  This paper develops an algorithmic framework for real-time optimization of
distribution-level distributed energy resources (DERs). The proposed framework
optimizes the operation of both DERs that are individually controllable and
groups of DERs (i.e., aggregations) at an electrical point of connection that
are jointly controlled. From an electrical standpoint, wye and delta single-
and multi-phase connections are accounted for. The algorithm enables (groups
of) DERs to pursue given performance objectives, while adjusting their
(aggregate) powers to respond to services requested by grid operators and to
maintain electrical quantities within engineering limits. The design of the
algorithm leverages a time-varying bi-level problem formulation capturing
various performance objectives and engineering constraints, and an online
implementation of primal-dual projected-gradient methods. The gradient steps
are suitably modified to accommodate appropriate measurements from the
distribution network and the DERs. By virtue of this approach, the resultant
algorithm can cope with inaccuracies in the distribution-system modeling, it
avoids pervasive metering to gather the state of non-controllable resources,
and it naturally lends itself to a distributed implementation. Analytical
stability and convergence claims are established in terms of tracking of the
solution of the formulated time-varying optimization problem. The proposed
method is tested in a realistic distribution system with real data.
