A multi-module dc-to-dc power transformation system that is constructed and arranged to transform power from a first high dc voltage node to a separate second high dc voltage node, having: (a) a column comprising a plurality of half-bridge modules connected in series, each half-bridge module comprising a capacitance configured to be either electrically inserted into the column or electrically isolated and electrically bypassed, wherein a first end of the column is electrically connected to ground; (b) first and second high voltage switches (12, 13), each in series with a reactor (70, 71); the first high-voltage switch adapted to electrically connect a second end of the column to the first high dc voltage node and the second high-voltage switch adapted to electrically connect the second end of the column to the second high dc voltage node; and (c) a controller adapted to control the states of switches within the half-bridge modules of the column and the first and second high voltage switches (12, 13) so as to transform power by resonant exchange of energy between multiple capacitances within the column and the first and second high dc voltage nodes (2, 3); characterized in that: the controller is configured to accomplish resonant switching that results in multiple positive half-cycles of resonant and sinusoidally varying current input to the multi-module dc-to-dc power transformation system and output from the multi-module dc-to-dc power transformation system, initiated by the connection of multiple capacitances of the column to the first and second high dc voltage nodes (2, 3) and interrupted at its first current-zero point, to achieve resonant exchange of energy between those multiple capacitances and the high voltage nodes (2, 3); wherein the resonant switching is characterized by: initially pre-charging all of the n capacitances of the column with the first high voltage switch open and the second high voltage switch closed; and then opening the second high voltage switch, and bypassing m capacitances, to electrically isolate m capacitances from the column, where m is less than n; and then closing the first high voltage switch to resonantly transfer charge from the first high dc voltage node to the n-m capacitances that are electrically inserted into the column; and then removing all of the bypasses and closing the second high dc voltage switch to resonantly discharge the capacitances of the column to the second high dc voltage node. (a) a column comprising a plurality of half-bridge modules connected in series, each half-bridge module comprising a capacitance configured to be either electrically inserted into the column or electrically isolated and electrically bypassed, wherein a first end of the column is electrically connected to ground; (b) first and second high voltage switches (12, 13), each in series with a reactor (70, 71); the first high-voltage switch adapted to electrically connect a second end of the column to the first high dc voltage node and the second high-voltage switch adapted to electrically connect the second end of the column to the second high dc voltage node; and (c) a controller adapted to control the states of switches within the half-bridge modules of the column and the first and second high voltage switches (12, 13) so as to transform power by resonant exchange of energy between multiple capacitances within the column and the first and second high dc voltage nodes (2, 3); the controller is configured to accomplish resonant switching that results in multiple positive half-cycles of resonant and sinusoidally varying current input to the multi-module dc-to-dc power transformation system and output from the multi-module dc-to-dc power transformation system, initiated by the connection of multiple capacitances of the column to the first and second high dc voltage nodes (2, 3) and interrupted at its first current-zero point, to achieve resonant exchange of energy between those multiple capacitances and the high voltage nodes (2, 3); wherein the resonant switching is characterized by: initially pre-charging all of the n capacitances of the column with the first high voltage switch open and the second high voltage switch closed; and then opening the second high voltage switch, and bypassing m capacitances, to electrically isolate m capacitances from the column, where m is less than n; and then closing the first high voltage switch to resonantly transfer charge from the first high dc voltage node to the n-m capacitances that are electrically inserted into the column; and then removing all of the bypasses and closing the second high dc voltage switch to resonantly discharge the capacitances of the column to the second high dc voltage node. initially pre-charging all of the n capacitances of the column with the first high voltage switch open and the second high voltage switch closed; and then opening the second high voltage switch, and bypassing m capacitances, to electrically isolate m capacitances from the column, where m is less than n; and then closing the first high voltage switch to resonantly transfer charge from the first high dc voltage node to the n-m capacitances that are electrically inserted into the column; and then removing all of the bypasses and closing the second high dc voltage switch to resonantly discharge the capacitances of the column to the second high dc voltage node.