Stabilized Benders decomposition for energy planning under climate uncertainty

TL;DR

The primary focus is stabilization, specifically comparing established bundle methods to a quadratic trust-region approach for continuous problems and an extensive computational comparison shows that all stabilization methods can significantly reduce computation time.

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.

Figures (15)

• Figure 1: Structure of closed two-stage problem
• Figure 2: Graph of years and scenarios for exemplary problem
• Figure 3: Structure of decomposed problem
• Figure 4: Dynamic trust-region adjustment
• Figure 5: Interpolation methods for convergence tolerance of SPs