The impact of different bus number order on some indices of evaluating static voltage stability

In static voltage stability study, the minimum absolute eigenvalue and the smallest singular value are widely used as an indicator to measure the static voltage stability, the bus sensitivity and participation factor is also used in weak bus ranking. It is all known that the minimum absolute eigenvalue and the smallest singular value based on power flow Jacobian matrix are independent of bus number order, recently reduced Jacobian matrix concerning the voltage/reactive power and 2×2 load matrix are frequently used in static voltage stability, but the effect of different bus number order on these indices based on reduced Jacobian matrix and 2×2 load matrix are usually neglected. This paper proposes some propositions, which shows the indices mentioned above have nothing to do with the bus number order when the balanced bus is selected, regardless of the form of matrix used.