In power system operation, the economic dispatch problem (EDP) aims to minimize the total generation cost while meeting the demand and satisfying generator capacity limits. This paper proposes an algorithm based on the gradient push-sum method to solve the EDP in a distributed manner over communication networks potentially with time-varying topologies and communication delays. This paper shows that the proposed algorithm is guaranteed to solve the EDP if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, the proposed algorithm is also able to handle arbitrarily large but bounded time-varying delays on communication links. Numerical simulations are used to illustrate and validate the proposed algorithm.