Physics-Informed Neural Networks for Power Systems

Misyris, George S.; Venzke, Andreas; Chatzivasileiadis, Spyros

doi:10.48550/arxiv.1911.03737

Cited by 4 publications

(7 citation statements)

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“…of [27], on tuning a NN to satisfy the output of an equation (algebraic or differential). Noticeable applications of the methodology came in the context of dynamical equations (ODEs and PDEs), including the so-called Sparse Identification of Nonlinear Dynamics (SINDy) [5], Physics Informed Neural Network (PINN) [44] which was also applied to the PS dynamics in [34], and Neural ODE [8] frameworks. See also most recent review [53], and references there in, e.g.…”

Section: A Physics-informed Modeling and Machine Learningmentioning

confidence: 99%

“…Some of these approaches also dealt with the partial observability [12,14,15,31,38], which is especially well pronounced on the lower voltage (distribution) side of the PS. The hybrid approach, attempting to mix the best of the two aforementioned approaches (and inspired by universal methodologies [5,27,43] suggesting to blend equations with modern ML) was also explored in [34] to estimate the PS dynamics. Ability to predict SE and learn physical models, i.e.…”

Section: State and Parameter Estimation In Power Systemsmentioning

confidence: 99%

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Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems

Pagnier,

Chertkov

2021

Preprint

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Parameter Estimation (PE) and State Estimation (SE) are the most wide-spread tasks in the system engineering. They need to be done automatically, fast and frequently, as measurements arrive. Deep Learning (DL) holds the promise of tackling the challenge, however in so far, as PE and SE in power systems is concerned, (a) DL did not win trust of the system operators because of the lack of the physics of electricity based, interpretations and (b) DL remained illusive in the operational regimes were data is scarce. To address this, we present a hybrid scheme which embeds physics modeling of power systems into Graphical Neural Networks (GNN), therefore empowering system operators with a reliable and explainable real-time predictions which can then be used to control the critical infrastructure. To enable progress towards trustworthy DL for PE and SE, we build a physics-informed method, named Power-GNN, which reconstructs physical, thus interpretable, parameters within Effective Power Flow (EPF) models, such as admittances of effective power lines, and NN parameters, representing implicitly unobserved elements of the system. In our experiments, we test the Power-GNN on different realistic power networks, including these with thousands of loads and hundreds of generators. We show that the Power-GNN outperforms vanilla NN scheme unaware of the EPF physics.

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Section: A Physics-informed Modeling and Machine Learningmentioning

confidence: 99%

Section: State and Parameter Estimation In Power Systemsmentioning

confidence: 99%

Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems

Pagnier,

Chertkov

2021

Preprint

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“…Physics-Informed Machine Learning (PIML) is the modern approach to resolve the model reduction bottleneck -that is to compensate for the lack of data (typical of online applications) by building models that are aware of the underlying physics [8], as, e.g., expressed in terms of differential equations [9]- [11]. (See also [12], [13] for discussion of the application of PIML to power systems. )…”

Section: Introductionmentioning

confidence: 99%

Toward Model Reduction for Power System Transients With Physics-Informed PDE

et al. 2022

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This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. Following Seymlyen (1974) and Thorpe, Seyler, and Phadke (1999), we suggest to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. We illustrate our method on the synchronous transmission grid of continental Europe. We show that, when properly coarse-grained, i.e., with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDEbased modeling will initialize a physics-informed machine learning approach for real-time modeling, n − 1 feasibility assessment and transient stability analysis of power systems.

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“…Physics Informed Machine Learning (PIML) is the modern approach to resolve the model reduction bottleneck -that is to compensate for the lack of data (typical of the on-line applications) by building models that are aware of the underlying physics [11], which may be expressed in terms of differential equations [12], [13], [14]. (See also [15], [16] for discussion of the application of PIML to power systems. )…”

Section: Introductionmentioning

confidence: 99%

“…Similarly to [15], we take advantage of the PIML approach and construct an on-line framework for simulating power system dynamics faster than real time. We are however aiming to capture the transient dynamics in a very large, continentalscale power system, a goal that has not been addressed by any earlier related approach we are aware of.…”

Section: Introductionmentioning

confidence: 99%

Model Reduction of Swing Equations with Physics Informed PDE

Pagnier,

Chertkov,

Fritzsch

et al. 2021

Preprint

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This manuscript is the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-ofseconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. We suggest, following Seymlyen (1974) and Thorpe, Seyler and Phadke (1999), to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. The continuous two-dimensional spatial domain is defined by a geographical map of the area served by the power grid, and associated with the PDE coefficients derived from smoothed graph-Laplacian of susceptances, machine inertia and damping. Inhomogeneous source terms represent spatially distributed injection/consumption of power. We illustrate our method on PanTaGruEl (Pan-European Transmission Grid and ELectricity generation model) [1], [2]. We show that, when properly coarse-grained, i.e. with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based reduced modeling will initialize a physics-informed machine learning approach for realtime modeling, n − 1 feasibility assessment and transient stability analysis of power systems.

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Physics-Informed Neural Networks for Power Systems

Cited by 4 publications

References 0 publications

Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems

Physics-Informed Graphical Neural Network for Parameter & State Estimations in Power Systems

Toward Model Reduction for Power System Transients With Physics-Informed PDE

Model Reduction of Swing Equations with Physics Informed PDE

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