Learning-based state estimation in distribution systems with limited real-time measurements

The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time, indicating the existence of multiple states that result in identical values for the available measurements. Certain existing approaches utilize historical data to infer the relationship between real-time available measurements and the state. Other learning-based methods aim to estimate the measurements acquired with a delay, generating pseudo-measurements. Our paper presents a methodology that utilizes the outcome of an underdetermined state estimator of an unobservable network state estimator to exploit information on the joint probability distribution between real-time available measurements and delayed ones to generate new physics-informed interpretable features. Through numerical simulations conducted on two realistic distribution grids of different size with insufficient real-time measurements, the proposed procedure showcases superior performance compared to existing state forecasting approaches and those relying on inferred pseudo-measurementsFunding for open access charge: Universidad de Málaga/CBU

Learning-based State Estimation in Distribution Systems with Limited Real-Time Measurements

The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time, indicating the existence of multiple states that result in identical values for the available measurements. Certain existing approaches utilize historical data to infer the relationship between real-time available measurements and the state. Other learning-based methods aim to estimate the measurements acquired with a delay, generating pseudo-measurements. Our paper presents a methodology that utilizes the outcome of an unobservable state estimator to exploit information on the joint probability distribution between real-time available measurements and delayed ones. Through numerical simulations conducted on a realistic distribution grid with insufficient real-time measurements, the proposed procedure showcases superior performance compared to existing state forecasting approaches and those relying on inferred pseudo-measurements

Control of partial differential equations via physics-informed neural networks

This paper addresses the numerical resolution of controllability problems for partial differential equations (PDEs) by using physics-informed neural networks. Error estimates for the generalization error for both state and control are derived from classical observability inequalities and energy estimates for the considered PDE. These error bounds, that apply to any exact controllable linear system of PDEs and in any dimension, provide a rigorous justification for the use of neural networks in this field. Preliminary numerical simulation results for three different types of PDEs are carried out to illustrate the performance of the proposed methodology.This research was supported by Fundación Séneca (Agencia de Ciencia y Tecnología de la Región de Murcia (Spain)) under contract 20911/PI/18 and grant number 21503/EE/21 (mobility program Jiménez de la Espada). F. Periago acknowledges the hospitality of the Mathematics Department at University of California, Santa Barbara, where part of this work was carried out. The authors also thank professor Lu Lu for very fruitful comments on the use of DeepXDE