arXiv subjects

Philippe Jacquod

Publications and source records attributed to Philippe Jacquod.

At least 19 recordsLinked to original sources

arXiv2026

Accurate Data-Based State Estimation from Power Loads Inference in Electric Power Grids

Accurate state estimation is a crucial requirement for the reliable operation and control of electric power systems. Here, we construct a data-driven, numerical method to infer missing power load values in large-scale power grids. Given partial observations of power demands, the method estimates the operational state using a linear regression algorithm, exploiting statistical correlations within synthetic training datasets. We evaluate the performance of the method on three synthetic transmission grid test systems. Numerical experiments demonstrate the high accuracy achieved by the method in reconstructing missing demand values under various operating conditions. We further apply the method to real data for the transmission power grid of Switzerland. Despite the restricted number of observations in this dataset, the method infers missing power loads rather accurately. Furthermore, Newton-Raphson power flow solutions show that deviations between true and inferred values for power loads result in smaller deviations between true and inferred values for flows on power lines. This ensures that the estimated operational state correctly captures potential line contingencies. Overall, our results indicate that simple data-based regression techniques can provide an efficient and reliable alternative for state estimation in modern power grids.

eess.SY↗

arXiv2026

Anomaly Detection with Machine Learning Algorithms in Large-Scale Power Grids

We apply several machine learning algorithms to the problem of anomaly detection in operational data for large-scale, high-voltage electric power grids. We observe important differences in the performance of the algorithms. Neural networks typically outperform classical algorithms such as k-nearest neighbors and support vector machines, which we explain by the strong contextual nature of the anomalies. We show that unsupervised learning algorithm work remarkably well and that their predictions are robust against simultaneous, concurring anomalies.

eess.SY↗

arXiv2025

Feasibility and Single Parameter Scaling of Extinctions in Large Ecological Communities

Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and what triggers species extinctions is a key, outstanding problem in theoretical ecology. Using standard methods of random matrix theory, I show that distributions of species abundances are Gaussian at equilibrium, in the weakly interacting regime. One consequence is that feasibility is generically broken before stability, for large enough number of species. I further derive an analytical expression for the probability that $n=0,1,2,...$ species go extinct and conjecture that a single-parameter scaling law governs species extinctions. These results are corroborated by numerical simulations in a wide range of system parameters.

q-bio.PE↗

arXiv2025

Route to Chaos in Multi-Species Ecosystems

We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in natural or lab-controlled ecosystems and in mathematical models. Here we emphasize the emergence of limit cycles following Hopf bifurcations tuned by the variability of interspecies interaction. As this variability increases, and owing to the large dimensionality of the system, limit cycles typically acquire a growing spectrum of frequencies. This often leads to the appearance of strange attractors, with a chaotic dynamics of species abundances characterized by a positive Lyapunov exponent. We observe that limit cycles and strange attractors preserve biodiversity to some extent, as they maintain dynamical stability without species extinction. We give numerical evidences that this route to chaos dominates in ecosystems with strong enough interactions and where predator-prey behavior dominates over competition and mutualism. Based on arguments from random matrix theory, we further conjecture that this scenario is generic in ecosystems with large number of species, and identify the key parameters driving it. Overall, we show that the model we consider provides a unifying framework, where a wide range of population dynamics emerge from a simple few-parameter model.

nlin.AO↗

arXiv2024

A large synthetic dataset for machine learning applications in power transmission grids

With the ongoing energy transition, power grids are evolving fast. They operate more and more often close to their technical limit, under more and more volatile conditions. Fast, essentially real-time computational approaches to evaluate their operational safety, stability and reliability are therefore highly desirable. Machine Learning methods have been advocated to solve this challenge, however they are heavy consumers of training and testing data, while historical operational data for real-world power grids are hard if not impossible to access. This manuscript presents a large synthetic dataset of power injections in an electric transmission grid model of continental Europe, and describes the algorithm developed for its generation. The method allows one to generate arbitrarily large time series from the knowledge of the grid -- the admittance of its lines as well as the location, type and capacity of its power generators -- and aggregated power consumption data, such as the national load data given by ENTSO-E. The obtained datasets are statistically validated against real-world data.

eess.SY↗

arXiv2023

Transmission grid stability with large interregional power flows

We propose a general methodology for identifying critical lines in the long-distance transmission of power across large electric grids. When the system is pushed to its operational limit, for instance by large power imbalances such as those generated by high penetration of variable renewable energy sources, the network gets destabilized and loses synchrony. We investigate a model of the synchronous AC grid of continental Europe under tunable large interregional power flows. When those flows exceed some critical value, we find that instabilities emerge due to topological constraints. We identify two different scenarios triggering these instabilities. In the first one, specific sets of lines reach their maximal load simultaneously, causing the grid to split into two desynchronized zones. In the second one, one or few lines become overloaded, which eventually renders one Lyapunov exponent positive. The first scenario is obviously less generic and we develop a numerical approach to force the splitting of the AC grid into disconnected areas. Remarkably, the critical lines identified in this way match those that triggered the separation of the synchronous grid of continental Europe in two instances in 2021. We further discuss how the modes of the system provide information on which areas are more susceptible to lose synchrony with each other.

physics.soc-ph↗

arXiv2023

Stabilizing Large-Scale Electric Power Grids with Adaptive Inertia

The stability of AC power grids relies on ancillary services that mitigate frequency fluctuations. The electromechanical inertia of large synchronous generators is currently the only resource to absorb frequency disturbances on sub-second time scales. Replacing standard thermal power plants with inertialess new renewable sources of energy (NRE) therefore jeopardizes grid stability against e.g. sudden power generation losses. To guarantee system stability and compensate the lack of electromechanical inertia in grids with large penetrations of NREs, virtual synchronous generators, that emulate conventional generators, have been proposed. Here, we propose a novel control scheme for virtual synchronous generators, where the provided inertia is large at short times -- thereby absorbing faults as efficiently as conventional generators -- but decreases over a tunable time scale to prevent coherent frequency oscillations from setting in. We evaluate the performance of this adaptive inertia scheme under sudden power losses in large-scale transmission grids. We find that it systematically outperforms conventional, electromechanical inertia and that it is more stable than previously suggested schemes. Numerical simulations show how a quasi-optimal geographical distribution of adaptive inertia devices not only absorbs local faults efficiently, but also significantly increases the damping of inter-area oscillations. Our results show that the proposed adaptive inertia control scheme is an excellent solution to strengthen grid stability in future low-inertia power grids with large penetrations of NREs.

eess.SY↗

arXiv2023

On the Robustness of Democratic Electoral Processes to Computational Propaganda

There is growing evidence of systematic attempts to influence democratic elections by controlled and digitally organized dissemination of fake news. This raises the question of the intrinsic robustness of democratic electoral processes against external influences. Particularly interesting is to identify the social characteristics of a voter population that renders it more resilient against opinion manipulation. Equally important is to determine which of the existing democratic electoral systems is more robust to external influences. Here we construct a mathematical electoral model to address these two questions. We find that, not unexpectedly, biased electorates with clear-cut elections are overall quite resilient against opinion manipulations, because inverting the election outcome requires to change the opinion of many voters. More interesting are unbiased or weakly biased electorates with close elections. We find that such populations are more resilient against opinion manipulations (i) if they are less polarized and (ii) when voters interact more with each other, regardless of their opinion differences, and that (iii) electoral systems based on proportional representation are generally the most robust. Our model qualitatively captures the volatility of the US House of Representatives elections. We take this as a solid validation of our approach.

physics.soc-ph↗

arXiv2022

Towards Model Reduction for Power System Transients with Physics-Informed PDE

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 PDE-based modeling will initialize a physics-informed machine learning approach for real-time modeling, $n-1$ feasibility assessment and transient stability analysis of power systems.

eess.SY↗

arXiv2022

Finite-time Correlations Boost Large Voltage-Angle Fluctuations in Electric Power Grids

Decarbonization in the energy sector has been accompanied by an increased penetration of new renewable energy sources in electric power systems. Such sources differ from traditional productions in that, first, they induce larger, undispatchable fluctuations in power generation and second, they lack inertia. Therefore, substituting new renewables for traditional generation induces stronger and more frequent disturbances and modifies the way disturbances propagate across AC electric power grids. Recent measurements have indeed reported long, non-Gaussian tails in the distribution of local grid-frequency data. Large frequency deviations may induce grid instabilities, leading in worst-case scenarios to cascading failures and large-scale blackouts. In this manuscript, we investigate how correlated noise disturbances, characterized by the cumulants of their distribution, propagate through meshed, high-voltage power grids. We show that for a single source of fluctuations, non-Gaussianities in the form of finite skewness and positive kurtosis of the noise distribution propagate over the entire network when the noise correlation time is larger than the network's intrinsic time scales, but that they vanish over short distances if the noise fluctuates rapidly. We furthermore show that a Berry-Esseen theorem leads to the vanishing of non-Gaussianities as the number of uncorrelated noise sources increases. Our results show that the persistence of non-Gaussian fluctuations of feed-in power have a global impact on power-grid dynamics when they fluctuate over time scales larger than the intrinsic time scales of the system, which, we argue, is the relevant regime in real power grids. Our predictions are corroborated by numerical simulations on realistic models of power grids.

nlin.AO↗

arXiv2022

Long Wavelength Coherency in Well Connected Electric Power Networks

We investigate coherent oscillations in large scale transmission power grids, where large groups of generators respond in unison to a distant disturbance. Such long wavelength coherent phenomena are known as inter-area oscillations. Their existence in networks of weakly connected areas is well captured by singular perturbation theory. However, they are also observed in strongly connected networks without time-scale separation, where applying singular perturbation theory is not justified. We show that the occurrence of these oscillations is actually generic. Applying matrix perturbation theory, we show that, because these modes have the lowest oscillation frequencies of the system, they are only moderately sensitive to increased network connectivity between well chosen, initially weakly connected areas, and that their general structure remains the same, regardless of the strength of the inter-area coupling. This is qualitatively understood by bringing together the standard singular perturbation theory and Courant's nodal domain theorem.

nlin.AO↗

arXiv2021

Reconstructing Network Structures from Partial Measurements

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. Here, we investigate the different problem of inferring network structures within the observed/measured agents. For symmetrically coupled dynamical systems close to a stable equilibrium, 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.

nlin.AO↗

arXiv2020

Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence

Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a certain value. We focus on Kuramoto oscillators with peaked, bimodal distribution of natural frequencies. We show that, in this case, the fixed-points for the extended model are made of certain numbers of independent clusters of oscillators, depending on the length of the confidence bound -- the interaction range -- and the distance between the two peaks of the bimodal distribution of natural frequencies. This allows us to construct the phase diagram of attractive fixed-points for the bimodal Kuramoto model with bounded confidence and to analytically explain clusterization in dynamical systems with bounded confidence.

nlin.AO↗

arXiv2020

Primary Control Effort under Fluctuating Power Generation in Realistic High-Voltage Power Networks

Many recent works in control of electric power systems have investigated their synchronization through global performance metrics under external disturbances. The approach is motivated by fundamental changes in the operation of power grids, in particular by the substitution of conventional power plants with new renewable sources of electrical energy. This substitution will simultaneously increase fluctuations in power generation and reduce the available mechanical inertia. It is crucial to understand how strongly these two evolutions will impact grid stability. With very few, mostly numerical exceptions, earlier works on performance metrics had to rely on unrealistic assumptions of grid homogeneity. Here we show that a modified spectral decomposition can tackle that issue in inhomogeneous power grids in cases where disturbances occur on time scales that are long compared to the intrinsic time scales of the grid. We find in particular that the magnitude of the transient excursion generated by disturbances with long characteristic times does not depend on inertia. For continental-size, high-voltage power grids, this corresponds to power fluctuations that are correlated on time scales of few seconds or more. We conclude that power fluctuations arising from new renewables will not require per se the deployment of additional rotational inertia. We numerically illustrate our results on the IEEE 118-Bus test case and a model of the synchronous grid of continental Europe.

eess.SP↗

arXiv2019

Network desynchronization by non-Gaussian fluctuations

Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization. Here we build a general theory for inertial oscillator network desynchronization by non-Gaussian noise. We compute the rate of desynchronization and show that higher-moments of noise enter at specific powers of coupling: either speeding up or slowing down the rate exponentially depending on how noise statistics match the statistics of a network's slowest mode. Finally, we use our theory to introduce a technique that drastically reduces the effective description of network desynchronization. Most interestingly, when instability is associated with a single edge, the reduction is to one stochastic oscillator.

nlin.AO↗

arXiv2019

Rate of change of frequency under line contingencies in high voltage electric power networks with uncertainties

In modern electric power networks with fast evolving operational conditions, assessing the impact of contingencies is becoming more and more crucial. Contingencies of interest can be roughly classified into nodal power disturbances and line faults. Despite their higher relevance, line contingencies have been significantly less investigated analytically than nodal disturbances. The main reason for this is that nodal power disturbances are additive perturbations, while line contingencies are multiplicative perturbations, which modify the interaction graph of the network. They are, therefore, significantly more challenging to tackle analytically. Here, we assess the direct impact of a line loss by means of the maximal Rate of Change of Frequency (RoCoF) incurred by the system. We show that the RoCoF depends on the initial power flow on the removed line and on the inertia of the bus where it is measured. We further derive analytical expressions for the expectation and variance of the maximal RoCoF, in terms of the expectations and variances of the power profile in the case of power systems with power uncertainties. This gives analytical tools to identify the most critical lines in an electric power grid.

nlin.AO↗

arXiv2019

Eigenstate thermalization and ensemble equivalence in few-body fermionic systems

We investigate eigenstate thermalization from the point of view of vanishing particle and heat currents between a few-body fermionic Hamiltonian prepared in one of its eigenstates and an external, weakly coupled Fermi-Dirac gas. The latter acts as a thermometric probe, with its temperature and chemical potential set so that there is neither particle nor heat current between the two subsystems. We argue that the probe temperature can be attributed to the few-fermion eigenstate in the sense that (i) it varies smoothly with energy from eigenstate to eigenstate, (ii) it is equal to the temperature obtained from a thermodynamic relation in a wide energy range, (iii) it is independent of details of the coupling between the two systems in a finite parameter range, (iv) it satisfies the transitivity condition underlying the zeroth law of thermodynamics and (v) it is consistent with Carnot's theorem. These conditions are essentially independent of the interaction between the few fermions. When the interaction strength is weak, however, orbital occupancies in the few fermion system differ from the Fermi-Dirac distribution so that partial currents from or to the probe will eventually change its state. We find that (vi) above a certain critical interaction strength, orbital occupancies become close to the Fermi-Dirac distribution, leading to a true equilibrium between the few-fermion system and the probe. We conclude that for few-body systems with sufficiently strong interaction, the eigenstate thermalization hypothesis of Deutsch and Srednicki is complemented by ensemble equivalence: individual many-body eigenstates define a microcanonical ensemble that is equivalent to a canonical ensemble.

quant-ph↗

arXiv2019

Optimal placement of inertia and primary control : a matrix perturbation theory approach

The increasing penetration of inertialess new renewable energy sources reduces the overall mechanical inertia available in power grids and accordingly raises a number of issues of grid stability over short to medium time scales. It has been suggested that this reduction of overall inertia can be compensated to some extent by the deployment of substitution inertia - synthetic inertia, flywheels or synchronous condensers. Of particular importance is to optimize the placement of the limited available substitution inertia, to mitigate voltage angle and frequency disturbances following a fault such as an abrupt power loss. Performance measures in the form of H2-norms have been recently introduced to evaluate the overall magnitude of such disturbances on an electric power grid. However, despite the mathematical conveniance of these measures, analytical results can be obtained only under rather restrictive assumptions of uniform damping ratio, or homogeneous distribution of inertia and/or primary control in the system. Here, we introduce matrix perturbation theory to obtain analytical results for optimal inertia and primary control placement where both are heterogeneous. Armed with that efficient tool, we construct two simple algorithms that independently determine the optimal geographical distribution of inertia and primary control. These algorithms are then implemented on a model of the synchronous transmission grid of continental Europe. We find that the optimal distribution of inertia is geographically homogeneous but that primary control should be mainly located on the slow modes of the network, where the intrinsic grid dynamics takes more time to damp frequency disturbances.

math.OC↗