Wideband Modeling of Toroidal Air-Core Reactors Based on Equipotential Conductor Elements and Terminal Capacitance Equivalence

Toroidal air-core reactors (TARs) exhibit significant advantages due to low leakage flux, making them suitable for compact applications, such as offshore wind power platsforms. Establishing a wideband equivalent circuit for TARs enables rapid calculation of transient voltage distribution, thereby assessing whether the existing structure meets insulation requirements. This paper proposes a modeling methodology for the transient voltage estimation of the TAR based on the concepts of equipotential conductor elements and terminal capacitance equivalence. The contributions lie in three aspects. First, wideband equivalent circuits are constructed at both the coil level and the TAR level. The capacitances in the model can all be explicitly defined by mathematical expressions, moving beyond behavioral equivalence and possessing clear physical meaning. Second, methods for extracting resistance, inductance, and capacitance parameters of the proposed models are presented, along with an analytical formula for the AC resistance of TARs. Finally, lightning impulse tests are conducted on a TAR prototype. The average errors between calculated and measured peak values of node-to-ground voltage, inter-coil voltage, and inter-turn voltage are 3.239%, 4.901%, and 8.603%, respectively, validating the accuracy of the proposed wideband equivalent circuit and parameter extraction methods.