{'fraction_non_alphanumeric': 0.01818181818181818, 'fraction_numerical': 0.0, 'mean_word_length': 5.754545454545455, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Decentralized Control of Thermostatic Loads for Flexible Demand Response

Thermostatically controlled loads (TCLs), such as refrigerators, air-conditioners and space heaters, offer significant potential for short-term modulation of their aggregate power consumption. This ability can be used in principle to provide frequency response services, but controlling a multitude of devices to provide a measured collective response has proven to be challenging. Many controller implementations struggle to manage simultaneously the short-term response and the long-term payback, whereas others rely on a real-time command-and-control infrastructure to resolve this issue. In this paper, we propose a novel approach to the control of TCLs that allows for accurate modulation of the aggregate power consumption of a large collection of appliances through stochastic control. By construction, the control scheme is well suited for decentralized implementation, and allows each appliance to enforce strict temperature limits. We also present a particular implementation that results in analytically tractable solutions both for the global response and for the device-level control actions. Computer simulations demonstrate the ability of the controller to modulate the power consumption of a population of heterogeneous appliances according to a reference power profile. Finally, envelope constraints are established for the collective demand response flexibility of a heterogeneous set of TCLs.