Benders Decomposition with Partial Non-Anticipativity Relaxation for Multi-Stage Stochastic Clean Energy Transition Planning

Abstract

We study clean energy transition planning for campus-scale integrated electricity-heat systems under both strategic level and operational level uncertainties. We formulate a multi-stage stochastic mixed-integer program that jointly optimizes investment and operational decisions for renewable generation, storage, and heat-transfer technologies whose costs and efficiencies evolve stochastically across stages. To account for short-term operational uncertainty, we further derive a robust reformulation based on box uncertainty sets for demand, renewable generation, and heat-transfer performance. To solve the resulting large-scale model, we develop a Benders decomposition algorithm with partial non-anticipativity relaxation. Investment variables and their non-anticipativity constraints are retained in the master problem while operational variables are assigned to scenario-wise subproblems where their non-anticipativity constraints are relaxed. Non-anticipativity of operational variables is restored only at termination through a smaller linear program. We prove that this correction step can only increase the objective function value by a finite bound. We improve the computational performance of the algorithm developed with valid inequalities and a two-phase cut-addition strategy. Using the proposed approach, we solve the Middle East Technical University campus case study at high temporal resolution within a reasonable computational budget, which is not otherwise possible with the extensive form or the classical Benders decomposition. We evaluate the resulting investment plans through rolling-horizon Monte Carlo simulations with an out-of-sample analysis and demonstrate that the added robustness can significantly improve the operational reliability of the transition plans with a moderate increase in total cost.