This paper considers islanded microgrids and is motivated by the need for decentralized control strategies with minimal communication among grid components to support a robust and plug-and-play operation. We focus on the problem of power allocation among the distributed generation units (DGs) to maintain low distribution power loss in the grid and develop a communication-free distributed power control approach for power loss minimization based on the extremum-seeking (ES) method. In this approach, the DGs implement ES simultaneously and separately to minimize their current outputs by controlling the active power. The total power loss is thus reduced and no grid structure information or communication is needed in the optimization process. The existence of a Nash equilibrium in the resulting non-cooperative game is proved. Numerical simulations are conducted to demonstrate the performance of the proposed communication-free power control approach and show that it is suitable for maintaining low power loss under different operating conditions in a plug-and-play manner.
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