SEARCH · Search NASA

Results for “high torque”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

DOE OSTI2018

Advanced High Torque Density Magnetically Geared Generator

The objective of this research project was to investigate the fundamental torque density limitations of multistage flux focusing magnetic gears and magnetically geared direct-drive generators for wind turbines. Magnetic gears create non-contact speed amplification by modulating the air-gap magnetic field harmonics created by magnetic rotors. By integrating a stator into the magnetic gear structure a very high torque density direct-drive generator can be created. Magnetic geared systems offer unique capabilities that are currently not available using existing mechanically geared systems, such as overload protection. Magnetic gears also offer the potential for higher reliability, higher efficiency and quieter operation than is currently achievable using a mechanically geared generator. By increasing reliability and design life magnetic gears could decrease the overall life-cycle costs when compared with equivalent mechanical or direct-drive drivetrains. This research project investigated and experimentally testing two sub-scale magnetic gearboxes (0.12 m diameter) and two large diameter magnetic gearboxes (0.56m and 0.63m diameter). The goal of the project was to demonstrate a torque density >300Nm/L for a multistage magnetic gearbox with integrated stator. A nested multistage magnetic gear structure was first proposed and studied. However, it was shown that the nested design greatly increased mechanical complexity and therefore a two-stage series typology was utilized. A multi-stage magnetic gear with a 59:1 gear ratio was successfully experimentally tested. A peak torque of 4.25 kN·m was measured and this resulted in an overall active region torque density of 141 N·m/L (when including support rings). The torque density was significantly reduced from what was computed using 2-D electromagnetic analysis. This reduction was due to the 3-D edge effects, increased power losses and the inclusion of additional mechanical support rings as well as other mechanical assembly design changes. At large diameters contiguous lamination parts could not be fabricated and so a segmented laminated rotor design had to be used. This reduced the mechanical strength of the design when compared to small diameter magnetic gears and resulted in the need for the addition of mechanical support rings to prevent deflection. The final experimentally tested design also had a high torque ripple and the power loss within the magnetic gear did not change significantly with load. This therefore resulted in the efficiency being high only at peak loads. Despite not experimentally achieving the 2-D calculated high torque density the analysis has shown that the problems encountered with the scaling can be overcome with careful design changes. For example, understanding the unique mechanical deflection requirements during the electromagnetic design of the large diameter magnetic gears is key to achieving both a high torque density based on the electromagnetic analysis and a high torque density based on the mechanical support needs. Furthermore, ensuring that end plates are made of non-conductive material and minimizing other conductive support elements within the magnetic structure is a key requirement for reducing eddy current losses. In summary, if the mechanical design can be made more robust and eddy current loss mitigation strategies are used in the mechanical design phase then the magnetic gear is capable of being scaled up whilst operating at a very high torque density. This will then enable it to be potentially performance and cost competitive with alternative direct-drive and mechanically geared wind turbine drivetrains.

17 WIND ENERGY↗

DOE OSTI2021

MADE3D: Enabling the next generation of high-torque density wind generators by additive design and 3D printing

Direct-drive wind turbine generators are increasing in popularity, thanks to recent project developments—especially offshore, where reliability and efficiency are major cost drivers. Yet, high capital costs are forcing many original equipment manufacturers to consider lightweight, high-torque density generators for next-generation multi-megawatt turbines that may be difficult to realize by traditional design or manufacturing methods. In this study, we present a new design framework enabled by advanced machine learning and multimaterial additive manufacturing to perform a magnetic topology optimization that maximizes the torque per rotor active mass for a 15-megawatt direct-drive permanent magnet wind generator. A comparison of the proposed approach against conventional topology optimization demonstrated a significant increase in computational efficiency and accuracy in performance predictions. Results using single and multimaterial compositions for rotor core and magnets identify a wider choice of 3D printable designs for a given specification. A hybrid combination of sintered and dysprosium-free polymer-bonded magnets shows good potential for torque performance by saving material costs up to 8.75%. More than 30% improvement in rotor torque densities is identified which can marginally improve the overall generator torque density. With the rapid evolution of multipowder deposition technolgies, this study can greatly inspire a new paradigm for design-driven manufacturing with novel material compositions and lightweight, low-cost, high-strength multimaterial geometries that were previously unexplored for direct-drive generators.

17 WIND ENERGY↗

DOE OSTI2021

MADE3D: Enabling the Next-Generation High-Torque- Density Wind Generators by Additive Design and 3D Printing

Direct-drive wind turbine generators are increasing in popularity, thanks to recent project developments - especially offshore, where reliability and efficiency are major cost drivers. Yet, high capital costs are forcing many original equipment manufacturers to consider lightweight, high-torque density generators for next-generation multi-megawatt turbines that may be difficult to realize by traditional design or manufacturing methods. In this study, we present a new design framework enabled by advanced machine learning and multimaterial additive manufacturing to perform a magnetic topology optimization that maximizes the torque per rotor active mass for a 15-megawatt direct-drive permanent magnet wind generator. A comparison of the proposed approach against conventional topology optimization demonstrated a significant increase in computational efficiency and accuracy in performance predictions. Results using single and multimaterial compositions for rotor core and magnets identify a wider choice of 3D printable designs for a given specification. A hybrid combination of sintered and dysprosium-free polymer-bonded magnets shows good potential for torque performance by saving material costs up to 8.75%. More than 30% improvement in rotor torque densities is identified which can marginally improve the overall generator torque density. With the rapid evolution of multipowder deposition technologies, this study can greatly inspire a new paradigm for design-driven manufacturing with novel material compositions and lightweight, low-cost, high-strength multimaterial geometries that were previously unexplored for direct-drive generators.

3D printing↗

DOE OSTI2019

Shaping of Cams for High-Torque Variable-Speed Drives

Attention focuses on the calculation of the working profile for three-dimensional cams in an oscillatory lever mechanism with a contacting spherical roller. That permits the creation of 3D surfaces for milling of the cams on CNC machine tools. Methods are proposed for determining the pressure angle and selecting the optimal parameters of the oscillatory mechanism in a nonfrictional high-torque variable-speed drive.

42 ENGINEERING↗

DOE OSTI2026

High-Torque Heavy-Rare-Earth-Free Electric Motor Thermal Management

This project is part of a multi-lab Next-Generation Reliable Electric Drive Systems for Medium and Heavy-Duty Vehicles (NEXT-DRIVE) project led by Oak Ridge National Laboratory (ORNL), and including NREL, Sandia National Laboratories (SNL), and Ames Laboratory that leverages research expertise and facilities of these national labs to develop tools and approaches for reducing the design and development time of new electric drive technologies for medium and heavy-duty vehicles (MHDVs) and their associated costs while increasing reliability and asset utilization. The Next-Drive project aligns with the DOE's goals by introducing high-fidelity multi-physics and AI/ML-based modeling to design low-cost, highly reliable, and longer-lifetime drivetrains, aiming to achieve 25 years of progress in 5 years. The efforts of this project will focus on NEXT-DRIVE Task 4 (led by ORNL, NREL, and AMES) - developing high-fidelity modeling framework and identifying technologies enabling heavy-rare-earth-free electric motors for medium- and heavy-duty vehicles to achieve 1 million miles of operation. Contrary to conventional approaches that optimize the motor for power density, the focus will be to identify motor designs that achieve the best trade-off between motor power density and durable operation. NREL tasks include development of high-fidelity motor thermal models incorporating rotor windage losses and identification, evaluation and measurement of motor interface materials in key thermal pathways. The poster summarizes NREL's accomplishments for the first half of FY 2025 and outlines future plans.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2015

System and method to allow a synchronous motor to successfully synchronize with loads that have high inertia and/or high torque

A mechanical soft-start type coupling is used as an interface between a line start, synchronous motor and a heavy load to enable the synchronous motor to bring the heavy load up to or near synchronous speed. The soft-start coupling effectively isolates the synchronous motor from the load for enough time to enable the synchronous motor to come up to full speed. The soft-start coupling then brings the load up to or near synchronous speed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Comprehensive Report on Design and Development of a 100-kW DSSRM

Switched reluctance machines (SRMs) are low cost and fault tolerant alternatives for traction applications. Due to their relatively low torque density and high torque ripple, these machines have not been used in commercialized electrified power trains yet. The double-stator magnetic configuration, where a segmental rotor shared between two stators, is proven to have superior torque density, lower acoustic noise, and torque pulsation. The double-stator SRM (DSSRM) has a high potential of being the next generation of traction motors since it combines the advantages of permanent magnet-free machines, such as low cost and independence from supply chain issues associated with rare metals, while providing high torque and power densities. In this paper, we introduce the complete design process of a 100-kW DSSRM including electromagnetic, structural, thermal, and system level design. The performance of the developed DSSRM is verified with the experimental data. This paper presents overall study of DSSRM and describes merits of DSSRM drive system.

42 ENGINEERING↗

DOE OSTI2022

Efficient, Compact, and Smooth Variable Propulsion Motor (Final Report)

In this project, a new architecture of highly efficient hydraulic motor was developed for the propulsion of off-highway vehicles. The motor uses an adjustable linkage driving a cam to vary the displacement of the piston, resulting in a Variable Displacement Linkage Motor (VDLM). The motor uses low friction rolling element bearings to significantly reduce mechanical friction, especially in the demanding low-speed high-torque conditions experienced by off-highway vehicles. The VDLM has high torque capabilities for its size due to the radial piston packaging and use of a multi-lobe cam. A VDLM is very smooth due to the ability to tune the torque ripple through the design of the cam profile. The project was divided into three periods. During the first period, a dynamic model was constructed of the motor to predict the performance of the motor and the vehicle. During the second period, a single-cylinder learning prototype was designed, built, and tested to validate the models constructed in the first period. In the third period, a multi-cylinder prototype motor was optimized, designed, fabricated, and tested. The motor demonstrated excellent mechanical efficiency (above 92.5% across the range of displacements), but the experimentally measure volumetric efficiency was lower than expected due to higher leakage rates created by the poor tolerance control on the prototype. To validate the dynamic models developed in the first period and better understand design trade-offs. In the third period a multi-cylinder concept demonstration prototype will be designed, fabricated, and tested. The final prototype will be tested on a motor dynamometer and will be utilized in hardware-in-the-loop testing to demonstrate its efficiency and performance impacts on the overall drive train. The experimental results were used in a drive train simulation of a compact track loader operating through a drive cycle. Using the VDLM in a hydrostatic circuit yielded 17.1% reduction in fuel consumption and 36.5% reduction in a series hybrid transmission.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2016

Discovery of stationary operation of quiescent H-mode plasmas with net-zero neutral beam injection torque and high energy confinement on DIII-D

Recent experiments in DIII-D [J. L. Luxon et al., in Plasma Physics and Controlled Nuclear Fusion Research 1996 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159] have led to the discovery of a means of modifying edge turbulence to achieve stationary, high confinement operation without Edge Localized Mode (ELM) instabilities and with no net external torque input. Eliminating the ELM-induced heat bursts and controlling plasma stability at low rotation represent two of the great challenges for fusion energy. By exploiting edge turbulence in a novel manner, we achieved excellent tokamak performance, well above the H{sub 98y2} international tokamak energy confinement scaling (H{sub 98y2} = 1.25), thus meeting an additional confinement challenge that is usually difficult at low torque. The new regime is triggered in double null plasmas by ramping the injected torque to zero and then maintaining it there. This lowers E × B rotation shear in the plasma edge, allowing low-k, broadband, electromagnetic turbulence to increase. In the H-mode edge, a narrow transport barrier usually grows until MHD instability (a peeling ballooning mode) leads to the ELM heat burst. However, the increased turbulence reduces the pressure gradient, allowing the development of a broader and thus higher transport barrier. A 60% increase in pedestal pressure and 40% increase in energy confinement result. An increase in the E × B shearing rate inside of the edge pedestal is a key factor in the confinement increase. Strong double-null plasma shaping raises the threshold for the ELM instability, allowing the plasma to reach a transport-limited state near but below the explosive ELM stability boundary. The resulting plasmas have burning-plasma-relevant β{sub N} = 1.6–1.8 and run without the need for extra torque from 3D magnetic fields. To date, stationary conditions have been produced for 2 s or 12 energy confinement times, limited only by external hardware constraints. Stationary operation with improved pedestal conditions is highly significant for future burning plasma devices, since operation without ELMs at low rotation and good confinement is key for fusion energy production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

Polyalkylene Glycol (PAG) Based Lubricant for Light & Medium Duty Axles

The axle lubricant (SAE 75W-140) widely used in the market place over the last few years is primarily formulated from polyalpha olefin (PAO) basestock. This investigation focused on polyalkylene glycol (PAG) base stock which is significantly different chemically from PAO and because of their polar nature it is hypothesized that it can adsorb relatively easily on contacting surfaces resulting in significant friction reduction and improve fuel economy. Axle efficiency is generally quite high at high torque range but it could be quite low at low torque range representative of EPA drive cycles. Therefore, this project primarily focus on improving axle efficiency in the low torque range while maintaining all durability attributes. The objective of this project is to develop novel lubricant formulations that are expected to improve the fuel efficiency of light, medium, heavy-duty, and military vehicles by at least 2% over Society of Automotive Engineers (SAE) 75W-140 axle lubricants (improvement based on comparative results from engine dynamometer testing, chassis dynamometer testing or test track, e.g., SAE J1321) without adverse impacts on vehicle performance or durability. The proposed research project followed a structured approach beginning with lubricant formulations by varying base oil chemistry and additive components followed by physical property characterization. Lubricant performance evaluations started with simple laboratory friction, wear, oxidation, and corrosion tests which guided into identification of performance areas requiring improvements. This required an iterative lubricant reformulation. Once a few acceptable formulations were identified, they are evaluated in more complex component tests including ASTM tests (L-37 - load carrying capacity under low speed and high torque, L42 – load carrying properties under high speed and shock loading, L-60 - thermal and oxidative stability, and L-33-1 moisture corrosion resistance). Two issues were observed following L-42 tests; toxicological and foaming. This required reformulation and repeating all ASTM tests. During repeat tests it was observed that some of the additives precipitated out of solution. Since it was discovered quite late in the program, and the time it may need to find a solution to this issue, the team changed direction of the program to switch to use of an oil soluble PAG as a co-basestock (15-30%) with mineral oil used in a commercial formulation (SAE 75W-85). This formulation strategy helped passing all ASTM tests. This was followed by Ford proprietary axle efficiency, gear wear, and chassis roll dynamometer tests for fuel economy evaluations. Axle efficiency was improved up to 7% when a full PAG formulation was used but no such significant improvement was observed with PAG as co-basestock formulation. Chassis roll fuel economy improved by 1.9% with PAG co-basestock formulation (conforming to SAE 75W-85) compared to SAE 75W-140 baseline. However, it was observed that the improvement is mostly due to reduced viscosity of candidate formulation when compared to a full mineral oil based SAE 75W-85 formulation. PAG as co-basestock also exhibited unacceptable wear in proprietary gear wear test. This investigation highlighted challenges with PAG formulations including identification of additive components that stay in PAG solution for intended duration, and meeting component durability requirement.

36 MATERIALS SCIENCE↗

DOE OSTI2017

Synthetic Fiber Capstan Drives for Highly Efficient, Torque Controlled, Robotic Applications

Here this paper describes the design and performance of a synthetic rope on sheave drive system. This system uses synthetic ropes instead of steel cables to achieve low weight and a compact form factor. We demonstrate how this system is capable of 28-Hz torque control bandwidth, 95% efficiency, and quiet operation, making it ideal for use on legged robots and other dynamic physically interactive systems. Component geometry and tailored maintenance procedures are used to achieve high endurance. Endurance tests based on walking data predict that the ropes will survive roughly 247,000 cycles when used on large (90 kg), fully actuated bipedal robot systems. The drive systems have been incorporated into two novel bipedal robots capable of three-dimensional unsupported walking. Robot data illustrate effective torque tracking and nearly silent operation. Finally, comparisons with alternative transmission designs illustrate the size, weight, and endurance advantages of using this type of synthetic rope drive system.

42 ENGINEERING↗

DOE OSTI2026

Electronic structure of the kagome compound CaTi 3⁢ Bi 4 using high-field torque magnetometry and density functional theory

Here, we report systematic torque magnetometry measurements to investigate the electronic properties of the newly discovered kagome compound CaTi 3 ⁢Bi 4 . Electrical transport, magnetic susceptibility, and thermal measurements reveal no evidence of a magnetic ground state in this material. Torque data obtained in magnetic fields up to 41.5 T exhibit clear de Haas–van Alphen (dHvA) oscillations, with nine distinct frequencies ranging from 13 to 6164 T. Angular-dependent dHvA measurements show that, with the exception of the lowest frequency (13 T), all observed frequencies nearly follow a 1/cos ⁡𝜃 dependence, where 𝜃 is the angle between the crystallographic 𝑐 axis and the magnetic field direction. This behavior is characteristic of quasi-two-dimensional Fermi-surface sheets with nearly circular cross sections. To further elucidate the electronic structure, we performed density functional theory (DFT) calculations of the band structure and Fermi surface. The calculated bands reveal the presence of multiple Dirac points (DP), flat bands (FB), and van Hove singularities (VHS) near the Fermi level. The resulting Fermi surface consists of several quasi-two-dimensional cylindrical sheets, consistent with the experimentally observed 1/cos⁡ 𝜃 dependence. Notably, the theoretical dHvA frequencies, derived from extremal Fermi-surface cross-sectional areas, agree well with the experimental values and reproduce their angular dependence. Remarkably, all experimentally observed frequencies are captured by the DFT predictions. Pressure-dependent calculations up to 10 GPa show that the electronic features—DP, FB, and VHS—evolve systematically with pressure. In particular, the VHS shifts closer to the Fermi level, demonstrating that pressure acts as an effective tuning parameter in this material. These combined experimental and theoretical results provide a comprehensive understanding of the electronic structure of CaTi 3 ⁢Bi 4 and demonstrate how pressure can be used to tune its key electronic features, offering valuable guidance for exploring related kagome materials.

Shtefiienko, Kyryl [West Texas A & M University, C↗

DOE OSTI2016

Parallel elastic elements improve energy efficiency on the STEPPR bipedal walking robot

This study describes how parallel elastic elements can be used to reduce energy consumption in the electric motor driven, fully-actuated, STEPPR bipedal walking robot without compromising or significantly limiting locomotive behaviors. A physically motivated approach is used to illustrate how selectively-engaging springs for hip adduction and ankle flexion predict benefits for three different flat ground walking gaits: human walking, human-like robot walking and crouched robot walking. Based on locomotion data, springs are designed and substantial reductions in power consumption are demonstrated using a bench dynamometer. These lessons are then applied to STEPPR (Sandia Transmission-Efficient Prototype Promoting Research), a fully actuated bipedal robot designed to explore the impact of tailored joint mechanisms on walking efficiency. Featuring high-torque brushless DC motors, efficient low-ratio transmissions, and high fidelity torque control, STEPPR provides the ability to incorporate novel joint-level mechanisms without dramatically altering high level control. Unique parallel elastic designs are incorporated into STEPPR, and walking data shows that hip adduction and ankle flexion springs significantly reduce the required actuator energy at those joints for several gaits. These results suggest that parallel joint springs offer a promising means of supporting quasi-static joint torques due to body mass during walking, relieving motors of the need to support these torques and substantially improving locomotive energy efficiency.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2018

Calculation of AC Magnetizing Loss of ReBCO Superconducting Tapes Subjected to Applied Distorted Magnetic Fields

In recent years, there are fast-increasing concerns on the utilizations of superconducting rotating electrical machines in different application areas, such as ship propulsion systems, aircraft drivers, and wind turbine generators, since these machines exhibit the merits of high current density, compact design, high power density, light weight, high torque density as well as high efficiency. One of the main limitations in front of the vast use of superconducting tapes in the fabrication of electrical machineries is AC magnetizing loss when tapes are exposed to an external magnetic field, which can decrease the critical current density of wires, as well. In the literature, most of the research works have been done on calculation of the AC magnetizing loss under a pure external magnetic field, while in reality, magnetic flux lines in AC electrical machines are usually distorted with harmonics because of different reasons such as distorted leakage flux, distributed coils of a winding in several slots, cogging fields, mechanical faults, etc. Since these distorted fields contain harmonics, then in this paper, the AC magnetizing loss of superconducting tapes has been electromagnetically modeled and calculated when they are subjected to nonsinusoidally distorted external magnetic fields. The magnetic field dependency of critical current density has been considered in a proposed finite element model. The results have shown that the AC magnetizing loss increases significantly under a distorted applied field compared with a sinusoidal one. In addition, the loss increase depends on the harmonic content which would increases drastically with total harmonic distortion of the applied magnetic field.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Comparative Analysis of Direct and Indirect Cooling of Wide-Bandgap Power Modules and Performance Enhancement of Jet Impingement-Based Direct Substrate Cooling

With the development of high-power and high-torque machines, requirements for high-power density electronics are increasing. Thermal management of such systems requires high heat extraction. Conventional air cooling based heat sinks and cold plate based liquid cooling have their own benefits for various applications but has limitations for high power density applications. The current study explores a jet impingement based direct substrate cooling system that was implemented for a SiC based direct bonded Cu substrate for various power losses. Numerical comparison between jet impingement cooling and conventional horizontal/indirect cooling (pin fin heat sink and genetic algorithm-optimized heat sink) showed that the area weighted average of the heat transfer coefficient (HTC) is high for both horizontal cooling designs, and the local HTC is higher for jet impingement. Design iterations were undertaken to resolve the bottleneck of this cooling system. Increasing the number of nozzles helped to cover more area at the direct bonded Cu bottom plate, which drops the chip temperature considerably. With a constant flow rate, increasing the number of nozzles would decrease local jet velocity, which reduces the heat extraction by jet impingement. This issue can be addressed by reducing the diameter of nozzle but doing so results in a high pressure drop where the design constraint is 2 psi. A flared nozzle design is proposed, which has a higher spreading angle of the jet that increases the flow coverage and reduces the pressure drop of the coolant loop.

Barua, Himel↗

DOE OSTI2023

Wave Energy Power Take-off Validation with a Hydraulicly Actuated Rotary Dynamometer and a Bi-Directional High-Power DC Supply

There are many organizations working towards the commercialization of wave energy converter technologies and are advancing their designs through the technology readiness levels (TRLs). A critical step before the field deployment of prototype wave energy converters is the validation of the subsystems and components that are contained in the wave energy converter through laboratory testing and performance characterization. In 2021, the National Renewable Energy Laboratory (NREL) developed and demonstrated a system for testing power takeoffs (PTO) with a low-speed, high-torque dynamometer and a grid-tied high-power DC power source and sink before field deployment. The hydraulic dynamometer allows for the simulation of PTO actuation from wave motion and is capable of a wide range of wave periods and heights which are represented as various speeds and torques from the dynamometer. The high-power bidirectional power supply allows for hardware in the loop and controller in the loop testing to be conducted on WEC power electronics. This presentation was made to describe the methods used by NREL research staff to test all components and sub-systems in the PTO of a novel wave energy converter before field deployment.

dynamometer↗

DOE OSTI2023

Wave Energy Power Take-Off Validation with a Hydraulicly Actuated Rotary Dynamometer and a Bidirectional High-Power DC Supply: Preprint

dynamometer↗

DOE OSTI2017

A Comprehensive Review of Permanent Magnet Transverse Flux Machines for Direct Drive Applications

The use of direct drive machines in renewable and industrial applications are increasing at a rapid rate. Transverse flux machines (TFM) are ideally suited for direct drive applications due to their high torque density. In this paper, a comprehensive review of the permanent magnet (PM) TFMs for direct drive applications is presented. The paper introduces TFMs and their operating principle and then reviews the different type of TFMs proposed in the literature. The TFMs are categorized according to the number of stator sides, types of stator cores and magnet arrangement in the rotor. The review covers different design topologies, materials used for manufacturing, structural and thermal analysis, modeling and design optimization and cogging torque minimization in TFMs. The paper also reviews various applications and comparisons for TFMs that have been presented in the literature.

24 POWER TRANSMISSION AND DISTRIBUTION↗