Impedance spectroscopy analysis of thermoelectric modules under actual energy harvesting operating conditions and a small temperature difference

Thermoelectric (TE) devices can convert heat into electricity and have gained great interest as energy harvesters in many applications, such as self-powered sensors, solar TE generators and industrial waste heat recovery. Not many techniques are usually available for their characterization under operating conditions. Consequently, only current-voltage (power output) curves are typically reported to account for their performance, which provide limited information. Impedance spectroscopy, which has been mainly applied to the study of TE modules suspended in air or vacuum, has the advantage to be used under operating conditions. Here, we exploit this advantage and provide an in-depth analysis of the impedance response of standard TE devices when they operate under a small temperature difference. First, we derive the physical models (equivalent circuits) for the two most common operating conditions: (i) constant temperature difference and (ii) constant heat power input. Then, we use the obtained equivalent circuit to successfully fit experimental impedance measurements in both operating modes, which show significant differences. From the fittings, it is possible to obtain the thermal contact resistance between the TE device and the heat exchangers (heat source and heat sink) among other key parameters. In addition, we analyze the variations found in the impedance spectra for different current output levels. Moreover, we show how different electrical resistances, extracted from the impedance results, directly relate to the slope of the I-V curve (power output), and can provide very valuable information about the different processes that determine its value. All these results establish impedance spectroscopy as a very powerful tool to characterize TE devices under operating conditions and as a method that can provide highly valuable insights into their performance.