Applied Mathematics Colloquium **SPECIAL DAY/TIME**

The need for improving security standards for electric power systems is well recognized.  Such efforts however, are hindered by lack of decision support tools that can incorporate security into the decision making process. The current practice is to protect the system against known or anticipated failures either by using a post-processing phase or by explicit enumeration of the known cases. These approaches not only lack scalability to larger systems or higher security standards, but also are limited to predicted failures, which is a significant shortcoming with the uncertainty of the renewable generation. In this talk, we will start with introducing our techniques for vulnerability analysis of electric power systems, where we try to find small groups of components, whose loss will cause significant disturbances. Then we will describe how our vulnerability analysis techniques can be incorporated into the decision making process, where vulnerability analysis becomes a constraint to another optimization problem. For instance, can we solve the unit-commitment problem such that the system can survive loss of any combination of a specified number of its elements? We will also briefly discuss our recent work on how to include uncertainty in these problems.