The potential of distributed energy resources in providing grid services can be maximized with the recent advancements in demand side control. Effective utilization of this control strategy requires the knowledge of aggregate flexibility of the distributed energy resources (DERs)... Recent works have shown that the aggregate flexibility of DERs can be modeled as a virtual battery (VB) whose state evolution is governed by a first order system including self-dissipation. The VB parameters (self-dissipation rate, energy capacity) are obtained by solving an optimization problem which minimizes the tracking performance of the ensemble and the proposed first-order model. For the identified first order model, time-varying power limits are calculated using binary search algorithms. Finally, this proposed framework is demonstrated for different homogeneous and heterogeneous ensembles consisting of air conditioners (ACs) and electric water heaters (EWHs). (read more)