Step-Wise Power Transformation

A system for transforming the voltage of AC electrical energy by resonant charge exchange between a first node and a second node. The system includes a capacitor or series-connected column of capacitors and a controller that is configured to cause the system to repetitively conduct a primary charge exchange by resonantly exchanging energy between the capacitor or the series-connected column of capacitors and the first node, and then electrically isolate the capacitor or the series-connected column of capacitors. During the electrical isolation the system can electrically reconfigure the series-connected column of capacitors. The system then conducts a secondary charge exchange by resonantly exchanging energy between the capacitor or the reconfigured series-connected column of capacitors and the second node.