  Distributed secondary frequency control for power systems, is a problem that
has been extensively studied in the literature, and one of its key features is
that an additional communication network is required to achieve optimal power
allocation. Therefore, being able to provide stability guarantees in the
presence of communication delays is an important requirement. Primal-dual and
distributed averaging proportional-integral (DAPI) protocols, respectively, are
two main control schemes that have been proposed in the literature. Each has
its own relative merits, with the former allowing to incorporate general cost
functions and additional operational constraints, and the latter being more
straightforward in its implementation. Although delays have been addressed in
DAPI schemes, there are currently no theoretical guarantees for the stability
of primal-dual schemes for frequency control, when these are subject to
communication delays. In fact, simulations illustrate that even small delays
can destabilize such schemes. In this paper, we show how a novel formulation of
prima-dual schemes allows to construct a distributed algorithm with delay
independent stability guarantees. We also show that this algorithm can
incorporate many of the key features of these schemes such as tie-line power
flow requirements, generation constraints, and the relaxation of demand
measurements with an observer layer. Finally, we illustrate our results through
simulations on a 5-bus example and on the IEEE-39 test system.
