Fractional-order equivalent impedance model for junction-case thermal characteristics of insulated gate bipolar transistor modules

Purpose Thermal characterization of power switching devices is critical for the performance and reliability of power electronic applications. This paper aims to characterize the junction-case thermal properties of insulated gate bipolar transistor (IGBT) modules by fractional calculus-related techniques. Design/methodology/approach A fractional-order thermal impedance model is proposed for IGBT modules. Riemann–Liouville definition of fractional calculus and Laplace transformations are used to describe the thermal impedance characteristics of IGBT modules, thus, a fractional-order equivalent model is derived. Furthermore, the task of identifying model parameters is transformed into the problem of finding the global optimal solution for the fractional-order model, where the Harris Hawks optimization algorithm is used. Findings The thermal impedance curves of IGBT modules generally exhibit a “long-tail distribution” over time. This work demonstrates that, there is a potential relationship between this distribution law and fractional calculus operation. Therefore, fractional-order equivalent models can be used to describe the thermal impedance characteristics of IGBT modules in effective and concise way. Originality/value This work proposes for the first time a fractional-order model for the junction-to-case thermal impedance characteristics of IGBT modules. Using the proposed fractional-order model and parameter identification scheme, the maximum relative error remains below 8% within a time range of 0.001–100 s and a power range of 14.5 W–273 W, demonstrating high accuracy across diverse operating conditions. This model’s advantages in accuracy and complexity provide theoretical support for the manufacturing and thermal characteristics analysis of IGBT modules, confirming the widespread presence of fractional-order properties in the physical world.