We use several realistic three-dimensional models of ionospheric currents to calculate geomagnetically induced currents (GIC) in the Finnish high-voltage power system. Of special interest are events during which the magnetic field changes rapidly and GIC are large. The geoelectric field driving GIC is determined with the complex image method, which is a fast and accurate tool for taking into account induction effects in the Earth. A detailed investigation is made applying a model of a westward traveling surge (WTS). It is capable of producing magnetic field variations and GIC which are of the same magnitude as the observed values. However, the WTS model yields too large time derivatives of the magnetic field. A much simpler line current model produces very realistic magnitudes of both the magnetic field and GIC. However, in contrast to WTS, it lacks the realistic spatial structure of the ground magnetic field. The requirement of accurate models of the Earth's conductivity is demonstrated by comparing a resistive and conductive structure in connection with a very rapid change of the magnetic field. Consideration of some other typical ionospheric events (Harang's discontinuity, omega band, pulsation) indicates that these phenomena probably cannot produce extremely large GIC. ¿ 1999 American Geophysical Union