Lumped and Distributed Parameter SPICE Models of TE Devices Considering   Temperature Dependent Material Properties
  Based on simplified one-dimensional steady-state analysis of thermoelectric phenomena and on analogies between thermal and electrical domains, we propose both lumped and distributed parameter electrical models for thermoelectric devices. For lumped parameter models, constant values for material properties are extracted from polynomial fit curves evaluated at different module temperatures (hot side, cold side, average, and mean module temperature). For the case of distributed parameter models, material properties are calculated according to the mean temperature at each segment of a sectioned device. A couple of important advantages of the presented models are that temperature dependence of material properties is considered and that they can be easily simulated using an electronic simulation tool such as SPICE. Comparisons are made between SPICE simulations for a single-pellet module using the proposed models and with numerical simulations carried out with Mathematica software. Results illustrate accuracy of the distributed parameter models and show how inappropriate is to assume, in some cases, constant material parameters for an entire thermoelectric element. 
D. Mitrani, J. Salazar, A. Turo, M. J. Garc\'ia, J. A. Ch\'avez