Flexibility pricing in the active distribution network including renewable and flexibility sources as a bi-level optimization model

This article models the flexibility services pricing (FSP) for an active distribution network (ADN) with renewable and flexibility resources. In this scheme, flexible resources include incentive-based demand response program and energy storage systems. The scheme is formulated as a bi-level problem. The upper-level formulation includes an objective function that maximizes the expected flexibility profits of flexible resources with considering constraints of the flexibility power model of these resources and the ADN. The lower-level problem is used to calculate the flexibility incentive price. Hence, it contains the ADN optimal operation formulation, where it minimizes the expected operating cost of the network limited to linearized AC optimal power flow equations, resources' models, and flexibility constraints of the ADN. The Karush-Kuhn-Tucker method obtains the single-level formulation for this scheme. Also, the stochastic programming is used to model the uncertainties of load, renewable power, and energy price. In the end, the mentioned method applies on the radial 69-bus network, then the obtained numerical results confirm the potential of the approach in the improvement of economic, operation, and flexibility indices of the ADN.