In this paper, we consider the optimal coordination problem for distributed energy resources (DERs), including distributed generators and energy storages. We first propose an algorithm based on the push-sum and gradient method to solve the optimal DER coordination problem in a distributed manner. In the proposed algorithm, each DER only maintains a set of variables and updates them through information exchange with a few neighboring DERs over a time-varying directed communication network. We show that the proposed distributed algorithm with appropriately chosen diminishing step sizes solves the optimal DER coordination problem if the time-varying directed communication network is uniformly jointly strongly connected. Moreover, in order to improve the convergence speed and to reduce the communication burden, we propose an accelerated distributed algorithm with a fixed step size. We show that the new proposed algorithm exponentially solves the optimal DER coordination problem if the cost functions satisfy an additional assumption and the selected step size is less than a certain critical value. Both proposed distributed algorithms are validated and evaluated using the IEEE 39-bus system.