This research develops comprehensive frequency-dependent analysis techniques to investigate surge arrester behaviour across the operational frequency spectrum. Through systematic characterization of gapless zinc oxide varistors, the study reveals previously overlooked loss mechanisms arising from distributed grain boundary effects within the polycrystalline microstructure. These findings demonstrate that conventional frequency-independent models significantly underestimate thermal stress during harmonic temporary overvoltages, explaining discrepancies between predicted and observed failure rates.

To address these limitations, a novel fractional-order circuit model is developed that captures both dielectric relaxation phenomena and voltage-dependent nonlinear conduction. The modelling framework employs phase-sensitive decomposition techniques to separate capacitive and resistive current components, enabling accurate representation of frequency-dependent behaviour. Validation against experimental data confirms that harmonic content fundamentally alters energy dissipation patterns in ways that existing models cannot predict.

The research establishes that surge arrester quality assessment must consider frequency-dependent effects as well as voltage magnitude. The developed characterization methodology and modelling tools provide essential capabilities for evaluating surge arrester performance in modern cable-intensive, renewable-integrated grids with significantly intermittent loads, contributing to more resilient protection systems for evolving power networks.