Thermostatically controlled loads (TCLs) account for approximately 50% of U.S. electricity consumption. Various techniques have been developed to model TCL populations. A High-fidelity analytical model of heterogeneous TCL populations facilitates the aggregate synthesis of power control in power networks. Such a model assists the utility manager to increase the stability margin of the network. The model, also, assists the customer to schedule his/her tasks in order to reduce his/her energy cost. We present a deterministic hybrid partial differential equation (PDE) model which accounts for heterogeneous populations of TCLs, and facilitates analysis of common scenarios like cold load pick up, cycling, and daily and/or seasonal temperature changes to estimate the aggregate performance of the system. The proposed technique is flexible in terms of parameter selection and ease of changing the set-point temperature and deadband width all over the TCL units. We provide guidelines to maintain the numerical stability of the discretized model during computer simulations. Moreover, the proposed model is a close fit to design output feedback algorithms for power control purposes. Our integral output feedback control, designed using the comparison principle, guarantees fast and efficient power tracking for various real-world scenarios. We present simulation results to verify the effectiveness of the proposed modeling and control technique.

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