Title: Resistance distance criterion for optimal 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.