Multistage reliability-based expansion planning of AC distribution networks using a mixed-integer linear programming model

Abstract

A new mathematical model for the multistage distribution network expansion planning problem considering reliability is proposed in this paper. Decisions related to substation and branch expansion are driven by the minimization of the total cost, which comprises investment and operating costs including the impact of reliability. The proposed model features two main novelties. First, a set of novel algebraic expressions is devised for a standard reliability index, namely the expected energy not supplied. As a result, the dependence of reliability on network topology is explicitly and effectively cast in the mathematical formulation of the planning problem at hand. In addition, the effect of the network is characterized by a computationally efficient piecewise linear representation of the ac power flow model that takes into account both real and reactive power. The resulting optimization problem is formulated as an instance of mixed-integer linear programming, which provides a suitable framework for the attainment of high-quality solutions with acceptable computational effort using efficient off-the-shelf software with well-known convergence properties. The effectiveness of the proposed planning methodology is empirically demonstrated by providing cheaper expansion plans that enhance system reliability and by achieving better computational results as compared with state-of-the-art models.