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 electric
power industry. The main objective of today’s SE is to estimate system state using redundant measurements
in the presence of bad data and constantly varying network topology. The hoped-for of this thesis contributions
concerns the use of embedding techniques to overcome problems related to non-linearities and
uncertainties.
First, in order to improve static SE when reliable historical data is unavailable, we reformulate the leastsquares
non-convex static SE currently used as a convex optimization problem by using an embedding
and convex relaxation techniques. We demonstrate a significant improvement in accuracy, particularly in
reactive power/voltage estimates. We propose that the added computational complexity caused by this embedding
can be managed by implementing the method as a distributed algorithm developed on the basis of
an underlying power system graph.
On the other hand, when reliable historical data is available, this thesis proposes utilizing them by using
both static and dynamic data-driven state estimation methods. The static estimator uses the an embedding
of the current measurements and learns the state estimator using similar measurement-state pairs in the historical
records. Several speedup techniques from machine learning are proposed for overcoming the initial
computational 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 capture
dynamics. 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 a
fully distributed probabilistic state estimation method. This thesis provides a Bayesian Network solution to
the SE problem in that setting. The proposed method employs a probabilistic graphical model and embeds
it in a ceratin probability space, which allow the use of a variational belief propagation method that is both
scalable and exact for tree networks in distribution systems.
To assess the improved performance achieved by applying the proposed methods in this thesis, we compare
them with currently used methods in various simulation scenarios. Using the results, a flow chart is
presented to determine which methods to apply in different scenarios.