Economic dispatch problem (EDP) is a fundamental optimization problem in power system operation, which aims at minimizing the total generation cost. In fact, the power grid is becoming a cyber-physical power system (CPPS). Therefore, the quality of communication is a key point. In this paper, considering two important factors, i.e., time delays and channel noises, a fully distributed consensus based algorithm is proposed for solving EDP. The critical maximum allowable upper bounds of heterogeneous communication delays and self-delays are obtained. It should be pointed out that the proposed algorithm can be robust against the time-varying delays and channel noises considering generator constraints. In addition, even with time-varying delays and channel noises, the power balance of supply and demand is not broken during the optimization. Several simulation studies are presented to validate the correctness and superiority of the developed results.