Systems and methods for power conversion are described. Symmetric topologies and modulation schemes are described that may reduce common-mode noise. For example, a system may include a transformer including a first secondary winding and a second secondary winding; a rectifier, including a set of switches, that connects taps of the first secondary winding and the second secondary winding to a first terminal and a second terminal, wherein the rectifier is symmetric with respect to the first secondary winding and the second secondary winding; a battery connected between the first terminal and the second terminal; and a processing apparatus that is configured to control the set of switches to rectify a multilevel voltage signal on the transformer, including: selecting a modulation scheme from among two or more modulation schemes based on a measured voltage level of the battery.