A scenario-based robust distribution expansion planning under ellipsoidal uncertainty set using second-order cone programming

作     者：Akbari, Tohid Moghaddam, Saeed Zolfaghari 

作者机构：Pooyesh Inst Higher Educ Fac Elect Engn Qom Iran Urmia Univ Technol Fac Ind Technol Dept Elect Engn Orumiyeh Iran 

出 版 物：《ELECTRIC POWER SYSTEMS RESEARCH》 (电力系统研究)

年 卷 期：2022年第213卷第0期

核心收录：

学科分类：0808[工学-电气工程] 080802[工学-电力系统及其自动化] 08[工学] 

主　　题：Distribution expansion planning Khachiyan algorithm Robust optimization Second -order cone programming Stochastic programming 

摘      要：This paper intends to propose a new mathematical framework for distribution expansion planning (DEP) based on which the uncertainties associated with electric demand and wind production are modeled through several plausible ellipsoidal uncertainty sets. In this regard, a hybrid model combining stochastic programming and robust optimization is constructed. Data related to the demand-wind scenarios are first divided into clusters of similar elements using an existing clustering technique. Then, an ellipsoidal uncertainty set is created corre-sponding to each of these generated clusters based on the theory of minimum volume covering ellipsoid (MVCE) using the Khachiyan algorithm (KA). The hybrid robust/stochastic scheme is formulated as a two-stage tri-level min-max-min optimization problem in which the convex conic relaxation of AC power flow is used to represent the electric distribution network. The multi-uncertainty-set-based model is then solved by employing the classic column-and-constraint-generation (C&CG) technique which guarantees the convergence to the optimal solution in a limited number of iterations. In this regard, a master problem and several subproblems related to each scenario will be solved, both of which are second-order cone programs. Numerical simulations reveal the su-periority of the hybrid model compared to the existing ones.