Derivation and Analysis of Dynamic Model of Peltier Module using Small Signal Approach for Heat Pump Application

Abstract

This paper aims at the dynamic modelling of the Peltier module with cooling load and heat sink. The governing equation for the system is derived and linearized with the induced perturbation to the variable quantities. Laplace transform is applied to the governing equations to obtain the transfer function, which accounts for the dynamics of the Peltier module system. The exact transfer function of the system demands a series expansion of a few terms, which results in a multi-order system with a larger number of poles. So, from an analytical point of view transfer function is reduced to second order system with optimal assumptions. Mathematical derivation is provided for this system which explains the physical essence of the transfer function having one zero and two poles and depends on the operating conditions.