Power Grid Parameter Estimation Without Phase Measurements: Theory and Empirical Validation

Reliable integration and operation of renewable distributed energy resources requires accurate distribution grid models. However, obtaining precise models is often prohibitively expensive, given their large scale and the ongoing nature of grid operations. To address this challenge, considerable efforts have been devoted to harnessing abundant consumption data for automatic model inference. The primary result of the paper is that, while the impedance of a line or a network can be estimated without synchronized phase angle measurements in a consistent way, the admittance cannot. Furthermore, a detailed statistical analysis is presented, quantifying the expected estimation errors of four prevalent admittance estimation methods. Such errors constitute fundamental model inference limitations that cannot be resolved with more data. These findings are empirically validated using synthetic data and real measurements from the town of Walenstadt, Switzerland, confirming the theory. The results contribute to our understanding of grid estimation limitations and uncertainties, offering guidance for both practitioners and researchers in the pursuit of more reliable and cost-effective solutions

Regularization for Distributionally Robust State Estimation and Prediction

The increasing availability of sensing techniques provides a great opportunity for engineers to design state estimation methods, which are optimal for the system under observation and the observed noise patterns. However, these patterns often do not fulfill the assumptions of existing approaches. We provide a direct method using samples of the noise to create a moving horizon observer for linear time-varying and nonlinear systems, which is optimal under the empirical noise distribution. Moreover, we show how to enhance the observer with distributional robustness properties in order to handle unmodeled components in the noise profile, as well as different noise realizations. We prove that, even though the design of distributionally robust estimators is a complex minmax problem over an infinite-dimensional space, it can be transformed into a regularized linear program using a system level synthesis approach. Numerical experiments with the Van der Pol oscillator show the benefits of not only using empirical samples of the noise to design the state estimator, but also of adding distributional robustness. We show that our method can significantly outperform state-of-the-art approaches under challenging noise distributions, including multi-modal and deterministic components.ISSN:2475-145

The effect of transmission-line dynamics on grid-forming dispatchable virtual oscillator control

In this work, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based AC power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, i.e., if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of AC power inverters with respect to a pre-specified solution of the AC power-flow equations. While this approximation is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system. In this work, we establish explicit bounds on the controller setpoints, branch powers, and control gains that guarantee almost global asymptotic stability of dVOC in combination with a dynamic model of the transmission network.ISSN:2325-587

Bayesian Methods for the Identification of Distribution Networks

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

Bayesian Error-in-Variables Models for the Identification of Distribution Grids

The increasing integration of renewable energy requires a good model of the existing power distribution infrastructure, represented by its admittance matrix. However, a reliable estimate may either be missing or quickly become obsolete, as distribution grids are continuously modified. In this work, we propose a method for estimating the admittance matrix from voltage and current measurements. By focusing on μPMU measurements and partially observed networks, we show that voltage collinearity and noisy samples of all electric variables are the main challenges for accurate identification. Moreover, the accuracy of maximum likelihood estimation is often insufficient in real-world scenarios. To overcome this problem, we develop a flexible Bayesian framework that allows one to exploit different forms of prior knowledge about individual line parameters, as well as network-wide characteristics such as the sparsity of the interconnections. Most importantly, we show how to use maximum likelihood estimates for tuning relevant hyperparameters, hence making the identification procedure self-contained. We also discuss numerical aspects of the maximum a posteriori estimate computation. Realistic simulations conducted on benchmark electrical systems demonstrate that, compared to other algorithms, our method can achieve significantly greater accuracy than previously developed methods.ISSN:1949-3053ISSN:1949-306