FAST CALCULATION OF A VOLTAGE STABILITY INDEX P-A L6f T Smed G Andersson

The minimum singular value of the power flow jacobian matrix has been used as a static voltage stability index, indicating the distance between the studied operating point and the steady state voltage stability limit. Here a fast method to calculate the minimum singular value and the corresponding (left and right) singular vectors is presented. The main advantages of the developed algorithm are the small amount of computation time needed, and that it only requires information available from an ordinary program for power flow calculations. Furthermore, the proposed method fully utilizes the sparsity of the power flow jacobian matrix and hence the memory requirements for the computation are low. These advantages are preserved when applied to various submatrices of the jacobian matrix, which can be useful in constructing special voltage stability indices. The developed algorithm was applied to small test systems as well as to a large (real size) system with over 1000 nodes, with satisfactory results.