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

Pagnier, Laurent; Chertkov, Michael

doi:10.48550/arxiv.2102.06349

Cited by 17 publications

(31 citation statements)

References 52 publications

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“…This fact has not gone unnoticed by researchers, and references to 'physics-informed neural networks can be found in the literature, e.g. [44], [45]. In this work we have briefly investigated physics informed neural networks in the context of spacecraft swarm trajectory planning.…”

Section: Supervised Learning Approachmentioning

confidence: 99%

Machine Learning Based Relative Orbit Transfer for Swarm Spacecraft Motion Planning

Sabol¹,

Yun²,

Adil³

et al. 2022

Preprint

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In this paper we describe a machine learning based framework for spacecraft swarm trajectory planning. In particular, we focus on coordinating motions of multi-spacecraft in formation flying through passive relative orbit(PRO) transfers. Accounting for spacecraft dynamics while avoiding collisions between the agents makes spacecraft swarm trajectory planning difficult. Centralized approaches can be used to solve this problem, but are computationally demanding and scale poorly with the number of agents in the swarm. As a result, centralized algorithms are ill-suited for real time trajectory planning on board small spacecraft (e.g. CubeSats) comprising the swarm. In our approach a neural network is used to approximate solutions of a centralized method. The necessary training data is generated using a centralized convex optimization framework through which several instances of the n=10 spacecraft swarm trajectory planning problem are solved. We are interested in answering the following questions which will give insight on the potential utility of deep learning-based approaches to the multispacecraft motion planning problem: 1) Can neural networks produce feasible trajectories that satisfy safety constraints (e.g. collision avoidance) and low in fuel cost? 2) Can a neural network trained using n spacecraft data be used to solve problems for spacecraft swarms of differing size?

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Section: Supervised Learning Approachmentioning

confidence: 99%

Machine Learning Based Relative Orbit Transfer for Swarm Spacecraft Motion Planning

Sabol¹,

Yun²,

Adil³

et al. 2022

Preprint

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“…One of the celebrated characteristics of PINNs is they can learn from sparse data [24] as physics doesn't generate humongous data as easily in other commercial fields. Upon the proposed PINN framework, various types of PINNs designed for different engineering applications emerge in fields, with their most renowned works in predicting fluid fields [25,26], but also include electronics [28,29]. Henceforth a question arose: can PINN be applied for dynamical systems?…”

Section: Inductormentioning

confidence: 99%

Physics-Informed Deep Operator Control: Controlling chaos in van der Pol oscillating circuits

Zhai,

Sands

2021

Preprint

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Controlling chaos is a long-standing problem in engineering. By linearizing nonlinear systems, traditional control methods cannot learn features from chaotic data for control. Here, we introduce Physics-Informed Deep Operator Control (PIDOC), by encoding control signal and initial position into the losses of a Physics-Informed Neural Network (PINN), the nonlinear system exhibits the desired route given the control signal. The framework has a clear application scenario: receiving signals as physics commands and learning chaotic data from the nonlinear van der Pol system, PIDOC is able to execute the controlled signal as the output of the PINN. PIDOC is first applied to a benchmark problem, unveils a fluctuating behavior of the acceleration that seemingly behave in the same frequency of the desired signal, indicating the learning of neural networks (NN) elicit stochasticity for higher-order terms, yet still successfully impose the control that enforces the system behave as in the same frequency of the control signal. PIDOC is also proved capable of converging to different desired trajectories based on case studies. Initial positions slightly affect the control accuracy at the beginning stage yet still converge to the control signal based on numerical experiments. To note, for highly nonlinear systems, PIDOC is not able to execute control as high accuracies compared with the benchmark problem, yet still, PIDOC converges to decent trajectories corresponding to given signals with fair predictable behavior. The depth and width of the NN structure did not heavily variate the convergence of PIDOC based on case studies on van der Pol systems with low and high nonlinearities. Surprisingly, by enlarging the control signal by multiplying a Lagrangian multiplier, PIDOC failed to converge to the desired trajectory, indicating enlarging the control signal does not increase control quality, which is not intuitive. The proposed framework can be potentially applied to many nonlinear systems for controlling chaos.

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“…Physics-informed neural networks have been first introduced in power systems in our previous work [18], and, since then, have extended in applications related to system identification [19], the transient response of interconnected systems [20], and DC optimal power flow [21]; along the same lines, sensitivity-informed NNs have been recently introduced for AC power flow optimization [22] and physics-informed graphical NNs for parameter estimation [23]. All of these works, however, have utilised a continuous formulation of the problem's underlying physics and have thus required simulated training data.…”

Section: Introductionmentioning

confidence: 99%

Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulation

Stiasny¹,

Chevalier²,

Chatzivasileiadis³

2021

Preprint

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In order to drastically reduce the heavy computational burden associated with time-domain simulations, this paper introduces a Physics-Informed Neural Network (PINN) to directly learn the solutions of power system dynamics. In contrast to the limitations of classical model order reduction approaches, commonly used to accelerate time-domain simulations, PINNs can universally approximate any continuous function with an arbitrary degree of accuracy. One of the novelties of this paper is that we avoid the need for any training data. We achieve this by incorporating the governing differential equations and an implicit Runge-Kutta (RK) integration scheme directly into the training process of the PINN; through this approach, PINNs can predict the trajectory of a dynamical power system at any discrete time step. The resulting Runge-Kutta-based physics-informed neural networks (RK-PINNs) can yield up to 100 times faster evaluations of the dynamics compared to standard time-domain simulations. We demonstrate the methodology on a single-machine infinite bus system governed by the swing equation. We show that RK-PINNs can accurately and quickly predict the solution trajectories.

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

Cited by 17 publications

References 52 publications

Machine Learning Based Relative Orbit Transfer for Swarm Spacecraft Motion Planning

Machine Learning Based Relative Orbit Transfer for Swarm Spacecraft Motion Planning

Physics-Informed Deep Operator Control: Controlling chaos in van der Pol oscillating circuits

Learning without Data: Physics-Informed Neural Networks for Fast Time-Domain Simulation

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