Stabilized Benders decomposition for energy planning under climate uncertainty

TL;DR

This paper enhances Benders decomposition with stabilization techniques, notably trust-region methods, to efficiently solve large-scale energy planning problems under climate uncertainty, enabling robust renewable energy system design with many climatic scenarios.

Contribution

It introduces and compares stabilization methods, especially trust-region approaches, for Benders decomposition tailored to energy planning under climate uncertainty, improving computational efficiency and robustness.

Findings

All stabilization methods reduce computation time.

Trust-region and box-step methods are most robust and easy to implement.

Parallelization yields a 100-fold speedup over vanilla Benders.

Abstract

This paper applies Benders decomposition to two-stage stochastic problems for energy planning under climate uncertainty, a key problem for the design of renewable energy systems. To improve performance, we adapt various refinements for Benders decomposition to the problem's characteristics -- a simple continuous master-problem, and few but large sub-problems. The primary focus is stabilization, specifically comparing established bundle methods to a quadratic trust-region approach for continuous problems. An extensive computational comparison shows that all stabilization methods can significantly reduce computation time. However, the quadratic trust-region and the non-quadratic box-step method are the most robust and straightforward to implement. When parallelized, the introduced algorithm outperforms the vanilla version of Benders decomposition by a factor of 100. In contrast to off-the-shelf solvers, computation time remains constant when the number of scenarios increases. In conclusion, the algorithm enables robust planning of renewable energy systems with a large number of climatic years. Beyond climate uncertainty, it can make an extensive range of other analyses in energy planning computationally tractable, for instance, endogenous learning and modeling to generate alternatives.