Abstracts

Yifei SUN: Goal-oriented data compression

Lossy compression a widely used when communications or storage resources are limited. Compression schemes try to find a trade-off between the distortion and the rate required to represent the compressed data. In most cases, the distortion is expressed in terms of mean square error (MSE) between the original and reconstructed data. Nevertheless, in several applications (fault localization, image segmentation, optimization), the MSE is not the most appropriate figure of merit when the compressed data are used to take some decision. This paper focuses on an Lp-norm optimization problem in which some parameters have been compressed. The aim is to design a compression scheme for the parameters such that the minimum of the cost function with compressed parameters is as close as possible to the minimum obtained without compression. For that purpose, we introduce a compression scheme consisting of a precoder, a quantizer, and a decoder, designed to get the most relevant representation of the parameters leading to a minimum optimality loss. Numerical examples show the benefits of the proposed approach compared to a classical compression scheme minimizing the MSE.

Yoshinari TAKAYAMA : Structure-Exploiting Optimization for Control with Signal Temporal Logic Specifications

Signal temporal logic (STL) is capable of expressing a broad range of temporal properties that controlled dynamical systems must satisfy. In order to solve optimal control problems with complex STL specifications, both mixed-integer programming (MIP) and nonlinear programming (NLP) methods have been applied in the literature; however, neither has succeeded in solving these problems. In this talk, we introduce a brief overview of our new optimization framework, termed STLCCP, which mitigates this issue by explicitly taking into account several structures of STL based on the convex-concave procedure (CCP). During this presentation, I will also briefly discuss my perspective on utilizing this algorithm for power systems.

Noureddine HENKA : Robust Electrical Segmentation for Power Grid Reduction

The intense renewable energy integration into the power grid shows a daily critical challenge for grid operators.This high renewable integration tends to surpass the human’s reaction to deal with because of its fast injection variations, flow inversion, voltage equilibrium, etc.This paradigm leads to new tools to assist the operators for gird management difficulties.Electrical segmentation offers a promising solution to reduce the grid’s complexity, which aims to divide the grid into coherent electrical zones.The electrical segmentation is based on electrical influence, which allows for constructing zones with high intra-zone influence and low inter-zone influence. It allows operators to focus on reduced zone of the grid.However, due to topological changes requested constantly to manage the grid, electrical segmentation in a single situation may not fairly represent the optimal and robust segmentation that adapts mainly to all situations. In our work, we model robust segmentation as the clustering of a multiplex graph that represents the changes that can occur in the grid.The main model is based on a flattening process that aims to compute a latent representation that adequately represents the grid’s variations. The proposed pipeline has demonstrated its relevance compared to single-situation segmentation in many cases.

Pierre HOUDOUIN : Certification of complex systems with Machine Learning

In answer to the fast growth of renewable power that complicates line congestion management, RTE developed NAZA automatons, designed to maintain the stability of the system. In parallel of their massive deployment, we wish to obtain security guarantees by identifying situations where NAZA's decisions do not prevent congestions. However, such situations are rare event since only extreme scenarios might threaten the security of the network. Also, evaluating a scenario is time consuming. A naïve approach that would consist in evaluating all scenarios sampled randomly becomes excessively long. In this talk, we present a new machine-lerning based workflow to quickly identify threatening scenarios. Sampling is handled using Reinforcement Learning and paired with a classifier to predict the output of a simulation and avoid simulating scenarios with obvious outcomes. For a fixed time budget, we aim to find much more interesting scenarios compared to the naïve approach.

Eva BOGUSLAWSKI : Congestion handling on Power Grid governed by complex automata

Renewable energy sources are forcing power grid operators to review their grid management policies. To limit the need to adapt and reinforce the grid, RTE is developing new adaptive zonal automatons. Each automaton monitors a zone of the power grid and can receive a target path from operators. RTE now needs to develop a decision support assistant for the supervision and coordination of automatons on the power grid. This thesis focuses on the development of a decision support assistant through the decentralized Multi-Agent Reinforcement Learning (MARL) approach. We think a decentralized approach could greatly improve scalability compared to traditional deep learning methods. The assistant will have to recommend relevant target paths for automatons. During this presentation, we will discuss some preliminary results obtained in a simplified setting with single Reinforcement Learning.

Noureddine HENKA : Robust Electrical Segmentation for Power Grid Reduction

The intense renewable energy integration into the power grid shows a daily critical challenge for grid operators. This high renewable integration tends to surpass the human’s reaction to deal with because of its fast injection variations, flow inversion, voltage equilibrium, etc. This paradigm leads to new tools to assist the operators for gird management difficulties. Electrical segmentation offers a promising solution to reduce the grid’s complexity, which aims to divide the grid into coherent electrical zones. The electrical segmentation is based on electrical influence, which allows for constructing zones with high intra-zone influence and low inter-zone influence. It allows operators to focus on reduced zone of the grid. However, due to topological changes requested constantly to manage the grid, electrical segmentation in a single situation may not fairly represent the optimal and robust segmentation that adapts mainly to all situations. In our work, we model robust segmentation as the clustering of a multiplex graph that represents the changes that can occur in the grid. The main model is based on a flattening process that aims to compute a latent representation that adequately represents the grid’s variations. The proposed pipeline has demonstrated its relevance compared to single-situation segmentation in many cases.

Guillaume GANET-LEPAGE : Towards a safe maximisation of renewables flexibility in power transmission sub-grids. An MPC approach

This presentation contributes to the current trend of development of a model-based predictive control laws for the operation of sub-transmission grids with storage devices and significant distributed generation. First, a framework for simulations and controls is presented. Second, it is shown that a receding horizon control law is able not only to automatically handle the curtailment levels but also to indicate the levels of relaxation for the curtailements, whenever they are admissible. The major difficulty in this process resides in the fact that a reduction of the curtailment implies potential increase of the generated power and can lead to congestion on the transmission lines. To avoid the ensuing safety constraint violations, an upper bound is used for the available power to cope with the lack of information when the curtailment is active. The controller's performance is evaluated via simulations through a case study of a real zone in the French power grid.

Corentin PRESVÔTS : Compression of current and voltage sample values via a multi-model coding system

We propose, based on the literature, to improve the existing approaches for compressing raw voltage and current signals with a compression ratio similar to PMUs. The approach consists of two stages of compression.  The first stage models the electrical waveform. The second stage encodes the residual signals involving a DCT or DWT. Additional models to the literature are taken into account in the first stage, notably the variational autoencoders traditionally used in image compression.  A new model of the distortion introduced by the quantization of model parameters on the reconstructed waveforms is proposed. Using this model, an optimal rate allocation between the two stages is performed by balancing the distortion introduced by the parameter quantization and the quantization of the transformed residuals. 

François PACAUD : Revisiting structure-exploiting optimal power flow methods

How far should you exploit the structure of your problem in nonlinear optimization? By design, many engineering problems are constrained by physical equations, leading to stringent restriction on the search-space. Hence, one can exploit the structure of the physical equations to split the optimization variables in two distinct sets, by isolating the independent variables (=degrees of freedom) from the dependent variables. If the number of degrees of freedom is small, we can drastically reduce the dimension of the problem by using a reduced-space approach, where we optimize only with relation to the independent variables. Dommel and Tinney have shown in 1968 that such reduced-space approach directly applies to the static optimal power flow problem (OPF), when one looks at optimizing the dispatch of generators in a power grid while satisfying the static (nonlinear) power flow equations. In that particular case, the reduced-space is directly associated to the manifold induced by the power flow equations. Incidentally, this approach has fallen out of flavor in the 1990s, with the development of mature sparse linear solvers able to solve frontally large-scale optimization problems. In this talk, we revisit the seminal method of Dommel and Tinney, with a modern glance. We exhibit the link existing between the reduced-space OPF approach and the classical OPF formulation. We show that by accelerating the computation of the reduced gradient and the reduced Hessian on GPUs, the method of Dommel and Tinney compares favorably with Ipopt, a state-of-the-art interior-point solver. We detail an extension of the method to solve stochastic and security-constrained OPF, interpreted here as two-stage stochastic nonlinear programs. We finish the talk by discussing potential extensions to transient-stability OPF, where this time the physical equations are encoded by a differential algebraic equations (DAE).

Matteo TACCHI: Robust data-driven Lyapunov analysis with finite data

This contribution proposes a new data-driven method to approximate the region of attraction of a system whose dynamics are unknown and difficult to simulate. In such case, no model is provided and obtaining new data is very expensive. Using a previously fixed sample, our algorithm evaluates the possibility of approximating (with robust, deterministic guarantees) the region of attraction of an equilibrium point and, in the affirmative, outputs such approximation under the form of a sub-level set of a Lyapunov function. The output certificate is a Lyapunov function for all systems that are consistent with the input data, and is computed through a tessellation of the set of admissible states combined with solving a second order cone programming problem.

Sofiane CHALAL : Qubo formulation for electrical grid problems

The Mincut problem is a fundamental problem in graph theory that involves finding the minimum cut in a graph, (i.e., the set of edges that, when removed, separates the graph into two disconnected components). In this project the approach is to use Quantum Adiabatic Computing (AQC) and encoding the Mincut problem as a Hamiltonian, finding the ground state of the Hamiltonian, corresponds to the minimum cut of the graph. The implementation can be done on PASQAL computers, which are particularly tailored towards solving quadratic unconstrained binary optimization problems (QUBOs).

Adrien LE FRANC: Minimal sparsity for scalable moment-SOS relaxations of the AC-OPF problem

The moment-SOS (Sums-Of-Squares) hierarchy has proved relevant to solve AC-OPF (Alternative Current - Optimal Power Flow) instances to global optimality. However, obtaining the convergence of the hierarchy may requires to go beyond the first step of the involved sequence of SDP (Semidefinite Programming) relaxations, and thus to solve semidefinite programs whose size grows drastically at each step of the hierarchy. Thus, the application of such relaxations to large scale AC-OPF problems (with thousands of variables) remains a challenging computing task. Large polynomial optimization problems can be tackled efficiently if they are sufficiently sparse. In this talk, we present a new sparsity pattern, that we call minimal sparsity, inspired by the specific structure of the AC-OPF problem. We show that minimal sparsity enables the computation of second order moment-SOS relaxations on instances with thousands of variables. Experimentally, we observe that it also provides tighter lower bounds to certify the global optimality of AC-OPF solutions compared with previous sparsity approaches.

Andrei BRAITOR: Distributed Bounded Consensus-Based Control for Multi-Agent Systems with Undirected Graphs

In this talk, a distributed consensus-based control method is presented that guarantees agent states limitation for networks of multi-agent systems with undirected communication graphs. This approach takes into account the general linear dynamic models of n identical agents and, by employing Lyapunov methods and ultimate boundedness theory, it ensures that each agent state remains within given bounds. This latter feature is particularly useful in scenarios where one must mitigate the occurrence of abnormal values being transmitted within the network, thus, maintaining a relatively safe consensus policy between agents. The developed strategy requires, at each agent node, information from their respective neighbours only, and it can be applied independently of any global information of the communication graph, hence, it is fully distributed. To highlight the developed controller capability and effectiveness, a multi-converter microgrid system with a meshed communication network has been used as a practical example. Subsequent to the asymptotic stability proof for the overall closed-loop microgrid system, the control framework has been tested in a predetermined simulation scenario.

Stéphane DROBOT :  SOStab: a Matlab Toolbox for Approximating Regions of Attraction of Nonlinear Systems

This talk presents a novel Matlab toolbox, aimed at facilitating the use of polynomial optimization for stability analysis of nonlinear systems. Indeed, in the past decade several decisive contributions made it possible to recast the difficult problem of computing stability regions of nonlinear systems, under the form of convex optimization problems that are tractable in modest dimensions. However, these techniques combine sophisticated frameworks such as algebraic geometry, measure theory and mathematical programming, and existing software still requires their user to be fluent in Sum-of-Squares and Moment programming, preventing these techniques from being used more widely in the control community. To address this issue, SOStab entirely automates the writing and solving of optimization problems, and directly outputs relevant data for the user, while requiring minimal input. In particular, no specific knowledge of optimization is needed to use it.

Hoai Nam NGUYEN: Adaptive PI Control of Wave Energy Converters with Force and Motion Constraints

This presentation provides the development of adaptive PI control design to a point absorber wave energy converter (WEC) under force and motion constraints. Adaptive PI control has several features that make it attractive for WEC system. In particular, it has a clear physical interpretation. The ”P” component converts the wave energy into useful energy, while the ”I” component changes the WEC system natural frequency allowing the absorber to be more in phase with the incoming waves. However, standard adaptive PI control schemes in the literature do not have the ability to incorporate the constraints in the design phase. The main objective of this paper is to fill this gap by proposing a new adaptive PI control law that can take the constraints into account. Simulation results show that the new control law can improve the performance while respecting system limitations.

We will consider a class of non-convex optimization problems involving a large number of agents. The cost function is formulated as a convex function of an "aggregate", i.e., the sum of contributions of all the agents. The applications of such problems concern in particular energy management problems involving a large number of small producers (or consumers) and a cost function penalizing the distance of the total production (or consumption) to some desired profile. We will introduce and analyze an iterative numerical method, relying at each iteration on the parallelizable computation of "best-responses" for all agents. Joint work with: Frédéric Bonnans (Inria and L2S CentraleSupélec), Kang Liu (Ecole Polytechnique, Inria, and L2S CentraleSupélec), Nadia Oudjane (EDF R&D), Cheng Wan (EDF R&D)