  This paper is concerned with the problem of coordinating a set of distributed
energy resources (DERs) in a lossy power distribution system to provide
frequency regulation services to a bulk power grid with the explicit
consideration of system losses. To this end, we formulate the problem as an
optimization problem, the objective of which is to minimize some cost function
subject to a set of constraints. The formulation requires knowledge of
incremental total system losses, which we approximate using the so-called loss
factors (LFs) that explicitly capture the impacts of both active and reactive
power injections on system losses. The LFs are estimated recursively using
power injection measurements; thus, they are adaptive to various phenomena that
impact the power system operation. Numerical simulation on a 33-bus
distribution test feeder validated the effectiveness of the proposed framework.
