Optimal Transient Operation in Thermoelectric Cooling and its Relation to Thermoelectric Properties

It has been well known for many decades that there exists an optimal Peltier current to achieve the best performance in steady-state Peltier cooling. At this constant current, there is a minimum steady-state cold-end temperature that can be achieved across a thermoelectric cooler. However, in a transient operation over a short time window, the temperature drop can be improved with a transient current pulse where the minimum transient temperature depends on the shape of the current pulse [1]. Here, we apply optimal control theory to find for the first time, a temperature minimizing <i>transient</i> current pulse. We consider a thermoelectric cooler with a heat load at the cold end, and model it as a discrete control system and use gradient descent to find a cost-minimizing current [2]. The optimal current diminishes the temperature rise due to the low frequency components of the heat loads, and this performance improvement depends strongly on thermal conductivity [3]. We also consider transient cooling of a thermoelectric below the minimum steady-state temperature. We observe that an optimal current pulse holds the temperature below its steady-state value for longer than a comparable constant current pulse. This work provides new insights into the upper li--mit of the transient performance of thermoelectric coolers.<br/> <br/>R. Yang, G. Chen, A. R. Kumar, G. J. Snyder, and J.-P. Fleurial, “Transient cooling of thermoelectric coolers and its applications for microdevices,” <i>Energy Conversion and Management</i>, 2005.<br/>D. P. Bertsekas, <i>Nonlinear programming</i>, 3rd ed. Belmont, Mass: Athena scientific, 2016<br/>P. E. Gray, <i>The Dynamic Behavior of Thermoelectric Devices</i>. The MIT Press, 1960.