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At least 73 records · Page 4

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DOE OSTI2021

Operation of Natural Gas Pipeline Networks With Storage Under Transient Flow Conditions

Here, we formulate a nonlinear optimal control problem for intraday operation of a natural gas pipeline network that includes storage reservoirs. The dynamics of compressible gas flow through pipes, compressors, reservoirs, and wells are considered. In particular, a reservoir is modeled as a rigid, hollow container that stores gas under isothermal conditions and uniform density, and a well is modeled as a vertical pipe. For each pipe, flow dynamics are described by a coupled partial differential equation (PDE) system in density and mass flux variables, with momentum dissipation modeled using the Darcy–Wiesbach friction approximation. Compressors are modeled as scaling up the pressure of gas between the inlet and outlet. The governing equations for all network components are spatially discretized and assembled into a nonlinear differential-algebraic equation (DAE) system, which synthesizes above-ground pipeline and subsurface reservoir dynamics into a single reduced-order model. We seek to maximize an objective function that quantifies economic profit and network efficiency subject to the flow equations and inequalities that represent operating limitations. The problem is solved using a primal–dual interior point solver, and the solutions are validated in computational experiments and simulations on several pipeline test networks to demonstrate the effectiveness of the proposed methodology.

03 NATURAL GAS↗

DOE OSTI2019

Quasi-Stochastic Approximation and Off-Policy Reinforcement Learning: Preprint

The Robbins-Monro stochastic approximation algorithm is a foundation of many algorithmic frameworks for reinforcement learning and often an efficient approach to solving (or approximating the solution to) complex optimal control problems. In many cases, however, practitioners are unable to apply these techniques because of an inherent high variance. This paper aims to provide a general foundation for 'quasi-stochastic approximation,' in which all of the processes under consideration are deterministic, much like quasi-Monte Carlo for variance reduction in simulation. The variance reduction can be substantial, subject to tuning of pertinent parameters in the algorithm. This paper introduces a new coupling argument to establish the optimal rate of convergence provided the gain is sufficiently large. These results are established for linear models and tested also in nonideal settings. A major application of these general results is a new class of reinforcement learning algorithms for deterministic state space models. In this setting, the main contribution is a class of algorithms for approximating the value function for a given policy, using a different policy designed to introduce exploration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

A Minimum Principle-Based Algorithm for Energy-Efficient Eco-Driving of Electric Vehicles in Various Traffic and Road Conditions

Our report presents an optimization algorithm for energy-efficient driving of electric vehicles. The algorithm is based on Pontryagin’s Minimum Principle by considering the driving mission as an optimal control problem. On a planned route, diverse application cases may occur due to various physical traits such as powertrain (e.g., switching between motor and generator operation), environmental variations (e.g., terrain grade change), traffic laws (e.g., speed limits), and safety concerns (e.g., headway to the leading vehicle). The proposed algorithm handles these real-world challenges by considering the perturbation to the system dynamics and the constraints to the control and state variables.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2023

Intracycle RPM control for vertical axis wind turbines

The wind energy market is currently dominated by horizontal axis wind turbines (HAWTs); however, vertical axis wind turbines (VAWTs) are emerging as a design alternative, especially for deep-water offshore siting due to their low center of gravity, ease of access to drivetrain components, and overall simplicity. Due to the absence of a pitch mechanism in large-scale Darrieus VAWTs, stall control has often been used to manage power and loads. Introducing a pitching mechanism in H-type VAWTs has been studied, but this diminishes the mechanical simplicity advantage, and the use of a pitching mechanism in a large-scale Darrieus-type VAWT is not practical. This work examines an innovative, alternative method to control the rotor dynamics of a large-scale 5 MW VAWT to maximize power while constraining loads without introducing any new or complex mechanical elements. This control strategy is termed intracycle revolution per minute (RPM) control, where the rotational speed of the turbine is allowed to vary in an optimal fashion with the azimuthal location of blades as opposed to typical constant RPM operation. An optimization framework is formulated for an open-loop optimal control problem and solved to maximize power subject to constraints on aerodynamic design loads. Results are presented to demonstrate the benefits and the performance limits of intracycle RPM control for large-scale 5 MW Darrieus VAWTs, namely, (1) power production (quantified in terms of AEP) that can be increased subject to baseline load limits and (2) opportunities to significantly increase AEP or decrease loads via intracycle RPM control that are examined for both two-bladed and three-bladed VAWTs.

17 WIND ENERGY↗

DOE OSTI2023

Real-time control of connected vehicles in signalized corridors using pseudospectral convex optimization

Recent advances in Connected and Automated Vehicle (CAV) technologies have opened up new opportunities to enable safe, efficient, and sustainable transportation systems. However, developing reliable and rapid speed control algorithms in highly dynamic environments with complex inter-vehicle interactions and nonlinear vehicle dynamics is still a daunting task. In this paper, we develop a novel speed control method for CAVs to produce optimal speed profiles that minimize the fuel consumption and avoid idling at signalized intersections. To this end, an optimal control problem is formulated using the information of the upcoming traffic signal to adapt vehicles' speeds to avoid frequent stop-and-go driving patterns. Here, by applying the pseudospectral discretization method and the sequential convex programming method, the computational efficiency is greatly improved, enabling potential real-time on-vehicle applications. In addition, the algorithm is implemented under a model predictive control framework to ensure online control with instant response for collision avoidance and robust vehicle coordination. The proposed algorithm is verified through numerical simulations of three different traffic scenarios. The convergence and accuracy of the proposed approach are demonstrated by comparing with a popular nonlinear solver. Furthermore, the benefit of the proposed method in both traffic mobility and fuel efficiency is validated using the speed profile determined from a traffic following model in a simulation software as the baseline.

42 ENGINEERING↗

DOE OSTI2025

A neural-network-enhanced parameter-varying framework for multi-objective model predictive control applied to buildings

Management of the electrical grid is becoming more complex due to the increased penetration of alternative energy generation technologies and a broadening diversity of electric loads. This complexity creates challenges in balancing demand and generation that can increase the potential for grid instabilities. One effective way to address this issue is to leverage previously unexploited demand flexibility through advanced control strategies. In this work, we propose an advanced control method, called adaptive neural parameter-varying model predictive control (ANPV-MPC), to control the temperature and energy consumption of a building via its Heating, Ventilation, and Air Conditioning system. ANPV-MPC combines key ideas in parameter-varying control, adaptive control, and online learning strategies to bridge the gap between computationally efficient linear model predictive control and more accurate nonlinear model predictive control. The novelty in ANPV-MPC is the use of a physics-inspired Bayesian neural network to estimate the coefficients of the parameter-varying linear control model. The Bayesian neural network additionally provides uncertainty estimates, triggering online training to capture evolving building system conditions. We show that ANPV-MPC can approximate the building system dynamics with a 28.39% higher accuracy than traditional linear model predictive control, resulting in 36.23% better control performance without increasing complexity of the optimal control problem. ANPV-MPC also adapts in real time to previously unseen conditions using online learning, further improving its performance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Restoring Distribution System Under Renewable Uncertainty Using Reinforcement Learning

Distributed energy resources (DERs) in distribution systems, including renewable generation, micro-turbine, and energy storage, can be used to restore critical loads following extreme events to increase grid resiliency. However, properly coordinating multiple DERs in the system for multi-step restoration process under renewable uncertainty and fuel availability is a complicated sequential optimal control problem. Due to its capability to handle system non-linearity and uncertainty, reinforcement learning (RL) stands out as a potentially powerful candidate in solving complex sequential control problems. Moreover, the offline training of RL provides excellent action readiness during online operation, making it suitable to problems such as load restoration, where in-time, correct and coordinated actions are needed. In this study, a distribution system prioritized load restoration based on a simplified single-bus system is studied: with imperfect renewable generation forecast, the performance of an RL controller is compared with that of a deterministic model predictive control (MPC). Our experiment results show that the RL controller is able to learn from experience, adapt to the imperfect forecast information and provide a more reliable restoration process when compared with the baseline controller.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2020

Restoring Distribution System Under Renewable Uncertainty Using Reinforcement Learning: Preprint

Distributed energy resources (DER) in distribution systems, including renewable generation, micro-turbine, and energy storage, can be used to restore critical loads following extreme events to increase grid resiliency. However, properly coordinating multiple DERs in the system for multi-step restoration process under renewable uncertainty and fuel availability is a complicated sequential optimal control problem. Due to its capability to handle system non-linearity and uncertainty, reinforcement learning (RL) stands out as a potentially powerful candidate in solving complex sequential control problems. Moreover, the offline training of RL provides excellent action readiness during online operation, making it suitable to problems such as load restoration, where in-time, correct and coordinated actions are needed. In this study, a distribution system prioritized load restoration based on a simplified single-bus system is studied: with imperfect renewable generation forecast, the performance of an RL controller is compared with that of a deterministic model predictive control (MPC). Our experiment results show that the RL controller is able to learn from experience, adapt to the imperfect forecast information and provide a more reliable restoration process when compared with the baseline MPC controller.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2021

Restoring Distribution System Under Renewable Uncertainty Using Reinforcement Learning

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗

DOE OSTI2022

Floating Wind Turbine Control Optimization

We present a framework for optimizing the control parameters of floating offshore wind turbines (FOWTs). The framework combines aeroelastic simulations with a systems engineering model and control software. In an example of the optimization framework, we minimize tower damage equivalent loading with generator speed constraints. We also study the effect of thrust-limiting control and quantify the trade off between fatigue loading and energy capture using a set of optimal controller designs. Finally, we optimize the controller of four different FOWT models and compare their dynamic responses. Additional details and other use cases for the framework are presented, which can optimize different control problems and evaluate FOWT designs.

controls↗

DOE OSTI2023

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Engineering↗

DOE OSTI2020

Optimization-based control using input convex neural networks

Input convex neural networks (ICNNs) are a family of deep learning models where the outputs are constructed to be convex functions of the inputs. By parameterizing system models using ICNNs, optimization-based control problems can be solved as convex optimization problems, leading to improved performance and robustness. This work proposes a novel framework where the control objective function and constraints are modelled using ICNNs. A case study of optimization-based control with output constraints is conducted on a process with input multiplicity and nonminimum phase behavior. The simulation results demonstrate improved economic yield compared with normal neural networks. Additionally, the input convexity formulation is compared with simple regularization techniques, and unique benefits such as improved data efficiency and robustness of the proposed formulation are shown. Finally, by explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the universal approximation power of deep learning and computational feasibility required by control.

42 ENGINEERING↗

DOE OSTI2024

Binary Quantum Control Optimization with Uncertain Hamiltonians

Optimizing the controls of quantum systems plays a crucial role in advancing quantum technologies. The time-varying noises in quantum systems and the widespread use of inhomogeneous quantum ensembles raise the need for high-quality quantum controls under uncertainties. In this paper, we consider a stochastic discrete optimization formulation of a discretized binary optimal quantum control problem involving Hamiltonians with predictable uncertainties. We propose a sample-based reformulation that optimizes both risk-neutral and risk-averse measurements of control policies, and solve these with two gradient-based algorithms using sum-up-rounding approaches. Furthermore, we discuss the differentiability of the objective function and prove upper bounds of the gaps between the optimal solutions to binary control problems and their continuous relaxations. We conduct numerical simulations on various sized problem instances based on two applications of quantum pulse optimization; we evaluate different strategies to mitigate the impact of uncertainties in quantum systems. In conclusion, we demonstrate that the controls of our stochastic optimization model achieve significantly higher quality and robustness compared with the controls of a deterministic model.

conditional value-at-risk (CVaR)↗

DOE OSTI2022

Multistage Stabilized Continuation for Indirect Optimal Control of Three-Dimensional Hypersonic Trajectories

This work presents the development of a multistaged stabilized continuation for the three-dimensional unpowered hypersonic trajectory planning problem using indirect optimal control methods. The stabilized continuation method is noniterative and guaranteed to terminate within a finite number of floating point operations, thereby making it well suited for onboard autonomous implementations. Here, we present a multistage formulation of the stabilized continuation scheme that involves starting with a “loose” integration tolerance during the first stage and ramping up toward a “strict” integration tolerance through subsequent stages. An important benefit of this approach is that even when the solution to the underlying optimal control problem is numerically unstable, such as with the hypersonic vehicle footprint generation problem, the stabilized continuation algorithm is shown to be successful in finding a solution while providing some additional insights into the underlying cause of the numerical instability.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Robust Control of Wave Energy Converters Using Unstructured Uncertainty

In the design of ocean wave energy converters, proper control design is essential to the maximization of the power generation performance for the device. However, in realistic applications, this control design must be undertaken in the presence of model uncertainty. This paper considers the use of robust control theory to optimize the nominal performance for a wave energy converter in stochastic waves, subject to the constraint that the controller be stability-robust to unstructured uncertainties. We formulate the problem as a multi-objective optimal control problem, in which the primary objective is the maximization of power generation for the nominal system, and the competing objective is the norm of the uncertainty input/output channel. This optimal control problem is nonconvex, and we therefore propose an iterative algorithm that can be used to arrive at a local optimal solution. This iterative approach employs the concept of Iterative Convex Overbounding, in the context of the classical Method of Centers. Here, the methodology is demonstrated on a model of a single, buoy- type wave energy converter.

16 TIDAL AND WAVE POWER↗

DOE OSTI2023

Load Shedding for Voltage Regulation With Probabilistic Agent Compliance

With the increased observability and controllability of distribution systems, the share of behind-the-meter systems is trending upwards rapidly. As a consequence, the impact of human behaviors on system performance can no longer be ignored and should be reflected in the energy management system models. In this paper, we discuss the problem of distribution system voltage control by active power curtailment where the agent compliance of the load curtailment signal is probabilistic. We discuss the modeling of the optimal voltage control problem with probabilistic agent compliance as a chance-constrained optimization problem, its tractable safe approximation using convex restriction, and a scenario-based mixed-integer reformulation as well as the associated solution method based on augmented Lagrangian method. The numerical simulation on IEEE test system validates the effectiveness of the proposed approach in obtaining high-quality feasible load curtailment signal with low computational cost, which makes it a viable tool for real time decision making.

augmented Lagrangian method↗