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DOE OSTI2020

Enhanced dynamic equivalent identification method of large-scale power systems using multiple events

The increasing complexity of the interconnected power system makes high-fidelity dynamic simulation models computationally more intensive. To improve computation efficiency, model reduction techniques have been investigated to only preserve the dynamics in a limited area of interest (study area), while deriving equivalent representation for the external area. For this purpose, a measurement-based reduction approach using system identification techniques has been previously proposed. Accordingly, external areas are represented by dynamic equivalent loads using transfer function estimation. In this paper, in order to enhance the accuracy of the reduced model in preserving dynamics of the study area, multiple “grid” events of different types and at different locations are considered for identifying the parameters of the equivalent loads. Additionally, case studies are carried out in the NPCC 140-bus system. Comparisons are made between multiple events training and single event training, highlighting the advantages of the proposed method in providing a better representation of the grid dynamics under different operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Enhanced Dynamic Equivalent Identification Method of Large-Scale Power Systems Using Multiple Event

The increasing complexity of the interconnected power system makes high-fidelity dynamic simulation models computationally more intensive. To improve computation efficiency, model reduction techniques have been investigated to only preserve the dynamics in a limited area of interest (study area), while deriving equivalent representation for the external area. For this purpose, a measurement-based reduction approach using system identification techniques has been previously proposed. In that case, external areas are represented by dynamic equivalent loads using transfer function estimation. In this paper, in order to enhance the accuracy of the reduced model in preserving dynamics of the study area, multiple “grid” events of different types and at different locations are considered for identifying the parameters of the equivalent loads. Case studies are carried out in the NPCC 140-bus system. Comparison are made between multiple events training and single event training, highlighting the advantages of the proposed method in providing a better representation of the grid dynamics under different operating conditions.

Xue, Yaosuo↗

DOE OSTI2015

Radial force on the vacuum chamber wall during thermal quench in tokamaks

The radial force balance during a thermal quench in tokamaks is analyzed. As a rule, the duration τ{sub tp} of such events is much shorter than the resistive time τ{sub w} of the vacuum chamber wall. Therefore, the perturbations of the magnetic field B produced by the evolving plasma cannot penetrate the wall, which makes different the magnetic pressures on its inner and outer sides. The goal of this work is the analytical estimation of the resulting integral radial force on the wall. The plasma is considered axially symmetric; for the description of radial forces on the wall, the results of V.D. Shafranov’s classical work [J. Nucl. Energy C 5, 251 (1963)] are used. Developed for tokamaks, the standard equilibrium theory considers three interacting systems: plasma, poloidal field coils, and toroidal field coils. Here, the wall is additionally incorporated with currents driven by ∂B/∂t≠0 accompanying the fast loss of the plasma thermal energy. It is shown that they essentially affect the force redistribution, thereby leading to large loads on the wall. The estimates prove that these loads have to be accounted for in the disruptive scenarios in large tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

Estimation of Permanent Magnet Synchronous Motor Parameters using a Linear Unknown Input Interval Observer

This paper develops and evaluate a technique to estimate the speed and unknown load torque of a permanent magnet synchronous motor (PMSM). An interval unknown input observer (UIO) for linear time-invariant (LTI) systems is designed and utilized to estimate the PMSM parameters. Interval UIOs are advantageous as they allow for the estimation of both states and unknown inputs, while accounting for varying uncertainty sources, such as model and measurement uncertainties inherent in dynamic systems and processes. First, the nonlinear PMSM model is linearized to transform it to a suitable form for application of the linear interval UIO. Then, the interval UIO is applied to jointly estimate the motor speed and the unknown load torque disturbance. Assuming that the measurement noise and disturbances are bounded, lower and upper bounds are first computed for the unmeasured state (motor speed) and then for the unknown input (load torque). The proposed approach and its limitations are demonstrated for the nonlinear PMSM model derived from its equivalent electrical circuit.

Elinirina I Robinson↗

NASA NTRSDate not supplied

An Ensemble Investigation of the Causes for Regional Air-Quality Model Critical Load Exceedances Prediction Variability in European and North American Domains Using Diagnostics From Phase 4 of the Air Quality Model Evaluation International Initiative

We summarize tentative findings from multi air quality model ensembles for the years 2009 and 2010 in Europe (EU), and 2010 and 2016 in North America (NA), under AQMEII-4. The model predictions of sulphur and nitrogen deposition were used to estimate exceedances of critical loads for acidification and eutrophication, to show the extent to which the ensemble members agree in the magnitude and the trend of ecologically meaningful impacts. Model exceedance variability was analyzed using AQMEII-4 diagnostics. Evaluation against concentration and wet deposition observations, coupled with these diagnostics, identified specific process representations as the causes for variability between model predictions and for reduced model performance. All models predicted reductions in ecosystem acidification impacts in North America between the years 2010 and 2016, in accord with SO2 emissions reduction legislation which started in 2010 (SO2 SIP) However, all models in EU and NA domains had net negative biases for wet deposition of sulphur and nitrogen relative to observations. The wet S deposition average mean bias for the NA ensemble was -0.17 eq ha-1 d-1, and for the EU ensemble -1.15 eq ha-1 d-1. The NA daily wet deposition average mean bias for NH4+ was -0.37 eq ha-1d-1; EU -1.19 eq ha-1 d-1. The daily NA wet NO3- deposition average mean bias was -0.24 eq ha-1d-1; EU -0.69 eq ha-1 d-1. The members of the ensemble diverged (factor of 10) in their North American predictions for Ndep and consequently their eutrophication exceedances. The models with the highest eutrophication predictions also predicted the highest levels of gas-phase ammonia dry deposition (standard deviation of ammonia dry deposition flux across ensemble members was larger than the ensemble average). These models also had negative biases of predicted ammonia concentrations; average mean biases of -0.63 (satellite NH3) and -0.85 ppbv (surface NH3) compared to ensemble averages of -0.30 and -0.34 ppbv. Diagnostics showed that these differences resulted from the manner in which bidirectional ammonia fluxes were parameterized within these models. The second largest source of NA eutrophication prediction variability were models with positive biases in particulate ammonium and nitrate concentrations, and higher particle nitrogen deposition levels ( particle ammonium concentration bias +0.35 ug m-3; ensemble bias +0.15 ug m-3). We believe two factors may have led to these latter overestimates: higher levels of fine mode particle nitrate formation compared to other models (due to the use of an inorganic heterogeneous chemistry algorithm which did not take base cation chemistry into account), and updates to particle dry deposition velocities carried out in the absence of concurrent updates to wet scavenging algorithms. The relative importance of dry gas, dry particulate, and wet deposition towards total sulphur and nitrogen deposition totals differed between EU and North American domains, though all models had negative biases in wet deposition as noted above. Parallel and subsequent work suggests that multiphase hydrometeor scavenging may improve model wet deposition performance. An increased research focus is recommended for four model processes: multiphase hydrometeor scavenging, ammonia bidirectional fluxes, base cation chemistry and emissions, and particle dry deposition.

regional air-quality model↗

DOE OSTI2020

Predictive and Cooperative Voltage Control with Probabilistic Load and Solar Generation Forecasting

This paper proposes predictive cooperative voltage control method in a power system with high penetration of photovoltaic (PV) units. Cooperative distributed control of the reactive power output of PV inverters is coordinated with operation of voltage regulators (VRs) to maintain system voltages within an appropriate bandwidth. Probabilistic forecasting of the solar power generation and the loads is applied to estimate voltage changes which, in turn, are used to set the VR tap positions for preventing large voltage fluctuations with the lowest risk considering the voltage distribution estimation. The fine tuning of voltage adjustment is achieved by cooperative control of PV inverters to maintain a uniform voltage profile across the system. The proposed method is tested on the modified IEEE 123-node test feeder with high PV penetration using real insolation data and with constant loads replaced by several different load profiles. Simulation results demonstrate the effectiveness of the coordinated approach for voltage control with cooperative PV and predictive VR controls taking into account probabilistic load and solar power forecasts.

Cooperative Control↗

DOE OSTI2012

Refinement of Modeling Techniques for the Structural Evaluation of Hanford Single-Shell Nuclear Waste Storage Tanks

ABSTRACT Several tanks at the Hanford Site (in Washington State, USA) belong to the first generation of underground nuclear waste storage tanks known as single shell tanks (SSTs). These tanks were constructed between 1943 and 1964 and are well beyond their design life. This article discusses the structural analysis approach and modeling challenges encountered during the ongoing analysis of record (AOR) for evaluating the structural integrity of the SSTs. There are several geometrical and material nonlinearities and uncertainties to be dealt with while performing the modern finite element analysis of these tanks. The analysis takes into account the temperature history of the tanks and allowable mechanical operating loads of these tanks for proper estimation of creep strains and thermal degradation of material properties. The loads prescribed in the AOR models also include anticipated loads that these tanks may see during waste retrieval and closure. Due to uncertainty in a number of inputs to the models, sensitivity studies were conducted to address questions related to the boundary conditions to realistically or conservatively represent the influence of surrounding tanks in a tank farm, the influence of backfill excavation slope, the extent of backfill and the total extent of undisturbed soil surrounding the backfill. Because of the limited availability of data on the thermal and operating history for many of the individual tanks, some of the data was assumed or interpolated. However, the models developed for the analysis of record represent the bounding scenarios and include the loading conditions that the tanks were subjected to or anticipated. The modeling refinement techniques followed in the AOR resulted in conservative estimates for force and moment demands at various sections in the concrete tanks. This article discusses the modeling aspects related to Type-II and Type-III SSTs. The modeling techniques, methodology and evaluation criteria developed for evaluating the structural integrity of SSTs at Hanford are in general applicable to any similar tanks or underground concrete storage structures.

Waste Managament, Single Shell Tanks, Structural E↗

NASA NTRS2022

Using Soil Moisture Information to Better Understand and Predict Wildfire Danger: A Review of Recent Developments and Outstanding Questions

Soil moisture conditions are represented in fire danger rating systems mainly through simple drought indices based on meteorological variables, even though better sources of soil moisture information are increasingly available. This review summarises a growing body of evidence indicating that greater use of in situ, remotely sensed, and modelled soil moisture information in fire danger rating systems could lead to better estimates of dynamic live and dead herbaceous fuel loads, more accurate live and dead fuel moisture predictions, earlier warning of wildfire danger, and better forecasts of wildfire occurrence and size. Potential uses of soil moisture information in existing wildfire danger rating systems include (1) as a supplement or replacement for drought indices, (2) for live and (3) dead fuel moisture modelling, (4) for estimating herbaceous fuel curing, and (5) for estimating fuel loads. We identify key remaining research questions and note the logistical challenge of convincing wildfire professionals of the importance of soil moisture compared with more familiar wildfire danger metrics. While obstacles remain, the path forward is clear. Soil moisture information can and should be used to improve fire danger rating systems and contribute to more effective fire management for the protection of communities and ecosystems worldwide.

fuel properties↗

NASA NTRS1977

Theoretical study of hull-rotor aerodynamic interference on semibuoyant vehicles

Theoretical methods are being developed to predict the mutual interference between rotor wakes and the hull for semibuoyant vehicles. The objective of the investigation is to predict the pressure distribution and overall loads on the hull in the presence of rotors whose locations, tilt angles, and disk loading are arbitrarily specified. The methods involve development of potential flow models for the hull alone in a nonuniform onset flow, a rotor wake which has the proper features to predict induced flow outside the wake, and a wake centerline specification technique which accounts for the reactions of the wake to a nonuniform crossflow. The flow models are used in sequence to solve for the mutual influence of the hull and rotor(s) on each other and the resulting loads. A flow separation model is included to estimate the influence of separation on hull loads at high sideslip angles. Only limited results have been obtained to date. These were obtained on a configuration which was tested in the Ames Research Center 7- by 10-Foot Low Speed Tunnel under Goodyear Aircraft Corporation sponsorship and indicate the nature of the interference pressure distribution on a configuration in hover.

Spangler, S. B.↗

DOE OSTI2015

Advanced Variable Speed Air-Source Integrated Heat Pump (AS-IHP) Development (Final Report)

Between August 2011 and September 2015, Oak Ridge National Laboratory (ORNL) and Nordyne, LLC (now Nortek Global HVAC LLC, NGHVAC) engaged in a Cooperative Research and Development Agreement (CRADA) to develop an air-source integrated heat pump (AS-IHP) system for the US residential market. Two generations of laboratory prototype systems were designed, fabricated, and lab-tested during 2011-2013. Performance maps for the system were developed using the latest research version of the DOE/ORNL Heat Pump Design Model, or HPDM, (Rice 1991; Rice and Jackson 2005; Shen et al 2012) as calibrated against the lab test data. These maps were the input to the TRNSYS (SOLAR Energy Laboratory, et al, 2010) system to predict annual performance relative to a baseline suite of equipment meeting minimum efficiency standards in effect in 2006 (combination of 13 SEER air-source heat pump (ASHP) and resistance water heater with Energy Factor (EF) of 0.9). Predicted total annual energy savings, while providing space conditioning and water heating for a tight, well insulated 2600 ft2 (242 m2) house at 5 U.S. locations, ranged from 46 to 61%, averaging 52%, relative to the baseline system (lowest savings at the cold-climate Chicago location). Predicted energy use for water heating was reduced 62 to 76% relative to resistance WH. Based on these lab prototype test and analyses results a field test prototype was designed and fabricated by NGHVAC. The unit was installed in a 2400 ft2 (223 m2) research house in Knoxville, TN and field tested from May 2014 to April 2015. Based on the demonstrated field performance of the AS-IHP prototype and estimated performance of a baseline system operating under the same loads and weather conditions, it was estimated that the prototype would achieve ~40% energy savings relative to the minimum efficiency suite. The estimated WH savings were >60% and SC mode savings were >50%. But estimated SH savings were only about 20%. It is believed that had the test house been better insulated (more like the house used for the savings predictions noted above) and the IHP system nominal capacity been a bit lower that the energy savings estimate would have been closer to 45% or more (similar to the analytical prediction for the cold climate location of Chicago).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS2005

Global Admittance Estimates of Elastic and Crustal Thickness of Venus: Results from Top, Hot Spot, and Bottom Loading Models

We have calculated admittance spectra using the spatio-spectral method [14] for Venus by moving the central location of the spectrum over a 1 grid, create 360x180 admittance spectra. We invert the observed admittance using top-loading (TL), hot spot (HS), and bottom loading (BL) models, resulting in elastic, crustal, and lithospheric thickness estimates (Te, Zc, and Zl) [0]. The result is a global map for interpreting subsurface structure. Estimated values of Te and Zc concur with previous TL local admittance results, but BL estimates indicate larger values than previously suspected.

Smrekar, S. E.↗

DOE OSTI2018

Vitrification Process for Idaho HLW Calcine - 18433

The majority of the liquid wastes produced from reprocessing of several types of spent nuclear fuel at the Department of energy's (DOE) Idaho site have been volume reduced by calcination. The resulting ∼155,600 ft{sup 3} of calcined waste is stored in 43 shielded stainless steel bins, which have a 500-year design life. The calcined material is both a high-level waste and a RCRA hazardous waste, which complicates treatment and disposal options. In addition to a potential direct disposal option, treatment options that have been considered include steam reforming, hot isostatic pressing (HIP), and vitrification. This paper describes testing and evaluation of a vitrification option for the calcine. Vitrification to produce a borosilicate glass has the advantage that it is the only treatment that provides a waste form that meets the current HLW repository waste acceptance criteria. It is therefore the lowest risk option in terms of regulatory and legislative concerns. The present work addressed several key questions: (i) Calcine waste loadings in glass, which determine the number of HLW canisters produced and the required glass production rate (throughput) for the system design; (ii) Melt rate per unit glass pool surface area of the melter, which determines the sizing of the vitrification system; and (iii) The ability to meet waste form acceptance requirements (PCT and TCLP) while achieving reasonable waste loadings. These are issues of fundamental importance to the sizing estimates for the unit operations and overall flow-sheet and they, therefore, directly impact the cost and schedule estimates. Fully compliant, high-waste-loading glasses were developed for two of the four Idaho calcine wastes. The results demonstrate that waste loadings of 35 wt% waste oxides are achievable for the two alumina calcines and about 30 wt% is achievable for the two zirconia calcines. Testing of these formulations in a joule-heated ceramic melter showed glass production rates of over 5000 kg/(m2/d) for the Alumina calcine and over 8500 kg/(m{sup 2}/d) for the Zirconium-Na Blend calcine. These extremely high production rates translate directly into smaller system size and shorter mission duration and, therefore, reduced costs. Based on these results, a preliminary design for the full-scale vitrification system was developed. The system consists of waste receipt, vitrification, off-gas treatment, and canister sealing and decontamination equipment. The calcine is blended with the appropriate glass forming chemicals (or glass frit) and fed to the melter as a solid stream. The melter has a glass pool surface area of about 2.5 m{sup 2} and is equipped with a bubbling system to increase processing rates. Glass production rates of about 6 metric tons per day are projected. The vitrification system would be installed into the existing Idaho Waste Treatment Unit Facility (IWTU) so that no new facilities are required to house the treatment system, thus greatly reducing overall cost, duration, and risk. The system would be designed to treat all of the calcine waste within a period of 12 years at an operating efficiency of 80%, producing a total of about 8500 canisters each weighing two metric tons. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1991

Delaminations in composite plates under impact loads

A method is presented for calculating the locations, shapes, and sizes of delaminations which occur in a fiber reinforced composite plate subjected to non-penetrating (low velocity) impact of a solid object. The plate may be simply supported, clamped, or free along its edges. A failure model of the delamination formation was developed. This model was then coupled with a finite element analysis. The model and the finite element analysis were then implemented by a computer code (IMPACT-ST) which can be used to estimate the damage initiation load and the locations, shapes, and sizes of the delaminations. Tests were performed measuring the geometries of the delaminations in graphite-epoxy, graphite-toughened epoxy, and graphite-PEEK plates impacted by a projectile with a spherical tip having masses ranging from 0.355 lbm to 0.963 lbm and velocities from 50 in/sec to 225 in/sec. The data were compared to the results of the model, and good agreements were found between the measured and the calculated delamination lengths and widths.

Finn, Scott R.↗

NASA NTRSDate not supplied

Improved Techniques for Measuring Static Ground Wind Loads on the NASA Space Launch System Mobile Launcher 2

Vertical distribution of static ground wind loads was directly measured on Mobile Launcher ground support hardware to the NASA Space Launch System (SLS) at 1.75% scale in the Langley Research Center 14- by 22-Foot Subsonic Tunnel. Low-speed wind tunnel testing in the liftoff phase of flight was conducted for the SLS Block 1B family of rockets with their associated ground support systems. Improved methods for measuring and estimating static ground wind loads on the launch tower assembly are introduced in detail. A novel, distributed loads measurement technique is introduced and compared against lower-fidelity, previously utilized methods.

Ground Wind Loads↗

DOE OSTI2020

Codisposal Waste Package Loading Options for DOE SNF and HLW PPT

The U.S. Department of Energy (DOE) is responsible for managing spent nuclear fuel (SNF) that is currently in, or will in the future come into, its possession. DOE must continue to safely store that SNF, transport it to an interim storage site or a repository, and dispose of it. These fuels come from a wide range of reactor types with various cladding materials and enrichments. Many of these reactors, now decommissioned, had unique design features, such as core configuration, fuel element and assembly geometry, moderator and coolant materials, operational characteristics, and neutron spatial and spectral properties, resulting in a large diversity of reactor and fuel designs. Because of the wide variety and conditions of SNF, a robust DOE Standard Canister was proposed that would confine radionuclides and preclude moderator. The DOE Standard Canister had four variations: 3.05-meter (10-foot) or 4.57-meter (15-foot) length, and 45.7-cm (18-inch) or 61.0-cm (24-inch) diameter. For ultimate disposal in the Yucca Mountain Repository, these canisters were to be grouped with 61.0-cm (24-inch) diameter high level waste (HLW) canisters in a 2.13-meter (84-inch) diameter co-disposal waste package. The smaller 45.7-cm (18-inch) diameter DOE Standard Canister could be placed in the middle of five HLW canisters. The larger 61.0-cm (24-inch) diameter DOE Standard Canister would take the place of one of the five HLW canisters on the outer ring in the co-disposal waste package. No DOE Standard Canisters have been loaded. A preliminary evaluation has estimated the number of elements of a fuel type that can fit into the different sizes of the DOE Standard Canister, but no definitive loading configuration has been selected. Changing the loading configuration could impact the number of loadable DOE Standard Canisters and the number of co-disposal waste packages needed for eventual disposition. This paper conveys the ranges of DOE Standard Canisters and HLW canisters that may be produced under certain conditions. It also examines the differences in the estimated number of co-disposal waste packages produced for eventual disposal when using different loading strategies in the DOE Standard Canister for Advanced Test Reactor (ATR), Peach Bottom, and High Flux Isotope Reactor (HFIR) SNF. Changing the loading configurations of ATR, Peach Bottom, and HFIR SNF slightly impacted the number of co-disposal waste packages that may be needed for ultimate disposal. The change in loading configuration was more impactful when a different canister was used, as opposed to varying the number of elements that could fit inside the same size canister. In one case, a reduction of co-disposal waste packages could be achieved by allowing mixing of short HLW canisters with long DOE Standard Canisters. The main conclusion from this analysis is that the ratio between HLW canisters and DOE Standard Canisters will drive the total number of co-disposal waste packages. If too many HLW canisters (i.e., more than five times the number of 18-inch DOE standard canisters) or DOE Standard Canisters are produced, some co-disposal waste packages may not have all positions filled. A co-disposal waste package may be filled with all HLW with no DOE Standard Canister, or a co-disposal waste package could be filled with a single DOE Standard Canister. A ratio that does not closely align to optimum could allow for the design of waste packages that hold just HLW canisters or just DOE SNF canisters.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Co-Disposal Waste Package Loading Options for DOE SNF and HLW - 20331

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Short-term apartment-level load forecasting using a modified neural network with selected auto-regressive features

Residential electricity load profiles and their diversity have become increasingly important to realize the benefits of Smart or Transactive Energy Networks (TENs). An important element of TENs will be practical, accurate, and implementable residential load forecasting techniques. While there have been many approaches to short-term load forecasting, few have included forecasting for individual households, partly because the high volatility and idiosyncrasies present in individual household load data can pose significant challenges. In this study, we develop a Convolutional Long Short-Term Memory-based neural network with Selected Autoregressive Features (termed a CLSAF model) to improve short-term household electricity load forecasting accuracy by employing three strategies: autoregressive features selection, exogenous features selection, and a “default” state to avoid overfitting at times of high load volatility. We include aggregations of apartments to floor and building level, because utilities may favor transactive approaches that rely on aggregator models, e.g., a cluster of consumers as opposed to an individual. We demonstrate that the CLSAF model, by virtue of its enhanced feature representation and modest computational resources, can accomplish load forecasting in a multi-family residential building across three spatial granularities (individual apartment/household, floor, and building levels), with an accuracy improvement of up to 25% compared to a persistence model. We propose a data screening technique to characterize time-series electricity-load data. This technique is suitable for integration into a TEN ecosystem and allows one to estimate confidence levels of the load forecasts to optimize computational resources and the risks associated with uncertain forecasts.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2002

Solar Electric Propulsion Vehicle Design Study for Cargo Transfer to Earth-moon L1

A design study for a cargo transfer vehicle using solar electric propulsion was performed for NASA's Revolutionary Aerospace Systems Concepts program. Targeted for 2016, the solar electric propulsion (SEP) transfer vehicle is required to deliver a propellant supply module with a mass of approximately 36 metric tons from Low Earth Orbit to the first Earth-Moon libration point (LL1) within 270 days. Following an examination of propulsion and power technology options, a SEP transfer vehicle design was selected that incorporated large-area (approx. 2700 sq m) thin film solar arrays and a clustered engine configuration of eight 50 kW gridded ion thrusters mounted on an articulated boom. Refinement of the SEP vehicle design was performed iteratively to properly estimate the required xenon propellant load for the out-bound orbit transfer. The SEP vehicle performance, including the xenon propellant estimation, was verified via the SNAP trajectory code. Further efforts are underway to extend this system model to other orbit transfer missions.

Sarver-Verhey, Timothy R.↗