In this paper, we investigate the impact of communication delays on the performance of power system automatic generation control (AGC). To this end, we formulate a hybrid system model that describes the power system electromechanical behavior, including the AGC system dynamics. Through linearization and discretization, this hybrid system model is converted into a discrete-time linear time-invariant system model that includes the effect of delays in the AGC system communication channels. The stability of the closed-loop system can then be determined by examining the characteristics of the state-transition matrix of the aforementioned discrete-time linear system. Interesting findings include that increasing communication delay may help decrease the largest eigenvalue magnitude of the state-transition matrix. However, in reality, the delay is not constant or deterministic. We carefully analyze the stability of systems with random communication delays and nonzero mean random disturbances. The proposed analysis methodology is illustrated and verified through numerical examples.