Power Divider

TL;DR

This paper introduces power divider laws that analytically relate nodal power injections to line flows in AC networks, aiding in network analysis and allocation tasks.

Contribution

It derives closed-form power divider laws from circuit theory, linking network topology and voltage profiles to power flows, a novel analytical approach.

Findings

Power divider laws accurately relate nodal injections to line flows.

Application examples include transmission-loss allocation and feasible injection identification.

The laws enhance understanding of power flow contributions in AC networks.

Abstract

This paper derives analytical closed-form expressions that uncover the contributions of nodal active- and reactive-power injections to the active- and reactive-power flows on transmission lines in an AC electrical network. Paying due homage to current- and voltage-divider laws that are similar in spirit, we baptize these as the power divider laws. Derived from a circuit-theoretic examination of AC power-flow expressions, the constitution of the power divider laws reflects the topology and voltage profile of the network. We demonstrate the utility of the power divider laws to the analysis of power networks by highlighting applications to transmission-network allocation, transmission-loss allocation, and identifying feasible injections while respecting line active-power flow set points.