  This paper considers distribution networks featuring inverter-interfaced
distributed energy resources, and develops distributed feedback controllers
that continuously drive the inverter output powers to solutions of AC optimal
power flow (OPF) problems. Particularly, the controllers update the power
setpoints based on voltage measurements as well as given (time-varying) OPF
targets, and entail elementary operations implementable onto low-cost
microcontrollers that accompany power-electronics interfaces of gateways and
inverters. The design of the control framework is based on suitable linear
approximations of the AC power-flow equations as well as Lagrangian
regularization methods. Convergence and OPF-target tracking capabilities of the
controllers are analytically established. Overall, the proposed method allows
to bypass traditional hierarchical setups where feedback control and
optimization operate at distinct time scales, and to enable real-time
optimization of distribution systems.
