Statistical and Intertemporal Methods Using Embeddings for Non-linear AC Power System State Estimation

This thesis aims to improve the robustness of state estimation (SE) methods currently used by the electricpower industry. The main objective of today’s SE is to estimate system state using redundant measurementsin the presence of bad data and constantly varying network topology. The hoped-for of this thesis contributionsconcerns the use of embedding techniques to overcome problems related to non-linearities anduncertainties.First, in order to improve static SE when reliable historical data is unavailable, we reformulate the leastsquaresnon-convex static SE currently used as a convex optimization problem by using an embeddingand convex relaxation techniques. We demonstrate a significant improvement in accuracy, particularly inreactive power/voltage estimates. We propose that the added computational complexity caused by this embeddingcan be managed by implementing the method as a distributed algorithm developed on the basis ofan underlying power system graph.On the other hand, when reliable historical data is available, this thesis proposes utilizing them by usingboth static and dynamic data-driven state estimation methods. The static estimator uses the an embeddingof the current measurements and learns the state estimator using similar measurement-state pairs in the historicalrecords. Several speedup techniques from machine learning are proposed for overcoming the initialcomputational complexity of the proposed method and making it potentially useful for online applications.A dynamic data-driven state estimator requires a much faster sampling of the historical data to capturedynamics. An expectation maximization algorithm for SE is proposed for learning in embedded state space.Finally, the uncertainties in SE caused by a massive number of distributed energy resources motivate afully distributed probabilistic state estimation method. This thesis provides a Bayesian Network solution tothe SE problem in that setting. The proposed method employs a probabilistic graphical model and embedsit in a ceratin probability space, which allow the use of a variational belief propagation method that is bothscalable and exact for tree networks in distribution systems.To assess the improved performance achieved by applying the proposed methods in this thesis, we comparethem with currently used methods in various simulation scenarios. Using the results, a flow chart ispresented to determine which methods to apply in different scenarios