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DOE OSTI2022

Distribution Function Instead of Steady-State Assumption in Time-Series Simulation

The quasi-steady-state assumption in time-series simulation is inadequate to model phenomena of interest to energy system integration such as inverter clipping, sell-back of excess electricity to a utility and utility hosting capacity, and battery throughput. Researchers are working on stochastic modeling, higher-resolution time series data, and machine learning approaches to address this need. This poster describes a distribution function that allows a maximum value, minimum value, and shape to the curve that can vary within each time-step based only on data inputs at the resolution of that time step (eg. Hourly). The distribution function is not used to synthesize high-resolution data, rather scalar integrals are used to calculate the quantities of interest within each time step. The form of the distribution function shows significant reduction in error when compared to 1 minute data and commercial software employing the distribution function (HOMER Pro version 14.3 and higher) shows a much improved estimate of inverter clipping in an example.

battery↗

DOE OSTI2021

Stochastic pre-event preparation for enhancing resilience of distribution systems

Extreme weather events are the common causes for power supply interruptions and power outages in electrical distribution systems. Improving the distribution system and enhancing its resilience is becoming crucial due to the increased frequency of extreme weather events. Preparation and allocation of multiple flexible resources, such as mobile resources, fuel resources, and labor resources before extreme weather events can mitigate the effects of extreme weather events and enhance the resilience of power distribution systems. Here, in this paper, a two-stage stochastic mixed-integer linear programming (SMILP) is proposed to optimize the preparation and resource allocation process for upcoming extreme weather events, which leads to faster and more efficient post-event restoration. The objective of the proposed two-stage SMILP is to maximize the served load and minimize the operating cost of flexible resources. The first stage in the optimization problem selects the amounts and locations of different resources. The second stage considers the operational constraints of the distribution system and repair crew scheduling constraints. The proposed stochastic pre-event preparation model is solved by a scenario decomposition method, Progressive Hedging (PH), to ease the computational complexity introduced by a large number of scenarios. Furthermore, to show the impact of solar photovoltaic (PV) generation on system resilience, three types of PV systems are considered during a power outage and the resilience improvements with different PV penetration levels are compared. Numerical results from simulations on a large-scale (more than 10,000 nodes) distribution feeder have been used to validate the effectiveness and scalability of the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Probability Density Function Control of Frequency Fluctuations in Renewable-Rich Power Systems

The stochastic nature of renewable energy sources (RESs) necessitates treating power system frequency response as a random process with a nonstationary probability density function (PDF). Here, based upon the stochastic distribution control theory originated by the second author, this paper proposes a novel stochastic controller to improve the frequency PDF in power grids when integrating a large amount of RESs, thereby minimizing the effects of uncertainties and enhancing overall system stability. The key idea is to manipulate the controllable power generation resources so that the frequency PDF is make to follow a target PDF by using the stochastic distribution control theory originated by the second author. The proposed method can easily be plugged into existing automatic generation controls for multi-area transmission grids. The proposed method is validated via a modified Kundar's two area system and 240-bus Western Electricity Coordinating Council systems. The simulation results show that the proposed control shapes the frequency PDF narrower and sharper, leading to a notable improvement toward minimizing the effects of randomness and uncertainty during grid operation.

frequency↗

DOE OSTI2024

The Transient Multi-Level method for Monte Carlo reactor statics calculations

The Transient Multi-Level (TML) method is applied to a time-dependent Monte Carlo transport solver to offload some of the computational burden of the expensive Monte Carlo solve to lower-order Coarse Mesh Finite Difference (CMFD) and Exact Point Kinetics Equations (EPKE) solvers via factorization of the neutron flux at the transport and CMFD levels using the Predictor Corrector Quasi-Static Method (PCQM). The Monte Carlo transient is solved by a modified fission source iteration scheme that introduces a single transient source bank. The method is implemented in the production-level Monte Carlo code, Shift, and verified with prescribed reactivity ramps from the two-dimensional version of the C5G7-TD reactor benchmark. The results show that, as compared to other quasi-static methods, the TML reduces the stochastic noise inherent to the transient Monte Carlo solver by factors of ~2 to 6 for various norm comparisons of the reactor power amplitude. Finally, the TML additionally reduces the number of Monte Carlo evaluations needed to simulate the transient, leading to roughly an order of magnitude improvement in CPU time relative to the standard PCQM for the problems tested.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

Extending the computational reach of a superconducting qutrit processor

Quantum computing with qudits is an emerging approach that exploits a larger, more connected computational space, providing advantages for many applications, including quantum simulation and quantum error correction. Nonetheless, qudits are typically afflicted by more complex errors and suffer greater noise sensitivity which renders their scaling difficult. In this work, we introduce techniques to tailor arbitrary qudit Markovian noise to stochastic Weyl–Heisenberg channels and mitigate noise that commutes with our Clifford and universal two-qudit gate in generic qudit circuits. We experimentally demonstrate these methods on a superconducting transmon qutrit processor, and benchmark their effectiveness for multipartite qutrit entanglement and random circuit sampling, obtaining up to 3× improvement in our results. To the best of our knowledge, this constitutes the first-ever error mitigation experiment performed on qutrits. Our work shows that despite the intrinsic complexity of manipulating higher-dimensional quantum systems, noise tailoring and error mitigation can significantly extend the computational reach of today’s qudit processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Benchmark for Fuel Shuffling and Depletion for Pebble-Bed Reactors

Pebble bed reactors have specific operational characteristics when their fuel-cycle and fueling operations are considered. They are specifically distinguished by other type of nuclear reactor designs by their online fuel recycling scheme, where the fuel elements that have not yet reached discharge burnup can be reloaded and recycled continuously during normal operation. The fuel in a pebble bed reactor is not stationary and stochastically moves through the core once or several times during its lifetime, which allows them to operate without requiring a large excess reactivity hold for the burnup. However, this characteristic of pebble bed reactors introduces challenges in simulation, as each pebble can take many different trajectories through the core, its composition depends on the details of the irradiation history that is unique to its aggregated path through the core. For predicting the safety performance characteristics, such as source term, maximum fuel temperatures and fuel failure rates, etc., it is important to accurately incorporate the movement of pebbles through the core during their lifetime in a multi-physics simulation together with other phenomena. The equilibrium core analysis for pebble bed reactors are performed with multi-physics tools including fuel depletion in a multi pass reload coupled to the fuel movement. Currently, there are only a few legacy multi-physics simulation tools that can implement the pebble flow characteristics and perform equilibrium core analysis for pebble bed reactors. However, there are development efforts on-going under Department of Energy's Nuclear Energy Advanced Modelling and Simulation program and also in private industry for including these capabilities into their modelling and simulation tools. Any new development in the modelling and simulation tools needs to be validated by using tools such as experiments, analytical solutions or code-to-code benchmarks. In this work, a code-to-code benchmark for the equilibrium core analysis capability of pebble bed reactors was developed. Multiple cases were identified to capture different fuel cycle strategies that can be used in PBRs. The results of each case are presented in terms of overall equilibrium core characteristics: the discharge burnup; spatial burnup distribution; spatial isotopic distributions; axial and radial neutron flux distributions and power history of fuel elements per pass through the core for both a prototypical pebble bed High Temperature Gas-cooled Reactor and a prototypical pebble bed Fluoride-salt cooled High temperature Reactor.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Understanding and Controlling Photoexcited Molecules in Complex Environments (Final Technical Report)

Predicting the outcome of a photochemical reaction is complicated by factors outside the scope of tradition theoretical chemistry. On such small scales, fluctuations of the environment render outcomes stochastic, nonadiabatic dynamics blur the separation between nuclear and electronic motion, and ultrafast relaxation renders typical assumptions of equilibrium inappropriate. This project aimed to elucidate and control nonadiabatic molecular dynamics in condensed phases. We developed accurate, efficient simulation tools to study irreversible molecular processes computational across a range of scales. We applied these methodological advances to study electron transfer under exotic conditions where spin and topology opened new pathways for reactivity. We also brought these ideas to bare on light harvesting systems, where energy and charge transport are coupled, and where long lifetimes can be deleterious to function. These advances helped to establish general principles for chemical efficiency and guide the design of nanoscale energy materials, molecular machines, and related technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Operator learning for predicting multiscale bubble growth dynamics

We report simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming “hand-shaking” interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh–Plesset (R–P) equation at the macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R–P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Efficient Ensemble-Based Stochastic Gradient Methods for Optimization Under Geological Uncertainty

Ensemble-based stochastic gradient methods, such as the ensemble optimization (EnOpt) method, the simplex gradient (SG) method, and the stochastic simplex approximate gradient (StoSAG) method, approximate the gradient of an objective function using an ensemble of perturbed control vectors. These methods are increasingly used in solving reservoir optimization problems because they are not only easy to parallelize and couple with any simulator but also computationally more efficient than the conventional finite-difference method for gradient calculations. In this work, we show that EnOpt may fail to achieve sufficient improvement of the objective function when the differences between the objective function values of perturbed control variables and their ensemble mean are large. On the basis of the comparison of EnOpt and SG, we propose a hybrid gradient of EnOpt and SG to save on the computational cost of SG. We also suggest practical ways to reduce the computational cost of EnOpt and StoSAG by approximating the objective function values of unperturbed control variables using the values of perturbed ones. We first demonstrate the performance of our improved ensemble schemes using a benchmark problem. Results show that the proposed gradients saved about 30–50% of the computational cost of the same optimization by using EnOpt, SG, and StoSAG. As a real application, we consider pressure management in carbon storage reservoirs, for which brine extraction wells need to be optimally placed to reduce reservoir pressure buildup while maximizing the net present value. Results show that our improved schemes reduce the computational cost significantly.

58 GEOSCIENCES↗

DOE OSTI2026

Scalable Generation of High-fidelity Synthetic Population Ensembles

Used within social simulations, synthetic population ensembles enable uncertainty quantification (UQ) methods for obtaining more robust model inference and prediction. A synthetic population ensemble is a series of plausible virtual reconstructions of an area’s population at the granularity of people and residences, generated stochastically to preserve privacy of the source population survey’s respondents. In this paper, we demonstrate the production of large synthetic population ensembles for the U.S. via Oak Ridge National Laboratory’s UrbanPop framework to support modeling of high spatial resolution energy affordability metrics from nationwide social surveys in collaboration with the fusionACS project. The study involves two scenarios: creating ensembles for (1) 17 U.S. metropolitan areas in 2019 and (2) full U.S. Census Divisions in 2023, with each scenario consisting of 41 population instances (a base realization and 40 replicates). To accomplish this task at scale, we configured an integrated system within a research cloud, comprised of virtual containerizations, GPU-enhanced functionality, and orchestrated deployments of UrbanPop’s maturing Likeness Python ecosystem. Results demonstrate we maintained high-fidelity approximations of residential totals by areas of interest and the demographic characteristics of neighborhoods while reducing manual workflow burdens. Finally, we discuss plans to fine-tune and further develop our automated workflows for truly distributed job orchestration to increase computational efficiency, as well as provide an outlook for broadening applications of the ensembles.

Cluster computing↗

DOE OSTI2023

Parameterization and Explicit Modeling of Cloud Microphysics: Approaches, Challenges, and Future Directions

Cloud microphysical processes occur at the smallest end of scales among cloud-related processes and thus must be parameterized not only in large-scale global circulation models (GCMs) but also in various higher-resolution limited-area models such as cloud-resolving models (CRMs) and large-eddy simulation (LES) models. Instead of giving a comprehensive review of existing microphysical parameterizations that have been developed over the years, this study concentrates purposely on several topics that we believe are understudied but hold great potential for further advancing bulk microphysics parameterizations: multi-moment bulk microphysics parameterizations and the role of the spectral shape of hydrometeor size distributions; discrete vs “continuous” representation of hydrometeor types; turbulence-microphysics interactions including turbulent entrainment-mixing processes and stochastic condensation; theoretical foundations for the mathematical expressions used to describe hydrometeor size distributions and hydrometeor morphology; and approaches for developing bulk microphysics parameterizations. Also presented are the spectral bin scheme and particle-based scheme (especially, super-droplet method) for representing explicit microphysics. Their advantages and disadvantages are elucidated for constructing cloud models with detailed microphysics that are essential to developing processes understanding and bulk microphysics parameterizations. Particle-resolved direct numerical simulation (DNS) models are described as an emerging technique to investigate turbulence-microphysics interactions at the most fundamental level by tracking individual particles and resolving the smallest turbulent eddies in turbulent clouds. Outstanding challenges and future research directions are explored as well.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

A Non-Cooperative Game-Based Distributed Beam Scheduling Framework for 5G Millimeter-Wave Cellular Networks

Here, this paper studies the problem of distributed beam scheduling for 5G millimeter-Wave (mm-Wave) cellular networks where base stations (BSs) belonging to different operators share the same spectrum without centralized coordination among them. Our goal is to design efficient distributed scheduling algorithms to maximize the network utility, which is a function of the achieved throughput by the user equipment (UEs), subject to the average and instantaneous power consumption constraints of the BSs. We propose a Media Access Control (MAC) and a power allocation/adaptation mechanism utilizing the Lyapunov stochastic optimization framework and non-cooperative games. In particular, we first decompose the original utility maximization problem into two sub-optimization problems for each time frame, which are a convex optimization problem and a non-convex optimization problem, respectively. By formulating the distributed scheduling problem as a non-cooperative game where each BS is a player attempting to optimize its own utility, we provide a distributed solution to the non-convex sub-optimization problem via finding the Nash Equilibrium (NE) of the game whose weights are determined optimally by the Lyapunov optimization framework. Finally, we conduct simulation under various network settings to show the effectiveness of the proposed game-based beam scheduling algorithm in comparison to that of several reference schemes.

42 ENGINEERING↗

DOE OSTI2021

Hybrid Simulation Framework

HYBRID is a modeling toolset to assess the economic viability of Nuclear-Renewable Integrated Energy Systems (N-R IES). The frameworks enabling this toolset are INL’s RAVEN, its CashFlow plugin and the Modelica language. The toolset includes sample RAVEN workflows performing economic assessments. These workflows consist of: generation of stochastic time series and application of probabilistic analysis and optimization algorithms (RAVEN); a library of Modelica models representing the physical behavior of N-R IES; and the CashFlow plugin mapping physical performance to economic performance. The toolset allows assembling existing and new models such as nuclear reactors, renewable energy sources, energy storage, gas turbines, industrial processes, etc. into an N-R IES. The toolset workflows evaluate the dynamics of the N-R IES responding to stochastic conditions (electricity demand, price, etc.) and optimize the dispatch economics as well as N-R IES capacity planning.

Epiney, Aaron↗

DOE OSTI2021

Space-Time Reduced-Order Modeling for Uncertainty Quantification

This work focuses on the space-time reduced-order modeling (ROM) method for solving large-scale uncertainty quantification (UQ) problems with multiple random coefficients. In contrast with the traditional space ROM approach, which performs dimension reduction in the spatial dimension, the space-time ROM approach performs dimension reduction on both the spatial and temporal domains, and thus enables accurate approximate solutions at a low cost. We incorporate the space-time ROM strategy with various classical stochastic UQ propagation methods such as stochastic Galerkin and Monte Carlo. Numerical results demonstrate that our methodology has significant computational advantages compared to state-of-the-art ROM approaches. By testing the approximation errors, we show that there is no obvious loss of simulation accuracy for space-time ROM given its high computational efficiency.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Latent Stochastic Differential Equations for Modeling Quasar Variability and Inferring Black Hole Properties

Quasars are bright and unobscured active galactic nuclei (AGN) thought to be powered by the accretion of matter around supermassive black holes at the centers of galaxies. The temporal variability of a quasar’s brightness contains valuable information about its physical properties. The UV/optical variability is thought to be a stochastic process, often represented as a damped random walk described by a stochastic differential equation (SDE). Upcoming wide-field telescopes such as the Rubin Observatory Legacy Survey of Space and Time (LSST) are expected to observe tens of millions of AGN in multiple filters over a ten year period, so there is a need for efficient and automated modeling techniques that can handle the large volume of data. Latent SDEs are machine learning models well suited for modeling quasar variability, as they can explicitly capture the underlying stochastic dynamics. In this work, we adapt latent SDEs to jointly reconstruct multivariate quasar light curves and infer their physical properties such as the black hole mass, inclination angle, and temperature slope. Our model is trained on realistic simulations of LSST ten year quasar light curves, and we demonstrate its ability to reconstruct quasar light curves even in the presence of long seasonal gaps and irregular sampling across different bands, outperforming a multioutput Gaussian process regression baseline. Our method has the potential to provide a deeper understanding of the physical properties of quasars and is applicable to a wide range of other multivariate time series with missing data and irregular sampling.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

FORCE-DISPATCHES Integration - Initial Demonstration

Integrated energy systems (IES) combine, in mutually beneficial ways, power from variable renewable energy sources and nuclear power plants (NPP) to improve economic viability under uncertain market and weather conditions. The open-source Framework for Optimization of Resources and Economics (FORCE) tool suite, developed at Idaho National Laboratory (INL), has enabled comprehensive modeling and simulation of IES. The capabilities within FORCE include grid portfolio optimization through the Holistic Energy Resource Optimization Network (HERON) and the transient process model analysis library HYBRID, among others. Continuous efforts and investments from the IES programs have been made to expand and improve the versatility of the FORCE toolset in fiscal year 2022. Code-coupling and cross-tool communication have been important methods for improving this versatility. This report focuses on an additional workflow in the HERON tool for capacity and dispatch stochastic optimization through integration with the external tool Design Integration and Synthesis Platform to Advance Tightly Coupled Hybrid Energy Systems (DISPATCHES). DISPATCHES was primarily developed by the National Energy Technology Laboratory, in collaboration with other national laboratories, which included INL, universities, and industry partners. It is coupled to a library of algebraic models for specific plant components, and to a framework for stochastic optimization different from that provided in the current Risk Analysis Virtual Environment (RAVEN)-running-RAVEN algorithm in HERON. HERON currently conducts stochastic optimization via an outer-inner loop: it optimizes over variable capacity on the outer loop, and at each step within the capacity parameter space, conducts an inner optimization over scenarios (of market signals, demand, and/or weather patterns) and hourly dispatch throughout a user-specified number of years. On the other hand, DISPATCHES conducts stochastic optimization via an “all-at-once” strategy in which capacity variables are optimized at the same level as dispatch variables, as all scenarios are considered at once. The latter method works especially well for projects of limited size and project length, as the necessary computational power and memory increases with the number of variables and scenarios. The new capability to use the DISPATCHES workflow in HERON enhances standalone simulations by leveraging FORCE tools—namely, the economic metrics from the Tool for Economic Analysis (TEAL) and reduced-order model (ROM) sampling from RAVEN. The initial demonstration of the DISPATCHES workflow simulates an existing nuclear-case flowsheet within the DISPATCHES repository—this models a NPP with a secondary revenue stream for hydrogen production. Electrical output from the plant is converted to hydrogen via a proton-exchange membrane (PEM) electrolyzer, hydrogen tanks are used for storage, and an additional turbine is added for hydrogen combustion. Continued work regarding this FORCE-DISPATCHES integration will include automatic generation of DISPATCHES models from HERON inputs, offering analysts the option of using either the RAVEN-runsRAVEN or DISPATCHES workflow to solve technoeconomic optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Uncertainty Quantification for Multiphase Computational Fluid Dynamics Closure Relations with a Physics-Informed Bayesian Approach

Multiphase Computational Fluid Dynamics (MCFD) based on the two-fluid model is considered a promising tool to model complex two-phase flow systems. MCFD simulation can predict local flow features without resolving interfacial information. As a result, the MCFD solver relies on closure relations to describe the interaction between the two phases. Those empirical or semi-mechanistic closure relations constitute a major source of uncertainty for MCFD predictions. In this paper, we leverage a physics-informed uncertainty quantification (UQ) approach to inversely quantify the closure relations’ model form uncertainty in a physically consistent manner. This proposed approach considers the model form uncertainty terms as stochastic fields that are additive to the closure relation outputs. Combining dimensionality reduction and Gaussian processes, the posterior distribution of the stochastic fields can be effectively quantified within the Bayesian framework with the support of experimental measurements. As this UQ approach is fully integrated into the MCFD solving process, the physical constraints of the system can be naturally preserved in the UQ results. Here, in a case study of adiabatic bubbly flow, we demonstrate that this UQ approach can quantify the model form uncertainty of the MCFD interfacial force closure relations, thus effectively improving the simulation results with relatively sparse data support.

42 ENGINEERING↗

DOE OSTI2020

MHD stability and disruptions in the SPARC tokamak

SPARC is being designed to operate with a normalized beta of $β_N$ = 1.0, a normalized density of $n_G$ = 0.37 and a safety factor of $q_{95}$ ≈ 3.4, providing a comfortable margin to their respective disruption limits. Further, a low beta poloidal $β_p$ = 0.19 at the safety factor $\textit{q}$ = 2 surface reduces the drive for neoclassical tearing modes, which together with a frozen-in classically stable current profile might allow access to a robustly tearing-free operating space. Although the inherent stability is expected to reduce the frequency of disruptions, the disruption loading is comparable to and in some cases higher than that of ITER. The machine is being designed to withstand the predicted unmitigated axisymmetric halo current forces up to 50 MN and similarly large loads from eddy currents forced to flow poloidally in the vacuum vessel. Runaway electron (RE) simulations using GO+CODE show high flattop-to-RE current conversions in the absence of seed losses, although NIMROD modelling predicts losses of ~80 %; self-consistent modelling is ongoing. A passive RE mitigation coil designed to drive stochastic RE losses is being considered and COMSOL modelling predicts peak normalized fields at the plasma of order 10 –2 that rises linearly with a change in the plasma current. Massive material injection is planned to reduce the disruption loading. A data-driven approach to predict an oncoming disruption and trigger mitigation is discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗