Decentralized robust operation of the unbalanced microgrids in distribution networks: A convex relaxation approach.

This work presents a distributed robust operation framework for the microgrids within the power distribution network. It addresses the uncertainties in photovoltaic generation, as well as active, and reactive loads in the network, by modeling them using polyhedral sets. The energy management problems are formulated as two-stage optimization problems in microgrids and power distribution networks for which Benders decomposition is used to solve the problems. The power flow constraints are relaxed using second-order cone relaxation and moment relaxation techniques in the power distribution network and microgrid energy management problems, respectively. The interaction between the microgrids and the power distribution network is represented using the price signal and the exchanged active and reactive power at the microgrids' points of common coupling. The effectiveness of the proposed framework is shown using two case studies on IEEE 37-bus and IEEE 123-bus systems. The effect of the energy storage system on the operational cost of the system is assessed. It is shown that total operation cost is decreased by 9.69% when the energy storage system is integrated into the power distribution network. Additionally, the solution derived from the robust problem is compared with that of the deterministic problem. • The energy management problems are modeled as two-stage robust optimization problems. • The formulated problems are solved using the Benders decomposition technique. • Two convex relaxation techniques were used to solve the energy management problems in the subproblems. • The coordination between the distribution network and microgrids was ensured using the price signal and power exchanged. [ABSTRACT FROM AUTHOR]