Simplified models for heating system optimisation using the thermal–electrical analogy

The well-known electrical analogy for thermal modelling is based on the observation that Fourier’s equation for one dimensional heat transfer takes the same form as Ohm’s law. This provides a system for creating and resolving complex heat transfer problems using an established set of physically–based laws. The present article illustrates the concept for adjacent rooms in a modern university building, and investigates some of the modelling issues involved. The electrical analogy is chosen so that the models can be extended and used for future research into demand–side control of multiple buildings on the university network, requiring a fast computation time. For illustrative purposes, the present article is limited to a relatively straightforward two–room system, for which the modelling equations are conveniently represented and solved using MATLAB–SIMULINK. The coefficients of this model are estimated from data using standard nonlinear optimisation tools. For comparison, the article also develops an equivalent multiple–input Transfer Function form of the model. Finally, suggestions are made for the inclusion of occupancy estimates in the model.