Power system steady-state stability and the load-flow Jacobian

Sauer, P. W. ; Pai, M. A. (1990) Power system steady-state stability and the load-flow Jacobian IEEE Transactions on Power Systems, 5 (4). pp. 1374-1383. ISSN 0885-8950

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Related URL: http://dx.doi.org/10.1109/59.99389


The relationship is presented between a detailed power system dynamic model and a standard load-flow model. The linearized dynamic model is examined to show how the load-flow Jacobian appears in the system dynamic-state Jacobian for evaluating steady-state stability. Two special cases are given for the situation when singularity of the load-flow Jacobian implies singularity of the system dynamic-state Jacobian. The standard load-flow Jacobian can provide information about the existence of a steady-state equilibrium point for a specified level of loading or interchange. There are two very special cases when the determinant of the standard load-flow Jacobian implies something about the steady-state stability of a dynamic model. Both of these cases involve very drastic assumptions about the synchronous machines and their control systems. The load level which produces a singular load-flow Jacobian should be considered an optimistic upper bound on maximum loadability.

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