A Game Theory Approach to Vulnerability Analysis: Integrating Power Flows with Topological Analysis


This paper presents a new framework for vulnerability analysis. Under this framework, we can identify the vulnerable components and the critical components of a power grid. Distinct from previous work, our model considers the interaction between the components of the power system, and models the dynamic evolving process of cascading failures. The impact of a component failure on the system is dynamically changing as the failure propagates. We analyze the vulnerability of a power grid using an optimization model based on game theory, and use linear programming method to solve it. Since instability is the reason of power outage, we use an instability index to measure the negative impact to the system. The results from this optimization problem suggest which component of the system is critical since its failure can most negatively impact the cyber-physical system.


Computer Science

Second Department

Electrical and Computer Engineering


National Science Foundation (U.S.)
United States. Department of Energy


This research work is supported in part by US National Science Foundation under Grants ECCS-1307458, CNS-1537538, CNS1545063, and CMMI-1551448. Dr. Crow is supported by multiple NSF - United States and DOE - United States grants.

Keywords and Phrases

Electric load flow; Electric power transmission networks; Embedded systems; Game theory; Linear programming; Optimization; Plasma stability; Topology; Cascading failures; Component failures; Cyber physical systems (CPSs); Optimization modeling; Optimization problems; Power flows; Topological analysis; Vulnerability analysis; Outages; Instability

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


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© 2016 Elsevier Ltd, All rights reserved.

Publication Date

01 Nov 2016