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The Optimal Power Flow (OPF) routine used in energy control centers allocates individual generator outputs by minimizing the overall cost of generation subject to system level operating constraints. The OPF relies on the outputs of two other modules, namely topology processor and state estimator. The topology processor maps the grid topology based on statuses received from the switches and circuit breakers across the system. The state estimator computes the system state, i.e., voltage magnitudes with phase angles, transmission line flows, and system loads based on real-time meter measurements. However, topology statuses and meter measurements are vulnerable to false data injection attacks. Recent research has shown that such cyber attacks can be launched against state estimation where adversaries can corrupt the states but still remain undetected. In this paper, we show how the stealthy topology poisoning attacks can compromise the integrity of OPF, and thus undermine economic operation. We describe a formal verification based framework to systematically analyze the impact of such attacks on OPF. The proposed framework is illustrated with an example. We also evaluate the scalability of the framework with respect to time and memory requirements.
Rahman et al. (Sun,) studied this question.