This paper investigates a load frequency control issue for multi-area interconnected unknown power systems with random communication delays. First, a model-free adaptive control scheme is established by building an equivalent data relationship model between area control error and corresponding control input. Then, a dynamic event-triggered scheme is designed to improve resource utilization and reduce computational burden. Furthermore, random communication delays in the feedback and forward channels are considered. The results show that the proposed method is independent of any model information about the power system, only using the controlled system's control input and output data. Several simulation results validate the effectiveness of the proposed control scheme.