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Geomagnetically induced currents (GIC) represent a challenge for society, given its strong dependence 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 to much weaker, but fast, processes. Here we consider several typical examples of such fast processes and their impact on power transmission lines at Kola peninsula and in Karelia: SC/SI impulses; TCV events; impulses embedded into substorms; and irregular Pi3 pulsations. Geomagnetic field variability is examined using data from the IMAGE magnetometer array. GIC are often modeled as fluctuations of intensity of the east-west auroral electrojet, so it is commonly supposed that they are most dangerous for technological systems extended in the longitudinal direction. We have shown that during the considered impulsive events the ionospheric currents fluctuate not just in the E-W direction, but chaotically in both the E-W and N-S directions, and they do induce GIC in the latitudinally extended electric power line. Information about GIC is important not only from a practical point of view, but also from a fundamental scientific view, revealing the fine structure of fast geomagnetic variations during storms and substorms.