Scheduling and Pricing of Load Flexibility in Power Systems

This paper proposes a fundamental approach for scheduling and pricing of load flexibility in power systems operation. An optimal control model is proposed to co-optimize the continuous-time flexibility of loads with the operation of generating units to supply the flexibility requirements of the net-load, while satisfying delay-based and deadline-based service quality constraints of the flexible loads. A function space-based solution method is developed to solve the continuous-time problem, which is based on reducing the dimensionality of the continuous-time decision and parameter trajectories by modeling them in a finite-order function space formed by Bernstein polynomials. The proposed method converts the continuous-time problem into a mixed-integer linear programming problem with the Bernstein coordinates of the trajectories as the decision variables. The proposed method not only allows for full exploitation of the load flexibility through higher order solution spaces, but also includes the traditional discrete-time solution as a special case. This paper proves that the Lagrange multiplier associated with the continuous-time power balance constraint is the continuous-time marginal price of electricity in the presence of flexible loads. The marginal price is calculated in a closed from, which demonstrates the dependence of the price on the incremental cost rates of generating units, on parameters of the flexible loads, as well as on ramping limitations of generating units and flexible loads. Numerical results, provided for the IEEE Reliability Test System, demonstrate the effectiveness of the proposed model in deploying load flexibility to reduce operation cost and ramping requirement of the system, as well as smoothing the load and marginal price trajectories of the system.