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The way in which electric power depends on the topology of circuits withmixed voltage and current sources is examined. The power flowing in anysteady-state DC circuit is shown to depend on a minimal set of key variablescalled fundamental node voltages and fundamental edge currents. Everysteady-state DC circuit can be decomposed into a voltage controlled subcircuitand a current controlled subcircuit. In terms of such a decomposition, the I^2Rlosses of a mixed source circuit are always the sum of losses on the voltagecontrolled subcircuit and the current controlled subcircuit. The paperconcludes by showing that the total power flowing in a mixed source circuit canbe found as critical points of the power expressed in terms of the key voltageand current variables mentioned above. The possible relationship to topologycontrol of electric grid operations is discussed.

A Novel Decomposition for Control of DC Circuits and Grid Models with Heterogeneous Energy Sources