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In the United States, buildings account for 35% of total energy-related carbon dioxide emissions, making them important contributors to decarbonization. Carbon intensities in the power grid are time-varying and can fluctuate significantly within hours, so shifting building loads in response to the carbon intensities can reduce a building's operational carbon emissions. This paper presents a rule-based carbon responsive control framework that controls the setpoints of thermostatically controlled loads responding to the grid's carbon emission signals in real time. Based on this framework, four controllers are proposed with different combinations of carbon accounting methods and control rules. To evaluate their performance, we performed simulation studies using models of a 27-home, all-electric, net zero energy residential community located in Basalt, Colorado, United States. The carbon intensity data of four future years from the Cambium data set are adopted to account for the evolving resource mix in the power grid. Various performance metrics, including energy consumption, carbon emission, energy cost, and thermal discomfort, were used to evaluate the performance of the controllers. Sensitivity analysis was also conducted to determine how the control thresholds and intervals affect the controllers' performance. Simulation results indicate that the carbon responsive controllers can reduce the homes' annual carbon emissions by 6.0% to 20.5%. However, the energy consumption increased by 0.9% to 6.7%, except in one scenario where it decreased by 2.2%. Compared to the baseline, the change in energy cost was between −2.9% and 3.4%, and thermal discomfort was also maintained within an acceptable range. The little impact on energy cost and thermal discomfort indicates there are no potential roadblocks for customer acceptance when rolling out the controllers in utility programs. [ABSTRACT FROM AUTHOR]