A Novel Decomposition for Control of DC Circuits and Grid Models with Heterogeneous Energy Sources
Provides a theoretical decomposition for power analysis in DC circuits, which may inform grid operations but is incremental as it extends known circuit theory.
The paper shows that power in steady-state DC circuits with mixed sources depends on fundamental node voltages and edge currents, and that I^2R losses decompose into separate contributions from voltage- and current-controlled subcircuits. Total power is found as critical points of these variables, with potential applications to grid topology control.
The way in which electric power depends on the topology of circuits with mixed voltage and current sources is examined. The power flowing in any steady-state DC circuit is shown to depend on a minimal set of key variables called fundamental node voltages and fundamental edge currents. Every steady-state DC circuit can be decomposed into a voltage controlled subcircuit and a current controlled subcircuit. In terms of such a decomposition, the I^2R losses of a mixed source circuit are always the sum of losses on the voltage controlled subcircuit and the current controlled subcircuit. The paper concludes by showing that the total power flowing in a mixed source circuit can be found as critical points of the power expressed in terms of the key voltage and current variables mentioned above. The possible relationship to topology control of electric grid operations is discussed.