Sparse Causal Temporal Modeling to Inform Power System Defense

Abstract The accurate estimation of system state variables at buses in the power-grid is crucial for determining the operational state of the power system. Spoofing attacks on meters at buses can bypass bad data detectors in Supervisory Control and Data Acquisition (SCADA) systems and undetectably manipulate state estimates. Existing methods for protection of the state estimate of critical buses against spoofing attacks assume the existence of a given set of set of critical buses/meters to be protected. Given budget constraints, determining the critical set of meters/buses to be protected against spoofing attacks is a crucial problem. In this paper, we address the issue of how best to determine the set of meters to be protected. We suggest the use of two sparse temporal modeling methods from the machine learning literature to evaluate the influence of each meter measurement on the power grid network. Based on the influence distribution as indexed by these methods we can populate a set of meter measurements which serves a dual purpose. First, this set can serve as the initial collection of nodes that is a required input for methods developed to defend against false injection attacks on power system state estimation. Second, the high influential power of meters in the set incentivizes their protection since they are pivotal for making real-time prediction in the absence of complete real-time data from other meters. Thus, we introduce influence as one of the primary criteria to be considered in the process of selecting nodes to protect. We also suggest a novel way to measure influence based on sparse structure learning. We provide results on a publicly available simulated dataset and discuss how to use the notion of the N50 statistic to calibrate the number of meter measurements that should be protected under a specified budget.