Invariant subspace parametric sensitivity (ISPS) of structure-preserving power system models

In this paper, the parametric sensitivities of structure-preserving power system model are derived. The parametric sensitivities give the sensitivities of an equilibrium point with respect to a particular parameter of interest. A new invariant subspace parametric sensitivity (ISPS) is derived by projecting the total parametric sensitivity onto a particular eigenspace of interest. The ISPS provides the sensitivity of system stability. At a particular eigensubspace, ISPS of all the parameters under consideration are represented by a right eigenvector multiplied by a scalar a. Then the parameter which has the most influence on the subspace can be determined by selecting the largest value of a. The methodology is applied to a New England 39-bus system to identify components and parameters that are responsible for a possible system instability.