Stochastic market equilibrium model for generation planning

It is widely accepted that medium-term generation planning can be advantageously modeled through market equilibrium representation. There exist several methods to define and solve this kind of equilibrium in a deterministic way. Medium-term planning is strongly affected by uncertainty in market and system conditions, thus extensions of these models are commonly required. The main variables that should be considered as subject to uncertainty include hydro conditions, demand, generating units failures and fuel prices. This paper presents a model to represent medium-term operation of electrical market that introduces this uncertainty in the formulation in a natural and practical way. Utilities are explicitly considered to be intending to maximize their expected profits and biddings are represented by means of a conjectural variation. Market equilibrium conditions are introduced by means of the optimality conditions of a problem, which has a structure that strongly resembles classical optimization of hydrothermal coordination. A tree-based representation to include stochastic variables and a model based on it are introduced. This approach for market representation provides three main advantages: robust decisions are obtained; technical constraints are included in the problem in a natural way, additionally obtaining dual information; and big size problems representing real systems in detail can be addressed.