Information Theoretic State Estimation in Power Systems

This thesis is a result of research work intended to shed some new light over the state estimation problem in power systems from perspective of information theory. The main motivation behind this investigation was enhancement of general robustness, reliability and flexibility in State Estimation process in respect to any type of inconsistencies that may appear in the input dataset. Moreover, all concepts presented in this thesis are built in a decentralized architecture in order to be compatible with modern power systems which are currently undergoing radical operational changes. One of the main hypotheses of this thesis addresses the issue of adoption of paradigms from Information Theoretic Learning as novel state estimation criterion with multiple valuable properties. As a result of this work, a novel state estimation model that maximizes Correntropy as a robust localized measure of similarity between input values and their estimated values, is proposed. Substitution of the least squares criterion with the Maximum Correntropy Criterion (MCC) results in a fast and reliable estimator that naturally embodies all key bad data analysis functions. Moreover, it offers a strong theoretical justification for all previous attempts of modification of quadratic function in WLS estimator intended for establishment of robust properties. The novel MCC estimator is further improved via fusion with a mosaic of semi-autonomous auto-associative local measurement screening. Thanks to decentralized and localized architecture of the method, a high level of robustness is attained without affecting the real time feasibility for large scale systems. The proposed information theoretic data screening is further extended to the problem of reconstruction of erroneous or incomplete information about system topology. The proposed competitive scheme of local autoencoders achieves remarkably efficient and robust reconstruction of entire topologies based on information backup between analog measurements and binary topology variables captured during the offline training process. Due to extreme robustness in respect to measurement redundancy and gross errors, the proposed topology estimator is particularly appropriate for state estimation in distribution power grids. As a significant support to the proposed state estimation methodologies, a novel concept named Statistical Observability is established. Unlike the classical definition of observability, concerned with the analytical solution of a system of equations, the concept of Statistical Observability relies on the information content of joint probability distributions incorporated in the Maximum Mutual Information criterion. This concept allows for an autonomous definition of a decentralization degree and the most relevant local areas thus contributing to efficient topology estimation with minimal computational and memory requirements. As the main contribution to theory of state estimation in power systems, this thesis paves the way towards new perspectives established on strong theoretical justification provided by Information Theory and Information Theoretic Learning. Moreover, it facilitates migration from global traditional concepts defined as problems of mathematical programming, towards decentralized local models that perceive state estimation as a problem of dealing with information.