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Distribution grids are experiencing a massive penetration of fluctuatingdistributed energy resources (DERs). As a result, the real-time efficient andsecure operation of distribution grids becomes a paramount problem. Whileinstalling smart sensors and enhancing communication infrastructure improvesgrid observability, it is computationally impossible for the distributionsystem operator (DSO) to optimize setpoints of millions of DER units. Thispaper proposes communication-free and model-free algorithms that can activelycontrol converter-connected devices, and can operate either as stand-alone orin combination with centralized optimization algorithms. We address the problemof loss minimization in distribution grids, and we analytically prove that ourproposed algorithms reduce the total grid losses without any prior informationabout the network, requiring no communication, and based only on localmeasurements. Going a step further, we combine our proposed local algorithmswith a central optimization of a very limited number of converters. The hybridapproaches we propose have much lower communication and computation requirementthan traditional methods, while they also provide performance guarantees incase of communication failure. We demonstrate our algorithms in four networksof varying sizes: a 5-bus network, an IEEE 141-bus system, a real Danishdistribution system, and a meshed IEEE 30-bus system.

Decentralized Model-free Loss Minimization in Distribution Grids with the Use of Inverters