A Game-Theoretic Framework for Controlled Islanding in the Presence of Adversaries

Controlled islanding effectively mitigates cascading failures by partitioning the power system into a set of disjoint islands. In this paper, we study the controlled islanding problem of a power system under disturbances introduced by a malicious adversary. We formulate the interaction between the grid operator and adversary using a game-theoretic framework. The grid operator first computes a controlled islanding strategy, along with the power generation for the post-islanding system to guarantee stability. The adversary observes the strategies of the grid operator. The adversary then identifies critical substations of the power system to compromise and trips the transmission lines that are connected with compromised substations. For our game formulation, we propose a double oracle algorithm based approach that solves the best response for each player. We show that the best responses for the grid operator and adversary can be formulated as mixed integer linear programs. In addition, the best response of the adversary is equivalent to a submodular maximization problem under a cardinality constraint, which can be approximated up to a (1− 1 e ) optimality bound in polynomial time. We compare the proposed approach with a baseline where the grid operator computes an islanding strategy by minimizing the power flow disruption without considering the possible response from the adversary. We evaluate both approaches using IEEE 9-bus, 14-bus, 30-bus, 39-bus, 57bus, and 118-bus power system case study data. Our proposed approach achieves better performance than the baseline in about 44% of test cases, and on average it incurs about 12.27 MW less power flow disruption.

[1]  Ali Peiravi,et al.  A fast algorithm for intentional islanding of power systems using the multilevel kernel k-means approach , 2009 .

[2]  Natalia Alguacil,et al.  Analysis of Electric Grid Interdiction With Line Switching , 2010, IEEE Transactions on Power Systems.

[3]  Daniel S. Kirschen,et al.  Criticality in a cascading failure blackout model , 2006 .

[4]  Deepak Rajan,et al.  Strong Mixed-Integer Formulations for Power System Islanding and Restoration , 2019, IEEE Transactions on Power Systems.

[5]  Lei Ding,et al.  Two-Step Spectral Clustering Controlled Islanding Algorithm , 2013, IEEE Transactions on Power Systems.

[6]  Branislav Bosanský,et al.  An Exact Double-Oracle Algorithm for Zero-Sum Extensive-Form Games with Imperfect Information , 2014, J. Artif. Intell. Res..

[7]  Avrim Blum,et al.  Planning in the Presence of Cost Functions Controlled by an Adversary , 2003, ICML.

[8]  Gabor Karsai,et al.  Vulnerability analysis of power systems based on cyber-attack and defense models , 2018, 2018 IEEE Power & Energy Society Innovative Smart Grid Technologies Conference (ISGT).

[9]  Heejo Lee,et al.  This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. INVITED PAPER Cyber–Physical Security of a Smart Grid Infrastructure , 2022 .

[10]  Naima Kaabouch,et al.  Cyber security in the Smart Grid: Survey and challenges , 2013, Comput. Networks.

[11]  Kai Sun,et al.  Splitting strategies for islanding operation of large-scale power systems using OBDD-based methods , 2003 .

[12]  Vincent Conitzer,et al.  A double oracle algorithm for zero-sum security games on graphs , 2011, AAMAS.

[13]  Sarit Kraus,et al.  Playing games for security: an efficient exact algorithm for solving Bayesian Stackelberg games , 2008, AAMAS.

[14]  Vincent Conitzer,et al.  On Stackelberg mixed strategies , 2015, Synthese.

[15]  R D Zimmerman,et al.  MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education , 2011, IEEE Transactions on Power Systems.

[16]  Rongxing Lu,et al.  Defending Against False Data Injection Attacks on Power System State Estimation , 2017, IEEE Transactions on Industrial Informatics.

[17]  V. Vittal,et al.  Slow coherency-based islanding , 2004, IEEE Transactions on Power Systems.

[18]  Jacek Mandziuk,et al.  Double-oracle sampling method for Stackelberg Equilibrium approximation in general-sum extensive-form games , 2020, AAAI.

[19]  G.T. Heydt,et al.  A Novel Slow Coherency Based Graph Theoretic Islanding Strategy , 2007, 2007 IEEE Power Engineering Society General Meeting.

[20]  Zhuo Lu,et al.  Cyber security in the Smart Grid: Survey and challenges , 2013, Comput. Networks.

[21]  J. M. Arroyo,et al.  A Genetic Algorithm Approach for the Analysis of Electric Grid Interdiction with Line Switching , 2009, 2009 15th International Conference on Intelligent System Applications to Power Systems.

[22]  Joe H. Chow,et al.  Time-Scale Modeling of Dynamic Networks with Applications to Power Systems , 1983 .

[23]  A. G. Expósito,et al.  Power system state estimation : theory and implementation , 2004 .

[24]  Haibo He,et al.  Supplementary File : Revealing Cascading Failure Vulnerability in Power Grids using Risk-Graph , 2013 .

[25]  Yang Xiao,et al.  Cyber Security and Privacy Issues in Smart Grids , 2012, IEEE Communications Surveys & Tutorials.

[26]  A.H.M.A. Rahim,et al.  Identification of coherent generators using energy function , 1990 .

[27]  Kai Sun,et al.  A study of system splitting strategies for island operation of power system: a two-phase method based on OBDDs , 2003 .

[28]  V. Terzija,et al.  Two-step spectral clustering controlled islanding algorithm , 2013, 2013 IEEE Power & Energy Society General Meeting.

[29]  Vincent Conitzer,et al.  Computing the optimal strategy to commit to , 2006, EC '06.

[30]  Elias Kyriakides,et al.  A Real-Time Controlled Islanding and Restoration Scheme Based on Estimated States , 2019, IEEE Transactions on Power Systems.

[31]  Zhipeng Liu,et al.  Controlled Islanding via Weak Submodularity , 2019, IEEE Transactions on Power Systems.

[32]  Sarit Kraus,et al.  Using Game Theory for Los Angeles Airport Security , 2009, AI Mag..

[33]  Andreas Krause,et al.  Submodular Function Maximization , 2014, Tractability.

[34]  Wei Yu,et al.  On False Data-Injection Attacks against Power System State Estimation: Modeling and Countermeasures , 2014, IEEE Transactions on Parallel and Distributed Systems.

[35]  V. E. Henner A network separation scheme for emergency control , 1980 .