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At least 55 records · Page 3

Life Cycle Assessment for Closed-Loop Pumped Hydropower Energy Storage in the United States

The federal government has initiated an aggressive set of policies to achieve a net-zero carbon emission goal for the electricity sector by 2050. As a result, rapid growth in deployment of renewable energy technologies is expected. Most commercially mature technologies are temporally variable and do not provide grid inertia, while renewable technologies with high projected deployment have intermittent generation methods. Energy storage technologies are needed to both dispatch power on-demand and help provide the needed grid inertia. Pumped storage hydro (PSH) is a well-established technology that has gained renewed interest in recent years offering energy-balancing, grid stability, control of electrical network frequency, and large-scale storage capacity. For widespread adoption of PSH, more information is needed regarding its current life cycle environmental impacts. The objective of this study is to perform a full life cycle assessment (LCA) of new closed-loop PSH in the U.S. The functional unit for this study is 1 kWh of electrical power delivered to the grid and the base case project lifetime is 80 years. The life cycle inventory for this project accounts for all material and energy flows associated with the green-field construction, operation, maintenance, and decommissioning of a closed-loop PSH plant in the U.S. Collected data represents a range of potential PSH specifications and geographic locations coming from all prospective closed-loop PSH installations in the U.S. with data available. In addition, existing PSH installations are used to provide assumptions for inventory inputs. Results presented will include the global warming potential (GWP IPCC 100a) and Energy Return on Investment (EROI) from our base case (average PSH installation) as well as from scenario analyses and model sensitivity. These results will be compared to the impacts from existing PSH sites and alternate storage technologies. Methods align with the assumptions and guidelines put in place by previous PSH LCAs to ensure an accurate comparison with the results from this report.

ENERGY PLANNING, POLICY, AND ECONOMY,HYDRO ENERGY↗

Selection of Global Climate Model Data for Downscaling With Generative Machine Learning and Use in the Power Planning for Alignment of Climate and Energy Systems Project

The range of results from climate models and scenarios is important to the understanding of uncertainty in power planning analysis. A U.S. Department of Energy-funded analytic project called Power Planning for Alignment of Climate and Energy Systems is developing data and analytic methods to reflect the effects of climate change on key variables for power system planning, as part of the Grid Modernization Lab Consortium. This project will select and prepare global climate model results for use in power system planning models. A related report (Evaluation of Global Climate Models for Use in Energy Analysis) assesses the performance of various global climate models from the Coupled Model Intercomparison Project Phase 6 data archive for their historical skill with respect to energy system performance and for their future projections under multiple climate change scenarios. Building from that report, we describe the selection of a climate scenario (Shared Socioeconomic Pathway [SSP] 2-4.5) and five climate models: TaiESM1, EC-Earth3-CC, GFDL-CM4, EC-Earth3-Veg, and MPI-ESM1-2-HR. We describe the model selection criteria, which were based on the quality of the match between model results under historical conditions and on the representation of the range of future values for several variables. These results will be downscaled via an open-source generative machine learning method called Super-Resolution for Renewable Energy Resource Data with Climate Change Impacts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Ordovician-Cambrian Units: Hierarchical Evaluation of Geologic Carbon Storage Resource Estimates

The Indiana Geological and Water Survey (IGWS) led subtask 1.1 to assess the regional distribution and estimate the storage capacity of Ordovician-Cambrian stratigraphic units located within the partnership region. A comprehensive data set of wireline logs and petrophysical information was used to generate these interpretations. These data include core analysis for porosity and permeability, mercury injection capillary pressure (MICP), and existing well data including location and stratigraphic information. This report includes storage resource estimates (SREs) for three potential storage reservoirs(limestone and dolostone from the Upper Ordovician Trenton Limestone/Black River Group and equivalent units, the Middle Ordovician St. Peter Sandstone, and primary target reservoir rocks of the Lower Ordovician and Upper Cambrian Knox Supergroup and equivalent units) calculated using six methodologies: (1) a fixed value of porosity of 10 percent in all units evaluated; (2) a unique average porosity (per well) from wireline-derived porosity (neutron, sonic, and/or density porosity for each unit); (3) porosity values from core analysis; (4) a depth-dependent porosity model (Knox Supergroup only); (5) porosity based on a model based on petrophysical facies; and (6) SREs using National Energy Technology Laboratory’s CO2 Storage prospeCtive Resource Estimation Excel aNalysis (CO2-SCREEN beta V2). All methods used the same values for thickness for each unit. However, the areal extent of each assessment was limited by the data available for each method. Estimated volumes were calculated in 1-by-1 kilometer grid cells and summarized as county and total stratigraphic unit volumes. The resultant SREs mass are displayed using boxplots, which allow for comparing data statistics (mean values and variability) between methods. Differences observed in SRE results from the six methods are mainly attributable to differences in the data and conceptual models used to interpret or estimate porosity in each method. Based on this systematic variability between methods, it is inferred that methods 1, 4, and 6 are best used for regional-scale reconnaissance estimates of storage capacity while methods 2, 3, and 5 are more appropriate for local scales where more data is required. All estimates are data-density dependent and different methods require different amounts of data for reasonable assessments. ArcMap 10.5.1 software was used to portray SREs to help visualize spatial variance of estimates for each methodology, and more importantly, to highlight those areas having the greatest total storage potential estimates.

01 COAL, LIGNITE, AND PEAT↗

A variable high-order shock-capturing finite difference method with GP-WENO

Here, we present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is an extension of the GP high-order method originally introduced in a finite volume framework by the same authors. The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. For shocks and discontinuities, this GP interpolation scheme uses a nonlinear shock handling strategy similar to Weighted Essentially Non-Oscillatory (WENO), with a novelty consisting in the fact that nonlinear smoothness indicators are formulated in terms of the Gaussian likelihood of the local stencil data, replacing the conventional L 2 -type smoothness indicators of the original WENO method. We demonstrate that these GP-based smoothness indicators play a key role in the new algorithm, providing significant improvements in delivering high – and selectable – order accuracy in smooth flows, while successfully delivering non-oscillatory solution behavior in discontinuous flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Representing lateral groundwater flow from land to river in Earth system models

Lateral groundwater flow (LGF) is an important hydrologic process in controlling water table dynamics. Due to the relatively coarse spatial resolutions of land surface models, the representation of this process is often overlooked or overly simplified. In this study, we developed a hillslope-based lateral groundwater flow model. Specifically, we first developed a hillslope definition model based on an existing watershed delineation model to represent the subgrid spatial variability in topography. Building upon this hillslope definition, we then developed a physical-based lateral groundwater flow using Darcy’s equation. This model explicitly considers the relationships between the groundwater table along the hillslope and the river water table levels. We coupled this intra-grid model to the land component (E3SM Land Model: ELM) and river component (MOdel for Scale Adaptive River Transport: MOSART) of the Energy Exascale Earth System Model (E3SM). We tested both the hillslope definition model and the lateral groundwater flow model and performed sensitivity experiments using different configurations. Simulations for a single grid cell at 0.5°×0.5° within the Amazon basin show that the definition of hillslope is the key to modeling lateral flow processes and the runoff partition between surface and subsurface can be dramatically changed using the hillslope approach. Although our method provides a pathway to improve the lateral flow process, future improvements are needed to better capture the subgrid structure to account for the spatial variability in hillslopes within the simulated grid of land surface models.

54 ENVIRONMENTAL SCIENCES↗

A Comparison of Linear Solvers for Resolving Flow in Three-Dimensional Discrete Fracture Networks

We compare various methods for resolving steady flow within three-dimensional discrete fracture networks, including direct methods, Krylov subspace methods with and without preconditioning, and multi-grid methods. We compared the performance of the methods based on compute times and scaling of the solution as a function of the number of grid nodes and log-variance of the hydraulic aperture. The methods are applied to three test cases: (a) variable density of networks with a truncated power-law distribution of fracture lengths, (b) a fixed network composed of monodisperse fracture sizes but varied permeability/aperture heterogeneity, (c) and a network based on field site in Nevada, US. We chose these cases to allow us to study the impact of the mesh size and flow properties, as well as to demonstrate our conclusions on a large-scale, realistic problem (more than 40 million mesh nodes). A direct solution using Cholesky factorization outperformed other methods for every example but was closely followed in performance by some algebraic multigrid (AMG) preconditioned Krylov subspace methods. Among the Krylov methods, conjugate gradients (CG) with an AMG preconditioner performs the best. Generally, Cholesky factorization is recommended, but CG with an AMG preconditioner may be suitable for very large problems beyond 40 million nodes where the entire linear system cannot reside in memory.

58 GEOSCIENCES↗

Design and Operation of a Sensible Heat Peaking Unit for Small Modular Reactors

Approximately 19% of the electricity produced in the United States comes from nuclear power plants. Traditionally, nuclear power plants, as well as larger coal-fired plants, operate in a baseload manner at or near steady-state for prolonged periods of time. Smaller, more maneuverable plants, such as gas-fired plants, are dispatched to match electricity supply and demand above the capacity of the baseload plants. However, air quality concerns and CO2 emission standards has made the burning of fossil fuels less desirable, despite the current low cost of natural gas. Wind and solar photovoltaic (PV) power generation are attractive options due to their lack of carbon footprint and falling capital costs. Yet, these renewable energy sources suffer from inherent intermittency. This inherent intermittency can strain electric grids, forcing carbon-based and nuclear sources of energy to operate in a load follow mode. For nuclear reactors, load follow operation can be undesirable due to the associated thermal and mechanical stresses placed on the fuel and other reactor components. Various methods of Thermal Energy Storage (TES) can be coupled to nuclear (or renewable) power sources to help absorb grid variability caused by daily load demand changes and renewable intermittency. Our previous research has shown that coupling a sensible heat TES system to a Small Modular Reactor (SMR) allows the reactor to run at effectively nominal full power during periods of variable electric demand by bypassing steam to the TES system during periods of excess capacity. In this study we demonstrate that this stored thermal energy can be recovered, allowing the TES system to act as a peaking unit during periods of high electric demand, or used to produce steam for ancillary applications such as desalination. For both applications the reactor is capable of operating continuously at approximately 100% power.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Developing Metrics to Evaluate the Skill and Credibility of Downscaling

In this project, our overarching goal was to evaluate the skill and credibility of statistical and dynamical downscaling techniques for reconstructing the historical climate record and projecting future climate change. This report summarizes our approach and accomplishments. In the first year of the project, the priority was to generate new data sets. For Year 2, the overall goal was to focus comparisons during the historical period and for a subset of variables, especially temperature and precipitation. In Year 3 and beyond, the focus was mainly on comparisons and metrics for future climate change simulations. To quantify the uncertainty associated with gridded dataset choice, the UCLA group compared eight gridded temperature datasets, examining climatologies, variability, and trends. The Scripps group completed statistical downscaling of NARR with the LOCA method, and UCLA and Scripps collaborated on a comparison of historical and end-of-century temperature and precipitation patterns over California from WRF, LOCA-WRF, and LOCA-Livneh. In addition to downscaling temperature and precipitation, the Scripps group has spent considerable time working on near-surface wind and humidity downscaling. The Santa Clara group assembled the Variable Infiltration Capacity (VIC) for nine snow-dominated river basins draining the western slopes of the Sierra Nevada range and assessed the role of snow albedo feedback in their VIC simulations. The results will help inform future downscaling studies.

54 ENVIRONMENTAL SCIENCES↗

Developing Metrics to Evaluate the Skill and Credibility of Downscaling (Final Report)

In this project, our overarching goal was to evaluate the skill and credibility of statistical and dynamical downscaling techniques for reconstructing the historical climate record and projecting future climate change. This report summarizes our approach and accomplishments. In the first year of the project, the priority was to generate new data sets. For Year 2, the overall goal was to focus comparisons during the historical period and for a subset of variables, especially temperature and precipitation. In Year 3 and beyond, the focus was mainly on comparisons and metrics for future climate change simulations. To quantify the uncertainty associated with gridded dataset choice, the UCLA group compared eight gridded temperature datasets, examining climatologies, variability, and trends. The Scripps group completed statistical downscaling of NARR with the LOCA method, and UCLA and Scripps collaborated on a comparison of historical and end-of-century temperature and precipitation patterns over California from WRF, LOCA-WRF, and LOCA-Livneh. In addition to downscaling temperature and precipitation, the Scripps group has spent considerable time working on near-surface wind and humidity downscaling. The Santa Clara group assembled the Variable Infiltration Capacity (VIC) for nine snow-dominated river basins draining the western slopes of the Sierra Nevada range and assessed the role of snow albedo feedback in their VIC simulations. The results will help inform future downscaling studies.

54 ENVIRONMENTAL SCIENCES↗

Autonomous Grid Support Functionality in Variable-Speed Drive-Based End-Use Loads

High penetration of inverter-based resources into power systems causes lower inertia, and it becomes more challenging to maintain grid stability during contingency events. While conventional demand response and shedding at the load side suffer from slow response, impact by unavailability, and issues from communication, variable-speed drives (VSDs) are becoming strong candidates for fast frequency response (FFR) thanks to their fast response and reduced user impact from variable power adjustment capability. In this letter, we propose an autonomous frequency support control method for a residential refrigerator with a VSD, a promising target small end-use load for FFR. We analyze the effect of the proposed controller on grid stability, and we verify the performance through laboratory experiments with a commercially available refrigerator.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Using Temporal Deep Learning Models to Estimate Daily Snow Water Equivalent Over the Rocky Mountains

Abstract In this study we construct and compare three different deep learning (DL) models for estimating daily snow water equivalent (SWE) from high‐resolution gridded meteorological fields over the Rocky Mountain region. To train the DL models, Snow Telemetry (SNOTEL) station‐based SWE observations are used as the prediction target. All DL models produce higher median Nash‐Sutcliffe Efficiency (NSE) values than a conceptual SWE model and interpolated gridded data sets, although mean squared errors also tend to be higher. Sensitivity of the SWE prediction to the model's input variables is analyzed using an explainable artificial intelligence (XAI) method, yielding insight into the physical relationships learned by the models. This method reveals the dominant role precipitation and temperature play in snowpack dynamics. In applying our models to estimate SWE throughout the Rocky Mountains, an extrapolation problem arises since the statistical properties of SWE (e.g., annual maximum) and geographical properties of individual grid points (e.g., elevation) differ from the training data. This problem is solved by normalizing the SWE with its historical maximum value to alleviate extrapolation for all tested DL models. Our work shows that the DL models are promising tools for estimating SWE, and sufficiently capture relevant physical relationships to make them useful for spatial and temporal extrapolation of SWE values.

54 ENVIRONMENTAL SCIENCES↗

A Comprehensive Comparison of Methods for Evaluating Dispatch of Long-Duration Energy Storage in Power Systems Models

Long-duration energy storage (LDES) could play a pivotal role in the transformation of electricity grids with high shares of variable renewable energy (VRE) such as solar and wind. However, the weather-dependent nature of VRE introduces challenges for grid balancing and stability, which LDES - along with short-duration energy storage (SDES) - can help address. However, modeling LDES in production cost models (PCMs) is particularly challenging due to the need for high temporal resolution over extended optimization windows while preserving chronology, which ensures the alignment of energy storage operations with VRE generation over multi-day periods. This report compares traditional dispatch methods with advanced LDES dispatch strategies, such as the extended horizon approach, across different PCM platforms and examines tradeoffs and scalability. The comparison reveals that the traditional 1-day optimization horizon within the PCM leads to inefficient utilization of LDES. In contrast, extending the optimization horizon as much as possible significantly reduces curtailment and improves storage dispatch, especially in renewable-dense systems. There is also promise in using state-of-charge or end volume targets set by an external model, however this requires an additional modeling set and generally increases computational burden. This paper presents a comparison of these various methods in a number of power systems, showing algorithms initially in small test systems and scaling up to large, country-wide simulations. Overall, the research presents the trade-offs of various computational methods and illustrates how LDES may play an essential role in power systems of the future.

14 SOLAR ENERGY↗

Impact of a dynamic grid mix and climate on operational carbon emissions modeling for different building typologies and climate zones

Calculating operational carbon emissions through a building’s lifecycle is complex due to the dynamic nature of influencing factors such as climate and energy grid mix. This paper introduces a novel methodology for modeling 30-year operational carbon impacts of buildings and applies this method to mid-rise office and residential typologies across various US climate zones. The method accounts for these temporal variabilities using new and scarcely cited data sources. Key findings indicate that future changes in the climate, while impactful, play a relatively modest role in operational carbon emissions compared to significant reductions with modeling scenarios using the projected decarbonization of the electricity grid. Here, the study also finds that using annual, month-hourly, or hourly grid emission factors have a minimal impact on carbon accounting, except in certain climates and program types where emission patterns do not align with a building’s energy consumption. Warmer climates like Miami, Florida and Tucson, Arizona, which rely heavily on cooling, demonstrate larger variations in carbon emissions when using higher temporal resolution emission factors. Ultimately, this study underscores the critical role of grid decarbonization in reducing long-term emissions and the importance of incorporating this variable in life cycle assessment (LCA) modeling.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Initial Uncertainty Analysis of Carbon Tetrachloride Contamination and Remediation in the Ringold A and Lower Mud Units at the Central Plateau

The long-term effectiveness of groundwater cleanup at the Hanford Site Central Plateau depends on predictive models that can capture key uncertainties in contaminant fate and transport. Carbon tetrachloride (CCl 4 ), a persistent and toxic compound, presents particular challenges due to variability in degradation rates, uncertainty in initial plume distribution, and subsurface heterogeneity. These uncertainties directly influence plume persistence, migration pathways, and remedy performance, and thus must be systematically evaluated to support long-term remediation planning. To address these gaps, a large-scale Monte Carlo analysis was conducted using the Plateau to River (P2R) model framework. The modeling approach parameterized three primary uncertainty factors: (1) degradation rate, (2) initial plume distribution, and (3) hydraulic conductivity. Degradation was represented as a first-order process, with half-lives ranging from 70 to 700 years. Initial plume distributions were created using a geostatistical simulation method (sgsim), which generates many equally plausible versions of how contaminants might be distributed underground. From this, 100 different scenarios were mapped onto the P2R grid. Variability in hydraulic conductivity was represented in a similar way, with 100 scenarios each for the Ringold Lower Mud and Ringold A units (layers 6 and 7), based on fitted exponential variograms and conditioned to well data. In total, more than 1000 realizations were simulated to assess plume behavior under uncertainty. Results demonstrate that degradation kinetics exert the strongest control over plume persistence: Shorter half-lives produced rapid mass reduction, while longer half-lives yielded persistent plumes with limited attenuation. A nonlinear response was observed, with steep mass reductions at half-lives greater than 200 years and near-linear declines beyond this threshold, reflecting interactions between degradation and pumping. The initial plume distribution strongly influenced early transport patterns, with broader sources generating larger plume footprints, although pump-and-treat operations constrained plume migration to managed areas. By comparison, hydraulic conductivity variability in the Ringold units had only a secondary influence, modifying spreading behavior without altering the dominant migration pathways governed by source configuration and hydraulic controls. Overall, the analysis highlights that uncertainty in degradation rate and initial plume configuration are the primary drivers of variability in plume predictions, while conductivity heterogeneity plays a limited role. These findings underscore the need for improved site-specific data on degradation processes and source characterization to enhance the reliability of long-term performance assessments and to better inform remedial decision-making at the Central Plateau.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Multi-agent voltage control in distribution systems using GAN-DRL-based approach

Active distribution grids can experience voltage fluctuations and violations due to the high penetration of variable distributed energy resources (DERs). These problems might occur because of the uncertain and variable generation natures of these resources, especially solar photovoltaic resources, during panel shadowing scenarios. Volt-VAR control (VVC) is an efficient method that controls the reactive power set-points of the inverters to regulate the voltage of distribution grids. Although several VVC approaches have been proposed recently, the performance of these approaches degrades significantly if behind-the-meter solar generation data are unobservable/missing. Therefore, it is necessary to impute missing/unobservable PV data accurately to be utilized in VVC approaches. Further, this paper proposes a model-free, data-driven, centrally trained, and decentrally executed multi-agent deep reinforcement learning-based VVC architecture to regulate the voltage of distribution networks. A generative adversarial network (GAN) is incorporated to impute the unobservable PV data accurately, which improves the performance of the proposed control architecture. The proposed multi-agent-soft-actor–critic algorithm (MASAC)-based VVC technique utilizes the actual PV dataset as well as the imputed dataset from the GAN framework to learn the optimal coordinated control policy for controlling the optimal reactive power set-points of PV inverters. The effectiveness of the proposed approach is analyzed on a modified IEEE 34-bus test case with added PV inverters. The results are compared and analyzed with a base case model with no VVC and VVC with a local droop control approach, genetic algorithm optimization, and a centralized soft actor–critic-based approach. Moreover, the performance of the proposed approach is compared with that of a multi-agent VVC framework without using the PV generation data and load information as the system state. The results illustrate that the proposed method with more state input improves the voltage profile and reduces the power loss of the network across various loading and PV generation scenarios.

14 SOLAR ENERGY↗

A reconstructed discontinuous Galerkin method for compressible flows in Lagrangian formulation

In this work, a high-order accurate reconstructed discontinuous Galerkin (rDG) method is developed for solving two-dimensional hydrodynamic problems in cell-centered updated Lagrangian formulation. This method is the Lagrangian limit of the unsplit rDG-ALE formulation, and is obtained by assuming the equality of the grid velocity to the fluid velocity only at cell boundaries. The conservative variables and the Taylor basis defined on the time-dependent moving mesh, provide the piece-wise polynomial expansion in the updated Lagrangian formulation. A multi-directional nodal Riemann solver is implemented for computing the grid velocity at the vertices and the numerical flux at the cell boundaries. A characteristic limiting procedure is extended from the primitive variable version to the conservative variable version, and its performance is compared with the limiter on physical variables. A number of benchmark test cases are conducted to assess the accuracy, robustness, and non-oscillatory property of the DG(P0), DG(P1) and rDG(P1P2) methods. The numerical experiments demonstrate that the developed rDG method is able to attain the designed order of accuracy and the characteristic limiting procedure outperforms the limiter on physical variables in terms of the monotonicity and symmetry preservation for shock problems.

42 ENGINEERING↗

Density effects on post-shock turbulence structure and dynamics

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles that density plays in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic VGT, PDF $(Q^{\ast },R^{\ast })$ , as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetric PDF $(Q^{\ast },R^{\ast })$ in heavy-fluid regions, while the light-fluid regions retain the characteristic tear-drop shape. To understand this behaviour and the return to ‘standard’ turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants is studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.

42 ENGINEERING↗

Evaluating Grid Strength under Uncertain Renewable Generation

The increasing displacement of synchronous generators with renewable resources such as wind and solar via power electronic interfaces causes a reduction in short-circuit strength and weak grid issues. The variation and uncertainty of renewable energy increase challenges for identifying weak grid conditions. This paper proposes an efficient method to analyze the impact of uncertain renewable energy on grid strength. The proposed method uses the probabilistic collocation method (PCM) to approximate the results of grid strength assessment under uncertain renewable generation, in order to reduce computational burden without compromising result accuracy when compared with traditional Monte Carlo simulation (MCS). To improve the accuracy of the approximation results, the proposed method integrates the K-means clustering technique with PCM to select the approximation samples of input variables. The efficacy of the proposed method is demonstrated by comparison with MCS on the modified IEEE 9-bus system and modified IEEE 39-bus system with multiple renewable generators.

grid strength↗