Scheduling and Pricing of Energy Generation and Storage in Power Systems

This paper proposes a fundamental model for continuous-time scheduling and marginal pricing of energy generation and storage in day-ahead power systems operation. The paper begins with formulating the economic operation problem of power systems with generating units and energy storage (ES) devices as a continuous-time optimal control problem, where the Lagrange multiplier trajectory associated with the continuous-time power balance constraint is proven to be the marginal price of energy generation and storage. The marginal price is calculated in closed-form, which reveals that in addition to the incremental cost rates of generating units, the marginal price embeds the financial ES charging offers and discharging bids that are defined as incremental charging utility and incremental discharging cost rates. This paper shows that the adjoint function associated with the ES state equation establishes a temporal dependence between the marginal prices during the ES charge and discharge states. A function space-based method is developed to solve the proposed model, which converts the continuous-time problem into a mixed-integer linear programming problem with finite dimensional decision space. The features of the proposed scheduling and pricing models are demonstrated using numerical studies conducted on the IEEE Reliability Test System.