The time-delay effect on load frequency control (LFC) for power smart grids systems based on microgrids (MGs) is analyzed. A new cyber-physical modeling approach is used to identify system signals that are vulnerable to communication constraints. An analytic approach based on the Rekasius substitution and sum of squares decomposition is proposed to find the time-delay stability margin of LFC in microgrids. The cyber physical modeling and time-delay margin analysis approaches are applied to a microgrid example based on a distributed diesel generator and a photo-voltaic generator. In addition, the impact of time-delays for these class of systems is shown in simulation. The proposed approach can be used to analyze other cybernetic constraints in smart grid power systems and the methodology used to find delay stability margin can be extended to power systems of larger scale, as interconnected microgrids.