Penalty-Free SDDP: Feasibility Cuts for Robust Multi-Stage Stochastic Optimization in Energy Planning

Multi-stage decision problems under uncertainty are often solved with the Stochastic Dual Dynamic Programming (SDDP) algorithm, which traditionally requires every stage problem to be feasible. Feasibility is usually enforced through slack variables penalized in the objective, a device that demands case-specific calibration and blurs the economic interpretation of results. This work proposes the Penalty-Free SDDP, an extension that introduces a Future Feasibility Function alongside the Future Cost Function. The new recursion handles infeasibilities automatically, distinguishes temporary from truly infeasible cases, and propagates feasibility information through dedicated feasibility cuts. The approach was validated on a large-scale deterministic case inspired by the Brazilian hydrothermal system, matching the benchmark feasibility while removing miscalibrated artificial penalties.