energies Article Identification of DC Thermal Steady-State Differential Inductance of Ferrite Power Inductors Salvatore Musumeci , Luigi Solimene * and Carlo Stefano Ragusa   Citation: Musumeci, S.; Solimene, L.; Ragusa, C.S. Identification of DC Thermal Steady-State Differential Inductance of Ferrite Power Inductors. Energies 2021, 14, 3854. https://doi.org/10.3390/en14133854 Academic Editor: Pavol Bauer Received: 28 May 2021 Accepted: 24 June 2021 Published: 26 June 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Dipartimento Energia “G. Ferraris”, Politecnico di Torino, 10129 Torino, Italy; salvatore.musumeci@polito.it (S.M.); carlo.ragusa@polito.it (C.S.R.) * Correspondence: luigi.solimene@polito.it Abstract: In this paper, we propose a method for the identification of the differential inductance of saturable ferrite inductors adopted in DC–DC converters, considering the influence of the operating temperature. The inductor temperature rise is caused mainly by its losses, neglecting the heating contribution by the other components forming the converter layout. When the ohmic losses caused by the average current represent the principal portion of the inductor power losses, the steady-state temperature of the component can be related to the average current value. Under this assumption, usual for saturable inductors in DC–DC converters, the presented experimental setup and charac- terization method allow identifying a DC thermal steady-state differential inductance profile of a ferrite inductor. The curve is obtained from experimental measurements of the inductor voltage and current waveforms, at different average current values, that lead the component to operate from the linear region of the magnetization curve up to the saturation. The obtained inductance profile can be adopted to simulate the current waveform of a saturable inductor in a DC–DC converter, providing accurate results under a wide range of switching frequency, input voltage, duty cycle, and output current values. Keywords: ferrite cores; DC–DC converters; saturable inductors 1. Introduction Inductors are key components in the design of high-power density DC–DC converters in high demand for automotive, aerospace, and telecommunications industries [1–3]. In these fields, the magnetic components need to have a small physical size, low power loss, and a high saturation magnetic flux density [4]. A further requirement is an ever- higher switching frequency in power converters, which reduces the inductor volume and increases the magnetic losses. Ferrite inductors represent a good trade-off between the required performance and cost of the component. However, their sharp inductance drop, even in gapped core components, often induce the designer to a conservative approach, ensuring that the inductor operates in the linear region of the core magnetization curve, where the inductance is nearly constant. The adoption of inductors operating in the weak saturation region allows optimizing the magnetic core to be used, reducing the volume and weight of the component [5–7]. However, the current ripple should be accurately computed to verify compliance with the application constraints. This task becomes even more challenging since the differential inductance profile of the component depends not only on the average current but also on the operating temperature of the core. In the literature, several methods for the characterization and modelling of the differential inductance of a saturable inductor for power electronics applications are described [8–12], some of which also consider the inductor operating temperature variation [13,14]. However, the temperature of a ferrite inductor is not easily measurable under normal operating conditions. Given the temperature dependence of the power dissipated by the component, some authors introduced a power-loss-dependent inductance model [15]. This approach allows describing the inductance of a saturable inductor as a function of operating current Energies 2021, 14, 3854. https://doi.org/10.3390/en14133854 https://www.mdpi.com/journal/energies