Improvement of thermal nodal models with negative compensation capacitors

The objective of the present study is to improve the modelling of heat tran sfer by elementary cells, aiming to increase the quality of their represent ation in the Laplace space. From the twoport representation and its connect ions with the classical nodal method, we show that the systematic increase of the order leads to improve the simulation results in transients. But, we would like to find a better reduced topology of the equivalent elementary network of heat conduction, closer to the analytical solution and verifying its terms for higher orders. The wall representation can be performed by a n impedance network with "II" or "T" shaped cells. The approximation of the se impedances leads to define a new cell topology, which introduces capacit ances with a negative value called "compensation capacitors". The value of these new elements only depends on the model nodal thermal capacitances in a wall. We study the transfer functions of these various equivalent network s as twoports that we will then compare to the analytical solution of the h eat transfer equation. Some interesting values of the negative compensation capacitors are then obtained from transfer function; however, the optimal value would only be given from simulation results. All the established resu lts will be confirmed by transient response simulations, which show the hig h performances of these new structures. These results are also validated by a modal analysis of these systems. The study of the model's accuracy show that the importance of the reduction for equivalent maximum errors correspo nds to the square of the number of elementary cells.