An analytical method is employed to characterize the reactive power loss of a single-phase transformer when subjected to geomagnetically induced current (GIC). A general closed-form formula is proposed to calculate the reactive power loss of the transformer as a function of the applied voltage, air-core inductance, and GIC. The developed equation reveals that the reactive power loss is a nonlinear function of the GIC and the applied voltage, implying that the reactive power loss is not scalable with the voltage or GIC.
The presented function can also be used to estimate the GIC from the measured transformer reactive power in the case of lacking direct GIC measurement. Based on high accuracy confirmed by the time-domain simulations, the developed formula can substitute for a large number of lookup tables required in a power system analysis program dealing with GIC studies.