Resistance distance criterion for optimal slack bus selection

TL;DR

This paper analyzes how the choice of slack bus affects transmission losses in high voltage AC networks, showing that selecting a single optimal slack bus minimizes losses, especially in networks with small, homogeneous r/x ratios.

Contribution

It provides an analytical framework linking slack bus selection to transmission losses using resistance distance, and validates findings with numerical tests on standard network models.

Findings

Optimal slack bus choice can reduce transmission losses by about 10%.

Transmission losses are minimized with a unique slack bus in networks with small, homogeneous r/x ratios.

Resistance distance serves as an effective indicator for slack bus selection.

Abstract

We investigate the dependence of transmission losses on the choice of a slack bus in high voltage AC transmission networks. We formulate a transmission loss minimization problem in terms of slack variables representing the additional power injection that each generator provides to compensate the transmission losses. We show analytically that for transmission lines having small, homogeneous resistance over reactance ratios ${r/x\ll1}$, transmission losses are generically minimal in the case of a unique \textit{slack bus} instead of a distributed slack bus. For the unique slack bus scenario, to lowest order in ${r/x}$, transmission losses depend linearly on a resistance distance based indicator measuring the separation of the slack bus candidate from the rest of the network. We confirm these results numerically for several IEEE and Pegase testcases, and show that our predictions qualitatively hold also in the case of lines having inhomogeneous ${r/x}$ ratios, with optimal slack bus choices reducing transmission losses by ${10}\%$ typically.