  This paper considers the dynamic economic dispatch problem for a group of
distributed energy resources (DERs) with storage that communicate over a
weight-balanced strongly connected digraph. The objective is to collectively
meet a certain load profile over a finite time horizon while minimizing the
aggregate cost. At each time slot, each DER decides on the amount of generated
power, the amount sent to/drawn from the storage unit, and the amount injected
into the grid to satisfy the load. Additional constraints include bounds on the
amount of generated power, ramp constraints on the difference in generation
across successive time slots, and bounds on the amount of power in storage. We
synthesize a provably-correct distributed algorithm that solves the resulting
finite-horizon optimization problem starting from any initial condition. Our
design consists of two interconnected systems, one estimating the mismatch
between the injection and the total load at each time slot, and another using
this estimate to reduce the mismatch and optimize the total cost of generation
while meeting the constraints.
