This paper introduces a novel fully distributed economic power dispatch (EPD) strategy for distribution networks, integrating dynamic tariffs. A two-layer model is proposed: the first layer comprises the physical power distribution network, including photovoltaic (PV) sources, wind turbine (WT) generators, energy storage systems (ESS), flexible loads (FLs), and other inflexible loads. The upper layer consists of agents dedicated to communication, calculation, and control tasks. Unlike previous EPD strategies, this approach incorporates dynamic tariffs derived from voltage constraints to ensure compliance with nodal voltage constraints. Additionally, a fast distributed optimization algorithm with an event-triggered communication protocol has been developed to address the EPD problem effectively. Through mathematical and simulation analyses, the proposed algorithm's efficiency and rapid convergence capability are demonstrated.