This paper investigates the economic dispatch problem in smart grids over an unbalanced directed graph and proposes a novel distributed optimization algorithm. It aims to minimize the total power generation cost by efficiently dispatching the output power of generator units. By introducing a momentum term, the algorithm ensures that the generator can obtain more previous historical information from itself and its neighbors, so as to achieve convergence in a shorter time. The momentum term and the step size in the algorithm are time-varying, making the execution of the algorithm more efficient. To avoid continuous communication between agents, the algorithm considers a new event-triggered condition with a simple choice of key parameters, and the agent only transmit information to their neighbors at the triggering time. Based on the assumptions of the cost functions (smoothness and strong convexity), the theoretical analysis proves that when the largest step-size and maximum momentum coefficient are within their limits, the method can achieve optimal dispatch. Finally, the superiority and correctness of the proposed algorithm is further demonstrated by several numerical examples.