https://inria.hal.science/hal-01857366v2Sun, KeKeSunACSE - Department of Automatic Control and Systems Engineering [ Sheffield] - University of Sheffield [Sheffield]Esnaola, IñakiIñakiEsnaolaACSE - Department of Automatic Control and Systems Engineering [ Sheffield] - University of Sheffield [Sheffield]ECE - Department of Electrical and Computer Engineering [Princeton] - Princeton University Perlaza, SamirSamirPerlazaNEO - Network Engineering and Operations - CRISAM - Inria Sophia Antipolis - Méditerranée - Inria - Institut National de Recherche en Informatique et en AutomatiqueECE - Department of Electrical and Computer Engineering [Princeton] - Princeton University Vincent Poor, HaroldHaroldVincent PoorECE - Department of Electrical and Computer Engineering [Princeton] - Princeton University Stealth Attacks on the Smart GridHAL CCSD2020Information-Theoretic SecurityMutual InformationProbability of DetectionData Injection AttacksStealth Attacks[MATH.MATH-IT] Mathematics [math]/Information Theory [math.IT][INFO.INFO-IT] Computer Science [cs]/Information Theory [cs.IT][SPI.NRJ] Engineering Sciences [physics]/Electric powerPerlaza, Samir M.2021-02-02 12:26:542023-03-15 08:58:092021-02-02 13:38:16enJournal articleshttps://inria.hal.science/hal-01857366v2/document10.1109/TSG.2019.2935353https://inria.hal.science/hal-01857366v1application/pdf2Random attacks that jointly minimize the amount of information acquired by the operator about the state of the grid and the probability of attack detection are presented. The attacks minimize the information acquired by the operator by minimizing the mutual information between the observations and the state variables describing the grid. Simultaneously, the attacker aims to minimize the probability of attack detection by minimizing the Kullback-Leibler (KL) divergence between the distribution when the attack is present and the distribution under normal operation. The resulting cost function is the weighted sum of the mutual information and the KL divergence mentioned above. The trade-off between the probability of attack detection and the reduction of mutual information is governed by the weighting parameter on the KL divergence term in the cost function. The probability of attack detection is evaluated as a function of the weighting parameter. A sufficient condition on the weighting parameter is given for achieving an arbitrarily small probability of attack detection. The attack performance is numerically assessed on the IEEE 30-Bus and 118-Bus test systems.