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We investigate the dependence of transmission losses on the choice of a slackbus in high voltage AC transmission networks. We formulate a transmission lossminimization problem in terms of slack variables representing the additionalpower injection that each generator provides to compensate the transmissionlosses. We show analytically that for transmission lines having small,homogeneous resistance over reactance ratios ${r/x\ll1}$, transmission lossesare generically minimal in the case of a unique \textit{slack bus} instead of adistributed slack bus. For the unique slack bus scenario, to lowest order in${r/x}$, transmission losses depend linearly on a resistance distance basedindicator measuring the separation of the slack bus candidate from the rest ofthe network. We confirm these results numerically for several IEEE and Pegasetestcases, and show that our predictions qualitatively hold also in the case oflines having inhomogeneous ${r/x}$ ratios, with optimal slack bus choicesreducing transmission losses by ${10}\%$ typically.

Resistance distance criterion for optimal slack bus selection