The communication networks of smart grids are often influenced by ubiquitous uncertainty. These uncertainties can directly influence the communication weights between generating units, consequently degrading the performance of economic dispatch (ED) algorithms. Despite this, much of the related work has been centered on ideal communication channels, thereby overlooking the impact of communication uncertainties. Consequently, this paper primarily delves into the economic dispatch problem (EDP) in smart grids with uncertain communication networks. Initially, we propose an adaptive algorithm grounded on an event-triggered strategy. This algorithm can effectively offset the communication uncertainties within a predefined upper limit, thereby facilitating optimal power allocation. Subsequently, we introduced a new self-triggered strategy. This strategy eliminates the need for continuous monitoring of neighboring statuses, leading to a reduction in controller updates and message transmissions, without negatively affecting the system's convergence performance. However, the effectiveness of the self-triggered strategy might be influenced by the accuracy of generator predictions. Finally, simulations demonstrate that the proposed approach effectively mitigates the impact of communication uncertainties on ED performance while reducing communication overhead.