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

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 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 that separates investments from operations and further decouples operational timesteps using budgeting variables in the the master model. This novel approach enables parallelization of operational subproblems and permits modeling of relevant constraints that couple decisions across time periods (e.g. policy constraints.) Runtime scales linearly with temporal resolution; numerical tests demonstrate substantial improvement in runtime relative to monolithic problems using state-of-the-art commercial solvers for all MILP formulations and for some LP formulations depending on problem size. Our algorithm is applicable to similar planning problems in other domains (e.g. water, transportation networks, production processes) and can solve large-scale, otherwise intractable, planning problems. We show that the increased resolution enabled by this algorithm mitigates structural uncertainty and improves recommendation accuracy.