Experimental characterization and comparative thermal modeling of thermoelectric cells: Lumped, multi-node, and fractional-order models

This work presents an experimental and computational framework for the characterization, identification and comparative evaluation of dynamic thermal models for thermoelectric cooling cells operating under PWM excitation. Five modeling approaches are investigated: a first-order model (PT1), a multi-node thermal model (PTN), a heterogeneous multi-time-constant model (PTN multi-tau), a classical three-node lumped thermal network (3N), and a fractional-order three-node model (F3N) based on a discrete Grünwald--Letnikov formulation. Experimental data were acquired using a dedicated embedded platform integrating thermal, electrical and environmental sensing under dynamic operating conditions. Model parameters were identified through a multi-objective optimization framework based on NSGA-II, simultaneously minimizing temperature reconstruction and dynamic response errors.A unified benchmarking methodology was developed to evaluate the models through temporal performance metrics, Pareto-front quality indicators, robustness analysis and parameter identifiability assessment. The comparative results indicate that increasing model complexity generally improves the representation of transient thermal dynamics, although this enhancement is accompanied by reduced robustness and lower parameter identifiability. Among the evaluated formulations, the PTN multi-tau model achieved the best overall compromise between prediction accuracy, dynamic fidelity and optimization stability, while the fractional-order model exhibited improved transient smoothing behavior but higher parameter dispersion. Statistical analysis confirmed significant differences among the evaluated models (p << 0.05), and the identifiability study revealed increasing parameter uncertainty as model dimensionality increased.The proposed framework provides a reproducible methodology for the comparative evaluation of thermoelectric thermal models under dynamic excitation and highlights the trade-offs between model accuracy, structural complexity and parameter stability in thermoelectric system identification.