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 primal-dual schemes allows to construct a distributed algorithm with delay independent stability guarantees. We also show that this algorithm can incorporate many 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.