State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

We consider the problem of estimating the states and detecting bad data in an unobservable power system. To this end, we propose novel graph signal processing (GSP) methods. The main assumption behind the proposed GSP approach is that the grid state vector, which includes the phases of the voltages in the system, is a smooth graph signal with respect to the system admittance matrix that represents the underlying graph. Thus, the first step in this paper is to validate the graph-smoothness assumption of the states, both empirically and theoretically. Then, we develop the regularized weighted least squares (WLS) state estimator, which does not require observability of the network. We propose a sensor (meter) placement strategy that aims to optimize the estimation performance of the proposed GSP-WLS estimator. In addition, we develop a joint bad-data and false data injected (FDI) attacks detector that integrates the GSP-WLS state estimator into the conventional J(theta)-test with an additional smoothness regularization. Numerical results on the IEEE 118-bus test-case system demonstrate that the new GSP methods outperform commonly-used estimation and detection approaches in electric networks and are robust to missing data.