Abstract The economic dispatch problem (EDP) in power systems is usually formulated as a category of convex optimization problems in which the collective cost function is expressed as the sum of all individual objectives of generators. It is inclined to be solved through a distributed way, which is to minimize the total generation cost while meet the demands under generator capability restrictions. In this paper, we consider this class of convex optimization problems that involve coupling linear constraint and individual box constraints. In order to make information communication of network decentralized, reliable and computationally inexpensive, an asynchronous distributed primal–dual optimization algorithm is proposed over stochastic networks. This algorithm allows nodes to use asynchronous communication strategy to update their state, and the step-sizes for seeking the optimum solution are uncoordinated constants. The asynchronous operation for generators takes link failures of networks into account. Under strongly convex assumption on objective functions, it is proved that the proposed algorithm can seek the exact optimal solution with probability one if the expectation of communication network is undirected connected. The effectiveness of the proposed optimization algorithm over stochastic networks is illustrated by provided simulation results.