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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Low-Order Preconditioning for the High-Order Finite Element de Rham Complex

Here, we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in H 1 , H(curl), and H(div) and is based on combining a low-order discretization posed on a refined mesh with a high-order basis for Nédélec and Raviart–Thomas elements that makes use of the concept of polynomial histopolation (polynomial fitting using prescribed mean values over certain regions). This spectral equivalence, coupled with algebraic multigrid methods constructed using the low-order discretization, results in highly scalable matrix-free preconditioners for high-order finite element problems in the full de Rham complex. Additionally, a new lowest-order (piecewise constant) preconditioner is developed for high-order interior penalty discontinuous Galerkin (DG) discretizations, for which spectral equivalence results and convergence proofs for algebraic multigrid methods are provided. In all cases, the spectral equivalence results are independent of polynomial degree and mesh size; for DG methods, they are also independent of the penalty parameter. These new solvers are flexible and easy to use; any “black-box” preconditioner for low-order problems can be used to create an effective and efficient preconditioner for the corresponding high-order problem. A number of numerical experiments are presented, based on an implementation in the finite element library MFEM. A range of challenging three-dimensional problems are used to corroborate the theoretical properties and demonstrate the flexibility and scalability of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Alternative Approaches to Traditional Net Energy Metering

Most jurisdictions in the United States originally implemented net energy metering (NEM) tariffs to support the deployment and interconnection of distributed generation (DG) resources (e.g., rooftop solar photovoltaic systems). Since then, NEM has proven effective in promoting adoption of DG resources. Recently, due to concerns about sufficient recovery of utilities’ revenue requirements and cost-shifting, there is increasing interest in—or statutory requirements to pursue—alternative compensation approaches, especially in U.S. states and territories with robust growth in distributed solar. Recent increases in other forms of distributed energy resources (DERs) that can potentially send power to the distribution grid (e.g., distributed battery energy storage system (BESS)) are further driving compensation reforms. This brief provides an overview of design elements associated with alternative approaches to traditional NEM, summarizes common arguments for and against them, and identifies implementation issues that utilities may need to address. Although this brief may be most useful in jurisdictions that are interested in or required to move beyond NEM, it is also applicable to those jurisdictions that have already done so—and are looking to further implement reforms to their existing compensation mechanisms. In the broadest sense, there are three primary tariff-related components when interconnecting a DER onto the local utility’s distribution system (adapted from Zinaman et al., 2017): 1. Metering and Billing Arrangements: How utilities measure and bill electricity consumption and production. 2. DER Export Tariff Design: The structure under which utilities compensate customers for electricity they export to the grid. 3. Consumption Tariff Design: The structure under which customers pay for electricity they consume from the grid. When implementing changes to any of these primary tariff-related components, there are likely implications for a utility’s metering system, billing system, and other technology systems. Where applicable, this brief explicitly identifies such implementation challenges.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Towards 50 Year Lifetime PV Modules: Double Glass vs. Glass/Backsheet

This award aims to increase the lifetime of c-Si modules by lowering the power degradation rate to the goal of 0.2 %/year, while also increasing the harvested irradiance per module using bifacial cells to achieve the 2030 SunShot goal of $0.03/kWh. Increasing the durability and lifetime of modules requires improved module packaging material choices and module architectures to exploit new cell improvements. Bifacial PERC cells (with backside aluminum fingers) are becoming a primary PV technology due to their decreased rear surface recombination and increased light absorption compared to traditional monofacial Al-BSF cells. Bifacial modules with double glass architectures have been deployed to capture the rear-side irradiance thereby increasing the light captured. The choice of a double glass (DG) or glass/backsheet (GB) module leads to two very different chemical (e.g., O 2 , H 2 O) and mechanical environments (e.g., mechanical stress levels) inside the PV module that impact the cell’s operational conditions. The recipient will fabricate 4-cell DG and GB minimodules with various module architectures or constructions (mono- & bifacial cells, transparent & white encapsulants), and conduct stepwise accelerated exposures and characterization.

14 SOLAR ENERGY↗
DOE OSTI2020

State-Constrained Grid-Forming Inverter Control for Robust Operation of AC Microgrids

The control of grid-forming inverters has become an important problem to achieve high efficiency, reliability, and resilience of the future power grid. The distributed control that utilizes a sparse communication network has been proposed for AC microgrids, in which each DG only has access to the information of a small number of its neighboring DGs, reducing the computational complexity and improving the resiliency to faults and unknown parameters. However, these approaches have not provided a clear analysis of the coupling between active/reactive power injections and the voltage magnitude/frequency or a distributed updating law with a solid theoretical foundation. Additionally, in the existing approaches, tracking the references from the secondary control may violate operational constraints.

Xu, Ying↗
DOE OSTI2022

Forming Interphase Microgrids in Distribution Systems Using Cooperative Inverters

Interphase-microgrids formed by three islanded single-phase feeders in distribution systems are proposed in this paper. Loss of utility caused by natural and human-made disasters may isolate each residential subdivision from the utility. In this case, the household loads are supplied by distributed generation (DG) units which may not be enough to meet the load demand. This can lead to deviations in voltage and frequency, and the deviations may vary for each phase. The proposed solution is to form an interphase-microgrid by seamlessly interconnecting the islanded single-phase feeders. This interphase-microgrid can effectively balance the load demands and DG generation in distribution systems after losing the utility supply. This paper presents different case studies to demonstrate the viability of forming interphase-microgrids for residential distribution systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

An Accurate SUPG-stabilized Continuous Galerkin Discretization for Anisotropic Heat Flux in Magnetic Confinement Fusion

We present a novel spatial discretization for the anisotropic heat conduction equation, aimed at improved accuracy at the high levels of anisotropy seen in a magnetized plasma, for example, for magnetic confinement fusion. The new discretization is based on a mixed formulation, introducing a form of the directional derivative along the magnetic field as an auxiliary variable and discretizing both the temperature and auxiliary fields in a continuous Galerkin (CG) space. Both the temperature and auxiliary variable equations are stabilized using the streamline upwind Petrov–Galerkin (SUPG) method, ensuring a better representation of the directional derivatives and therefore an overall more accurate solution. This approach can be seen as the CG-based version of our previous work (Wimmer, Southworth, Gregory, Tang, 2024), where we considered a mixed discontinuous Galerkin (DG) spatial discretization including DG-upwind stabilization. We prove consistency of the novel discretization, and demonstrate its improved accuracy over existing CG-based methods in test cases relevant to magnetic confinement fusion. This includes a long-run tokamak equilibrium sustainment scenario, demonstrating a 35% and 32% spurious heat loss for existing primal and mixed CG-based formulations versus 4% for our novel SUPG-stabilized discretization.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Equity-driven Planning of Distributed Solar PV using Optimal Transport

Typically, distribution system planning processes do not explicitly incorporate energy equity considerations, such as identifying consumers most affected by energy costs and determining how investments in the distribution system can address existing energy burden imbalances. This paper proposes a novel optimal transport (OT)-based method to improve the energy burden distribution of consumers. The approach involves the strategic siting and sizing of solar PV in order to assist customers with high energy burden and improve the overall energy burden distribution of the community. The desired energy burden distribution is defined using the equal distribution equivalent (EDE) concept. The OT-based method is then used to estimate the distributed solar PV capacity to be installed at various locations and the tariffs to be adjusted, all while improving the energy burden distribution and providing valuable insights into distributed generation (DG) planning. The results on IEEE 37 bus test system demonstrate how DG planning, considering EDE and OT, can help reduce the energy burden of low-income consumers. Additionally, the approach also reveals optimal tariff adjustments needed to ensure revenue neutrality for distribution utilities.

Optimal transport, equal distribution equivalent, ↗
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

MPC-Based Local Voltage Control Strategy of DGs in Active Distribution Networks

The increasing penetration of distributed generators (DGs) exacerbates the voltage violations in active distribution networks (ADNs). The commonly used centralized voltage control may aggravate the burden of computation and communication. Local voltage control can realize fast response to frequent voltage fluctuations. However, effective local control for DGs still needs to be further investigated. In this paper, a model predictive control (MPC)-based local voltage control strategy of DGs is proposed to cope with voltage violation problems and enhance the adaptation to the DG volatility. DGs are regulated with local Q-V control curves to respond to voltage fluctuations rapidly. Based on the dynamic network partition, a unified control curve for DGs is set in the same area to realize efficient operation. To further improve the performance of voltage control, the parameter tuning of control curves is regularly conducted based on decentralized inter-area coordination with the rolling of the control horizon. Finally, case study is verified on the modified IEEE 33-node distribution system. The proposed local control strategy of DGs can effectively improve the voltage profile and reduce power losses of the whole network without high computation and communication burden.

active distribution network (ADN)↗
DOE OSTI2022

Evaluation of Adaptive Volt-VAR to Mitigate PV Impacts [Slides]

Distributed generation (DG) sources like photovoltaic (PV) systems with advanced inverters are able to perform grid-support functions, like autonomous Volt-VAR that attempts to mitigate voltage issues by injecting or consuming reactive power. However, the Volt-VAR function operates with VAR priority, meaning real power may be curtailed to provide additional reactive power support. Since some locations on the grid may be more prone to higher voltages than others, PV systems installed at those locations may be forced to curtail more power, adversely impacting the value of that PV system. Adaptive Volt-VAR (AVV) could be implemented as an alternative, whereby the Volt-VAR reference voltage changes over time, but this functionality has not been well-explored in the literature. In this work, the potential benefits and grid impacts of AVV were investigated using yearlong quasi-static time-series (QSTS) simulations. After testing a variety of allowable AVV settings, we found that even with aggressive settings AVV resulted in <0.01% real power curtailment and significantly reduced the reactive power support required from the PV inverter compared to conventional Volt-VAR but did not provide much mitigation for extreme voltage conditions. The reactive power support provided by AVV was injected to oppose large deviations in voltage (in either direction), indicating that it could be useful for other applications like reducing voltage flicker or minimizing interactions with other voltage regulating devices.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Semi-Lagrangian nodal discontinuous Galerkin method for the BGK model

In this work, we propose a semi-Lagrangian (SL) nodal discontinuous Galerkin (DG) solver for the BGK equation. The BGK model was introduced by Bhatnagar, Gross, and Krook [1] as a relaxation model for the fundamental Boltzmann equation [5], which describes the kinetic dynamic of rarefied gases with a probability distribution function. The challenges of designing efficient numerical schemes for the Boltzmann equation mainly come from its high dimensionality and complicated nonlinear collision operator. The BGK model gains interests since it has much lower computational cost, due to the relatively simple structure of the relaxation operator in replacement of the collision operator, while simultaneously preserving several important physical properties, such as macroscopic quantities and dissipation of entropy.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An IIPG-Based Finite Element Framework in MOOSE for Modeling Fiber Reinforced Composite Failure Governed by Extrinsic Cohesive Laws

Many material and structure failures are initiated at the interface between two distinctive materials, such as the debonding of interfaces of matrix/fiber of composites or bulk matrix/inclusion in metals at micro-scales. Accurate and robust modeling of these interface failures is critical to the design of novel material and structure with improved functionality. This paper presents a robust implementation of a discontinuous Galerkin finite element method in MOOSE based on the Incomplete Interior Penalty Galerkin scheme for modeling material interface behavior. This DG-based interface method naturally accommodates important extrinsic cohesive zone material models and is capable of modeling the failures of material interfaces across which material properties are highly distinctive. We demonstrate a good performance of the proposed method using single fiber and multiple fiber debonding problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Droop-Free Distributed Control for AC Microgrids

In this chapter, droop-free distributed control for AC microgrids is discussed. The hierarchical structure of microgrid control is first introduced. Secondary level controls both with and without droop are discussed. Then two droop-free distributed controls are presented: one achieves average voltage regulation and perfect power sharing, and the other one achieves average voltage regulation, voltage variance regulation, and relaxed reactive power sharing. For the latter droop-free control, the relaxed reactive power sharing is achieved through a special distributed generator (DG) that will not participate in reactive power sharing.

Mohiuddin, Sheik Mohammad↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗
DOE OSTI2024

Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A discontinuous Galerkin spectral element method for compressible reacting flows

High-order methods have recently been shown to be an effective tool for high-fidelity flow computations like direct numerical simulations and large-eddy simulations because of their strong balance between accuracy and computational cost. In this work, a high-order discontinuous Galerkin spectral element method (DGSEM) is developed to solve the chemically reacting Navier-Stokes equations. To handle the disparate length and time scales associated with these equations, we develop a novel method which combines the spectral accuracy of the SEM with the flexibility of the DG approach. The framework, implemented in the spectral element code Nek5000, is well suited to capture turbulence in smooth regions of the flow, while maintaining numerical stability in the presence of shocks. An entropy-residual based artificial viscosity is added to smooth shocked regions of flow, and a positivity-preserving limiter is implemented to suppress non-physical oscillations. These enhancements support the numerical stability of the hydrodynamic sub-step, which is decoupled from the chemistry integration through a second-order operator splitting method. Here, a series of smooth and discontinuous validation cases are presented in increasing physical and computational complexity for both inviscid and viscous flows. In particular, simulations of canonical one-dimensional and two-dimensional detonations are performed, and the high-order numerical results are validated against available literature data. Additional validation studies are carried out for classical three-dimensional numerical simulations of incompressible and compressible turbulent flows.

Compressible reacting flows↗
DOE OSTI2025

Direct Discontinuous Galerkin methods for the reacting multi-component flow equations

The Direct Discontinuous Galerkin (DDG (Liu and Yan, 2008)) method and a counterpart with Interface Correction (DDGIC (Danis and Yan, 2022)) are extended to compute diffusion terms that arise when solving the compressible multi-component flow equations in thermochemical nonequilibrium. Thermodynamic properties, transport properties, chemical reaction rates, and energy exchange terms are computed using Mutation++ (Scoggins et al., 2020). The DG method is applied on unstructured grids, where the accuracy and convergence rates can be sensitive to the numerical method chosen for parabolic terms. A method for determining the homogeneity tensor of the flow equations required for DDGIC is shown. The convergence properties of the DDG methods are studied and compared to the Interior Penalty (IP) method. A number of numerical experiments are conducted to assess the accuracy and performance of the method. The numerical results and convergence studies indicate that DDG and DDGIC provide accurate solutions and perform well for general flows in thermochemical nonequilibrium.

Diffusion↗
DOE OSTI2021

MPC-based double-layer real-time conditional cSelf-restoration for interconnected microgrids

In this report, we propose a novel model predictive control(MPC)-based real-time conditional self-restoration energy management system (CSR-EMS) for interconnected microgrids (IMGs) integrated with renewable energy sources (RESs) and energy storage systems (ESSs). Superior to the existing IMG self-restoration methods, the “conditionality” of the proposed CSR-EMS can economically realize self-restoration and grid-assisted restoration during energy deficiency or faults, in both islanded and grid-connected modes. Cost minimization is implemented as the objective function to judge in real-time which restoration mode is economically preferred. The proposed CSR-EMS comprises two layers–the lower layer operates locally to eliminate electricity fluctuations created by RESs and ensure economic effectiveness within an MG, whereas the upper layer oversees the real-time operational status of the IMG system and determines power exchange among microgrids (MGs) during abnormalities. In detail, when a microgrid inside the IMG system experiences an energy deficiency, the CSR-EMS, on an MPC basis, intelligently optimizes power production from each dispatchable distributed generator (DG), ESS, power imported from the main grid, and power exchange among the IMGs to maintain the demand–supply balance, while considering system recovery cost, state of charge (SoC) of ESSs and operation modes of the IMGs (i.e., grid-connected or islanded mode). Simulation results and comparisons with existing IMG self-healing EMSs demonstrate the economic efficacy of the proposed CSR-EMS strategy during normal and abnormal operations, which can be used as an energy control framework for modern power systems with multiple interconnected microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗