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The normal operation of power system relies on accurate state estimation thatfaithfully reflects the physical aspects of the electrical power grids.However, recent research shows that carefully synthesized false-data injectionattacks can bypass the security system and introduce arbitrary errors to stateestimates. In this paper, we use graphical methods to study defendingmechanisms against false-data injection attacks on power system stateestimation. By securing carefully selected meter measurements, no false datainjection attack can be launched to compromise any set of state variables. Wecharacterize the optimal protection problem, which protects the state variableswith minimum number of measurements, as a variant Steiner tree problem in agraph. Based on the graphical characterization, we propose both exact andreduced-complexity approximation algorithms. In particular, we show that theproposed tree-pruning based approximation algorithm significantly reducescomputational complexity, while yielding negligible performance degradationcompared with the optimal algorithms. The advantageous performance of theproposed defending mechanisms is verified in IEEE standard power systemtestcases.

Graphical Methods for Defense Against False-data Injection Attacks on Power System State Estimation