This paper presents an integrated approach for the control and scheduling of Distributed Energy Resources (DERs) that are managed by a central supervisor over a resource-constrained communication network. The objective is to enhance the performance and disturbance-handling capabilities of the DERs while keeping the communication requirements with the supervisor to a minimum in order to reduce the susceptibility of the DERs to communication outages. To this end, the rate of data transfer from the DERs to the supervisor is initially minimized by embedding in the supervisor a set of models that are used to generate the necessary control action when measurements are not transmitted over the network, and then updating the models' states at discrete time instances. Only a subset of the DERs are allowed to transmit their data at any given time to provide updates to their target models according to a certain scheduling strategy. By formulating the networked closed-loop system as a hybrid system, an explicit characterization of the interdependence between the performance of the DERs, the communication rate, the transmission schedule and times, and the plant-models' mismatch is obtained. It is shown that by judicious selection of the transmission schedule and models, it is possible to optimize the performance of the DERs while simultaneously reducing network utilization beyond what is possible with concurrent transmission configurations. Finally, the results are demonstrated through an application to a collection of solid oxide fuel cells in a distributed power network.