Algorithms for Power System State Estimation with Phasor Measurement Units

Power system state estimation (PSSE) is one of the key components in the suite of computational tools which assist in managing the day to day operations of electric grids. In recent years, two trends have emerged as the world transitions towards smart grids: The first is the introduction of new measurement and protection devices called phasor measurement units (PMUs). The second is the creation of transmission system operators (TSOs) as part of a general move away from vertically integrated monopolies. These TSOs are charged with ensuring the fair and reliable operation of the power system. This thesis proposes new algorithms for PSSE which address the implications of these trends. This thesis introduces a novel approach to state estimation with PMUs where we decouple the estimation of PMU observable and PMU unobservable state variables. We show that this approach has several advantages like improved numerical stability, reduced computational complexity and robustness to time-skew errors. Next, we develop a signal-dependent scheme to choose how many PMU measurements to average over to obtain a more precise estimate of the underlying voltages. This method shows an improvement over the state-of-the-art approach. This thesis also develops methods for using PMUs for multi-area state estimation (MASE). These methods are based on a novel information exchange scheme called clustered gossip and share. We derive analytical results which prove that this approach always results in reduced information exchange when compared to a naive approach to network gossiping. This approach is applied to the traditional measurement-approach, the previously derived reduced-order approach, and also a novel privacy preserving approach for linear power system state estimation. Also presented in this thesis is a novel event-triggered approach to hierarchical multi-area state estimation. The main idea of this algorithm is that the state estimator in each area communicates with neighboring areas only when such an action is informative. This approach is shown to reduce the amount of communication, and also reduces the computational load involved in calculating the state estimation.