## Fast Post-Contingency Eigenvalue Calculation

**Rodney Yeu with adviser Peter W. Sauer**

Dynamic security assessment is an analysis of a power system made to determine if the system can withstand contingencies or certain probable disturbances and still operate in a satisfactory manner. A part of this assessment is the small-signal stability assessment of a power system that is traditionally done by looking at the eigenvalues of a linearized system. As an example, Figure 44 shows the eigenvalues on the complex plane of a nine-bus three-machine system before and after a line outage. As can be seen by the figure, two of the eigenvalues moved from the left-hand plane to the right-hand plane indicating that the system became unstable.

Eigenvalue analysis is a very helpful tool in determining the stability of a power system. However, it is computationally burdensome to calculate the eigenvalues for all the considered contingencies and cannot be done online. The current research is looking to develop a fast method to compute the eigenvalues of a power system after line outages. Initial work is investigating the use of the fast-linear-load-flow method on a decoupled system that separates the machines from the power system network.