This invention relates to methods and systems for limiting 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 arrangements in which the aggregated power load of a plurality of appliances is capped to a selected value (which may be arbitrary, or may be dictated by conditions) while seeking to minimize the deviation from target environmental conditions within the building through a combination of distributed decision making by the appliances themselves and centralized orchestration, which may be informed by real-time sensor readings and/or known properties of the building. The distributed decision-making by individual devices may be based on projected deviation from the target conditions after a period of activity or inactivity but with a central controller which determines which devices should be switched on.