arXiv subjects

Samuel Chevalier

Publications and source records attributed to Samuel Chevalier.

At least 37 records · Page 2Linked to original sources

arXiv2024

A Parallelized, Adam-Based Solver for Reserve and Security Constrained AC Unit Commitment

Power system optimization problems which include the nonlinear AC power flow equations require powerful and robust numerical solution algorithms. Within this sub-field of nonlinear optimization, interior point methods have come to dominate the solver landscape. Over the last decade, however, a number of efficient numerical optimizers have emerged from the field of Machine Learning (ML). One algorithm in particular, Adam, has become the optimizer-of-choice for a massive percentage of ML training problems (including, e.g., the training of GPT-3), solving some of the largest unconstrained optimization problems ever conceived of. Inspired by such progress, this paper designs a parallelized Adam-based numerical solver to overcome one of the most challenging power system optimization problems: security and reserve constrained AC Unit Commitment. The resulting solver, termed QuasiGrad, recently competed in the third ARPA-E Grid Optimization (GO3) competition. In the day-ahead market clearing category (with systems ranging from 3 to 23,643 buses over 48 time periods), QuasiGrad's aggregated market surplus scores were within 5% of the winningest market surplus scores. The QuasiGrad solver is now released as an open-source Julia package: QuasiGrad.jl. The internal gradient-based solver (Adam) can easily be substituted for other ML-inspired solvers (e.g., AdaGrad, AdaDelta, RMSProp, etc.). Test results from large experiments are provided.

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arXiv2023

GPU-Accelerated Verification of Machine Learning Models for Power Systems

Computational tools for rigorously verifying the performance of large-scale machine learning (ML) models have progressed significantly in recent years. The most successful solvers employ highly specialized, GPU-accelerated branch and bound routines. Such tools are crucial for the successful deployment of machine learning applications in safety-critical systems, such as power systems. Despite their successes, however, barriers prevent out-of-the-box application of these routines to power system problems. This paper addresses this issue in two key ways. First, for the first time to our knowledge, we enable the simultaneous verification of multiple verification problems (e.g., checking for the violation of all line flow constraints simultaneously and not by solving individual verification problems). For that, we introduce an exact transformation that converts the "worst-case" violation across a set of potential violations to a series of ReLU-based layers that augment the original neural network. This allows verifiers to interpret them directly. Second, power system ML models often must be verified to satisfy power flow constraints. We propose a dualization procedure which encodes linear equality and inequality constraints directly into the verification problem; and in a manner which is mathematically consistent with the specialized verification tools. To demonstrate these innovations, we verify problems associated with data-driven security constrained DC-OPF solvers. We build and test our first set of innovations using the $α,β$-CROWN solver, and we benchmark against Gurobi 10.0. Our contributions achieve a speedup that can exceed 100x and allow higher degrees of verification flexibility.

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arXiv2022

Towards Optimal Kron-based Reduction Of Networks (Opti-KRON) for the Electric Power Grid

For fast timescales or long prediction horizons, the AC optimal power flow (OPF) problem becomes a computational challenge for large-scale, realistic AC networks. To overcome this challenge, this paper presents a novel network reduction methodology that leverages an efficient mixed-integer linear programming (MILP) formulation of a Kron-based reduction that is optimal in the sense that it balances the degree of the reduction with resulting modeling errors in the reduced network. The method takes as inputs the full AC network and a pre-computed library of AC load flow data and uses the graph Laplacian to constraint nodal reductions to only be feasible for neighbors of non-reduced nodes. This results in a highly effective MILP formulation which is embedded within an iterative scheme to successively improve the Kron-based network reduction until convergence. The resulting optimal network reduction is, thus, grounded in the physics of the full network. The accuracy of the network reduction methodology is then explored for a 100+ node medium-voltage radial distribution feeder example across a wide range of operating conditions. It is finally shown that a network reduction of 25-85% can be achieved within seconds and with worst-case voltage magnitude deviation errors within any super node cluster of less than 0.01pu. These results illustrate that the proposed optimization-based approach to Kron reduction of networks is viable for larger networks and suitable for use within various power system applications.

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arXiv2022

Optimization-Based Exploration of the Feasible Power Flow Space for Rapid Data Collection

This paper provides a systematic investigation into the various nonlinear objective functions which can be used to explore the feasible space associated with the optimal power flow problem. A total of 40 nonlinear objective functions are tested, and their results are compared to the data generated by a novel exhaustive rejection sampling routine. The Hausdorff distance, which is a min-max set dissimilarity metric, is then used to assess how well each nonlinear objective function performed (i.e., how well the tested objective functions were able to explore the non-convex power flow space). Exhaustive test results were collected from five PGLib test-cases and systematically analyzed.

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arXiv2022

Emission-Aware Optimization of Gas Networks: Input-Convex Neural Network Approach

Gas network planning optimization under emission constraints prioritizes gas supply with the least CO$_2$ intensity. As this problem includes complex physical laws of gas flow, standard optimization solvers cannot guarantee convergence to a feasible solution. To address this issue, we develop an input-convex neural network (ICNN) aided optimization routine which incorporates a set of trained ICNNs approximating the gas flow equations with high precision. Numerical tests on the Belgium gas network demonstrate that the ICNN-aided optimization dominates non-convex and relaxation-based solvers, with larger optimality gains pertaining to stricter emission targets. Moreover, whenever the non-convex solver fails, the ICNN-aided optimization provides a feasible solution to network planning.

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arXiv2022

Interpretable Machine Learning for Power Systems: Establishing Confidence in SHapley Additive exPlanations

Interpretable Machine Learning (IML) is expected to remove significant barriers for the application of Machine Learning (ML) algorithms in power systems. This letter first seeks to showcase the benefits of SHapley Additive exPlanations (SHAP) for understanding the outcomes of ML models, which are increasingly being used. Second, we seek to demonstrate that SHAP explanations are able to capture the underlying physics of the power system. To do so, we demonstrate that the Power Transfer Distribution Factors (PTDF) -- a physics-based linear sensitivity index -- can be derived from the SHAP values. To do so, we take the derivatives of SHAP values from a ML model trained to learn line flows from generator power injections, using a simple DC power flow case in the 9-bus 3-generator test network. In demonstrating that SHAP values can be related back to the physics that underpin the power system, we build confidence in the explanations SHAP can offer.

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arXiv2022

Closing the Loop: A Framework for Trustworthy Machine Learning in Power Systems

Deep decarbonization of the energy sector will require massive penetration of stochastic renewable energy resources and an enormous amount of grid asset coordination; this represents a challenging paradigm for the power system operators who are tasked with maintaining grid stability and security in the face of such changes. With its ability to learn from complex datasets and provide predictive solutions on fast timescales, machine learning (ML) is well-posed to help overcome these challenges as power systems transform in the coming decades. In this work, we outline five key challenges (dataset generation, data pre-processing, model training, model assessment, and model embedding) associated with building trustworthy ML models which learn from physics-based simulation data. We then demonstrate how linking together individual modules, each of which overcomes a respective challenge, at sequential stages in the machine learning pipeline can help enhance the overall performance of the training process. In particular, we implement methods that connect different elements of the learning pipeline through feedback, thus "closing the loop" between model training, performance assessments, and re-training. We demonstrate the effectiveness of this framework, its constituent modules, and its feedback connections by learning the N-1 small-signal stability margin associated with a detailed model of a proposed North Sea Wind Power Hub system.

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arXiv2021

Accelerating Dynamical System Simulations with Contracting and Physics-Projected Neural-Newton Solvers

Recent advances in deep learning have allowed neural networks (NNs) to successfully replace traditional numerical solvers in many applications, thus enabling impressive computing gains. One such application is time domain simulation, which is indispensable for the design, analysis and operation of many engineering systems. Simulating dynamical systems with implicit Newton-based solvers is a computationally heavy task, as it requires the solution of a parameterized system of differential and algebraic equations at each time step. A variety of NN-based methodologies have been shown to successfully approximate the trajectories computed by numerical solvers at a fraction of the time. However, few previous works have used NNs to model the numerical solver itself. For the express purpose of accelerating time domain simulation speeds, this paper proposes and explores two complementary alternatives for modeling numerical solvers. First, we use a NN to mimic the linear transformation provided by the inverse Jacobian in a single Newton step. Using this procedure, we evaluate and project the exact, physics-based residual error onto the NN mapping, thus leaving physics ``in the loop''. The resulting tool, termed the Physics-pRojected Neural-Newton Solver (PRoNNS), is able to achieve an extremely high degree of numerical accuracy at speeds which were observed to be up to 31% faster than a Newton-based solver. In the second approach, we model the Newton solver at the heart of an implicit Runge-Kutta integrator as a contracting map iteratively seeking a fixed point on a time domain trajectory. The associated recurrent NN simulation tool, termed the Contracting Neural-Newton Solver (CoNNS), is embedded with training constraints (via CVXPY Layers) which guarantee the mapping provided by the NN satisfies the Banach fixed-point theorem.

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arXiv2021

Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment

Nonlinear power flow constraints render a variety of power system optimization problems computationally intractable. Emerging research shows, however, that the nonlinear AC power flow equations can be successfully modeled using Neural Networks (NNs). These NNs can be exactly transformed into Mixed Integer Linear Programs (MILPs) and embedded inside challenging optimization problems, thus replacing nonlinearities that are intractable for many applications with tractable piecewise linear approximations. Such approaches, though, suffer from an explosion of the number of binary variables needed to represent the NN. Accordingly, this paper develops a technique for training an "optimally compact" NN, i.e., one that can represent the power flow equations with a sufficiently high degree of accuracy while still maintaining a tractable number of binary variables. We show that the resulting NN model is more expressive than both the DC and linearized power flow approximations when embedded inside of a challenging optimization problem (i.e., the AC unit commitment problem).

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arXiv2021

Accelerated Probabilistic Power Flow in Electrical Distribution Networks via Model Order Reduction and Neumann Series Expansion

This paper develops a computationally efficient algorithm which speeds up the probabilistic power flow (PPF) problem by exploiting the inherently low-rank nature of the voltage profile in electrical power distribution networks. The algorithm is accordingly termed the Accelerated-PPF (APPF), since it can accelerate "any" sampling-based PPF solver. As the APPF runs, it concurrently generates a low-dimensional subspace of orthonormalized solution vectors. This subspace is used to construct and update a reduced order model (ROM) of the full nonlinear system, resulting in a highly efficient simulation for future voltage profiles. When constructing and updating the subspace, the power flow problem must still be solved on the full nonlinear system. In order to accelerate the computation of these solutions, a Neumann expansion of a modified power flow Jacobian is implemented. Applicable when load bus injections are small, this Neumann expansion allows for a considerable speed up of Jacobian system solves during the standard Newton iterations. APPF test results, from experiments run on the full IEEE 8500-node test feeder, are finally presented.

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arXiv2021

Uncertainty Quantification in LV State Estimation Under High Shares of Flexible Resources

The ongoing electrification introduces new challenges to distribution system operators (DSOs). Controllable resources may simultaneously react to price signals, potentially leading to network violations. DSOs require reliable and accurate low-voltage state estimation (LVSE) to improve awareness and mitigate such events. However, the influence of flexibility activations on LVSE has not been addressed yet. It remains unclear if flexibility-induced uncertainty can be reliably quantified to enable robust DSO decision-making. In this work, uncertainty quantification in LVSE is systematically investigated for multiple scenarios of input availability and flexibility utilization, using real data. For that purpose, a Bayesian neural network (BNN) is compared to quantile regression. Results show that frequent flexibility activations can significantly deteriorate LVSE performance, unless secondary substation measurements are available. Moreover, it is demonstrated that the BNN captures flexibility-induced voltage drops by dynamically extending the prediction interval during activation periods, and that it improves interpretability regarding the cause of uncertainty.

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arXiv2021

Network Topology Invariant Stability Certificates for DC Microgrids with Arbitrary Load Dynamics

DC microgrids are prone to small-signal instabilities due to the presence of tightly regulated loads. This paper develops a decentralized stability certificate which is capable of certifying the small-signal stability of an islanded DC network containing such loads. Utilizing a novel homotopy approach, the proposed standards ensure that no system eigenmodes are able to cross into the unstable right half plane for a continuous range of controller gain levels. The resulting "standards" can be applied to variety of grid components which meet the specified, but non-unique, criteria. These standards thus take a step towards offering plug-and-play operability of DC microgrids. The proposed theorems are explicitly illustrated and numerically validated on multiple DC microgrid test-cases containing both buck and boost converter dynamics.

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arXiv2021

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

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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arXiv2021

Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

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arXiv2021

Accelerated Probabilistic State Estimation in Distribution Grids via Model Order Reduction

This paper applies a custom model order reduction technique to the distribution grid state estimation problem. Specifically, the method targets the situation where, due to pseudo-measurement uncertainty, it is advantageous to run the state estimation solver potentially thousands of times over sampled input perturbations in order to compute probabilistic bounds on the underlying system state. This routine, termed the Accelerated Probabilistic State Estimator (APSE), efficiently searches for the solutions of sequential state estimation problems in a low dimensional subspace with a reduced order model (ROM). When a sufficiently accurate solution is not found, the APSE reverts to a conventional QR factorization-based Gauss-Newton solver. It then uses the resulting solution to preform a simple basis expansion of the low-dimensional subspace, thus improving the reduced model solver. Simulated test results, collected from the unbalanced three-phase 8500-node distribution grid, show the resulting algorithm to be almost an order of magnitude faster than a comparable full-order Gauss-Newton solver and thus potentially fast enough for real-time use.

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arXiv2020

Dynamic Linepack Depletion Models for Natural Gas Pipeline Networks

Given the critical role played by natural gas in providing electricity, heat, and other essential services, better models are needed to understand the dynamics of natural gas networks during extreme events. This paper aims at establishing appropriate and fast simulation models to capture the slow dynamics of linepack depletion for ideal isothermal natural gas pipeline networks. Instead of solving partial differential equations (PDE) on a large scale, three alternative implicit ordinary differential equation (ODE) simulation techniques are derived and discussed. The first one is commonly used in the literature with a slack node assumption. We show that the system of equations associated with this model is degenerate when flux injections are controlled (i.e. specified) at all nodes. To recover regularity under such a condition, two novel implicit ODE models are proposed, both with different techniques for specifying boundary conditions. They are easy to derive and efficient to simulate with standard ODE solvers. More importantly, they present useful frameworks for analyzing how networks respond to system-wide mass flux imbalances. These techniques offer different alternatives for simulating system dynamics based on how sources and loads are chosen to be modeled, and they are all proven to be regular (non-degenerate) in tree-structured networks. These proposed techniques are all tested on the 20-node Belgium network. The simulation results show that the conventional model with the slack node assumption cannot effectively capture linepack depletion under long term system-wide mass flux imbalance, while the proposed models can characterize the network behavior until the linepack is completely depleted.

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arXiv2020

A Bayesian Framework for Power System Components Identification

Having actual models for power system components (such as generators and loads or auxiliary equipment) is vital to correctly assess the power system operating state and to establish stability margins. However, power system operators often have limited information about the actual values for power system component parameters. Even when a model is available, its operating parameters and control settings are time-dependent and subject to real-time identification. Ideally, these parameters should be identified from measurement data, such as phasor measurement unit (PMU) signals. However, it is challenging to do this from the ambient measurements in the absence of transient dynamics since the signal-to-noise ratio (SNR) for such signals is not necessarily large. In this paper, we design a Bayesian framework for on-line identification of power system component parameters based on ambient PMU data, which has reliable performance for SNR as low as five and for certain parameters can give good estimations even for unit SNR. We support the framework with a robust and time-efficient numerical method. We illustrate the approach efficiency on a synchronous generator example.

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arXiv2020

A Passivity Interpretation of Energy-Based Forced Oscillation Source Location Methods

This paper develops a systematic framework for analyzing how low frequency forced oscillations propagate in electric power systems. Using this framework, the paper shows how to mathematically justify the so-called Dissipating Energy Flow (DEF) forced oscillation source location technique. The DEF's specific deficiencies are pinpointed, and its underlying energy function is analyzed via incremental passivity theory. This analysis is then used to prove that there exists no passivity transformation (i.e. quadratic energy function) which can simultaneously render all components of a lossy classical power system passive. The paper goes on to develop a simulation-free algorithm for predicting the performance of the DEF method in a generalized power system, and it analyzes the passivity of three non-classical load and generation components. The proposed propagation framework and performance algorithm are both tested and illustrated on the IEEE 39-bus New England system and the WECC 179-bus system.

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