geomagnetically induced currents (gics), which are generated due to geomagnetic disturbances (gmds), can saturate the cores of power transformers and their associated current transformers (cts). to avoid maloperation of transformer differential relays in the presence of gics, this family of relays is often equipped with harmonic blocking (hb) or harmonic restrain (hr) functions. these two functions, however, negatively impact the sensitivity and dependability of differential relays during gics. thus, if an internal fault occurs in the presence of gics, it might remain uninterrupted. on this basis, this study proposes an auxiliary framework for single-phase transformers or threephase transformer banks to address the above-mentioned issues for differential relays and their cts without sacrificing the sensitivity and/or speed of differential protection. this framework benefits from the linear parameter varying (lpv) state-space equations of cts and power transformers, and convert them to their polytopic form. then, it employs lpv observers to estimate the states of the transformer and its cts. to counter ct saturation, the framework precisely calculates the primary currents of cts based on their secondary currents, allowing the differential scheme to use the estimated primary currents rather than distorted secondary currents. furthermore, the proposed framework detects internal faults by comparing the estimated primary current of the transformer with the measured one. the difference between the estimated and measured currents is almost zero when no internal fault is present during gmds; however, the discrepancy between the two grows as soon as an internal fault occurs. the effectiveness of the proposed framework is validated through simulations in electromagnetic transient program (emtp)