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

TL;DR

This paper introduces a new decomposition method for analyzing steady-state DC circuits with mixed sources, simplifying power flow calculations and offering insights into grid topology control.

Contribution

It presents a novel decomposition into voltage and current controlled subcircuits, enabling simplified analysis of power flow and losses in mixed source DC circuits.

Findings

Power flow depends on fundamental node voltages and edge currents.

Total I^2R losses are sum of losses in subcircuits.

Power can be found as critical points of a key variable expression.

Abstract

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.