Eigenvalue sensitivity with respect to operating points for eigenvalue control of power system.

Eigenvalue and Eigenvector Sensitivities Applied to Power System Steady-state Operating Point

This paper proposes techniques used in finding a power system operating point that is both economically optimal and stable in the small-signal sense. To make the system small-signal stable, we should choose a power system operating point such that changes in system state variables due to small disturbances die out quickly. Thus, we need to know how changes in the power system operating point af...

II. Eigenvalue Sensitivity Analysis

Properties of eigenvalue function

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

Eigenvalue statistics and lattice points

One of the more challenging problems in spectral theory and mathematical physics today is to understand the statistical distribution of eigenvalues of the Laplacian on a compact manifold. There are now several challenging conjectures about these, originating in the physics literature. In this survey, a version of a talk delivered as the Colloquio De Giorgi at the Scuola Normale Superiore of Pis...

Eigenvalue calculator for Islanded Inverter-Based Microgrids

The stability analysis of islanded inverter-based microgrids (IBMGs) is increasingly an important and challenging topic due to the nonlinearity of IBMGs. In this paper, a new linear model for such microgrids as well as an iterative method to correct the linear model is proposed. Using the linear model makes it easy to analyze the eigenvalues and stability of IBMGs due to the fact that it derive...