Bridging uncertainty and profitability: A chance-constrained optimization approach for day-ahead hydro-power operations

This paper addresses the issue of optimizing short-term hydro-power generation under multiple sources of uncertainty by proposing a Chance-Constrained Mixed-Integer Nonlinear Programming (MINLP) model for the Valentín Gómez Farías Hydro-Power Plant in Mexico. The optimization problems incorporate realistic stochastic behaviors in electricity prices and demand requirements, utilizing derived probability distributions, where stochasticity increases as the modeling progresses. Initially, this paper analyzes the sensitivity of the revenue regarding a risk level under a normally distributed parameter approach. Further, two formulations are developed, one using deterministic forecasts and the other incorporating a stochastic objective function via Monte Carlo simulation. The study addresses the Sample Average Approximation (SAA) and the Bonferroni approach to manage joint chance constraints under an operational risk. Our work’s technical contribution proposes an integrated and validated use of a hydro-technical model within a stochastic market environment. Specifically, we embed realistic nonlinear hydro-generation equations with friction head losses directly into a chance-constrained optimization framework, a practice rarely seen in the hydro-power domain where linearized dispatch models are often used. Using actual system data from the Mexican electricity market introduces operational realism, which is often missing in theoretical formulations. Numerical results from Julia’s programming language demonstrate that the validated optimal solution achieves a maximum expected revenue under a risk tolerance of ɛ = 0.08, while maintaining a feasible solution with a maximum violation probability of 0.06913, as confirmed through Monte Carlo-based validation. We demonstrate the impact of feasible water dispatch strategies by interacting with physical Hydro constraints, probabilistic demand constraints, and market price signals over short-term horizons, highlighting the immediate applicability of our work and bridging uncertainty and profitability with optimal solutions for the day-ahead Hydro-Power Plant operation policy. • Stochastic optimization is applied using Bonferroni and SAA to manage uncertainties. • Robust three-stage modeling strategy that incrementally incorporates uncertainty. • Upper and lower bound validation mechanism for solution feasibility and optimality. • Models tested on Real-World Case Study: Valentín Gómez Farías hydro-power plant. • Distributed Approach for risk-level sensitivity analysis in hydro-power dispatch.