This invention relates to methods and systems for controlling consumption, particularly power consumption, more particularly by appliances in a building, and is generally suitable for integration with building management systems. Embodiments of the invention provide methods and systems which probabilistically limit the aggregated power load of a plurality of climate control appliances in a building to a selected value, while seeking to minimize the deviation from target environmental conditions within the building. The embodiments of the invention propose distributed decision-making by individual devices based on projected deviation from the target conditions after a period of activity or inactivity.