Generator bidding in oligopolistic electricity markets using optimal control: fundamentals and application

In this paper, optimal control is applied to study generator bidding in an oligopolistic electricity market. The repeated bidding process in (hourly-based) real-time electricity markets is modeled as a dynamic feedback system; an optimal control problem is then formulated to explore individual generator's long-term/multiperiod optimization behavior. Particularly in our formulation, the periodic property of the system demand is considered. Several lemmas are included for concerning system stability. Based on the necessary conditions for optimality from the Pontryagin maximum principle, a sweeping method is proposed, and an optimal state-feedback control rule is then obtained via backward induction. Numerical results suggest that the generator who unilaterally applies optimal control for generation decisions will obtain more profits. A sensitivity analysis is also performed, identifying these market factors that affect the performance of optimal control.