Mathematical model of a thermoelectric system based on steady- and rapid-state measurements

Abstract

The paper presents the development of a complete analytical model of a thermoelectric generator (TEG). Based on data coming from a small number of easily obtainable measurements, the model makes it possible to determine basic parameters of the TEG. Owing to measurements performed in the steady state and immediately after a rapid change of the TEG electrical state, the following quantities can be established analytically: the Seebeck coefficient, thermal conductivity and thermal resistance between heat exchangers and the TEG. The applied rapid method is based on the large difference in inertia between the electric and the thermal field. A rapid change from the short-circuit to the open-circuit electrical state makes it possible to record the voltage for the system thermal state corresponding to the short circuit. Experimental tests were carried out on a commercially available thermoelectric generator and the results proved the developed model usefulness. The simulation results show that the thermal resistance of the contact layers between the heat exchangers and the thermoelectric generators caused a loss of the temperature difference of the junctions from 30% at the recommended mechanical load to even over 50% if the clamping force was too low. Due to that, the determined power ratio, being an indicator of the utilization of the theoretical power capacity of a system burdened with thermal resistance, reaches values lower than 40% for the required clamping force and is below 20% for improper contact conditions The impact of the accuracy of the measurements on the values of the system parameters obtained from the model is evaluated by means of sensitivity analysis.