  In this paper, we consider the problem of optimally coordinating the response
of a group of distributed energy resources (DERs) so they collectively meet the
electric power demanded by a collection of loads, while minimizing the total
generation cost and respecting the DER capacity limits. This problem can be
cast as a convex optimization problem, where the global objective is to
minimize a sum of convex functions corresponding to individual DER generation
cost, while satisfying (i) linear inequality constraints corresponding to the
DER capacity limits and (ii) a linear equality constraint corresponding to the
total power generated by the DERs being equal to the total power demand. We
develop distributed algorithms to solve the DER coordination problem over
time-varying communication networks with either bidirectional or unidirectional
communication links. The proposed algorithms can be seen as distributed
versions of a centralized primal-dual algorithm. One of the algorithms proposed
for directed communication graphs has geometric convergence rate even when
communication out-degrees are unknown to agents. We showcase the proposed
algorithms using the standard IEEE 39-bus test system, and compare their
performance against other ones proposed in the literature.
