Planning Macro-energy Systems with Multiple Climatic Years: A Quadratic Trust-region Approach for Benders Decomposition

Abstract

This paper applies Benders decomposition to two-stage stochastic problems for energy planning with multiple climatic years, a key problem for the design of renewable energy systems. First, we implement Benders decomposition with existing enhancements suited for the characteristics of the problem, a simple continuous masterproblem and fewbut large sub-problems. Next, we develop a novel trust-region method using a quadratic constraint that is continuously adapted to further improve the algorithm. In a quantitative case-study our method accelerates Benders decomposition by a factor of four to six slightly increasing solve time of the master-problem, but greatly reducing the number of iterations. With the computational resources at our disposal, Benders decomposition with quadratic trust-region outperforms closed optimization if planning covers more than six climatic years, because run-time does not increase with the number of scenarios thanks to distributed computing. Furthermore, results show that the quadratic trust-region approach benefits from a heuristic starting solution but does not depend on it to be performative. Finally, we suggest further improvements of the algorithm. First, heuristic methods to narrow the solution space of the master-problem. Second, approximations of the sub-problems to faster add inexact but valid cuts.