Based on a proposed analytical approach and time- domain simulation, this paper investigates the operating condition of single-phase transformers under steady-state and quasi-dc transient of the geomagnetically induced current (GIC). The analytical approach employs a two-slope piecewise linear magnetization characteristic and facilitates the development of generic characteristics for system studies to reduce the risk of power system instability and blackout during geomagnetic disturbances (GMDs). In addition, such characteristics can be used to estimate the transformer GIC, reactive power, and harmonic currents in the absence of direct measurements. The results obtained from the proposed approach are compared with the laboratory GIC test results of 500-kV and 230-kV transformers. In addition, the estimated dynamic behavior of a 500-kV autotransformer during aGMD event is compared with the measurements obtained from Hydro One SCADA and GIC monitoring systems. The study results reveal that under steady-state conditions, the transformer reactive power increases with GIC with an initial slope equal to the transformer ac peak voltage which is equivalent to 2.0 on a per-unit basis. Depending on the transformer air-core inductance, the slope decreases at higher GIC levels. Unlike the steady-state conditions, the GIC behavior of the transformer during a GMD event is influenced by the core kneepoint and the transformer delta winding.