Load frequency control (LFC) requires transmitting measurements from remote RTUs to control center and control signals from the control center to plant side. Constant delays exist in the conventional dedicated communication channels, while the future usage of open communication networks will introduce time-varying delays. Those delays would degrade the dynamic performance of LFC and in the worst case, cause instability. The maximal delay time which allows an LFC scheme embedded with controllers to retain stable is defined as the delay margin. This paper investigates the delay-dependent stability of the LFC scheme by using Lyaponuv-theory based delay-dependent criterion and linear matrix inequalities (LMIs) techniques. Case studies are carried out based on one-area and multi-area LFC schemes installed with proportional-integral (PI) controllers, respectively. Relationship between the gains of PI controller and the delay margin of the LFC scheme are investigated and results obtained can be used to tune the PI controllers to achieve a compromise between the dynamic performance and the delay margin. Both constant and time-varying delays are considered. The effectiveness of the criterion used is verified by simulation studies.