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

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