Formulation of Radiality Constraints for Optimal Microgrid Formation

Forming microgrids (MG) in distribution systems (DSs) is an operational measure proposed to enhance power system flexibility. The computational performance of the applied optimization techniques varies greatly according to the constraints ensuring network radiality. Formulations of radiality constraints differ from each other by model complexity and the search space of the relaxed linear programming (LP) problem. In this paper, widely used formulations of radiality constraints are first revisited and flexibly enhanced to address the complex operating environment of modern DSs. To incorporate various radiality constraints and provide an optimization basis for comparison, a flexible MG formation problem is proposed with the ability to automatically allocate distributed generators (DGs) into multiple MGs. Combined formulations with parent-child (PC) constraints are then developed to shrink the LP feasible region. Moreover, to accelerate the branching process by applying the branch-and-cut (B&C) algorithm, an efficient formulation of radiality constraints is proposed by adding extra constraints that exclude fundamental loops into the single-commodity flow formulation. To further accelerate the branching process, a dynamic constraint generation algorithm is developed without substantially increasing the complexity of the LP problem. DSs of various complexities and sizes are employed to verify the computational efficiency of the proposed formulations. The paper concludes by suggesting the most efficient formulations of radiality constraints according to the scale of the targeted DS.