Home energy management problem: towards an optimal and robust solution

A home automation system basically consists of household appliances linked via a communication network allowing interactions for control purposes (Palensky & Posta, 1997). Thanks to this network, a load management mechanism can be carried out: it is called distributed control in (Wacks, 1993). Load management allows inhabitants to adjust power consumption according to expected comfort, energy price variation and CO2 equivalent rejection. For instance, during the consumption peak periods when power plants rejecting higher quantities of CO2 are used and when energy price is high, it could be possible to decide to delay some services, to reduce some heater set points or to run requested services even so according to weather forecasts and inhabitant requests. Load management is all the more interesting that local storage and production means exist. Indeed, battery, photovoltaic panels or wind mills provide additional flexibilities. Combining all these elements lead to systems with many degrees of freedom that are very complex to manage by users. The objective of this study is to setup a general mathematical formulation that makes it possible to design optimized building electric energy management systems able to determine the best energy assignment plan, according to given criteria. A building energy management system consists in two aspects: the load management and the local energy production management. (House & Smith, 1995) and (Zhou & Krarti, 2005) have proposed optimal control strategies for HVAC (Home Ventilation and Air Conditioning) system taking into account the natural thermal storage capacity of buildings that shift the HVAC consumption from peakperiod to off-peak period. Zhou & Krarti (2005) has shown that this control strategy can save up to 10% of the electricity cost of a building. However, these approaches do not take into account the energy resource constraints, which generally depend on the autonomy needs of off-grid systems (Muselli et al., 2000) or on the total power production limits of the suppliers in grid connected systems. The household load management problem can be formulated as a assignment problem where energy is considered as a resource shared by appliances, and tasks are energy consumptions of appliances. Ha et al. (2006a) presents a three-layers household energy control system that is both able to satisfy the maximum available electrical power constraint and to maximize user satisfaction criteria. This approach carries out more reactivity to adapt consumption to the energy provider requirements. Ha et al. (2006b) proposes a global solution for the household load management problem. In order to adapt the consumption to the available energy, the home automation system controls the appliances in housing by determining the 5