The rate of change in classic thyristor-based onload tap-changing ac stabilizers is limited to that of the load current zero crossing (once per half cycle) due to the natural turnoff method involved. The growth of the power rate of insulated-gate bipolar transistor and other gate turnoff switches allows exploring of stabilizers that are able to change taps several times in a half cycle of the mains wave (subcyclic commutation). This paper analyzes the best four solutions for the power circuit of this new class of tap-changers in the multitap version, developed through an iterative analysis and synthesis cost comparative method that moves the tap-changing stabilizers over to the world of low-frequency voltage harmonics, oscillations, flicker, and instability phenomena attenuators. These topologies allow changing times as low as 150 /spl mu/s by using a multicoil inductance to perform current limitation and voltage clamping tasks during the switching operation, as it shall be shown in a second paper dedicated to the synthesis and experimental aspects.