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DOE OSTI2025

Frequency Control and Disturbance Containment Using Grid-Forming Embedded Storage Networks

The paper presents a distributed approach for operating a network of inverter-based energy storage resources embedded in a bulk power system. Departing from their traditional role of steady-state reserves, the storage assets in the network are utilized as frequency-responsive resources shaping system dynamics. The power electronics converter systems interfacing the storage resources are equipped with local controllers designed to respond under transient disturbances. To this end, a safety-constrained distributed control strategy is explored. The paper compares the performance of converter-interfaced grid-forming and grid-following storage networks for fast frequency control and disturbance containment/localization. Sensitivity studies are performed to study the impact of storage size, steady-state dispatch, and controller design on dynamic performance. The findings are presented through case studies with results from the IEEE test systems.

Chatterjee, Kaustav (ORCID:0000000153273860)↗

DOE OSTI2018

Scaling laws for dynamical plasma phenomena

A scaling and similarity technique is a useful tool for developing and testing reduced models of complex phenomena, including plasma phenomena. Similarity and scaling arguments will be applied to highly dynamical systems where the plasma is evolving from some initial to some final state, which may differ dramatically from each other in size and plasma parameters. A question then arises whether, in order to better understand the behavior of one such system, is it possible to create another system, possibly much smaller (or larger) than the original one, but whose evolution would accurately replicate that of the original one, from its initial to its final state. This would allow a researcher, by an experimental study of this second system, to make confident predictions about the behavior of the first one (which may be otherwise inaccessible, as is the case of some astrophysical objects, or too expensive and hard to diagnose, as in the case of fusion applications of pulsed plasma systems, or for other reasons). The scaling and similarity techniques for dynamical plasma systems will be presented as a set of case studies of problems from various domains of plasma physics, including collisional and collisionless plasmas. Finally, among the results discussed are similar for MHD systems with an emphasis on high-energy-density laboratory astrophysics, interference between collisionless and collisional phenomena in the context of shock physics, and similarity for liner-imploded plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from a small dataset of recorded observations of the perturbed system's dynamics and the control law is optimized offline by interaction with the learned system model. The DPC method is based on two sequential steps, i) system identification using a constrained neural state-space model, and ii) optimization of an explicit control law parametrized by another neural network in closed-loop simulation with the identified neural state-space model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. By incorporating domain knowledge and leveraging established techniques from optimal control, our method leverages deep neural networks as nonlinear function approximators for system identification and control while avoiding concomitant costs of intractably large datasets, and computationally expensive over-parametrized models. The scalability, data efficiency, and constrained optimal control capability of the proposed DPC method are demonstrated in simulation using a multi-zone building emulator.

Drgona, Jan↗

DOE OSTI2024

Holistic Small-Signal Stability Analysis for Large-Scale Inverter-Intensive Power Systems with Coupled and Full-Order Dynamics from Control Systems and Power Networks

The increasing penetration of inverter-based resources (IBRs) into the existing power systems introduces tremendous benefits for enhanced sustainability but also poses inevitable challenges in terms of insufficient inertia, potential instability, and complex network dynamics, among others. However, the additional coupling introduced by the interactions among gridfollowing (GFL) and grid-forming (GFM) IBRs and the other components (i.e., synchronous generators [SGs], loads, and network, etc.) has not been clearly explored. A holistic, scalable, and quantitative stability analysis framework with the control systems and power networks is still missing. Here, in this paper, to fill in the technical gaps, a holistic small-signal model of the entire system with both rotating generation units and IBRs is established. An extended power flow model with operation dynamics from both generator control schemes and power networks is proposed to provide the varying steady-state operating points for small-signal modeling. The proposed method is compared with MATLAB solvers, and the results show that the proposed approach has a minimum calculation time, which can be less than 12 seconds for a large-scale power system with up to 2,000 buses. Furthermore, a quantitative method is developed to identify the impacts of IBRs on system performance with emphases on the potential stability issues with GFL IBRs, additional benefits of employing GFM IBRs, the feasibility of replacing SGs with GFM IBRs, and the impact of penetration level of different kinds of generation units. Finally, a field island power system is used to verify the proposed approach, and hardware-in-the-loop (HIL) tests are provided to further demonstrate the effectiveness of the proposed analysis.

14 SOLAR ENERGY↗

DOE OSTI2020

A Model-Free Voltage Control Approach to Mitigate Motor Stalling and FIDVR for Smart Grids

Electric power networks are large and highly nonlinear dynamical systems that present unique challenges to control design. Though there is a large number of dynamic models for power system stability and control, many models are only useful with right assumptions and wrong for other tasks. Moreover, the dynamic behavior of the grid is increasingly complex under the banner of smart grids. These lead to the difficulty of developing appropriate dynamic modeling, and thus an efficient control strategy. To avoid such modeling challenges, here we present a novel dynamic voltage control strategy based on a model-free control (MFC) approach, requiring no modeling procedure. In particular, it focuses on fault-induced delayed voltage recovery (FIDVR) events, which require complex and accurate dynamic load models to replicate such events. This work utilizes MFC as an online controller to achieve the desired voltage stability under the FIDVR event. The proposed MFC strategy allows simple implementation and low computational cost for efficient mitigation of FIDVR. For benchmarking, a reasonably accurate dynamic performance model is explored. Simulation results with the IEEE 57 bus test network demonstrate the enhanced dynamic voltage profile for load buses having induction motors with the support of reactive power resources.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Generative learning for slow manifolds and bifurcation diagrams

In dynamical systems characterized by separation of time scales, the approximation of so called “slow manifolds”, on which the long term dynamics lie, is a useful step for model reduction. Initializing on such slow manifolds is a useful step in modeling, since it circumvents fast transients, and is crucial in multiscale algorithms (like the equation-free approach) alternating between fine scale (fast) and coarser scale (slow) simulations. In a similar spirit, when one studies the infinite time dynamics of systems depending on parameters, the system attractors (e.g., its steady states) lie on bifurcation diagrams (curves for one-parameter continuation, and more generally, on manifolds in state parameter space. Sampling these manifolds gives us representative attractors (here, steady states of ODEs or PDEs) at different parameter values. Algorithms for the systematic construction of these manifolds (slow manifolds, bifurcation diagrams) are required parts of the “traditional” numerical nonlinear dynamics toolkit. In more recent years, as the field of Machine Learning develops, conditional score-based generative models (cSGMs) have been demonstrated to exhibit remarkable capabilities in generating plausible data from target distributions that are conditioned on some given label. It is tempting to exploit such generative models to produce samples of data distributions (points on a slow manifold, steady states on a bifurcation surface) conditioned on (consistent with) some quantity of interest (QoI, observable). In this work, we present a framework for using cSGMs to quickly (a) initialize on a low-dimensional (reduced-order) slow manifold of a multi-time-scale system consistent with desired value(s) of a QoI (a “label”) on the manifold, and (b) approximate steady states in a bifurcation diagram consistent with a (new, out-of-sample) parameter value. This conditional sampling can help uncover the geometry of the reduced slow-manifold and/or approximately “fill in” missing segments of steady states in a bifurcation diagram. Finally, the quantity of interest, which determines how the sampling is conditioned, is either known a priori or identified using manifold learning-based dimensionality reduction techniques applied to the training data.

Dynamical systems↗

NASA NTRS2007

Fault Detection and Correction for the Solar Dynamics Observatory Attitude Control System

The Solar Dynamics Observatory is an Explorer-class mission that will launch in early 2009. The spacecraft will operate in a geosynchronous orbit, sending data 24 hours a day to a devoted ground station in White Sands, New Mexico. It will carry a suite of instruments designed to observe the Sun in multiple wavelengths at unprecedented resolution. The Atmospheric Imaging Assembly includes four telescopes with focal plane CCDs that can image the full solar disk in four different visible wavelengths. The Extreme-ultraviolet Variability Experiment will collect time-correlated data on the activity of the Sun's corona. The Helioseismic and Magnetic Imager will enable study of pressure waves moving through the body of the Sun. The attitude control system on Solar Dynamics Observatory is responsible for four main phases of activity. The physical safety of the spacecraft after separation must be guaranteed. Fine attitude determination and control must be sufficient for instrument calibration maneuvers. The mission science mode requires 2-arcsecond control according to error signals provided by guide telescopes on the Atmospheric Imaging Assembly, one of the three instruments to be carried. Lastly, accurate execution of linear and angular momentum changes to the spacecraft must be provided for momentum management and orbit maintenance. In th~sp aper, single-fault tolerant fault detection and correction of the Solar Dynamics Observatory attitude control system is described. The attitude control hardware suite for the mission is catalogued, with special attention to redundancy at the hardware level. Four reaction wheels are used where any three are satisfactory. Four pairs of redundant thrusters are employed for orbit change maneuvers and momentum management. Three two-axis gyroscopes provide full redundancy for rate sensing. A digital Sun sensor and two autonomous star trackers provide two-out-of-three redundancy for fine attitude determination. The use of software to maximize chances of recovery from any hardware or software fault is detailed. A generic fault detection and correction software structure is used, allowing additions, deletions, and adjustments to fault detection and correction rules. This software structure is fed by in-line fault tests that are also able to take appropriate actions to avoid corruption of the data stream.

Starin, Scott R.↗

NASA NTRS1995

Influence of backup bearings and support structure dynamics on the behavior of rotors with active supports

Progress made in the current year is listed, and the following papers are included in the appendix: Steady-State Dynamic Behavior of an Auxiliary Bearing Supported Rotor System; Dynamic Behavior of a Magnetic Bearing Supported Jet Engine Rotor with Auxiliary Bearings; Dynamic Modelling and Response Characteristics of a Magnetic Bearing Rotor System with Auxiliary Bearings; and Synchronous Dynamics of a Coupled Shaft/Bearing/Housing System with Auxiliary Support from a Clearance Bearing: Analysis and Experiment.

Flowers, George T.↗

DOE OSTI2026

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

Advanced Kalman Filter for Real-Time Responsiveness in Complex Systems

Complex engineering systems pose fundamental challenges in real-time operations and control because they are highly dynamic systems consisting of a large number of elements with severe nonlinearities and discontinuities. Today’s tools for real-time complex system operations are mostly based on steady state models, unable to capture the dynamic nature and too slow to prevent system failures. We developed advanced Kalman filtering techniques and the formulation of dynamic state estimation using Kalman filtering techniques to capture complex system dynamics in aiding real-time operations and control. In this work, we looked at complex system issues including severe nonlinearity of system equations, discontinuities caused by system controls and network switches, sparse measurements in space and time, and real-time requirements of power grid operations. We sought to bridge the disciplinary boundaries between Computer Science and Power Systems Engineering, by introducing methods that leverage both existing and new techniques. While our methods were developed in the context of electrical power systems, they should generalize to other large-scale scientific and engineering applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1998

Charting Multidisciplinary Team External Dynamics Using a Systems Thinking Approach

Using the formalism provided by the Systems Thinking approach, the dynamics present when operating multidisciplinary teams are examined in the context of the NASA Langley Research and Technology Group, an R&D organization organized along functional lines. The paper focuses on external dynamics and examines how an organization creates and nurtures the teams and how it disseminates and retains the lessons and expertise created by the multidisciplinary activities. Key variables are selected and the causal relationships between the variables are identified. Five "stories" are told, each of which touches on a different aspect of the dynamics. The Systems Thinking Approach provides recommendations as to interventions that will facilitate the introduction of multidisciplinary teams and that therefore will increase the likelihood of performing successful multidisciplinary developments. These interventions can be carried out either by individual researchers, line management or program management.

Barthelemy, Jean-Francois↗

NASA NTRS2014

Lunar Cube Transfer Trajectory Options

Contingent upon the modification of an initial condition of the injected or deployed orbit. Additionally, these designs can be restricted by the selection of the Cubesat subsystem design such as propulsion or communication. Nonetheless, many trajectory options can be designed with have a wide range of transfer durations, fuel requirements, and final destinations. Our investigation of potential trajectories highlights several design options including deployment into low Earth orbit (LEO), geostationary transfer orbits (GTO), and higher energy direct lunar transfer orbits. In addition to direct transfer options from these initial orbits, we also investigate the use of longer duration Earth-Moon dynamical systems. For missions with an intended lunar orbit, much of the design process is spent optimizing a ballistic capture while other science locations such as Sun-Earth libration or heliocentric orbits may simply require a reduced Delta-V imparted at a convenient location along the trajectory. In this article we examine several design options that meet the above limited deployment and subsystem drivers. We study ways that both impulsive and low-thrust Solar Electric Propulsion (SEP) engines can be used to place the Cubesat first into a highly eccentric Earth orbit, enter the Moon's Sphere of Influence, and finally achieve a highly eccentric lunar orbit. We show that such low-thrust transfers are feasible with a realistic micro-thruster model, assuming that the Cubesat can generate sufficient power for the SEP. Two examples are shown here: (1) A Cubestat injected by Exploration Mission 1 (EM-1) then employing low thrust; and (2) a CubSat deployed in a GTO, then employing impulsive maneuvers. For the EM-1 injected initial design, we increase the EM-1 targeted lunar flyby distance to reduce the energy of the lunar flyby to match that of a typical lMoon system heteroclinic manifold. Figure 1 presents an option that encompasses the similar dynamics as that of the ARTEMIS mission design. Low-thrust maneuvers are used along the manifold trajectory to raise perigee to that of a lunar orbit, adjust the timing with respect to the Moon, rotate the line of apsides, and target a ballistic lunar encounter. In this design a second flyby decreases the orbital energy with respect to the Moon, so that C3 -0.1 km2s2. Another design, shown in Figure 2 emanates from a GTO then uses impulsive maneuvers to phase onto a local Earth-Moon manifold, which then transfers the CubeSat to a lunar encounter.

Dynamical System↗

NASA NTRS1994

Towards an integral computer environment supporting system operations analysis and conceptual design

VITROCISET has in house developed a prototype tool named System Dynamic Analysis Environment (SDAE) to support system engineering activities in the initial definition phase of a complex space system. The SDAE goal is to provide powerful means for the definition, analysis, and trade-off of operations and design concepts for the space and ground elements involved in a mission. For this purpose SDAE implements a dedicated modeling methodology based on the integration of different modern (static and dynamic) analysis and simulation techniques. The resulting 'system model' is capable of representing all the operational, functional, and behavioral aspects of the system elements which are part of a mission. The execution of customized model simulations enables: the validation of selected concepts with respect to mission requirements; the in-depth investigation of mission specific operational and/or architectural aspects; and the early assessment of performances required by the system elements to cope with mission constraints and objectives. Due to its characteristics, SDAE is particularly tailored for nonconventional or highly complex systems, which require a great analysis effort in their early definition stages. SDAE runs under PC-Windows and is currently used by VITROCISET system engineering group. This paper describes the SDAE main features, showing some tool output examples.

Barro, E.↗

DOE OSTI2020

Sampling Low-Dimensional Markovian Dynamics for Preasymptotically Recovering Reduced Models from Data with Operator Inference

This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with classical projection-based model reduction techniques. Thus, the proposed approach learns models that are guaranteed to have the well-studied properties of reduced models known from model reduction, without requiring full knowledge of the governing equations and without requiring the operators of the high-dimensional systems. The key ingredient is a new data sampling scheme to obtain re-projected trajectories of high-dimensional systems that correspond to Markovian dynamics in low-dimensional subspaces. The exact recovery of reduced models from these re-projected trajectories is guaranteed pre-asymptotically under certain conditions for finite amounts of data and for a large class of systems with polynomial nonlinear terms. Numerical results demonstrate that the low-dimensional models learned with the proposed approach match reduced models from traditional model reduction up to numerical errors in practice. In conclusion, the numerical results further indicate that low-dimensional models fitted to re-projected trajectories are predictive even in situations where models fitted to trajectories without re-projection are inaccurate and unstable.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

An Integrated Transmission-Distribution Co-Simulation for a Distribution System with High Renewable Penetration

Traditionally, transmission and distribution system dynamic simulations are performed independently. However, dynamic co-simulation of transmission-distribution systems can be beneficial in analyzing distribution systems with high penetration of distributed renewable resources. The authors describe a framework for conducting transmission-distribution dynamic co-simulation (TDDS). A model of a real network including detailed models of solar photovoltaic units in the distribution system is constructed. The initial operating point of the network is validated against field measurements. The TDDS tool is used to simulate a single line-to-ground fault on the distribution system, highlighting the need for conducting transmission-distribution co-simulations.

14 SOLAR ENERGY↗

NASA NTRS1973

Structural Aspects of System Identification

The problem of identifying linear dynamical systems is studied by considering structural and deterministic properties of linear systems that have an impact on stochastic identification algorithms. In particular considered is parametrization of linear systems so that there is a unique solution and all systems in appropriate class can be represented. It is assumed that a parametrization of system matrices has been established from a priori knowledge of the system, and the question is considered of when the unknown parameters of this system can be identified from input/output observations. It is assumed that the transfer function can be asymptotically identified, and the conditions are derived for the local, global and partial identifiability of the parametrization. Then it is shown that, with the right formulation, identifiability in the presence of feedback can be treated in the same way. Similarly the identifiability of parametrizations of systems driven by unobserved white noise is considered using the results from the theory of spectral factorization.

Glover, Keith↗

NASA NTRS2007

Recent Developments in Smart Adaptive Structures for Solar Sailcraft

The "Smart Adaptive Structures for Solar Sailcraft" development activity at MSFC has investigated issues associated with understanding how to model and scale the subsystem and multi-body system dynamics of a gossamer solar sailcraft with the objective of designing sailcraft attitude control systems. This research and development activity addressed three key tasks that leveraged existing facilities and core competencies of MSFC to investigate dynamics and control issues of solar sails. Key aspects of this effort included modeling and testing of a 30 m deployable boom; modeling of the multi-body system dynamics of a gossamer sailcraft; investigation of control-structures interaction for gossamer sailcraft; and development and experimental demonstration of adaptive control technologies to mitigate control-structures interaction.

Whorton, M. S.↗

NASA NTRS2007

Recent Developments in Smart Adaptive Structures for Solar Sailcraft

Worton, M. S.↗