Simplified models for heating system optimisation using a 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.