Temperature dependent iterative model of thermoelectric generator including thermal losses in passive elements

Design and development of a thermoelectric module and in its use in real application require an accurate simulation tool, which provides electrical and thermal characterizations as a function of temperature. The problem of correctly solving the basic thermoelectric equations originates from the fact that junctions temperatures are unknown and normally cannot be measured, whereas only external temperatures are available in testing and real applications. Due to thermal losses in passive layers, the internal temperatures can be significantly different. At the same time all the equations contains temperature dependent parameters. Many approximations are usually introduced to achieve results. Here we propose a simple iterative method to obtain the temperature losses and calculate all thermoelectric performances with corrected temperatures. The method, developed in Matlab language, takes into account temperature dependent material properties, thermal and electrical resistance of passive elements (electrodes, ceramics, interfaces, contact pad, etc.). Joule heating, Peltier and Thomson effects are considered in determine the temperatures. The effectiveness of the proposed procedure and the differences between approximated methods are investigated. The accuracy is proved with two commercial modules: the deviation were found to be within 4% and 3%. The code demonstrates to converge in few iterations in both cases. Moreover, the robustness has been investigated as a function of different parameters confirming that the code is suitable also for parametric simulations.