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At least 937 records · Page 52

Scenario generation for stochastic optimization problems via the sparse grid method

We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.

97 MATHEMATICS AND COMPUTING↗

Electricity Markets and Long-Duration Energy Storage: A Survey of Grid Services and Revenue Streams

Purpose of Review Long Duration Energy Storage (LDES) is increasingly viewed as a potential resource for providing grid services that enhance the stability and flexibility of electricity systems. While some LDES services are integrated into existing market frameworks, traditional mechanisms may not fully account for their operational characteristics, potentially leading to undervaluation. Within this context, this paper reviews the literature and industry practices to assess potential grid services for LDES, evaluates existing compensation mechanisms, and identifies challenges to full market integration. Recent Findings We first review existing literature and identify key grid services unique to LDES, including enhancing grid resilience during extreme weather events, enabling long-term energy shifting, and providing flexible and firm energy in systems with limited dispatchable resources. Here, we also review how LDES services are compensated in current market frameworks and the challenges associated with the full realization of LDES values. Additionally, we summarize market mechanisms for storage technologies across U.S. wholesale markets. We find that some markets are adjusting incentive structures, such as incorporating storage duration in capacity accreditation, to better align with system needs and LDES contributions to the grid. However, further refinements in capacity remuneration and dispatch timeframes may be needed for more effective realization of LDES value. Summary This review evaluates potential grid services for LDES, examines existing compensation mechanisms for LDES technologies, and identifies gaps between these mechanisms and LDES operational characteristics. The review concludes by outlining potential market enhancements for more effective LDES integration and articulating additional research needs to support its efficient participation in future power systems.

Flexible resources↗

Translating climate change and heating system electrification impacts on building energy use to future greenhouse gas emissions and electric grid capacity requirements in California

Climate change and increased electrification of space and water heating in buildings can significantly affect future electricity demand and hourly demand profiles, which has implications for electric grid greenhouse gas emissions and capacity requirements. We use EnergyPlus to quantify building energy demand under historical and under several climate change projections of 32 kinds of building prototypes in 16 different climate zones of California and imposed these impacts on a year 2050 electric grid configuration by simulation in the Holistic Grid Resource Integration and Deployment (HIGRID) model. We find that climate change only prompted modest increases in grid resource capacity and negligible difference in greenhouse gas emissions since the additional electric load generally occurred during times with available renewable generation. Heating electrification, however, prompted a 30-40% reduction in greenhouse gas emissions but required significant grid resource capacity increases, due to the higher magnitude of load increases and lack of readily available renewable generation during the times when electrified heating loads occurred. Overall, this study translates climate change and electrification impacts to system-wide endpoint impacts on future electric grid configurations and highlights the complexities associated with translating building-level impacts to electric system-wide impacts.

54 ENVIRONMENTAL SCIENCES↗

Non-orthogonal computational grids for studying dislocation motion in phase field approaches

In this work, new non-orthogonal computational grids are implemented into a phase field model called Phase Field Dislocation Dynamics (PFDD). We demonstrate that the new non-orthogonal grid can accommodate multiple slip planes in either the face centered cubic (FCC) or body centered cubic (BCC) crystallographic systems. Here, we show that they avoid numerical errors induced when modeling glide on inclined slip planes in an orthogonal grid. The Gibbs effect that arises in the orthogonal or rotated orthogonal grids is substantially diminished when a non-orthogonal grid is employed. A few test cases demonstrate the effectiveness of using non-orthogonal grids in solving systems with multiple non-planar slip systems.

36 MATERIALS SCIENCE↗

Thermal and electric multidomain dynamic model for integration of power grid distribution with behind-the-meter devices

As renewable energy sources like solar and wind power become more integrated into the grid, coordinated control of behind-the-meter devices is crucial for enhancing grid flexibility and reliability and for meeting cost targets, with standardized models being developed to support this transition. The increasing flexibility and uncertainty of integrated renewable energy grids, along with interactions between various subsystems, make traditional steady-state modeling insufficient to capture transient and dynamic behaviors. Current models (e.g., composite load and battery equivalent models) focus on thermodynamic or electrical characteristics but overlook critical electromechanical interactions. This limits the ability to share performance information for grid services and hampers fast dynamic simulations. In addition, motor stalling is usually triggered by a fault event and attributed to the characteristics of the mechanical torque of the motor, resulting in absorption of a large amount of reactive power during the stalling period. Further, this significant withdrawal of reactive power will deteriorate the dynamic voltage stability of power grids and cause delayed voltage recovery. Therefore, an in-depth modeling of the thermodynamics or mechanical torque is essential to study the impacts of the realistic torque characteristics of those behind-the-meter devices on power system voltage stability. This study developed a dynamic multidomain model for building HVAC systems, such as air-source heat pumps, to simulate their thermal and electrical responses to grid transients. The model can accurately predict power metrics with a mean absolute percentage error of 10%, by validating against with power system computer-aided design performance data. Case studies demonstrate the model capability of capturing the transient response to sudden voltage changes, rapid load fluctuations, and system shutdowns respectively. During a sudden voltage drop (30% for 0.1s), a fully loaded heat pump’s motor speed dropped, continued declining, and shut down after 3.6s, with severe power oscillations and a torque spike. A partially loaded unit experienced temporary oscillations but stabilized. Under higher building loads, compressor speed increased from 64% to 100%, with power and torque rising before stabilizing. In safety-triggered shutdowns, power decreased after minor fluctuations, and torque briefly spiked before dropping to zero.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Propagation of non-Gaussian voltage angle fluctuations in high-voltage power grids

Recent measurements have reported non-Gaussian tails in the distribution of frequency data in electric power grids. Large frequency deviations may induce grid instabilities and it is therefore crucial to understand how noise disturbances with long, non-Gaussian tails propagate. Here, we investigate how fluctuations in power feed-in, characterized by non-zero cumulants of their distribution, propagate through high-voltage power grids. Unlike previous investigations which focused on the white-noise limit, we consider the limit of long noise correlation time, where power feed-in fluctuates over times longer than the inherent dynamical time scales of the grid - the relevant regime for large-scale, high-voltage distribution grids. In this work, we show that in this limit, the skewness and kurtosis of the power feed-in distribution propagate similarly as its variance, independently of the distribution of inertia. Non-Gaussianities from individual sources of noise therefore persist throughout the entire network. This finding is corroborated by numerical results on a realistic model of the synchronous grid of continental Europe.

42 ENGINEERING↗

Coordinated frequency regulation among asynchronous AC grids with an MTDC system

With the increasing penetration level of renewable power, the power systems’ inertias are decreasing. To ensure that the frequency is above the threshold of the under frequency load shedding, one effective way is to share the spinning reserves among asynchronous AC grids through HVDC systems. In this paper, a coordinated frequency regulation scheme that enables spinning reserves sharing is proposed for such hybrid AC/DC grids. This scheme is a communication-free method that consists of the droop control, the inertia emulation control and the frequency safety control. The combined response of the three controls can increase not only the frequency nadir but also the settled frequency of the disturbed grid. In addition, the hysteresis comparators and the power injection limits are adopted in the frequency regulation scheme to reduce the coupling effect among AC grids. Thus, under small and harmless disturbance, the frequency regulation scheme will be inactive; the disturbance in strong AC grids would not affect the weak AC systems. The frequency regulation scheme coordinates well with the automatic generation control of the grids. Furthermore, the feasibility and effectiveness of the proposed frequency regulation scheme are verified through simulation studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗

High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form

High-order accurate upwind approximations for the wave equation in second-order form on overlapping grids are developed. Although upwind schemes are well established for first-order hyperbolic systems, it was only recently shown by Banks and Henshaw how upwinding could be incorporated into the second-order form of the wave equation. This new upwind approach is extended here to solve the time-domain Maxwell's equations in second-order form; schemes of arbitrary order of accuracy are formulated for general curvilinear grids. Taylor time-stepping is used to develop single-step space-time schemes, and the upwind dissipation is incorporated by embedding the exact solution of a local Riemann problem into the discretization. Second-order and fourth-order accurate schemes are implemented for problems in two and three space dimensions, and overlapping grids are used to treat complex geometry and problems with multiple materials. Stability analysis of the upwind-scheme on overlapping grids is performed using normal mode theory. The stability analysis and computations confirm that the upwind scheme remains stable on overlapping grids, including the difficult case of thin boundary grids when the traditional non-dissipative scheme becomes unstable. The accuracy properties of the scheme are carefully evaluated on a series of classical scattering problems for both perfect conductors and dielectric materials in two and three space dimensions. Finally, the upwind scheme is shown to be robust and provide high-order accuracy.

97 MATHEMATICS AND COMPUTING↗

Sparse-grid discontinuous Galerkin methods for the Vlasov–Poisson–Lenard–Bernstein model

Sparse-grid methods have recently gained interest in reducing the computational cost of solving high-dimensional kinetic equations. In this paper, we construct adaptive and hybrid sparse-grid methods for the Vlasov–Poisson–Lenard–Bernstein (VPLB) model. This model has applications to plasma physics and is simulated in two reduced geometries: a 0x3v space homogeneous geometry and a 1x3v slab geometry. Here we use the discontinuous Galerkin (DG) method as a base discretization due to its high-order accuracy and ability to preserve important structural properties of partial differential equations. We utilize a multiwavelet basis expansion to determine the sparse-grid basis and the adaptive mesh criteria. We analyze the proposed sparse-grid methods on a suite of three test problems by computing the savings afforded by sparse-grids in comparison to standard solutions of the DG method. The results are obtained using the adaptive sparse-grid discretization library ASGarD.

97 MATHEMATICS AND COMPUTING↗

Grid-to-rod flow-induced impact study for PWR fuel in reactor

The source for grid-to-rod fretting in a pressurized water nuclear reactor (PWR) is the dynamic contact impact from hydraulic flow-induced fuel assembly vibration. In order to support grid-to-rod fretting wear mitigation research, finite element analysis (FEA) was used to evaluate the hydraulic flow-induced impact intensity between the fuel rods and the spacer grids. Three-dimensional FEA models, with detailed geometries of the dimple and spring of the actual spacer grids along with fuel rods, were developed for flow impact simulation. The grid-to-rod dynamic impact simulation provided insights of the contact phenomena at grid-rod interface. Finally, it is an essential and effective way to evaluate contact forces and provide guidance for simulative bench fretting-impact tests.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Machine learning from RANS and LES to inform coarse grid simulations

Nuclear system thermal hydraulic analysis has historically relied on computationally inexpensive 1D codes. However, such tools are unable to capture multiscale multidimensional effects in large nuclear reactor enclosures. On the other hand, simulations with higher fidelity can be too expensive for such purposes. One of the ways to reduce computational cost is to perform simulations on a coarse grid, which, unfortunately, introduces large discretization errors. In this paper, two high-to-low data-driven approaches are investigated: (1) a coarse grid turbulence model to predict eddy viscosity and (2) correction of errors in coarse grid velocity fields. The approaches aim to reduce grid- and turbulence model-induced errors in coarse grid Reynolds-averaged Navier–Stokes (RANS) simulations. Two sources of high-fidelity data, RANS and large eddy simulations (LES), are explored. To extract the eddy viscosity from the LES data, an inverse optimization problem is solved. However, the LES eddy viscosity is shown to be comparable to the RANS eddy viscosity in terms of error reduction. Therefore, the directly available RANS eddy viscosity was used to develop a coarse grid data-driven turbulence model. Additionally, error correction in velocity is used to reduce the remaining uncertainties and bring the results closer to reality. In conclusion, the performance of the frameworks is demonstrated for a scaled upper plenum of a gas-cooled reactor facility.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Risk Assessment at the Edge: Applying NERC CIP to Aggregated Grid-Edge Resources

Distributed energy resources (DERs) promise to deliver benefits for both utilities and consumers by dynamically interoperating utility systems with customer-owned grid-edge technologies. These small energy-consuming devices are increasingly being aggregated for participation in grid markets, planning and operations. A cyber attack penetrating the control system of aggregated DERs could negatively impact the operation of the grid. In the worst case, the power grid could be severely damaged and physical safety compromised. In this paper we analyze cybersecurity risks associated with the aggregation of DERs and develop an approach to mitigating that risk. The approaches to both cyber risk analysis and mitigation were developed during a recent research project that serves as an example of how the approaches could be applied. However, both the risk analysis and mitigation are applicable to the broader domain of all DERs. An important conclusion is that the successful cyber compromise of aggregated DERs could have a significant impact on the bulk power system. This is the case even if each individual DER falls below the threshold of compliance with bulk-grid cybersecurity standards. For this reason, we specifically investigate how National Electricity Reliability Corporation's Critical Infrastructure Protection requirements could flow down to interactions between DER aggregators and the DERs themselves in order to protect the grid from these bulk-scale cyber attack impacts.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Investigating grid-to-rod fretting wear of nuclear fuel claddings using a unique autoclave fretting rig

Fuel rods in a pressurized water nuclear reactor (PWR) experience coolant flow-induced relative motion against the grid support features, a phenomenon called grid-to-rod fretting (GTRF), which may cause progressive fretting wear damage. Wear-through of the cladding on fuel rods will leak the radioactive fuel into the coolant loop to significantly increase the radiation level in PWR primary loop and often trigger expensive Post Irradiation Examination. In this work, a unique autoclave fretting test rig was designed and fabricated to allow studying GTRF using actual cladding and grid materials. Water temperature was up to 220 °C, which was designed to mimic the environment in an industry full-assembly reactor core simulator. The contact load (0.1–1 N), oscillation frequency (20–30 Hz) and stroke (50–150 µm), and work rate (1–3 mW) were defined based on simulations of GTRF in an actual reactor. Using this autoclave GTRF rig, tests were conducted to learn the effect of water temperature and to investigate the wear behavior of different cladding-grid material combinations currently used in actual PWRs, including Zr alloy claddings without and with pre-oxidation against Zr alloy and Inconel grids. Higher water temperature evidently increased the cladding wear, and pre-oxidation of the Zr alloy and/or using the Inconel grid effectively reduced the wear rate. In conclusion, results were correlated with the data of a full-size industry reactor core simulator in terms of both wear rate and wear scar morphology.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Low-Z FIB Grids for Reducing Spurious Fluorescence and X-ray Overlaps

Low-Z nanocrystalline diamond (NCD) grids have been developed to reduce spurious fluorescence and avoid X-ray peak overlaps or interferences between the specimen and conventional metal grids. Here, the low-Z NCD grids are non-toxic and safe to handle, conductive, can be subjected to high-temperature heating experiments, and may be used for analytical work in lieu of metal grids. Both a half-grid geometry, which can be used for any lift-out method, or a full-grid geometry that can be used for ex situ lift-out or thin film analyses, can be fabricated and used for experiments.

47 OTHER INSTRUMENTATION↗

Separating Physics and Dynamics Grids for Improved Computational Efficiency in Spectral Element Earth System Models

Previous studies have shown that atmospheric models with a spectral element grid can benefit from putting physics calculations on a relatively coarse finite volume grid. Here we demonstrate an alternative high-order, element-based mapping approach used to implement a quasi-equal-area, finite volume physics grid in E3SM. Unlike similar methods, the new method in E3SM requires topology data purely local to each spectral element, which trivially allows for regional mesh refinement. Simulations with physics grids defined by 2 × 2, 3 × 3, and 4 × 4 divisions of each element are shown to verify that the alternative physics grid does not qualitatively alter the model solution. The model performance is substantially affected by the reduction of physics columns when using the 2 × 2 grid, which can increase the throughput of physics calculations by roughly 60%–120% depending on whether the computational resources are configured to maximize throughput or efficiency. A pair of regionally refined cases are also shown to highlight the refinement capability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Geospatial mapping of distribution grid with machine learning and publicly-accessible multi-modal data

Abstract Detailed and location-aware distribution grid information is a prerequisite for various power system applications such as renewable energy integration, wildfire risk assessment, and infrastructure planning. However, a generalizable and scalable approach to obtain such information is still lacking. In this work, we develop a machine-learning-based framework to map both overhead and underground distribution grids using widely-available multi-modal data including street view images, road networks, and building maps. Benchmarked against the utility-owned distribution grid map in California, our framework achieves > 80% precision and recall on average in the geospatial mapping of grids. The framework developed with the California data can be transferred to Sub-Saharan Africa and maintain the same level of precision without fine-tuning, demonstrating its generalizability. Furthermore, our framework achieves a R 2 of 0.63 in measuring the fraction of underground power lines at the aggregate level for estimating grid exposure to wildfires. We offer the framework as an open tool for mapping and analyzing distribution grids solely based on publicly-accessible data to support the construction and maintenance of reliable and clean energy systems around the world.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Numerical study of the plasma wall-bias effect on the ion flux through acceleration grid hole

In the extraction of ion beams from a source plasma through a grid acceleration structure, one of the key improvement issues is the fluence of the ion flux. Theoretical research has usually been focused on the structure of the grid system and the distribution of the electrostatic voltages over the grid layers. In the present work, using a self-consistent computer simulation between the plasma source, sheath potential, and the grid system, the effect of the source-wall biasing on the fluence of the ion flux through a three-grid acceleration system has been examined. It is found that a strongly positive wall-biasing can significantly enhance the ion flux by improving the shape of the plasma sheath potential meniscus at the entrance to the grid hole structure.

43 PARTICLE ACCELERATORS↗