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In this paper, we consider a distributed economic dispatch problem (EDP) in smart grids, where each generator only communicates with its neighbors and minimizes its own cost in the presence of network-wide equality constraints and local capacity limits. Distributed algorithms to solve this problem have become an attractive focus of engineering research due to their multiple advantages. Many existing methods are time-triggered, whereas few works have been dedicated to solving the problem using an event-triggered approach. This problem gets more challenging when further accelerated convergence is desired. To solve such a problem, we carefully design an event-triggered parameter distributed accelerated algorithm, named as ET-PDA. On the one hand, the choice of different parameters in ET-PDA will lead to different momentum (Nesterov or heavy-ball) methods, which facilitates the accelerated convergence of the algorithm. On the other hand, the event-triggered mechanism in ET-PDA makes the time gap between two continuous interaction moments of each generator larger than the iteration interval, contributing to improved communication efficiency. In particular, ET-PDA achieves linear convergence when the local cost function of each generator is smooth and strongly convex, moreover, it precludes Zeno-like behavior. The effectiveness of ET-PDA is also verified through a series of simulation experiments. [ABSTRACT FROM AUTHOR]