A Computationally Efficient Benders Decomposition for Energy Systems Planning Problems with Detailed Operations and Time-Coupling Constraints

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 analogous 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. Funding: Funding for this work was provided by the Princeton Carbon Mitigation Initiative (funded by a gift from BP) and the Princeton Zero-carbon Technology Consortium (funded by gifts from GE, Google, ClearPath, and Breakthrough Energy). Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoo.2023.0005 .