Bayesian Methods for the Identification of Distribution Networks

Abstract

The increasing integration of intermittent renewable generation, especially at the distribution level, necessitates advanced planning and optimisation methodologies contingent on the knowledge of the admittance matrix, capturing the topology and line parameters of an electric network. However, a reliable estimate of the admittance matrix may either be missing or quickly become obsolete for temporally varying grids. In this work, we propose a data-driven identification method utilising voltage and current measurements collected from micro-PMUs. More precisely, we first present a maximum likelihood approach and then move towards a Bayesian framework, leveraging the principles of maximum a posteriori estimation. In contrast with most existing contributions, our approach not only factors in measurement noise on both voltage and current data, but is also capable of exploiting available a priori information such as sparsity patterns and known line admittances. Simulations conducted on benchmark cases demonstrate that, compared to other algorithms, our method can achieve greater accuracy.

Primary Frequency Control Provision by Distributed Energy Resources in Active Distribution Networks

“…The covariances σ v and σ i might be time-varying, but there is no temporal or spatial correlation in the measurement noise. Note that other noise models may be applicable [16,25].…”

“…Poor conditioning is common to least squares approaches [10,11,13] and arises even in the estimation of small-size networks due to high correlations in voltage or current measurements. Significant computational burden and memory requirements arise when solving the weighted total least squares [16,17] since a substantial amount of measurements is required for accuracy, and a large number of parameters contained within the admittance matrix need to be estimated.…”

“…(i.e., topology) [6][7][8], line parameters [9], or both [10][11][12][13][14][15][16][17], using bus voltage, current injection, or branch flow measurements. In this work, we address the problem of estimating the admittance matrix using µPMU measurements of bus voltage and current injection phasors.…”

“…This limitation of the least squares approaches can be successfully tackled by error-in-variables methods, such as total least squares [15]. A weighted total least squares method is introduced in [16] and then extended in [17] to a Bayesian framework that allows exploiting different forms of prior knowledge of the admittance matrix, thus creating a flexible framework that can achieve high estimation accuracy.…”

“…Expanding on these works, we use the eigendecomposition of the admittance matrix to generalize the notion of stationarity to electrical signals in power networks with a constant reactance-resistance ratio. Subsequently, we demonstrate how a Maximum a Posteriori (MAP) estimation method (resembling [16,17]) can be simplified when the current injections are stationary.…”