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Geomagnetically induced currents (GICs) represent a significant challenge for society on a stable electricity supply. Space weather activates global electromagnetic and plasma processes in the near-Earth environment, however, the highest risk of GICs is related not directly to those processes with enormous energy yield, but too much weaker, but fast, processes. Here we consider several typical examples of such fast processes and their impact on power transmission lines in the Kola Peninsula and in Karelia: interplanetary shocks; traveling convection vortices; impulses embedded in substorms; and irregular Pi3 pulsations. Geomagnetic field variability is examined using data from the IMAGE (International Monitor for Auroral Geomagnetic Effects) magnetometer array. We have confirmed that during the considered impulsive events the ionospheric currents fluctuate in both the East-West and North-South directions, and they do induce GIC in latitudinally extended electric power line. It is important to reveal the fine structure of fast geomagnetic variations during storms and substorms not only for a practical point of view but also for a fundamental scientific view.