A computationally efficient Benders decomposition for energy systems planning problems with detailed operations and time-coupling constraints

TL;DR

This paper introduces a novel Benders decomposition method for energy systems planning that significantly improves computational efficiency and scalability, enabling detailed, large-scale, and time-coupled optimization problems to be solved more effectively.

Contribution

The paper presents a new Benders decomposition approach that separates investments from operations and uses budgeting variables to decouple time periods, allowing parallelization and improved scalability.

Findings

Runtime scales linearly with temporal resolution

Substantial runtime improvements over monolithic models

Enhanced modeling of policy constraints across time

Abstract

Energy systems planning models identify least-cost strategies for expansion and operation of energy systems and provide decision support for investment, planning, regulation, and policy. Most are formulated as linear programming (LP) or mixed integer linear programming (MILP) problems. Despite the relative efficiency and maturity of LP and MILP solvers, large scale problems are often intractable without abstractions that impact quality of results and generalizability of findings. We consider a macro-energy systems planning problem with detailed operations and policy constraints and formulate a computationally efficient Benders decomposition separating investments from operations and decoupling operational timesteps using budgeting variables in the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints coupling decisions across time periods (e.g. policy constraints) within a decomposed framework. Runtime scales linearly with temporal resolution; tests demonstrate substantial runtime improvement for all MILP formulations and for some LP formulations depending on problem size relative to analagous monolithic models solved with state-of-the-art commercial solvers. Our algorithm is applicable to planning problems in other domains (e.g. water, transportation networks, production processes) and can solve large-scale problems otherwise intractable. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty, improving recommendation accuracy.