Inferring power-grid topology in the face of uncertainties

Basiri, Farnaz; Casadiego, Jose; Timme, Marc; Witthaut, Dirk

doi:10.1103/physreve.98.012305

Cited by 11 publications

(5 citation statements)

References 42 publications

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“…In theory

1

, observations are needed to completely infer the network, though symmetries in the data usually mean

is required in practice ( 52 ). In this experiment, we purposefully underdetermine the problem by only using

1

steps; additionally, we train the network on data recorded 1 simulated second after the power cut, where many nodes will still be close to equilibrium.…”

Section: Inferring Line Failures In the British Power Gridmentioning

confidence: 99%

Inferring networks from time series: A neural approach

Gaskin,

Pavliotis,

Girolami

2024

PNAS Nexus

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Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations of the dynamics to which they give rise. In this work we present a powerful computational method to infer large network adjacency matrices from time series data using a neural network, in order to provide uncertainty quantification on the prediction in a manner that reflects both the degree to which the inference problem is underdetermined as well as the noise on the data. This is a feature that other approaches have hitherto been lacking. We demonstrate our method's capabilities by inferring line failure locations in the British power grid from its response to a power cut, providing probability densities on each edge and allowing the use of hypothesis testing to make meaningful probabilistic statements about the location of the cut. Our method is significantly more accurate than both Markov-chain Monte Carlo sampling and least squares regression on noisy data and when the problem is underdetermined, while naturally extending to the case of non-linear dynamics, which we demonstrate by learning an entire cost matrix for a non-linear model of economic activity in Greater London. Not having been specifically engineered for network inference, this method in fact represents a general parameter estimation scheme that is applicable to any high-dimensional parameter space.

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“…In theory

1

, observations are needed to completely infer the network, though symmetries in the data usually mean

is required in practice ( 52 ). In this experiment, we purposefully underdetermine the problem by only using

1

steps; additionally, we train the network on data recorded 1 simulated second after the power cut, where many nodes will still be close to equilibrium.…”

Section: Inferring Line Failures In the British Power Gridmentioning

confidence: 99%

Inferring networks from time series: A neural approach

Gaskin,

Pavliotis,

Girolami

2024

PNAS Nexus

View full text Add to dashboard Cite

show abstract

“…The system (13) is overdetermined if the number M of time points at which state data of y is recorded exceeds 2N , twice the number of units. Due to inexact measurement data and numerical inaccuracies, we are searching for a robust solution of the overdetermined system of equations (13). Hence, we minimize the…”

Section: B Inference Of Interaction Topologymentioning

confidence: 99%

“…Depending on the field of interest, the available data and the (mathematical) understanding of the underlying system, different inference methods prove viable. Inference methods range from Bayesian networks and information theoretical methods based on mutual information or maximal entropy [10], [11] over compressed sensing [12], [13] and deep VOLUME 4, 2016 learning approaches [14] to network inference from response dynamics [7], see [2], [3] for comprehensive reviews. Such methods are useful to gain a better understanding of the structure and function of the network at hand, whether it is natural or engineered.…”

mentioning

confidence: 99%

“…Uncovering the interacting topology of networks from time series in the presence of hidden dynamical variables has been successful under certain conditions by heuristic means, see for instance [18]. Aside from applications of inference methods on biological networks, such as gene-regulation [22] or neuronal networks [23], or communication networks [24], [25], there are also several methods for parameter estimation in power systems, see [13] for an overview.…”

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confidence: 99%

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Inferring Topology of Networks With Hidden Dynamic Variables

et al. 2022

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Inferring the network topology from the dynamics of interacting units constitutes a topical challenge that drives research on its theory and applications across physics, mathematics, biology, and engineering. Most current inference methods rely on time series data recorded from all dynamical variables in the system. In applications, often only some of these time series are accessible, while other units or variables of all units are hidden, i.e. inaccessible or unobserved. For instance, in AC power grids, frequency measurements often are easily available whereas determining the phase relations among the oscillatory units requires much more effort. Here, we propose a network inference method that allows to reconstruct the full network topology even if all units exhibit hidden variables. We illustrate the approach in terms of a basic AC power grid model with two variables per node, the local phase angle and the local instantaneous frequency. Based solely on frequency measurements, we infer the underlying network topology as well as the relative phases that are inaccessible to measurement. The presented method may be enhanced to include systems with more complex coupling functions and additional parameters such as losses in power grid models. These results may thus contribute towards developing and applying novel network inference approaches in engineering, biology and beyond.INDEX TERMS complex networks, inverse problems, nonlinear dynamics, network inference, power grids I. INTRODUCTION

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“…There is a rather vast literature on network inference from dynamical measurements of agents and many data-based methods have been constructed. Early approaches use a probe injection signal and measure the response dynamics of the agents [14][15][16][17][18][19][20]. The successful reconstruction of the network topology, through e.g., the Laplacian matrix, the Jacobian matrix of dynamical flows or the adjacency matrix, requires then not only to record the dynamics of all agents, but also that one can control and inject specially tailored probe signals.…”

mentioning

confidence: 99%

Reconstructing Network Structures from Partial Measurements

Tyloo

Delabays

Jacquod

2021

Preprint

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The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is therefore highly desirable, for instance to develop efficient control schemes, to accurately predict the dynamics or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series, on each and every agent. These methods implicitly presuppose that, even though the network is not known, all its nodes are. A major shortcoming of theirs is that they cannot provide any reliable information, not even on partial network structures, as soon as some agents are unobservable. Here, we construct a novel method that determines network structures even when not all agents are measurable. We establish analytically and illustrate numerically that velocity signal correlators encode not only direct couplings, but also geodesic distances in the coupling network, within the subset of measurable agents. When dynamical data are accessible for all agents, our method is furthermore algorithmically more efficient than the traditional ones, because it does not rely on matrix inversion.

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Inferring power-grid topology in the face of uncertainties

Cited by 11 publications

References 42 publications

Inferring networks from time series: A neural approach

Inferring networks from time series: A neural approach

Inferring Topology of Networks With Hidden Dynamic Variables

Reconstructing Network Structures from Partial Measurements

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