Robust recovery of missing data in electricity distribution systems

The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore, paramount. In this context, an algorithm for recovering missing state variable observations in electricity distribution systems is presented. The proposed method exploits the low rank structure of the state variables via a matrix completion approach while incorporating prior knowledge in the form of second order statistics. Specifically, the recovery method combines nuclear norm minimization with Bayesian estimation. The performance of the new algorithm is compared to the information-theoretic limits and tested trough simulations using real data of an urban low voltage distribution system. The impact of the prior knowledge is analyzed when a mismatched covariance is used and for a Markovian sampling that introduces structure in the observation pattern. Numerical results demonstrate that the proposed algorithm is robust and outperforms existing state of the art algorithms

Robust Recovery of Missing Data in Electricity Distribution Systems

This journal paper was submitted to IEEE Transactions on Smart Grid.The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore, paramount. In this context, an algorithm for recovering missing state variable observations in electricity distribution systems is presented. The proposed method exploits the low rank structure of the state variables via a matrix completion approach while incorporating prior knowledge in the form of second order statistics. Specifically , the recovery method combines nuclear norm minimization with Bayesian estimation. The performance of the new algorithm is compared to the information-theoretic limits and tested trough simulations using real data of an urban low voltage distribution system. The impact of the prior knowledge is analyzed when a mismatched covariance is used and for a Markovian sampling that introduces structure in the observation pattern. Numerical results demonstrate that the proposed algorithm is robust and outperforms existing state of the art algorithms

Sparsity and Coordination Constraints on Stealth Data Injection Attacks

In this thesis, data injection attacks (DIAs) to smart grid within Bayesian framework is studied from two perspectives: centralized and decentralized systems. The fundamental limits of the data injection attacks are characterized by the information measures. Specifically, two metrics, mutual information and the Kullback-Leibler (KL) divergence, quantifies the disruption caused by the attacks and the corresponding stealthiness, respectively. From the perspective of centralized system, a unique attacker constructs the attacks that jointly minimize the mutual information acquired from the measurements about the state variables and the KL divergence between the distribution of measurements with and without attacks. One of the main contributions in the centralized attack construction is the sparsity constraints. Two scenarios where the attacks between different locations are independent and correlated are studied, respectively. In independent attacks, the challenge of the combinatorial character of identifying the support of the sparse attack vector is circumvented by obtaining the closed-form solution to single measurement attack problem followed by a greedy construction that leverages the insight distilled. In correlated attacks, the challenge is tackled by incorporating an additional measurement that yields sequential sensor selection problem. The sequential procedure allows the attacker to identify the additional sensor first and character the corresponding covariances between the additional measurement and the compromised measurements. Following the studies on sparse attacks, a novel metric that describes the vulnerability of the measurements on smart grids to data integrity attacks is proposed. The new metric, coined vulnerability index (VuIx), leverages information theoretic measures to assess the attack effect on the fundamental limits of the disruption and detection tradeoff. The result of computing the VuIx of the measurements in the system yields an ordering of the measurements vulnerability based on the level of the exposure to data integrity attacks. The assessment on the measurements vulnerability of IEEE test systems observes that power injection measurements are overwhelmingly more vulnerable to data integrity attacks than power flow measurements. From the perspective of decentralized system, the attack constructions are determined by a group of attackers in a cooperative manner. The interaction between the attackers is formulated as a game with a normal form. The uniqueness of the Nash Equilibrium (NE) is characterized in different games where the attackers have different objectives. Closed-form expression for the best response of the attackers in different games are obtained and followed by best response dynamics that leads to the NEs. The sparsity constraint is considered in decentralized system where the attackers have limited access to sensors. The attack construction with sparsity constraints in decentralized system is also formulated as a game with a normal form. The uniqueness of the NE and the closed-form expression for the best response are obtained