  Distribution grids are experiencing a massive penetration of fluctuating
distributed energy resources (DERs). As a result, the real-time efficient and
secure operation of distribution grids becomes a paramount problem. While
installing smart sensors and enhancing communication infrastructure improves
grid observability, it is computationally impossible for the distribution
system operator (DSO) to optimize setpoints of millions of DER units. This
paper proposes communication-free and model-free algorithms that can actively
control converter-connected devices, and can operate either as stand-alone or
in combination with centralized optimization algorithms. We address the problem
of loss minimization in distribution grids, and we analytically prove that our
proposed algorithms reduce the total grid losses without any prior information
about the network, requiring no communication, and based only on local
measurements. Going a step further, we combine our proposed local algorithms
with a central optimization of a very limited number of converters. The hybrid
approaches we propose have much lower communication and computation requirement
than traditional methods, while they also provide performance guarantees in
case of communication failure. We demonstrate our algorithms in four networks
of varying sizes: a 5-bus network, an IEEE 141-bus system, a real Danish
distribution system, and a meshed IEEE 30-bus system.
