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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Synchronous Machine Governor Upgrade

Conventional generation sources play a critical role in the stability and reliability of the electrical grid, particularly as we transition towards more renewable energy sources. To understand and accurately emulate their behavior for optimizing grid operations and ensuring seamless integration with renewable technologies, it is essential to better emulate the grid- and plant-level impacts of conventional generation sources, such as natural gas (NG) driven heat recovery steam generators (HRSGs) and combustion turbines (CTs). Therefore, a governor model is developed in a programmable logic controller (PLC) to investigate the performance of the conventional generator under various dynamic operating conditions and to identify the impact on grid stability in a controlled environment. The governor model aims to enable the hardware-in-the-loop (HIL) based emulation of these conventional generation sources using the existing 2 MVA synchronous machine/generator that is driven by a flexible 2.5 MW variable speed drive. This setup will allow us to replicate the dynamic characteristics and response behaviors of NG-driven HRSGs and CTs. The controls for the emulated conventional plants follow the industry standard and are adjustable, ensuring they accurately reflect the operational capabilities and limitations of real-world systems. These controls include load-following capabilities, ramp rates, startup and shutdown sequences, and emissions characteristics. By incorporating these adjustable controls, we aim to capture the nuanced impacts of conventional generation, such as their ability to provide ancillary services like frequency regulation, voltage support, and spinning reserve. In this report, we simulate two types of dynamic operations: grid-connected and islanding. For each dynamic operation, representative starting sequences are tested, including turbine purge, ignition, speed ramping up, generator excitation and synchronizing, and breaker close. The HIL based tests provides insights for field deployment, specifically the high-fidelity governor model provides results to predict the potential stability and reliability risk and suggest possible integration measures (e.g., generation and load balancing, tuning of governor control parameters). Ultimately, this enhanced emulation capability will be integrated into our Advanced Research on Integrated Energy Systems (ARIES), enabling us to conduct comprehensive studies on the interactions between conventional and renewable energy sources. By better understanding these interactions, we can develop strategies to optimize the overall performance and reliability of the grid. This will support the deployment of advanced grid management techniques, such as demand response, grid-forming inverters, and energy storage systems. The main contributions are summarized as follows: (1) This report introduces a PLC-based governor model for gas turbines. This model accurately simulates the dynamic behavior of conventional generation sources under various operational scenarios; (2) The model is integrated with an HIL testbed that includes a 2.5 MW variable speed drive and a 2 MVA synchronous machine. This setup enables realistic, real-time emulation of conventional power plants, particularly NG driven HRSGs and CTs; (3) The developed model is adaptable to various gas turbine configurations and allows for precise control over parameters such as MW ramp rates. This flexibility makes it a valuable tool for future research and industry collaboration; and (4) By incorporating the model into the National Renewable Energy Laboratory's Advanced Research on Integrated Energy Systems, the report lays the groundwork for future studies on interactions between conventional and renewable energy sources, enhancing the ability to develop advanced grid management strategies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Utility Experience with Inverter-Based Resource Impacts on Transmission Protection

High penetration of inverter-based resources (IBR) can adversely affect the transmission protection schemes in the area. With the proliferation of IBRs, utilities are finding out that conventional protection schemes are not adequately equipped to protect the electric systems because the existing system has been designed based on the fault current response of conventional rotating-machine-based generators. This report identifies various protection challenges due to IBRs that industry is facing.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Addressing the Split Incentive Challenge for Enhanced Solar Adoption in Multifamily Rental Properties [Abstract]

The split incentive problem is particularly pronounced in rental markets, where landlords prioritize investments that directly increase property value or rental income. Since energy savings from solar photovoltaic (PV) systems primarily benefit tenants, landlords may perceive little return on investment unless mechanisms exist to recapture some of the financial gains. The primary objective of this project is to develop a publicly available, web-based tool to analyze the U.S. Department of Energy’s ResStock database, which models the U.S. residential building stock. The tool allows users to filter buildings by location, type, HVAC system, square footage, and other characteristics, and outputs typical electric load profiles. By leveraging location-specific electric load data, Fram Energy aims to advance business strategies that address the split incentive barrier and promote the adoption of solar PV installations in rental properties. In addition, a machine learning model will be developed to weigh the marginal contribution of building features across the dataset in predicting electricity demand, supporting guided decision making in forecasting electric load profiles. Lastly, based on each building’s location, load profile, and utility’s electricity rate, an optimized solar photovoltaic array and battery energy storage system will be sized to provide energy arbitrage opportunities.

14 SOLAR ENERGY↗
DOE OSTI2022

Machine Learning Derived Dynamic Operating Reserve Requirements in High-Renewable Power Systems

Accurately forecasting wind and solar power output poses challenges for deeply decarbonized electricity systems. Grid operators must commit resources to provide reserves to ensure reliable operations in the face of forecast errors, a process which can increase fuel consumption and emissions. We apply neural network-based machine learning to expand the usefulness of median point forecast data by creating probabilistic distributions of short-term uncertainty in demand, wind, and solar forecasts that adapt to prevailing grid conditions. Machine learning derived estimates of forecast errors compare favorably to estimates based on incumbent methods. Reserves derived from machine learning are usually smaller than values derived using incumbent methods, which enables fuel savings during most hours. Machine learning reserves are generally larger than incumbent reserves during times of higher forecast error, potentially improving system reliability. Performance is tested using multi-stage production simulation modeling of the California Independent System Operator (CAISO) system. Machine learning reserves provide production cost and greenhouse gas (GHG) emission reductions of approximately 0.3% relative to historical 2019 requirements. Savings in the 2030 timeframe are highly dependent on battery storage capacity. At lower levels of battery capacity, savings of 0.4% from machine learning reserves are shown. Significant quantities of battery storage are expected to be added to meet California's resource adequacy needs and GHG reduction targets. Addition of these batteries saturate reserve needs and results in minimal within-hour balancing costs in 2030.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

GeoThermalCloud: Machine Learning for Geothermal Resource Exploration

Geothermal is a renewable energy source that can provide reliable and flexible electricity generation for the world. In the past decade, the U.S. Geological Survey's resource assessments, Play Fairway Analyses (PFA), and GeoVision report by the U.S. Department of Energy's Geothermal Technologies Office provided insights on enormous untapped potential for geothermal energy to contribute to the U.S. domestic energy needs. The past studies identified that geothermal resources without surface expression (e.g., blind/hidden hydrothermal systems) comprise a huge potential. These blind systems can significantly increase power generation. But a primary challenge is locating and quantifying these hidden resources, which do not have any thermal manifestations on the surface. PFA has successfully identified some blind systems in the western USA (e.g., specific locations in the Great Basin region within Nevada). However, a comprehensive search for these blind systems can be time-consuming, expensive, and resource-intensive with a low probability of success. Accelerated discovery of these blind resources is needed with growing energy needs and higher chances of exploration success. Recent advances in machine learning (ML) have shown promise in shortening the timeline for this discovery. This paper presents a novel ML-based methodology for geothermal exploration towards PFA applications. Our methodology is provided through our open-source ML framework called GeoThermalCloud \url{https://github.com/SmartTensors/GeoThermalCloud.jl}. GeoThermalCloud uses a series of unsupervised, supervised, and physics-informed ML methods available in SmartTensors AI platform \url{https://github.com/SmartTensors}. Here, the presented analyses are performed using our unsupervised ML algorithm called NMF$k$, which is available in the SmartTensors AI platform. Our ML algorithm facilitates the discovery of new phenomena, hidden patterns, and mechanisms that helps us to make informed decisions. Moreover, the GeoThermalCloud enhances the collected PFA data and discovers signatures representative of geothermal resources. Through GeoThermalCloud, we were able to identify hidden patterns in the geothermal field data needed for the efficient discovery of blind systems. Crucial geothermal signatures often overlooked in traditional PFA are extracted using GeoThermalCloud and analyzed by the subject matter experts to provide ML-enhanced PFA, which is informative for efficient exploration. We applied our ML methodology on various open-source geothermal datasets within the U.S. (some of these are collected by past PFA work), and the results provide valuable insights on resource types within those explored regions. This ML-enhanced workflow makes GeoThermalCloud attractive for the geothermal community to improve existing datasets and extract valuable information often unnoticed during geothermal exploration.

machine learning (ML), geothermal energy↗
DOE OSTI2025

Rotation of electrothermal-instability-driven overheating structure due to helically oriented surface magnetic field on a high-current-density aluminum rod

Experiments on the 1-MA, 100-ns-rise-time Mykonos Facility demonstrate rotation of electrothermal instability (ETI)-driven overheating structure on 1.00-mm-diameter, 10-nm-surface roughness, 99.999%-pure aluminum rods, which are pulsed with helically polarized surface magnetic field. Rods are machined to include pairs of 10-micron-scale quasi-hemispherical voids or “engineered defects (ED)” which provide the dominant current density perturbation from which ETI grows most rapidly. Experiments include an axial magnetic field component through the addition of a helically wound return-current electrode or “helical return can (HRC).” For a given HRC design, azimuthal field (B ɵ ) and axial field (B z ) components rise at a prescribed and fixed ratio, driving an increasing magnetic field of constant polarization at the rod's surface; most experiments generated surface magnetic field at a 15-degree field polarization angle (from horizontal) defined as ɸ B = arctan(B z /B ɵ ). ETI-driven emission patterns from individual ED are observed to rotate along ɸ B , while emission patterns from dielectric-coated ED pairs are shown to elongate and preferentially merge along ɸ B , in qualitative agreement with 3D-magnetohydrodynamic simulations. These data strongly support that for a randomized distribution of current density perturbations on a high-current density conductor, nearby perturbations will favorably merge about ɸ B , with the degree of merging increasing with current. Such observations offer fundamental new understanding of the seeding mechanisms of the helical magneto-Rayleigh Taylor (MRT) instabilities observed from axially magnetized magnetically driven imploding liners.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Establishing nationwide power system vulnerability index across US counties using interpretable machine learning

Power outages have become increasingly frequent, intense, and prolonged in the US due to climate change, aging electrical grids, and rising energy demand. However, largely due to the absence of granular spatiotemporal outage data, we lack data-driven evidence and analytics-based metrics to quantify power system vulnerability. This limitation has hindered the ability to effectively evaluate and address vulnerability to power outages in US communities. Here, in this work, we collected ∼179 million power outage records at 15-min intervals across 3022 US contiguous counties (96.15 % of the area) from 2014 to 2023. We developed a power system vulnerability assessment framework based on three dimensions (intensity, frequency, and duration) and applied interpretable machine learning models (XGBoost and SHAP) to compute Power System Vulnerability Index (PSVI) at the county level. Our analysis reveals a consistent increase in power system vulnerability across the US counties over the past decade. We identified 318 counties across 45 states as hotspots for high power system vulnerability, particularly in the West Coast (California and Washington), the East Coast (Florida and the Northeast area), the Great Lakes megalopolis (Chicago-Detroit metropolitan areas), and the Gulf of Mexico (Texas). Our heterogeneity analysis indicates that urban counties and those located along regional transmission boundaries tend to exhibit significantly higher vulnerability. Our results highlight the significance of the proposed PSVI for evaluating the vulnerability of communities to power outages. The findings underscore the widespread and pervasive impact of power outages across the country and offer crucial insights to support infrastructure operators, policymakers, and emergency managers in formulating policies and programs aimed at enhancing the resilience of the US power infrastructure.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Field evaluation of semi‐automated moisture estimation from geophysics using machine learning

Geophysical methods can provide three-dimensional (3D), spatially continuous estimates of soil moisture. However, point-to-point comparisons of geophysical properties to measure soil moisture data are frequently unsatisfactory, resulting in geophysics being used for qualitative purposes only. This is because (1) geophysics requires models that relate geophysical signals to soil moisture, (2) geophysical methods have potential uncertainties resulting from smoothing and artifacts introduced from processing and inversion, and (3) results from multiple geophysical methods are not easily combined within a single soil moisture estimation framework. To investigate these potential limitations, an irrigation experiment was performed wherein soil moisture was monitored through time, and several surface geophysical datasets indirectly sensitive to soil moisture were collected before and after irrigation: ground penetrating radar, electrical resistivity tomography (ERT), and frequency domain electromagnetics (FDEM). Data were exported in both raw and processed form, and then snapped to a common 3D grid to facilitate moisture prediction by standard calibration techniques, multivariate regression, and machine learning. A combination of inverted ERT data, raw FDEM, and inverted FDEM data was most informative for predicting soil moisture using a random regression forest model (one-thousand 60/40 training/test cross-validation folds produced root mean squared errors ranging from 0.025–0.046 cm 3 /cm 3 ). This cross-validated model was further supported by a separate evaluation using a test set from a physically separate portion of the study area. Machine learning was conducive to a semi-automated model-selection process that could be used for other sites and datasets to locally improve accuracy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Visualizing Intrinsic 3D-Strain Distribution in Gold Coated ZnO Microstructures by Bragg Coherent X-Ray Diffraction Imaging and Transmission Electron Microscopy with Respect to Piezotronic Applications

Novel devices ranging from bio magnetic field sensors to energy harvesting nano machines utilize the piezotronic effect. For optimal function, understanding the interaction of electrical and strain phenomena within the semiconductor crystal is necessary. Here, studies of a model piezotronic system are presented, consisting of a ZnO microrod coated by a thin layer of gold, which forms a Schottky contact with the piezoelectric ZnO material. Coherent X-ray diffraction imaging (CXDI) and transmission electron microscopy (TEM) are used to visualize the structure and strain distribution, showing that the ZnO microrod exhibits strains of multiple origins in the bulk and at the interface. Strain values of -6 × 10 -4 have been measured by CXDI at the ZnO/Au interface. The origin is shown to be a combination of an interface strain, possibly caused by the Schottky contact formation, and distinct, localized electrical fields inside the crystal which are assigned to electron depletion and screening in a bent ZnO/Au piezotronic rod. These findings will contribute to sensor development and to a better understanding of piezotronic applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Fusion welding of refractory metals and ZrB 2 -SiC-ZrC ceramics

Molybdenum and a molybdenum alloy were fusion welded to ZrB2-based ceramics to determine if the electrical and thermal properties of the metals and ceramics affected their weldability. Commercial ceramic powders were hot pressed, machined into coupons, and preheated to 1600 °C before joining the ceramics to commercial metals using plasma arc welding. Weldability varied as indicated by the range of porosity observed within the fusion zones. Measured thermal and electrical properties appeared to have little to no effect on the weldability of metal-ceramic welds despite the large range of values measured across each property. Differences in melting temperatures between metal and ceramic coupons did affect weldability by changing the weld penetration depth into ceramic coupons. Finally, future studies on metal-ceramic welds are suggested to investigate the effect that work function, melt viscosity, wetting, or other properties have on weldability.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Why Dissolving Salt in Water Decreases Its Dielectric Permittivity

The dielectric permittivity of salt water decreases on dissolving more salt. For nearly a century, this phenomenon has been explained by invoking saturation in the dielectric response of the solvent water molecules. Herein, we employ an advanced deep neural network (DNN), built using data from density functional theory, to study the dielectric permittivity of sodium chloride solutions. Notably, the decrease in the dielectric permittivity as a function of concentration, computed using the DNN approach, agrees well with experiments. Detailed analysis of the computations reveals that the dominant effect, caused by the intrusion of ionic hydration shells into the solvent hydrogen-bond network, is the disruption of dipolar correlations among water molecules. Accordingly, the observed decrease in the dielectric permittivity is mostly due to increasing suppression of the collective response of solvent waters.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2023

Fabrication of the Fermilab Pre-Series Cold Mass for the HL-LHC Accelerator Upgrade Project

Fermilab is fabricating ten full length cold masses for the high-luminosity Large Hadron Collider Accelerator Upgrade Project (HL-LHC AUP). One practice assembly and one pre-series assembly have been completed. Here this paper summarizes the construction details. Topics include incoming inspection, bus assembly, component machining, shell forming, beam tube insertion, bus expansion loop installation, instrumentation installation, electrical testing, heat exchanger installation and final assembly welding. In-process surveys, alignment measurements and testing are presented and explained. Problems encountered during construction and their solutions are discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Celeritas R&D Report: Accelerating Geant4

Celeritas is a new Monte Carlo (MC) detector simulation code designed for computationally intensive applications on high-performance heterogeneous architectures. In the past two years Celeritas has advanced from prototyping a Graphics Processing Unit (GPU)-based single physics model in infinite medium to implementing a full set of electromagnetic (EM) physics processes in complex geometries. The current release of Celeritas, version 0.4, has incorporated full device-based navigation, an event loop in the presence of magnetic fields, and detector hit scoring. New functionality incorporates a scheduler to offload electromagnetic physics to the GPU within a Geant4-driven simulation, enabling straightforward integration of Celeritas into the high energy physics (HEP) experimental frameworks CMSSW and ATLAS FullSimLight. On the Perlmutter supercomputer, Celeritas performs EM physics between 3× and 18× faster using the machine’s Nvidia GPUs compared to using only CPUs, corresponding to an electrical power efficiency up to a factor of 5. When running a multithreaded Geant4 ATLAS test beam application with full hadronic physics, using Celeritas to accelerate the EM physics results in an overall simulation speedup of 1.7–2.2× on GPU and 1.2× on CPU. In a CMS test application using tt¯ events and the prototype Run 4 configuration, compared to Geant4 CPU, Celeritas with a Nvidia A100 improves overall throughput up to a factor of 2.7× but cannot be efficiently shared with more than 8 cores.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Deploying E3’s RESERVE Tool to Enable Advanced Operation of Clean Grids

Energy and Environmental Economics, Inc. (E3) developed an open-source machine learning model, RESERVE, for deriving ancillary services timeseries in deeply decarbonized electricity grids. E3 used a bespoke PLEXOS production simulation model of the California Independent System Operator’s (CAISO) balancing area to validate RESERVE’s ability to enable production cost, greenhouse gas emissions (GHG), and renewable energy curtailment savings. These savings were modeled by comparing PLEXOS cases with RESERVE’s outputs to PLEXOS cases with CAISO’s incumbent reserve product in the Western Energy Imbalance Market (EIM)’s 15-minute market. E3 also tested cases with solar operating flexibly to provide reserves. E3 found that, in a 2030 modeling year, using RESERVE and flexible solar enabled significant production cost, GHG and curtailment savings versus the incumbent CAISO method in cases with low penetrations of lithium-ion batteries. However, with the full 14 gigawatts (about 30% of peak CAISO demand) of 4-hour lithium-ion batteries that are expected to be installed by 2030, these savings approach zero due to batteries saturating ancillary services markets. E3 also found significant savings under a 2019 benchmarking year.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2024

Finite Element Analysis and Machine Learning Guided Design of Carbon Fiber Organosheet-Based Battery Enclosures for Crashworthiness

Carbon fiber composite can be a potential candidate for replacing metal-based battery enclosures of current electric vehicles (E.V.s) owing to its better strength-to-weight ratio and corrosion resistance. However, the strength of carbon fiber-based structures depends on several parameters that should be carefully chosen. Here, in this work, we implemented high throughput finite element analysis (FEA) based thermoforming simulation to virtually manufacture the battery enclosure using different design and processing parameters. Subsequently, we performed virtual crash simulations to mimic a side pole crash to evaluate the crashworthiness of the battery enclosures. This high throughput crash simulation dataset was utilized to build predictive models to understand the crashworthiness of an unknown set. Our machine learning (ML) models showed excellent performance (R 2 > 0.97) in predicting the crashworthiness metrics, i.e., crush load efficiency, absorbed energy, intrusion, and maximum deceleration during a crash. We believe that this FEA-ML work framework will be helpful in down select process parameters for carbon fiber-based component design and can be transferrable to other manufacturing technologies.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A novel machine learning based identification of potential adopter of rooftop solar photovoltaics

With the proliferation of rooftop solar photovoltaic installations, there is a need to proactively predict consumer potential for solar photovoltaic adoption, for improved electric utility planning and operation. Traditional analytical modeling approaches are limited to a few survey features and a larger part of the survey would remain untouched by the decision model. This article presents a novel, data-driven modeling approach that strategically prunes a large set of consumer profile features using a machine learning framework to train a model for predicting potential solar adoption. The approach utilizes the Gradient Boosting Decision Tree model through a Light Gradient Boosting framework that improves significantly over the poor prediction accuracy of the existing approaches. Model training using focal-loss based supervision is used to overcome the difficulty in identifying the potential adopters that is inherent in conventional data-driven models. In addition, to overcome possible data sparsity in a limited survey sample, a Generative Adversarial Network is presented to create synthetic user samples and its effectiveness on model performance is assessed. A Bayesian optimization approach is used to systematically arrive at the hyperparameters of the proposed model. Validation of the presented approach on a survey data collected by the National Rural Electric Cooperative Association in Virginia in 2018 demonstrates the excellent predictive capability of the machine learning based approach to modeling solar adoption reliably.

14 SOLAR ENERGY↗
DOE OSTI2024

Coal-derived electrically conductive asphalt pavements for snow/ice melting: From laboratory to field

Timely removal of ice and snow from roads is critical to safe, fast, and uninterrupted transportation networks in cold regions. Constructing electrically conductive asphalt pavements to melt the ice and snow on the roads through resistive eating is an emerging alternative technology to traditional snow/ice removal approaches such as utilizing snowplow machines and deicing chemicals. Carbon-based fibers and fillers including carbon fiber and graphite have been widely reported to make electrically conductive hot mix asphalt mixtures for pavement snow/ice-melting applications. This study aimed to develop and demonstrate a novel type of electrically conductive asphalt pavements for snow/ice-melting, which utilizes electrically conductive cold mix asphalt (CMA) mixtures incorporating coal-derived carbon-based coke aggregate as resistive heating elements. Both laboratory experiments and field tests were conducted to investigate the electrical, mechanical, and thermal properties of such electrically conductive asphalt mixtures and pavements. The laboratory experiment results indicated that the electrically conductive CMA mixtures incorporating coke aggregate had sufficiently high electrical conductivity and satisfactory mechanical performance and the pavement prototype slab utilizing a thin layer of such CMA mixtures could successfully raise the pavement surface temperatures to 8.3–11.7 °C rom a low temperature of –5 °C with an input power density of 473 W/m 2 . The field test results showed that the full-scale coal-derived electrically conductive asphalt pavements were able to increase the pavement surface temperatures when electricity was applied, but the magnitude of temperature increase was highly dependent on the power density. Furthermore, it is promising to use coke aggregate to construct coal-derived electrically conductive asphalt pavements for snow/ice melting.

36 MATERIALS SCIENCE↗