function into a linear solvable form. An efficient decomposition algorithm, named column-and-constraints generation (C&CG), is used to solve the model, which can further improve the computational efficiency of the algorithm. Numerical tests on different test systems demonstrate that the proposed robust restoration methodology yields obvious advantages in resisting system uncertainties by contrast with the existing deterministic restoration methods.