A Novel Fractional-Order Equivalent Circuit Model for Characterizing Multifrequency Impedance Dynamics in Polymeric Insulation

This article presents a novel fractional-order equivalent circuit model (FO-ECM) for multifrequency impedance characterization of insulation systems in power assets. The proposed FO-ECM distinguishes itself by incorporating both a frequency-independent circuit module and adjustable frequency-dependent relaxation branches, making it a physics-based, modular approach capable of accurately representing complex impedance dynamics in polymeric insulation. The theory analysis, model construction, and analytical derivations of the FO-ECM are presented systematically. Eight study cases involving epoxy resin, polyester-imide resin, polyethylene terephthalate, and crosslinked polyethylene insulation are designed as a proof of concept to validate the model. The mapping relationship between dynamic mechanisms and the corresponding circuit model is analyzed. Additionally, the effectiveness and feasibility of the FO-ECM are validated by integrating varied measurement conditions, including voltage magnitudes (3 V, 100 V, and 140 V, rms), frequencies (1 mHz to 1 MHz), temperatures (25 °C to 150 °C above glass transition temperature), aging states (thermal aging), and instrument differences. Compared with the conventional RC impedance and Cole-Cole models, the proposed FO-ECM enables physics-based reconstruction of multifrequency impedance responses and exhibits enhanced applicability to insulation systems in practical power equipment. Thus, this study establishes a reliable modelling foundation for polymeric insulation under multifrequency voltages.