Equilibrium approach to the single solution of longer- and shorter-term hydro-thermal scheduling problems

A bilevel optimization problem formulation based on mathematical programs with equilibrium constraints (MPEC) to coordinate longer-(LTHS) and shorter-term hydro-thermal scheduling problems (STHS), as an alternative perspective to classical decomposition strategies is presented. The motivation to use MPEC to formulate the coordination of LTHS and STHS models as an equilibrium problem is both educational and methodological. It allows us to learn from a single and consistent framework how the optimal solution is affected by inconsistencies in LTHS and STHS modeling assumptions. Secondly, its methodological motivation is that of the one-level equivalent formulation of MPEC enabling the devise of approximate dynamic coordination strategies aiming to minimize these inconsistencies while keeping additional computational burden low. In this paper we explore the first motivation by presenting two small, simple examples in different economic scenarios: a classical monopoly model with central planning, and a competitive market model with a price maker hydroelectric producer.