Fecha: Jueves 3 de julio
Hora: 16:15hrs.
Lugar: Sala B05 (Beauchef 851, piso -1)
Speaker: Matías Vera (Universidad de Chile)
Abstract: In this talk, we present a joint problem in which a centralized entity, called the Independent System Operator (ISO), intends to minimize the joint cost of operation and investment in a network structure. The problem is formulated through operational and investment control variables; we discuss the hierarchy between them and use the so-called Day Ahead Problem to find an explicit form of the optimal operational variable, which allows us to reformulate the problem as a stochastic control problem with state constraints. We extend results of state-constrained stochastic control to fit our setting. Particularly, we use a version of the Pointing Inward Condition to fully characterize the value of the problem as the unique viscosity solution of a constrained HJB equation. We then assign a specific dynamic to the capacity-demand process and discuss how the assumptions for the HJB characterization result in a budget constraint for the planning. Finally, we run simulations for a three node setting, that resembles the Chilean market, for short-term planning and long-term planning.