A bi-level optimization model for operation of distribution networks with micro-grids

•Operation of DISCO with MGs is modeled as a bi-level optimization problem.•The proposed model creates a cooperative environment between DISCO and MGs.•The proposed model is solved using KKT conditions and dual theory.•The proposed model creates a retail electricity market in distribution grid level.•Two frameworks are presented to illustrate the structure of this market.

Active distribution grids (ADGs) consist of several distributed generations (DGs) and controllable loads (CLs). These resources are utilized in the form of several microgrids (MGs) which in turn facilitate managing of ADGs. Therefore, the problem of distribution company (DISCO) and MGs operation requires a hierarchical decision-making framework. An attempt is made in this paper to model such framework as a bi-level optimization problem. In the proposed bi-level model, the objective of the upper level (leader) problem is to maximize the profit of DISCO, and the objective of the lower level (follower) problems is to minimize the cost of MGs. The resulting model is a nonlinear bi-level problem which is transformed into a linear single-level problem through Karush–Kuhn–Tucker (KKT) conditions and dual theory. Since the proposed model creates a retail electricity market in distribution grid, two frameworks are considered for this market: various and uniform retail electricity prices. To illustrate the effectiveness of the model, a hypothetical distribution grid is considered as the case study. The impacts of the market price and various demand levels of MGs on the results are investigated in two scenarios.