Physics-Informed Deep Neural Network Method for Limited Observability State Estimation

Abstract

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power.In this paper, we consider the case when the distribution grid becomes partially observable, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

Physics-Conditioned Generative Adversarial Networks for State Estimation in Active Power Distribution Systems with Low Observability

“…In this regard, our work is more related to the studies such as in [10], where a new data-driven method is proposed based on training a deep neural network model to solve the DSSE problem by adding physical information of the underlying power distribution feeder, such as the parameters of the distribution lines to further increase the accuracy. Our approach, on the other hand, optimizes the output of a GAN model to estimate the unknown power injection at unobservable loads by utilizing the available measurements in physical equations.…”

“…where the left-hand-side indicates the total number of unknowns in (3) while the right-hand-side indicates the total number of independent equations. To be exact, we shall express (10) as 2N 3 > 2(N 1 − 1) due to the analysis being in complex domain; however, once we divide both sides by two, we can reach (10). Under the condition in (10), the system of linear equations in (3) is under-determined, i.e., it has an infinite number of solutions.…”

Multi-Area Distribution System State Estimation via Distributed Tensor Completion

“…The authors of [8] presented a data-driven, learning-based neural network that can accommodate several types of measurements as well as pseudo-measurements. Also, [9] proposed a novel neural network model that uses the physical structure of distribution power systems; [10] leveraged a deep neural network by incorporating physical information of the grid topology and line/shunt admittance; [11]- [13] proposed the constrained matrix completion method by combining the conventional matrix completion model with the power flow constraints; and [14] developed a spatio-temporal learning approach to enhance the observability of DERs; however, these machine learning methods require pseudo-measurements or accurate knowledge of the network model (topology of the grid or the bus admittance matrix). Unfortunately, pseudo-measurements [15] can introduce large estimation errors [16], and accurate distribution system topology is difficult to obtain because of frequent distribution grid reconfigurations and insufficient knowledge about the status of the network [17], [18].…”

Embedding Power Flow into Machine Learning for Parameter and State Estimation

“…This manuscript continues the thread, started in our recent paper [21] and in a companion submission to CDC [29], suggesting application of the Physics-Informed ML (PIML) to SE and PE in PS models. Essence of PIML is in resolving the problem as a regression based on the PF equations in their static or dynamic (then working with the so-called swing equations) [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. We focus here on the static PF setting, therefore assuming access to a static (or quasi-static) data consistent with solutions of the PF Eqs.…”