Resistance distance criterion for optimal slack bus selection
For power system operators, this provides a simple criterion to reduce transmission losses by selecting the optimal slack bus.
The paper shows that transmission losses in high voltage AC networks are minimized by using a single slack bus rather than a distributed one, and that the optimal slack bus can be identified via a resistance distance indicator, achieving typical loss reductions of 10%.
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.