The sparse formulation of ISPS and its application to voltage stability margin sensitivity and estimation

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Abstract
The sparse formulation of the invariant sub-space parametric sensitivity (ISPS) of the structure preserving power system model is derived. The ISPS is the projection of parametric sensitivity onto a particular critical eigensubspace of interest. In this paper, major modifications are proposed to extend the applicability of the ISPS. ISPS is computed while tracing simultaneously the trajectory of both dynamic and algebraic state variables. By doing so, the sparsity of total Jacobian (the Jacobian that corresponds to both dynamic and algebraic variables) is fully exploited. The authors also derived a new voltage stability margin estimation from the measure of ISPS. It is shown here that the derived margin sensitivity vector can be calculated with essentially no further cost once the measure of ISPS is available. The voltage stability margin for any other parameter variations can be easily estimated without re-computing the P-V curves. With this methodology, effective controls can be easily coordinated by quantifying the relative importance of a wide range of control parameters. Numerical studies with the IEEE New England 39-bus system shows the potential applications of the method.