Stolen heating or cooling energy evaluation in collective buildings using model inversion techniques

In the case of collective buildings, heat fluxes between adjacent units are generally not taken into account and induce an over- or an under-estimation of every unitary heating or cooling demand. We show that the heat fluxes between adjacent units can be considered as unknown solicitations and then estimated with inverse methods. We propose a definition of an individual reference consumption. In order to be usable in practice, the whole proposed methodology verifies the confidentiality of measured data concerning every unit. The direct model used in the inversion process is a state model that describes all the heat transfer in the units; it is obtained by using a usual spatial discretisation method. It is assumed that the required experimental measurements for indoor temperature, heating power and for all climatic solicitations applied to the units are available. We illustrate the methodology with a unit controlled at a particular set point temperature and bordered by neighbour units controlled at different set points temperature (three cases are studied). The obtained results are commented and show that the seasonal energy stolen can be a high percentage of the whole energy demand of a unit.