Distributed generators are integrated into microgrids or geographically distributed subsystems in active distribution networks and may belong to various entities. Centralized solutions cannot meet future requirements such as high resilience and privacy protection. Therefore, fully distributed economic dispatch (ED) methods are needed and most existing algorithms exhibit linear or sublinear convergence. This paper introduces an efficient fully distributed dynamic ED solution for minimizing photovoltaic power curtailment, based on a parallel primal-dual interior-point algorithm with a quasi-Newton technique. In this method, each area optimizes its own problem with limited information exchanged with its neighbors, and no central coordinator is needed. Based on a peer-to-peer communication paradigm, this method can achieve a global optimum while the privacy of each area is obliquely protected. Numerical tests demonstrated that the algorithm outperforms gradient-based methods such as ADMM and maintains stability under a partial communication failure.