Digital compensation framework for transport AC loss measurements in multistack superconducting coils

High-temperature superconducting (HTS) coils are used in high-current, high-field applications such as fusion magnets and electric aviation. In many designs, several tapes or stacks are connected within each turn to increase current capacity while maintaining low operating voltage. However, these multistack configurations can develop non-uniform current distributions, which affect AC losses and complicate their experimental characterisation. This work presents and evaluates a digital compensation framework for transport AC loss measurements in multi-stack HTS coils. The proposed framework is formulated as a common post-processing procedure in which three elements can vary: the inductive reference signal, its representation during compensation, and the fitting region used to estimate the compensation coefficient. Two global reference strategies are investigated under the same experimental conditions: a Rogowski-based reference and a secondary-coil reference obtained from a dedicated primary-secondary compensation circuit. For each, both full-waveform and phase-guided compensation approaches are assessed. The framework is evaluated across a hierarchy of coil topologies, including single-tape, single-stack, balanced double-stack, and unbalanced double-stack coils. The results show that the secondary-coil full-waveform implementation provides the most robust performance and is recommended as the preferred default when available. In contrast, Rogowski-based compensation is more sensitive to coil topology, frequency, sensor placement, and current redistribution. Full-waveform compensation generally gives the closest agreement with manual compensation, whereas secondary phase-guided compensation often remains close to the corresponding full-waveform implementation despite using reduced reference information. It therefore provides a useful reduced-information alternative when the reference phase is stable. A fitting-window sensitivity study shows that window location is more critical than window size, with the best performance obtained for low-current windows placed near, but slightly shifted from, the current zero crossing. Overall, the proposed framework provides a practical method-selection and qualification route for AC loss characterisation in complex HTS windings and clarifies when simplified reference representations remain valid.