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DOE OSTI2015

Final Technical Report: Distributed Controls for High Penetrations of Renewables

The goal of this effort was to apply four potential control analysis/design approaches to the design of distributed grid control systems to address the impact of latency and communications uncertainty with high penetrations of photovoltaic (PV) generation. The four techniques considered were: optimal fixed structure control; Nyquist stability criterion; vector Lyapunov analysis; and Hamiltonian design methods. A reduced order model of the Western Electricity Coordinating Council (WECC) developed for the Matlab Power Systems Toolbox (PST) was employed for the study, as well as representative smaller systems (e.g., a two-area, three-area, and four-area power system). Excellent results were obtained with the optimal fixed structure approach, and the methodology we developed was published in a journal article. This approach is promising because it offers a method for designing optimal control systems with the feedback signals available from Phasor Measurement Unit (PMU) data as opposed to full state feedback or the design of an observer. The Nyquist approach inherently handles time delay and incorporates performance guarantees (e.g., gain and phase margin). We developed a technique that works for moderate sized systems, but the approach does not scale well to extremely large system because of computational complexity. The vector Lyapunov approach was applied to a two area model to demonstrate the utility for modeling communications uncertainty. Application to large power systems requires a method to automatically expand/contract the state space and partition the system so that communications uncertainty can be considered. The Hamiltonian Surface Shaping and Power Flow Control (HSSPFC) design methodology was selected to investigate grid systems for energy storage requirements to support high penetration of variable or stochastic generation (such as wind and PV) and loads. This method was applied to several small system models.

14 SOLAR ENERGY↗

DOE OSTI2018

Hybrid methods for muon accelerator simulations with ionization cooling

Muon ionization cooling involves passing particles through solid or liquid absorbers. Careful simulations are required to design muon cooling channels. New features have been developed for inclusion in the transfer map code COSY Infinity to follow the distribution of charged particles through matter. To study the passage of muons through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map-Monte-Carlo approach in which transfer map methods describe the deterministic behavior of the particles, and Monte-Carlo methods are used to provide corrections accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics are represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed are expected to simplify the optimization of cooling channels which is usually computationally demanding. In conclusion, progress on the development of the required algorithms and their application to modeling muon ionization cooling channels is reported.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Optimized attenuated interaction: Enabling stochastic Bethe–Salpeter spectra for large systems

We develop an improved stochastic formalism for the Bethe–Salpeter equation (BSE), based on an exact separation of the effective-interaction W into two parts, W = (W – vW) + vW, where the latter is formally any translationally invariant interaction, vW(r – r'). When optimizing the fit of the exchange kernel vW to W, using a stochastic sampling W, the difference W – vW becomes quite small. Then, in the main BSE routine, this small difference is stochastically sampled. Furthermore, the number of stochastic samples needed for an accurate spectrum is then largely independent of system size. While the method is formally cubic in scaling, the scaling prefactor is small due to the constant number of stochastic orbitals needed for sampling W.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Monte Carlo Explicitly Correlated Second-Order Many-Body Green’s Function Calculations of Semiconductor Band Gaps

A systematically converging series of ab initio, post-density-functional, size-consistent, electron-correlated approximations is desired for predictive computing of felectronic band structures of insulating, semiconducting, and metallic solids. A series that meets all of these desiderata (except the applicability to metals) is ab initio many-body Green's function theory based on Gaussian-type-orbital (GTO) basis sets. Here, its leading-order approximation, the second-order Green's function (GF2) method in the diagonal and frequency-independent approximations with the aug-cc-pVDZ basis set, is applied to the fundamental band gaps of three semiconductors (diamond, silicon, and silicon carbide in the zincblende structure) using cluster models. Corrections are made to the basis-set-incompleteness errors by the explicit-correlation (F12) ansatz (GF2-F12) for the valence band edges. The crystals are modeled as surface-passivated clusters of increasing sizes, whose wave functions are expanded by up to 2709 GTO basis functions. Immense computational costs of these calculations are overcome by the highly scalable stochastic algorithm of the Monte Carlo GF2-F12 method, whose operation cost per state increases only as a cubic power of system size, which has a tiny memory footprint and easily achieves near-perfect parallel efficiency on thousands of CPUs or on hundreds of GPUs. The correlated, F12-corrected highest-occupied and lowest-unoccupied molecular-orbital energy (HOMO-LUMO) gap is 5.78 ± 0.07 eV for C 87 H 76 as compared with the experimental value of the fundamental (indirect) band gap of bulk diamond at 5.48 eV. The correlated, F12-corrected HOMO-LUMO gaps for Si 75 H 76 and Si 32 C 43 H 76 are 2.56 ± 0.15 eV and 3.50 ± 0.12 eV, respectively, which are expected to decrease further with increasing cluster sizes. As a result, the experimental fundamental (indirect) band gaps of bulk silicon and silicon carbide are 1.17 eV and 2.42 eV, respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2015

Predicting laser weld reliability with stochastic reduced-order models. Predicting laser weld reliability

Laser welds are prevalent in complex engineering systems and they frequently govern failure. The weld process often results in partial penetration of the base metals, leaving sharp crack-like features with a high degree of variability in the geometry and material properties of the welded structure. Furthermore, accurate finite element predictions of the structural reliability of components containing laser welds requires the analysis of a large number of finite element meshes with very fine spatial resolution, where each mesh has different geometry and/or material properties in the welded region to address variability. We found that traditional modeling approaches could not be efficiently employed. Consequently, a method is presented for constructing a surrogate model, based on stochastic reduced-order models, and is proposed to represent the laser welds within the component. Here, the uncertainty in weld microstructure and geometry is captured by calibrating plasticity parameters to experimental observations of necking as, because of the ductility of the welds, necking – and thus peak load – plays the pivotal role in structural failure. The proposed method is exercised for a simplified verification problem and compared with the traditional Monte Carlo simulation with rather remarkable results.

36 MATERIALS SCIENCE↗

NASA NTRS2014

A Multiscale Progressive Failure Modeling Methodology for Composites that Includes Fiber Strength Stochastics

A multiscale modeling methodology was developed for continuous fiber composites that incorporates a statistical distribution of fiber strengths into coupled multiscale micromechanics/finite element (FE) analyses. A modified two-parameter Weibull cumulative distribution function, which accounts for the effect of fiber length on the probability of failure, was used to characterize the statistical distribution of fiber strengths. A parametric study using the NASA Micromechanics Analysis Code with the Generalized Method of Cells (MAC/GMC) was performed to assess the effect of variable fiber strengths on local composite failure within a repeating unit cell (RUC) and subsequent global failure. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a unidirectional SCS-6/TIMETAL 21S metal matrix composite tensile dogbone specimen at 650 degC. Multiscale progressive failure analyses were performed to quantify the effect of spatially varying fiber strengths on the RUC-averaged and global stress-strain responses and failure. The ultimate composite strengths and distribution of failure locations (predominately within the gage section) reasonably matched the experimentally observed failure behavior. The predicted composite failure behavior suggests that use of macroscale models that exploit global geometric symmetries are inappropriate for cases where the actual distribution of local fiber strengths displays no such symmetries. This issue has not received much attention in the literature. Moreover, the model discretization at a specific length scale can have a profound effect on the computational costs associated with multiscale simulations.models that yield accurate yet tractable results.

Generalized Method of Cells↗

DOE OSTI2020

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch

A significant difficulty associated with the use of stochastic programming to solve optimal power flow problems on a 5-minute timescale is the quality of renewable energy scenarios input by the user. This is especially true when considering power systems with high penetrations of renewable energy, e.g. wind power. This paper introduces the use of stochastic programming to solve the DC optimal power flow problem with scenarios drawn directly from high-fidelity data sets. Hence, the proposed method avoids the problem of lost physics by finding high-fidelity analogs that can describe future states of the system. Furthermore, this method can be simply extended to output multi-period scenarios to the stochastic program. We demonstrate the effectiveness of this technique by simulating dispatch operations on a synthetic test system over the course of a week.

94 GMLC - Grid Modernization Laboratory Consortium↗

DOE OSTI2021

Scenario Creation and Power-Conditioning Strategies for Operating Power Grids with Two-Stage Stochastic Economic Dispatch

analog forecast↗

DOE OSTI2015

Stochastic Optimal Scheduling of Residential Appliances with Renewable Energy Sources

This paper proposes a stochastic, multi-objective optimization model within a Model Predictive Control (MPC) framework, to determine the optimal operational schedules of residential appliances operating in the presence of renewable energy source (RES). The objective function minimizes the weighted sum of discomfort, energy cost, total and peak electricity consumption, and carbon footprint. A heuristic method is developed for combining different objective components. The proposed stochastic model utilizes Monte Carlo simulation (MCS) for representing uncertainties in electricity price, outdoor temperature, RES generation, water usage, and non-controllable loads. The proposed model is solved using a mixed integer linear programming (MILP) solver and numerical results show the validity of the model. Case studies show the benefit of using the proposed optimization model.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2012

THE PANCHROMATIC HUBBLE ANDROMEDA TREASURY. III. MEASURING AGES AND MASSES OF PARTIALLY RESOLVED STELLAR CLUSTERS

The apparent age and mass of a stellar cluster can be strongly affected by stochastic sampling of the stellar initial mass function (IMF), when inferred from the integrated color of low-mass clusters ({approx}<10{sup 4} M {sub Sun }). We use simulated star clusters to show that these effects are minimized when the brightest, rapidly evolving stars in a cluster can be resolved, and the light of the fainter, more numerous unresolved stars can be analyzed separately. When comparing the light from the less luminous cluster members to models of unresolved light, more accurate age estimates can be obtained than when analyzing the integrated light from the entire cluster under the assumption that the IMF is fully populated. We show the success of this technique first using simulated clusters, and then with a stellar cluster in M31. This method represents one way of accounting for the discrete, stochastic sampling of the stellar IMF in less massive clusters and can be leveraged in studies of clusters throughout the Local Group and other nearby galaxies.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1987

Stochastic model theory of broadband shock associated noise from supersonic jets

A method based on the work of Tam and Tanna (1982) for calculating the near field noise spectrum and the spatial distribution of broadband shock associated noise from supersonic jets is proposed. Multiple-scales expansion is used to decompose the quasi-periodic shock cells into time-independent waveguide modes of the jet flow, and the interaction of the instability waves with each of the waveguide modes is shown to generate unsteady disturbances which become part of the broadband shock associated noise when radiated to the far field. The observed broadband shock associated noise is composed of a superposition of the various distinct spectra of the different waveguide modes, and the multispectra can be easily identified in many of the existing far and near field noise measurements.

Tam, C. K. W.↗

DOE OSTI2024

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗

DOE OSTI2021

A stochastic solver based on the residence time algorithm for crystal plasticity models

Abstract The deformation of crystalline materials by dislocation motion takes place in discrete amounts determined by the Burgers vector. Dislocations may move individually or in bundles, potentially giving rise to intermittent slip. This confers plastic deformation with a certain degree of variability that can be interpreted as being caused by stochastic fluctuations in dislocation behavior. However, crystal plasticity (CP) models are almost always formulated in a continuum sense, assuming that fluctuations average out over large material volumes and/or cancel out due to multi-slip contributions. Nevertheless, plastic fluctuations are known to be important in confined volumes at or below the micron scale, at high temperatures, and under low strain rate/stress deformation conditions. Here, we develop a stochastic solver for CP models based on the residence-time algorithm that naturally captures plastic fluctuations by sampling among the set of active slip systems in the crystal. The method solves the evolution equations of explicit CP formulations, which are recast as stochastic ordinary differential equations and integrated discretely in time. The stochastic CP model is numerically stable by design and naturally breaks the symmetry of plastic slip by sampling among the active plastic shear rates with the correct probability. This can lead to phenomena such as intermittent slip or plastic localization without adding external symmetry-breaking operations to the model. The method is applied to body-centered cubic tungsten single crystals under a variety of temperatures, loading orientations, and imposed strain rates.

42 ENGINEERING↗

DOE OSTI2021

A Data-Driven Multi-Period Importance Sampling Strategy for Stochastic Economic Dispatch

Power systems with high penetrations of renewable energy (e.g., wind power) require sophisticated approaches to optimize system performance due to uncertainty in short-term system generation capacity. In this paper, we combine a data-driven analog scenario selection method with importance sampling to create a novel scenario construction approach for two-stage stochastic economic dispatch problems with a large number of wind farms on a network. The proposed method produces scenarios with realistic physics by finding high-fidelity analogs that can describe future states of the system. We show how to extend this method to multi-period operations and demonstrate the effectiveness of this technique by simulating economic dispatch operations on a synthetic test system over the course of a week.

data-driven forecasting↗

DOE OSTI2019

High-throughput 3D reconstruction of stochastic heterogeneous microstructures in energy storage materials

Abstract Stochastic heterogeneous microstructures are widely applied in structural and functional materials, playing a crucial role in determining their performance. X-ray tomography and focused ion beam serial sectioning are frequently used methods to reconstruct three-dimensional (3D) microstructures, yet are demanding techniques and are resolution-limited. Here, a high-throughput multi-stage 3D reconstruction method via distance correlation functions is developed using a single representatively large-sized 2D micrograph for stochastic microstructures, and verified by X-ray micro-tomography datasets of isotropic and anisotropic solid oxide fuel cell electrodes. This method provides an economic, easy-to-use and high-throughput approach for reconstructing stochastic heterogeneous microstructures for energy conversion and storage devices, and can readily be extended to other materials.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Deep Reinforcement Learning for Distribution System Restoration Using Distributed Energy Resources and Tie-Switches

Distributed energy resources (DERs), such as solar PVs and energy storage, can be used to restore distribution system critical loads after the extreme weather events to increase grid resilience. However, coordinating multiple DERs together with tie-switches for multi-step restoration process under renewable uncertainty is challenging. This paper proposes a deep reinforcement learning to control discrete actions of switching on/off tie switches and DERs for critical load restoration. The restoration problem is first cast into the Markov decision process suitable for DRL. Then, the original soft actor critic (SAC) method for continuous actions has been extended to handle discrete and continuous actions. Numerical comparison results with other stochastic optimization-based approaches on the modified IEEE 33-bus system show that the proposed method can achieve fast critical load restoration in the presence of substation power outage while maintaining system voltage limit throughout the restoration process.

active distribution systems↗

NASA NTRS1988

Analysis and improvement of the vector quantization in SELP (Stochastically Excited Linear Prediction)

The Stochastically Excited Linear Prediction (SELP) algorithm is described as a speech coding method employing a two-stage vector quantization. The first stage uses an adaptive codebook which efficiently encodes the periodicity of voiced speech, and the second stage uses a stochastic codebook to encode the remainder of the excitation signal. The adaptive codebook performs well when the pitch period of the speech signal is larger than the frame size. An extension is introduced, which increases its performance for the case that the frame size is longer than the pitch period. The performance of the stochastic stage, which improves with frame length, is shown to be best in those sections of the speech signal where a high level of short-term correlations is present. It can be concluded that the SELP algorithm performs best during voiced speech where the pitch period is longer than the frame length.

Kleijn, W. B.↗

DOE OSTI2019

Path-accelerated stochastic molecular dynamics: Parallel-in-time integration using path integrals

Massively parallel computer architectures create new opportunities for the performance of long-time scale molecular dynamics (MD) simulations. Here, we introduce the path-accelerated molecular dynamics method that takes advantage of distributed computing to reduce the wall-clock time of MD simulation via parallelization with respect to stochastic MD time steps. The marginal distribution for the time evolution of a system is expressed in terms of a path integral, enabling the use of path sampling techniques to numerically integrate MD trajectories. By parallelizing the evaluation of the path action with respect to time and by initializing the path configurations from a nonequilibrium distribution, the algorithm enables significant speedups in terms of the length of MD trajectories that can be integrated in a given amount of wall-clock time. The method is demonstrated for Brownian dynamics, although it is generalizable to other stochastic equations of motion including open systems. We apply the method to two simple systems, a harmonic oscillator and a Lennard-Jones liquid, and we show that in comparison to the conventional Euler integration scheme for Brownian dynamics, the new method can reduce the wall-clock time for integrating trajectories of a given length by more than three orders of magnitude in the former system and more than two in the latter. This new method for parallelizing MD in the dimension of time can be trivially combined with algorithms for parallelizing the MD force evaluation to achieve further speedup.

Rosa-Raíces, Jorge L.↗