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DOE OSTI2026

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

AI-Based Faster-Than-Real-Time Stability Assessment of Large Power Systems with Applications on WECC System

Achieving clean energy goals will require significant advances in regard to addressing the computational needs for next-generation renewable-dominated power grids. One critical obstacle that lies in the way of transitioning today’s power grid to a renewable-dominated power grid is the lack of a faster-than-real-time stability assessment technology for operating a fast-changing power grid. This paper proposes an artificial intelligence (AI) -based method that predicts the system’s stability margin information (e.g., the frequency nadir in the frequency stability assessment and the critical clearing time (CCT) value in the transient stability assessment) directly from the system operating conditions without performing the conventional time-consuming time-domain simulations over detailed dynamic models. Since the AI method shifts the majority of the computational burden to offline training, the online evaluation is extremely fast. This paper has tested the AI-based stability assessment method using multiple dispatch cases that are converted and tuned from actual dispatch cases of the Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. The results show that the AI-based method could accurately predict the stability margin of such a large power system in less than 0.2 milliseconds using the offline-trained AI agent. Therefore, the proposed method has great potential to achieve faster-than-real-time stability assessment for practical large power systems while preserving sufficient accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Seasonal stabilization effects slowed the greening of the Northern Hemisphere over the last two decades

Rising atmospheric CO₂ and warming spring temperatures increase vegetation growth and the terrestrial carbon sink. However, drought, heat stress, phenology, and resource limitations may stabilize or limit theses projected increases. We investigate the balance between these amplifying and stabilizing ecological factors by asking whether enhanced early-season growth leads to continued late-season growth. Using the Moderate Resolution Imaging Spectroradiometer (MODIS) leaf area index (LAI) dataset, we identify three seasonal growth patterns based on early- and peak-season positive LAI anomalies: (1) amplification, where late-season LAI anomalies exceed earlier ones; (2) weak stabilization, where late-season anomalies remain similar or slightly lower; and (3) strong stabilization, where late-season anomalies become negative. Weak and strong stabilization events dominate across 67% and 26% of Northern Hemisphere ecosystems above 30°N, respectively. The absence of any trend in amplifying or stabilizing events suggests stabilizing factors seasonally offset CO₂ and temperature-induced spring greening. Terrestrial biosphere models underestimate strong stabilization and overestimate amplification events. This inconsistency arises from the models’ underestimation late-season LAI sensitivity to precipitation in water-limited regions; overlook negative legacy effects of early enhanced LAI on late-season soil moisture via evapotranspiration losses in energy-limited regions. Our findings suggest water/heat stress and resource limitations limit greening and the land carbon sink.

Zhang, Wen↗

DOE OSTI2020

Theoretical analysis of energetic-ion-driven resistive interchange mode stabilization strategies using a Landau closure model

The aim of the present study is to perform a theoretical analysis of different strategies to stabilize energetic-ion-driven resistive interchange mode (EIC) in Large Helical Device (LHD) plasma. In this work, we use a reduced MHD for the thermal plasma coupled with a gyrofluid model for the energetic particles (EP) species. The hellically trapped EP component is introduced through a modification of the drift frequency to include their precessional drift. The stabilization trends of the 1/1 EIC observed experimentally with respect to the thermal plasma density and temperature are reproduced by the simulations, showing a reasonable agreement with the data. The LHD operation scenarios with stable 1/1 EIC are identified, leading to the stabilization of the 1/1 EIC if the thermal plasma density and temperature are above a given threshold. Additionally, the 1/1 EIC are also stabilized if the rotational transform is modified in a way that the 1/1 rational surface is located further away than 0.9 times the normalized radius, or the magnetic shear in the plasma periphery is enhanced. Also, LHD discharges with large magnetic fields show a higher EIC destabilization threshold with respect to the thermal plasma density. If the perpendicular NBI deposition region is moved further inward than 0.875 times the normalized radius the 1/1 EIC are also stabilized. Furthermore, increasing the perpendicular NBI voltage such that the EP energy is higher than 30 keV stabilizes the 1/1 EIC. Moreover, deuterium plasmas show a higher stability threshold for the 1/1 EIC than hydrogen plasmas. The experimental data shows a larger time interval between EIC events as the power of the tangential NBI is increased providing that the perpendicular NBI power is at least 13 MW. This implies a stabilizing effect of the tangential NBI.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Measurement of Stability Diagram at IOTA at Fermilab

Nonlinear focusing elements can enhance the stability of particle beams in high-energy colliders by means of Landau Damping, through the tune spread which is introduced. We propose an experiment at Fermilab’s Integrable Optics Test Accelerator (IOTA) to investigate the influence of nonlinear focusing elements on the transverse stability of the beam. In this experiment, we employ an anti-damper, an active transverse feedback system, as a controlled mechanism to induce coherent beam instability. By utilizing the anti-damper, we can examine the impact of the nonlinear focusing element on the beam’s transverse stability. The stability diagram, a tool used to determine the system’s stability, will be measured using a recently demonstrated method at the LHC. This measurement is carried out experimentally by selecting specific threshold gains and measuring them for a range of phases. The stability diagram is represented by gei¿ on the complex plane. The experiment at IOTA adds insight towards the stability diagram measurement method by supplying a reduced machine impedance, to investigate the impedance’s effect on the stability diagram, as well as a larger range of phase measurements.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Thermodynamic and kinematic drivers of atmospheric boundary layer stability in the central Arctic during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC)

Observations collected during the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) provide a detailed description of the impact of thermodynamic and kinematic forcings on atmospheric boundary layer (ABL) stability in the central Arctic. This study reveals that the Arctic ABL is stable and near-neutral with similar frequencies, and strong stability is the most persistent of all stability regimes. MOSAiC radiosonde observations, in conjunction with observations from additional measurement platforms, including a 10 m meteorological tower, ceilometer, microwave radiometer, and radiation station, provide insight into the relationships between atmospheric stability and various atmospheric thermodynamic and kinematic forcings of ABL turbulence and how these relationships differ by season. We found that stronger stability largely occurs in low-wind (i.e., wind speeds are slow), low-radiation (i.e., surface radiative fluxes are minimal) environments; a very shallow mixed ABL forms in low-wind, high-radiation environments; weak stability occurs in high-wind, moderate-radiation environments; and a near-neutral ABL forms in high-wind, high-radiation environments. Surface pressure (a proxy for synoptic staging) partially explains the observed wind speeds for different stability regimes. Cloud frequency and atmospheric moisture contribute to the observed surface radiation budget. Unique to summer, stronger stability may also form when moist air is advected from over the warmer open ocean to over the colder sea ice surface, which decouples the colder near-surface atmosphere from the advected layer, and is identifiable through observations of fog and atmospheric moisture.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Design and Development of Stable Nanocrystalline High‐Entropy Alloy: Coupling Self‐Stabilization and Solute Grain Boundary Segregation Effects

Abstract Grain growth is prevalent in nanocrystalline (NC) materials at low homologous temperatures. Solute element addition is used to offset excess energy that drives coarsening at grain boundaries (GBs), albeit mostly for simple binary alloys. This thermodynamic approach is considered complicated in multi‐component alloy systems due to complex pairwise interactions among alloying elements. Guided by empirical and GB‐segregation enthalpy considerations for binary‐alloy systems, a novel alloy design strategy, the “ pseudo‐binary thermodynamic ” approach, for stabilizing NC‐high entropy alloys (HEAs) and other multi‐component‐alloy variants is proposed. Using Al 25 Co 25 Cr 25 Fe 25 as a model‐HEA to validate this approach, Zr, Sc, and Hf, are identified as the preferred solutes that would segregate to HEA‐GBs to stabilize it against growth. Using Zr, NC‐Al 25 Co 25 Cr 25 Fe 25 HEAs with minor additions of Zr are synthesized, followed by annealing up to 1123 K. Using advanced characterization techniques— in situ X‐ray diffraction (XRD), scanning/transmission electron microscopy (S/TEM), and atom probe tomography, nanograin stability due to coupling self‐stabilization and solute‐GB segregation effects is reported in HEAs up to substantially high temperatures. The self‐stabilization effect originates from the preferential GB‐segregation of constituent HEA‐elements that stabilizes NC‐Al 25 Co 25 Cr 25 Fe 25 up to 0.5 T m ( T m –melting temperature). Meanwhile, solute‐GB segregation originates from Zr segregation to NC‐Al 25 Co 25 Cr 25 Fe 25 GBs; this results in further stabilization of the phase and grain‐size (≈14 nm) up to ≈0.58 and ≈0.64 T m , respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Region-Based Stability Analysis of Resilient Distribution Systems with Hybrid Grid-Forming and Grid-Following Inverters

In this paper, distribution system stability considering mixed grid-forming (GFM) and grid-following (GFL) inverters is discussed. A holistic small-signal model of the distribution feeder accommodating both GFM and GFL inverters is derived. In contrast to conventional point-by-point stability analysis, a region-based stability assessment approach is proposed and implemented to evaluate small-signal system stability with both GFM and GFL controls. Furthermore, to enhance the computational efficiency, an Artificial Intelligence (AI) assisted Kernel Ridge Regression (KRR) approach is developed to obtain the stability region boundary. Therefore, with the derived stability region, the impact of critical parameters on system stability is intuitively shown, and more importantly, the relationship between the maximum penetration level and the corresponding feasible range of the selected control parameters can be quantified. The proposed approach has been validated using MATLAB/Simulink.

grid-following↗

DOE OSTI2021

TPCPF: Three-Phase Continuation Power Flow Tool for Voltage Stability Assessment of Distribution Networks With Distributed Energy Resources

This article presents a three-phase unbalanced continuation power flow algorithm for voltage stability assessment of distribution systems with high penetration of distributed energy resources (DERs). Analyzing distribution system voltage stability with DER will allow high penetration of renewable energy necessary for the sustainability goals. The developed algorithm can analyze voltage stability for both the meshed and radial systems and the balanced and unbalanced three-phase distribution systems. The developed tool allows the voltage stability analysis to facilitate the planning, operation, control, and distribution system management. The impact of DER on the voltage stability of several test cases has been analyzed considering constant power (P Q) and regulated-voltage (P V ) modes of operation for DER units. Moreover, different voltage stability case studies are presented to demonstrate the impact of unbalance, load increment, and network topology on the maximum loading capacity. Finally, results using the IEEE 13-node feeder, the 18-bus balanced shipboard system, the 13-node CIGRE benchmark system, and the 136-bus redial distribution feeder demonstrate that the developed continuation power flow tool can efficiently perform voltage stability analysis for active distribution systems.

42 ENGINEERING↗

DOE OSTI2023

Stabilizing a strongly nonlinear structure through shaker dynamics in fixed frequency voltage control tests

Bifurcations are commonly encountered during force controlled swept and stepped sine testing of nonlinear structures, which generally leads to the so-called jump-down or jump-up phenomena between stable solutions. There are various experimental closed-loop control algorithms, such as control-based continuation and phase-locked loop, to stabilize dynamical systems through these bifurcations, but they generally rely on specialized control algorithms that are not readily available with many commercial data acquisition software packages. A recent method was developed to experimentally apply sequential continuation using the shaker voltage that can be readily deployed using commercially available software. By utilizing the stabilizing effects of electrodynamic shakers and the force dropout phenomena in fixed frequency voltage control sine tests, this approach has been demonstrated to stabilize the unstable branch of a nonlinear system with three branches, allowing for three multivalued solutions to be identified within a specific frequency bandwidth near resonance. Recent testing on a strongly nonlinear system with vibro-impact nonlinearity has revealed jumping behavior when performing sequential continuation along the voltage parameter, like the jump phenomena seen during more traditional force controlled swept and stepped sine testing. Here, this paper investigates the stabilizing effects of an electrodynamic shaker on strongly nonlinear structures in fixed frequency voltage control tests using both numerical and experimental methods. The harmonic balance method is applied to the coupled shaker-structure system with an electromechanical model to simulate the fixed voltage control tests and predict the stabilization for different parameters of the model. The simulated results are leveraged to inform the design of a set of experiments to demonstrate the stabilization characteristics on a fixture-pylon assembly with a vibro-impact nonlinearity. Through numerical simulation and experimental testing on two different strongly nonlinear systems, the various parameters that influence the stability of the coupled shaker-structure are revealed to better understand the performance of fixed frequency voltage control tests.

42 ENGINEERING↗

DOE OSTI2023

Water Contamination Impacts on Biodiesel Antioxidants and Storage Stability

Biodiesel (fatty acid methyl esters) can oxidize in storage to form acids and gums that negatively impact engine performance and durability. Antioxidant additives are used to increase biodiesel storage stability, and previous studies that evaluated the effectiveness of antioxidants demonstrated that more polar antioxidants tend to be the most effective (provide the largest improvement in stability per unit of antioxidant added). However, polar antioxidants have significant water solubility, and diesel fuel storage tanks are commonly contaminated with water (forming a layer of water under the fuel). This study investigates whether nonpolar antioxidants, which are less effective in dry environments, might be more effective under wet conditions simulating real-world storage. Biodiesel blends treated with polar and nonpolar antioxidants were subjected to accelerated aging using the ASTM D4625 protocol (storage at 43 °C, open to air, for up to 24 weeks) both with and without added water. Fuels treated with polar/higher-effectiveness compounds and stored in contact with water (simulating water in a storage tank) or high humidity showed accelerated loss of stability compared to dry storage. The same fuel treated with a nonpolar antioxidant and stored in the same conditions did not exhibit accelerated stability loss and thus had higher storage stability over the long term despite treatment with an initially less effective additive. Analysis of the fuels during aging showed that this loss of stability was not due to oxidation but rather extraction of the polar antioxidant into the water layer. Antioxidant additives that are incompatible with wet or humid storage conditions were found to cause faster-than-anticipated loss of stability, which was preventable with use of nonpolar additives.

09 BIOMASS FUELS↗

DOE OSTI2026

Unraveling Fundamental Activity–Stability Relationships in Rutile Oxides

The oxygen evolution reaction (OER) is a key anodic half-cell reaction that accompanies several critical electrochemical reduction reactions of interest to a variety of applications. Despite steady advances in understanding and qualitatively predicting OER activity and selectivity trends, a comprehensive description or prediction of material aqueous (in)stability and degradation mechanisms remains elusive, even though these processes critically influence device lifetime and economic feasibility. In this work, we investigate the interplay, or lack thereof, between OER activity and material aqueous stability across rutile oxides, with a particular focus on iridium oxide (IrO 2 ). By applying a Born–Haber cycle, we calculate the thermodynamic driving force for metal dissolution as a function of the applied bias and electrolyte conditions. We apply interpretable machine learning techniques, including principal component analysis and symbolic regression, to analyze trends across rutile oxides and find that key thermodynamic descriptors for OER activity and surface stability are only very weakly correlated. Instead, the local atomic environment─especially electronic structure signatures for interactions between the active site and its neighbors─plays a more important role in predicting material stability. Leveraging these insights, we investigate the impact of doping IrO 2 with a range of transition metals and show that the stability of Ir active sites can be tuned largely independently of its predicted OER activity. These insights lay the foundation for material design to improve stability with respect to corrosion, with the ultimate aim to enhance long-term stability without sacrificing catalytic performance in the OER.

evolution reactions↗

DOE OSTI2022

Comparison of Kill Switch Toxins in Plant-Beneficial Pseudomonas fluorescens Reveals Drivers of Lethality, Stability, and Escape

Kill switches provide a biocontainment strategy in which unwanted growth of an engineered microorganism is prevented by expression of a toxin gene. A major challenge in kill switch engineering is balancing evolutionary stability with robust cell killing activity in application relevant host strains. Understanding host-specific containment dynamics and modes of failure helps to develop potent yet stable kill switches. To guide the design of robust kill switches in the agriculturally relevant strain Pseudomonas fluorescens SBW25, we present a comparison of lethality, stability, and genetic escape of eight different toxic effectors in the presence of their cognate inactivators (i.e., toxin–antitoxin modules, polymorphic exotoxin–immunity systems, restriction endonuclease–methyltransferase pair). We find that cell killing capacity and evolutionary stability are inversely correlated and dependent on the level of protection provided by the inactivator gene. Decreasing the proteolytic stability of the inactivator protein can increase cell killing capacity, but at the cost of long-term circuit stability. By comparing toxins within the same genetic context, we determine that modes of genetic escape increase with circuit complexity and are driven by toxin activity, the protective capacity of the inactivator, and the presence of mutation-prone sequences within the circuit. Here, the results of our study reveal that circuit complexity, toxin choice, inactivator stability, and DNA sequence design are powerful drivers of kill switch stability and valuable targets for optimization of biocontainment systems.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Stabilization of kink/peeling modes by coupled rotation and ion diamagnetic drift effects in quiescent H-mode plasmas in DIII-D and JT-60U

Magnetohydrodynamic stability at the edge pedestal in several quiescent H-mode (QH-mode) plasmas in DIII-D and JT-60U experiments was analyzed by considering plasma rotation and ion diamagnetic drift effects. It was identified that a kink/peeling mode, which is a prime candidate for a trigger of edge harmonic oscillation in QH-mode, is stabilized by plasma rotation when considering the ion diamagnetic drift simultaneously in both experiments. Furthermore, the stabilizing effect by rotation becomes more effective in case using the rotation profile of the main ion species evaluated by assuming radial force balance. In addition, when inverting the rotation direction, it was found that the kink/peeling mode is more stabilized when considering the rotation of the main ion species, though the mode is less stabilized by the rotation of impurity ion species. The result implies that the kink/peeling mode stability in QH-mode plasmas is sensitive to how the rotation profile is evaluated, but it is shown that a qualitative trend stabilizing the kink/peeling mode by rotation can be reproduced with the poloidal rotation profile of an impurity predicted numerically based on the neoclassical theory.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Comparison of MHD stability properties between QH-mode and ELMy H-mode plasmas by considering plasma rotation and ion diamagnetic drift effects

Magnetohydrodynamic (MHD) stability at tokamak edge pedestal in a quiescent H-mode (QH-mode) and type-I ELMy H-mode plasmas in DIII-D experiment was analyzed by considering plasma rotation and ion diamagnetic drift effects. QH-mode plasma is marginally stable to kink/peeling mode (K/PM), but ELMy H-mode one is almost unstable to peeling-ballooning mode (PBM). It was identified that there are three physics features responsible for the difference in the MHD stability properties between QH-mode plasma and ELMy H-mode one. These are the distance of pedestal foot from the last closed flux surface (LCFS), the amount of the ion diamagnetic drift frequency at pedestal, and impact of coupled rotation and ion diamagnetic drift effects. These features were confirmed through the numerical experiments that the stability properties of the QH-mode plasma can be changed to that of the ELMy H-mode one by shifting the plasma profiles inward in the radial direction and halving the ion diamagnetic drift frequency. The reasons of the change in the stability properties are thought as that K/PM is stabilized due to the inward shift of the bootstrap current profile, and PBM is destabilized due to the reduction of the coupled rotation and ion diamagnetic drift stabilizing effect. Importance of these features was validated through numerical experiments with experimental data of other QH-mode plasmas in DIII-D. All the results show that MHD stability properties of QH-mode plasma can be obtained in case that pedestal foot is close to LCFS, ion diamagnetic drift frequency is large due to high ion temperature, and strong rotation shear exists near pedestal.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Study of Inverter Control Strategies on the Stability of Low-Inertia Microgrid Systems

This paper investigates the stability of low-inertia microgrid systems with two control strategies that have different percentages of grid-forming (GFM) inverters. The first control strategy has approximately 50% GFM inverters, and all the battery inverters are working in GFM control mode. Originally, the second control strategy has approximately 10% GFM inverters, with only two battery inverters working in GFM control mode and the rest working in grid-following (GFL) PQ control mode based on current control, which cannot stabilize the microgrid system. Then, the second control strategy is modified to change the GFM inverters from droop control to isochronous control and the GFL battery inverters from traditional current control to voltage control for power control. Both control strategies can maintain system stability; however, the first control strategy can better handle contingency events. The study indicates that 1) a microgrid system with a higher percentage of GFM inverters has better stability; and 2) a microgrid with a lower percentage of GFM inverters can have poor stability, but improved control strategies in inverters can improve system stability. This study improves the understanding of how different percentages of GFM inverters and inverter control strategies affect the system stability of low-inertia microgrids.

droop control↗

DOE OSTI2023

ML-Based Power System Stability Assessment Considering Network Topology Changes: WECC 20,000+ Bus System Case Study

Modern power grids are fast-changing and thus require real-time monitoring and online stability assessment. With the rapid development of machine learning (ML) techniques, using data-driven models to provide fast and accurate estimations of power system stability marginal information, such as frequency nadir for frequency stability and critical clearing time (CCT) for transient stability, have become possible. However, despite the numerous research on ML-based methods for frequency nadir and CCT prediction, there is limited work on the impact of different network topology changes. Furthermore, most previous studies only focused on small or synthetic systems, and there is a lack of research on actual large power system models. In this paper, the above issues are addressed by studying the actual U.S. Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. Massive simulations are conducted in PowerWorld Simulator to study the impact of various topology change scenarios on both frequency stability and transient stability. System operating information is extracted from the success dispatch cases of various network topologies to generate a comprehensive dataset for ML-based models. Two ML methods, random forest (RF) and multilayer perceptron (MLP) neural network, are trained and tested for both frequency nadir prediction and CCT prediction. Test results have proven the models are capable of online stability assessment for large power networks such as the WECC system with sufficient accuracy.

critical clearing time↗

DOE OSTI2026

Transient Stability Study of IEEE 2800-2022 Standard Negative-Sequence-Current Compliant GFM IBRs

The primary function of grid-forming (GFM) inverter-based resources (IBRs) is to maintain voltage and fre- quency/phase angle stability; however, during unbalanced grid faults, IEEE Std. 2800-2022 requires IBRs to inject both positive- and negative-sequence reactive current. Enforcing compliance with this standard could compromise the stability of GFM IBRs under such fault conditions. This paper presents a preliminary transient stability study focused on the power angle stability of GFM IBRs operating in compliance with IEEE Std. 2800 during unbalanced faults. The goal is to assess potential stability issues associated with the standard's current injection requirements under fault ride-through conditions. The results show that injecting positive-sequence current with d-axis priority during unbalanced faults better preserves the power angle stability than the q-axis priority while still enabling negative-sequence current injection. These findings suggest that, to ensure stability, GFM IBRs might need to partially comply with IEEE Std. 2800 by prioritizing positive-sequence current injection along the d-axis.

14 SOLAR ENERGY↗