Distributed State Estimation in Power Systems using Probabilistic Graphical Models

AB We present a detailed study on application of factor graphs and the belief propagation (BP) algorithm to the power system state estimation (SE) problem. We start from the BP solution for the linear DC model, for which we provide a detailed convergence analysis. Using BPbased DC model we propose a fast real-time state estimator for the power system SE. The proposed estimator is easy to distribute and parallelize, thus alleviating computational limitations and allowing for processing measurements in real time. The presented algorithm may run as a continuous process, with each new measurement being seamlessly processed by the distributed state estimator. In contrast to the matrixbased SE methods, the BP approach is robust to illconditioned scenarios caused by significant differences between measurement variances, thus resulting in a solution that eliminates observability analysis. Using the DC model, we numerically demonstrate the performance of the state estimator in a realistic real-time system model with asynchronous measurements. We note that the extension to the non-linear SE is possible within the same framework. Using insights from the DC model, we use two different approaches to derive the BP algorithm for the non-linear model. The first method directly applies BP methodology, however, providing only approximate BP solution for the non-linear model. In the second approach, we make a key further step by providing the solution in which the BP is applied sequentially over the non-linear model, akin to what is done by the Gauss-Newton method. The resulting iterative Gauss-Newton belief propagation (GN-BP) algorithm can be interpreted as a distributed GaussNewton method with the same accuracy as the centralized SE, however, introducing a number of advantages of the BP framework. The thesis provides extensive numerical study of the GN-BP algorithm, provides details on its convergence behavior, and gives a number of useful insights for its implementation. Finally, we define the bad data test based on the BP algorithm for the non-linear model. The presented model establishes local criteria to detect and identify bad data measurements. We numerically demonstrate that the BP-based bad data test significantly improves the bad data detection over the largest normalized residual test. Accepted by Scientific Board on ASB 2018/09/27 Defended on DE Defend Board DB Advisor: Dr Dejan Vukobratović, Associate Professor Department of Power, Electronics and Communication Engineering, University of Novi Sad, Serbia. Thesis Committee Members: Dr Andrija Sarić, Full Professor Department of Power, Electronics and Communication Engineering, University of Novi Sad, Serbia. Dr Petar Popovski, Full Professor Department of Electronic Systems, Aalborg University, Denmark. Dr Čedomir Stefanović, Associate Professor Department of Electronic Systems, Aalborg University Copenhagen, Denmark. Dr Izudin Džafić, Full Professor, Department of Electrical Engineering, International University of Sarajevo, Bosnia and Herzegovina. Dr Dušan Jakovetić, Assistant Professor Department of Mathematics and Informatics, University of Novi Sad, Serbia. Distributed State Estimation in Power Systems using Probabilistic Graphical Models by Mirsad Ćosović Mr.-Ing. Power Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina, 2013. Dipl.-Ing. Power Electrical Engineering, University of Sarajevo, Bosnia and Herzegovina, 2009.