Graphical Evolutionary Game Model of Virus-Based Intrusion to Power System for Long-Term Cyber-Security Risk Evaluation

Through virus-based reconnaissances, the attacker may compromise critical power substations and induce power outages. Meanwhile, the power system operator may conduct defensive measures to prevent virus-spreading. In this paper, a graphical evolutionary game model is developed to solve the equilibrium of competitions between virus propagations and countermeasures, which helps to evaluate the cyber-security risk of power systems under long-term virus-based intrusions. In the proposed game model, the virus is supposed to propagate itself in a cyber network connecting cyber nodes belonging to power substations. Each cyber node may play as an attacker or a defender according to its state. A death-birth rule is adopted to model probabilistic strategies and state transfers, which reflects the bounded rationality of the viruses. Then, an evolution dynamic equation is derived to obtain the portion of the infected substations when the equilibrium is reached, and simulation algorithm is also given to estimate the infection probability of each substation under the persistent virus-based intrusion. Assuming a virus may trip all breakers in the infected substation, the cyber-security risk is evaluated to identify system-level vulnerabilities. The IEEE 118-bus system with a layered cyber network is used for case studies. Test results validate the proposed model and provide further insights into the virus-based intrusion.