Here are a very short description of the different projects I am working. (The last two are not active.)
Power Systems with Renewable sources
For my Postdoc at Los Alamos, I started completly new projects in a new research field for me: Power Systems.
I am part of the Advanced Network Science Initiative (ANSI) at Los Alamos National Laboratory.
Renewable Energy, such as provided by wind and sun, is a major novel source of generation.
However, it is not reliable as coming in spikes.
Having sufficient battery resources can help to mitigate the uncertainty, but even though battery technology has advanced significantly during the last decade, it is still very far from being able to level fluctuations even in a relatively small energy system (a small town, 100 MW scale) caused by the renewable sources.
This flexible battery problem is the topic of my first project at Los Alamos.
At the same time estimating how this uncertainty affects power grids is necessary to build reliable systems. This is the topic of my second project.
Control of Virtual Battery aggregates
The statistical behavior of large aggregates of Thermostatic Constrolled Loads (TCLs), e.g. Air conditioners, Fridges.
These aggregates of flexible loads can be seen as giant power source reservoir (so called virtual batteries) that can for example compensate for the fluctuations in renewable energy generation.
See for example, these two motivational press articles here and there.
We use statistical physics tools like Mean Field interactions to develop an efficient control for these aggregates.
○ Métivier D., Chertkov C. (2019). Mean Field Control of the Energy Load Ensemble with Disorder.
(Submitted).
○ Métivier D., Chertkov C. (2018). Mean Field Control for Efficient Mixing of Energy Loads.
arXiv:1810.00450 (Submitted).
○ Métivier, D., Luchnikov I., Chertkov C. (2019). Power of Ensemble Diversity and Randomization for Energy Aggregation.
Scientific reports 9 (1), 5910; arXiv:1808.09555.
Uncertainty Quantification in Power Systems
Traditional power systems operational planning and management is being challenged by the increased penetration of renewable energy and distributed energy resources.
The variability of power consumption and generation inherent to these additions calls for new control and optimization tools capable of accurately handling the impact of uncertainty on a faithful, nonlinear description of the power grid.
In this paper, we develop a framework for integrating uncertainty into AC Optimal Power Flow (ACOPF) problem in a scalable way with Polynomial Chaos Expansion. We consider the chance constrained ACOPF which ensures that safety limits are enforced with a prescribed probability.
○ Métivier, D., Vuffray M., Misra S. (2019). Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems.
arXiv:1910.06498 (Submitted to PSCC 2020)
Bifurcation in Vlasov and Kuramoto systems
I started working on this topic during my PhD thesis.
Long-range interacting systems are known to display particular statistical and dynamical properties. To
describe their dynamical evolution, we can use kinetic equations describing their density in the phase space.
To study their (infinite dimensional nonlinear) dynamics, we can look at bifurcations around unstable steady states.
In some cases, one might hope to obtain an exact reduced model describing the bifurcation,
while in some other cases it is not possible because of the resonance between the unstable mode and the continuous spectrum on the imaginary axis.
This project global goal is to classify and describe these bifurcations for systems described by Vlasov-like equations (plasma, self gravitating systems, ...) and Kuramoto-like systems (for coupled oscillators).
You can find animated simulations of such bifurcations in the Vlasov-HMF Videos section, which is the Vlasov equation for a simple interaction potential.
○ Barré J., Métivier D., Yamaguchi Y. Y. (2019). Towards a classification of bifurcations in Vlasov equations.
arXiv:1909.11344 (Submitted)
○ Métivier D., L Wetzel, S Gupta (2019). Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops.
arXiv:1906.02643 (Submitted).
○ Métivier D., Gupta S. (2019). Bifurcations in the time-delayed Kuramoto model of coupled oscillators: Exact results.
J Stat Phys; arXiv:1808.10436.
○ Barré J., Métivier D. (2018). Vlasov-Fokker-Planck equation: stochastic stability of resonances and unstable manifold expansion.
Nonlinearity 31 4667; arXiv:1703.01668.
○ Barré J., Métivier D. (2016). Bifurcations and singularities for coupled oscillators with inertia and frustration.
Physical Review Letters, 117(21), 214102.; arXiv:1605.02990.
○ Barré J., Métivier D., Yamaguchi Y. Y. (2016). Trapping scaling for bifurcations in the Vlasov systems.
Physical Review E, 93(4), 042207.; arXiv:1511.07645
Debye length in Magneto-Optical Traps
This was a collaboration with an experimental team to measure correlation effects characteristic of long range systems in a cold atom trap.
Magneto-Optical Traps are widely-used device, operating with a large number of atoms, they are supposed to display effective Coulomb interactions coming from photon rescattering.
We worked to propose experimental tests to highlight the analog of a Debye length.
○ Barré J., Kaiser R., Labeyrie G., Marcos B., Métivier, D. (2019). Towards a measurement of the Debye length in very large Magneto-Optical traps. Phys. Rev. A 100, 013624
arXiv:1808.02098.
Lieb-Robinson bound
This was a project I worked during a three month internship in South Africa. Lieb-Robinson-type bounds are the non-relativistic analog of the light cone, i.e. they control how correlations travels in space and time for quantum or classical lattices.
In particular for short-range interacting lattice, this bound has the usual cone shape of special relativity. For long range interactions the shape of the 'cone' is different leading to new phenoma.
○ Métivier, D., Bachelard, R., Kastner, M. (2014). Spreading of Perturbations in Long-Range Interacting Classical Lattice Models.
Physical Review Letters, 112(21), 210601.; arXiv:1405.7556