This paper shows how to exploit the degree of freedom represented by the common-mode voltage, which is inherent in three-phase Cascaded H-Bridge (CHB) converters, to minimize the total Root Mean Square (RMS) current value of the distributed dc sources. An optimal common-mode voltage injection law is derived, constituting a Maximum Power Per Ampere (MPPA) modulation strategy with respect to the currents of the dc sources. The potential benefits introduced by the proposed algorithm are analyzed in the context of battery-fed CHB converters and validated experimentally with a three-time-constant Randles model of a battery cell. The MPPA strategy is compared with traditional common-mode voltage injection methods, and battery loss reduction is demonstrated. The obtained battery energy saving is dependent on the converter modulation index and power factor. Experimental tests on a 36-cell full-bridge CHB converter validates the simulation and numerical derivation. To demonstrate the efficacy of the proposed method in practical applications, a 3 MW Energy Storage System (ESS) and a 110 kW Battery Electric Vehicle (BEV) undergoing standard drive cycles are presented as case studies. Compared to traditional modulation strategies, the MPPA strategy reduces the battery losses by up to 10.9% in the ESS and 27.5% in the BEV application.