Power Density Of System Research Articles

Renewable energy driven on-road wireless charging infrastructure for electric vehicles in smart cities: A prototype design and analysis

The adoption of electrical vehicles (EVs) has increased due to the increasing concerns about fossil fuel shortages, rising costs, and environmental impacts. This increasing adoption of EVs significantly increase power demand on utility grids. Moreover the EVs require more time for charging compared to fossil fuel vehicles. To address these challenges, this study proposes a renewable energy-based on-road wireless charging (ORWC) infrastructureto reducing charging time and utilizing renewable energy within a smart city framework. This study develops a prototype of the ORWC system and examines its techno-economic and environmental benefits. Moreover, the study also evaluates annualized energy share, energy economics, and cost-effectiveness. The results of the proposed study indicate that the ORWC system in combination with RERs, effectively reduces the cost of energy from $0.112/kWh to $0.30/kWh and lowers carbon emissions from 76.9 tons/year to 29.5 tons/year. Furthermore, the results also reveals optimal energy distribution among different energy resources PV, BESS, and the grid. These results highlight that ORWC infrastructure can reduce peak load demand on existing grids and enhance the power density of EV charging systems. This has potential implications for future-oriented fast charging stations and policy development to support the widespread adoption of EVs.

Review on high-temperature superconducting REBCO trapped field magnets

Abstract Superconducting (SC) magnets can generate exceptionally high magnetic fields and can be employed in various applications to enhance system power density. In contrast to conventional coil-based SC magnets, high-temperature superconducting (HTS) trapped field magnets (TFMs), namely HTS trapped field bulks (TFBs) and trapped field stacks (TFSs), can eliminate the need for continuous power supply or current leads during operation and thus can function as super permanent magnets. TFMs can potentially trap very high magnetic fields, with the highest recorded trapped field reaching 17.89 T, achieved by TFSs. TFMs find application across diverse fields, including rotating machinery, magnetic bearings, energy storage flywheels, and magnetic resonance imaging (MRI). However, a systematic review of the advancement of TFMs over the last decade remains lacking, which is urgently needed by industry, especially in response to the global net zero target. This paper provides a comprehensive overview of various aspects of TFMs, including simulation methods, experimental studies, fabrication techniques, magnetisation processes, applications, and demagnetisation issues. Several respects have been elucidated in detail to enhance the understanding of TFMs, encompassing the formation of HTS bulk composites and TFSs, trapped field patterns, enhancement of trapped field strength through pulsed field magnetisation (PFM), as well as their applications such as SC rotating machines, levitation, and Halbach arrays. Challenges such as demagnetisation, mechanical failure, and thermal instability have been illuminated, along with proposed mitigation measures. The different roles of ferromagnetic materials in improving the trapped field during magnetisation and in reducing demagnetisation have also been summarised. It is believed that this review article can provide a useful reference for the theoretical analysis, manufacturing, and applications of TFMs within various domains such as materials science, power engineering, and clean energy conversion.

Design and performance analysis of a coupled burner for the Solid Oxide Fuel Cell system

The Solid Oxide Fuel Cell (SOFC) system is characterized by high energy conversion efficiency and low emissions. The energy supply and recovery of the SOFC system are facilitated through the ignition burner and the off-gas burner, respectively. This study proposes a coupled design of the ignition burner and the off-gas burner to reduce the burner volume, thereby enhancing the power density of the SOFC system. The ignition burner employs radially opposed jet combustion with fully premixed natural gas, while the off-gas burner uses swirl diffusion combustion with the anode off gas. When the premixed gas and lean anode off gas are unable to sustain the flame, catalytic combustion is initiated. Simulation and experiment methods are utilized to analyze the performance of the coupled burner in this paper. The results indicate that uniform mixing is achieved with a high swirl number (s1 = 2.6) for the premixed gas, and the maximum excess air coefficient for stable flame combustion at 400 °C is 2.47. As the temperature of the cathode off gas increases, the flameout boundary for the premixed gas gradually increases; conversely, with increasing burner power, the flameout boundary gradually decreases. The intersection cooling effect of mixed air and circumferential high-temperature flue gas is effective, and the flame does not exceed the tolerance temperature of the catalytic carrier. The diffusion combustion of anode off gas with a swirl number (s2 = 0.5) exhibits great gas mixing uniformity without a high-temperature core region. When transitioning from flame to catalytic combustion with premixed natural gas and anode off gas, there is a temperature lag of approximately 60 s. The isotropic cylindrical cordierite catalytic carrier with a 400 mesh and a coating of 60 g/ft3 Pt0.1Pd0.5 achieves stable catalytic combustion in an environment with preheated air temperatures ranging from 400 to 600 °C and H2 concentrations of 0.25–2.91 %.

Semiconducting minerals participated extracellular electron transfer in red soil of Ningxia Plain, China

In recent years, exploring interactions between sunlight, semiconducting minerals and microorganisms in nature has attracted great attention. However, relatively little research has been conducted on the interaction between minerals and microorganisms in the plain areas of the Yellow River Basin under sunlight. In this study, the mineral composition and microbial community of red soil from the Ningxia Plain, China were analyzed. X–ray diffraction (XRD) results showed that red soil contained semiconducting minerals such as birnessite, hematite and goethite. 16S rRNA analysis found that electroactive microorganisms such as Proteobacteria, Firmicutes and Actinobacteriota were enriched in in–situ microbial community of red soil. Afterwards, electrochemical tests such as linear sweep voltammetry (LSV) and I–t curves, indicated that red soil exhibited good semiconducting properties under light irradiation. Finally, a dual chamber system and electrochemical techniques were used to explore the electron transfer relationship between red soil and microorganisms. The open circuit voltage (350 mV) and maximum power density (1242.72 mW/m2) of red soil cathode system were significantly improved compared to blank graphite electrode, indicating that red soil could serve as electron acceptors for microbial extracellular respiration. Red soil electrode in live bacteria exhibited the highest photocurrent density (0.29 μA/cm2) and the lowest charge transfer resistance (Rct) (223 Ω) under light conditions, indicating that red soil accelerated the rapid transfer of electrons, reduced polarization loss, and enhanced extracellular electron transfer (EET) process under light conditions. This study demonstrated that the participation of semiconducting minerals in microbial EET processes under sunlight in the Ningxia Plain, China.

The Role of the Working Fluid and Non-Ideal Thermodynamic Effects on Performance of Gas Lubricated Bearings

Abstract Small-scale turbomachinery operating at high rotational speed is a key technology for increasing the power density of energy and propulsion systems. A notable example is the turbine of an organic Rankine cycle turbogenerator for thermal recuperation from prime engines and industrial processes. Such systems typically operate with organic compounds characterized by complex molecular structures, to allow the design of efficient fluid machinery and flexibility in matching the heat source and sink temperature profiles. Gas bearings are considered advantageous compared to traditional oil-lubricated rolling element bearings for supporting the turbine rotor, enabling greater machine compactness and reduced complexity, and to avoid contamination of the working fluid. In certain operating conditions, however, the lubricant of the bearing is in thermodynamic states near the saturated vapor line or in the vicinity of the fluid critical point whereby non-ideal effects are relevant and may affect bearing performance. This work investigates the physics of thin film flows in gas bearings operating with fluids made by complex molecules. The influence of non-ideal thermodynamic effects on gas bearing performance is discussed by analysis of the fluid bulk modulus. Reduced values of the non-dimensional bulk modulus near the critical point or saturated vapor line decrease bearing performance. The main parameter characterizing the influence of molecular complexity on bearing performance is shown to be the acentric factor. For complex fluids with large acentric factors, the impact of non-ideal thermodynamic effects on non-dimensional bearing load capacity and rotor-dynamic characteristics is less pronounced.

Enhancement of power density and hydrogen productivity of the reverse electrodialysis process by optimizing the temperature gradient between the working solutions

Reverse electrodialysis (RED) is an emerging technology that converts the salinity gradient energy (SGE) embedded in two solutions of different concentrations into electricity or hydrogen productivity. Given that two solutions containing SGE in nature are often at different temperatures, this study experimentally investigated the effects of the temperature and salinity ratio of the working solutions on the performance of RED systems. The results show that the power density and hydrogen productivity of RED systems could be markedly improved by adjusting the imposed temperature difference on the basis of the salinity gradient. The degree of improvement mainly depends on the magnitude and direction of the temperature difference between the high- and low-concentration solutions. The enhancement effect was more pronounced under a negative temperature difference (NTD) than under a positive temperature difference (PTD). Additionally, the improvement in system performance owing to the temperature difference was not affected by the endothermic or exothermic effects of different solutes in the water. At a NTD of 25℃ and a concentration of 0.1 M aqueous NaOH as the electrode solution, a RED system based on LiBr solution with a salinity ratio of 4.5 M/0.02 M as the working solution achieved a maximum power density of 0.754 ± 0.006 W∙m−2 and the highest hydrogen productivity of 1.128 ± 0.019 mol∙m−2∙h−1, which was 15.1% and 5.5% higher than the hydrogen productivity under LiCl and NaCl solution conditions, respectively. These results show the great potential of LiBr solution in the field of RED hydrogen productivity.

Energy-efficient Vienna rectifier for electric vehicle battery charging stations

Global DC fast-charging infrastructure is being rapidly developed to accommodate the ever-increasing demand from the electric vehicle market. A major complication in the electric power system's process is the proliferation of ultra-fast charging (UFC) stations, which are known for their enormous power consumption and unpredictable, intermittent performance. By implementing grid-supportive features and ensuring an improved power consumption profile for the grid, installing regional energy storage can solve these challenges. This study presents a control approach for managing the grid-side AC/DC converters of rapid charging stations focused on future-oriented regulation. The paper primarily concentrates on various Vienna rectifier topologies. The technology, characteristics, benefits, and operational aspects of Vienna rectifier topologies are vital to improving the performance, efficiency, and grid integration of electric vehicle charging systems. Fast charging, grid stability, energy economy, and the smooth integration of electric vehicles into the electrical grid are all made possible by Vienna rectifiers. When used in battery energy storage systems (BESS) for electric vehicle charging infrastructure, Vienna rectifiers allow for effective discharge and charging of the batteries. The configurations and assessments of these converters are examined, assessed, and compared based on power output parameters, element count, power factor, THD, and efficiency. The Vienna rectifier has been identified as the best suitable DC fast-charging converter architecture for power levels exceeding 15 kW due to its exceptional efficiency, limited output voltage ripples, high power density, reduced current ripples, and reliable performance. Research on ways to improve electric vehicle charging infrastructure can be spurred by a better grasp of the Vienna rectifier's technological complexities and performance benefits, leading to greener and more efficient transportation options. As a result, the system's power density will eventually rise and elemental stress will decrease.

Design of Radial Flux PM Synchronous Motor for EV Applications

Abstract: High-performance electric propulsion systems are becoming increasingly important as the automotive industry rapidly shifts to electric cars (EVs). The electric motor is an essential part of these systems as it determines the power, efficiency, and overall performance of the vehicle.This project uses Altair Flux, a full-featured finite element analysis (FEA) software suite, to build and optimize a radial flux motor (RFM) with permanent magnet synchronous motor (pmsm) . The main goal is to increase the power density and efficiency of the electric propulsion system for electric cars by utilizing Altair Flux's simulation and analytical capabilities.

Graphene thermionic energy converter integrated with two-stage thermoelectric generator for energy cascade utilization

For the purpose of energy cascade utilization, a new coupling system consisting of a graphene-based thermionic energy converter and a two-stage thermoelectric generator is proposed, in which the waste heat of graphene-based thermionic energy converter is recovered by the two-stage thermoelectric generator for generating extra power. Based on thermionic emission, semiconductor physics, and non-equilibrium thermodynamics, mathematical equations for power, efficiency, and exergy efficiency of the coupling system are presented, and the general performance features of the hybrid system are revealed. Numerical analysis shows that the maximum efficiency, maximum power density, and maximum exergy efficiency of the coupling system are 54.99%, 7.93Wcm−2, and 68.75%, respectively. Moreover, the maximum efficiency and maximum power density of the coupling system are enhanced by 28.39% and 28.52%, respectively, and the maximum exergy efficiency is improved by 28.39% compared to the stand-alone graphene-based thermionic energy converter. Subsequently, comprehensive parametric analyses are carried out to derive the effects of the heat source temperature, Fermi level of graphene, cathode work function, semiconductor element area-length ratio, and the Thomson effect on the performance of the coupled system. The obtained results may be useful for the design and running of this kind of energy cascade utilization system.

Surrogate-based multi-objective design optimization of tree-shaped fins with uniform branch end distribution for latent heat thermal energy storage

The enhancement of latent heat thermal energy storage (LHTES) systems through fin geometry optimization remains a critical challenge for leveraging the full potential of renewable energy sources. This study focuses on optimizing the geometries of tree-shaped fins to enhance power and energy densities in LHTES systems. The goal is to find branch designs with high energy and power density through a novel surrogate model-based optimization strategy that explores a broad design space. The surrogate models applied, including linear regression, principal component analysis-based linear regression, artificial neural networks, and random forest, are evaluated for their predictive performance. The random forest model demonstrates superior accuracy in predicting targets. The optimization process results in a Pareto-optimal design with a volume fraction of 33.9%. This optimal design substantially enhances the system's power density by 61.6% compared to conventional plate fins at an equivalent energy density. This optimized design improves energy and power density, achieving a uniform end-to-branch distribution, which is a pivotal factor for consistent temperature distribution and improved thermal efficiency. By integrating surrogate-based optimization with broad ranges of the tree-shaped fin design, this research has significantly improved the operational efficiency of LHTES systems. This research promises more effective thermal management and provides a methodological framework for design innovation in thermal energy storage.

Thermodynamic performance analysis of direct methanol solid oxide fuel cell hybrid power system for ship application

Methanol is a fuel that can be directly supplied to solid oxide fuel cell (SOFC) without carbon deposition. This paper introduces the direct methanol SOFC-Internal combustion engine (ICE) hybrid power and SOFC-Gas turbine (GT) hybrid power systems. Thermodynamic performance analysis of the hybrid power systems and an investigation into the impact of various parameters were conducted. The results indicate that the electric efficiency of the SOFC-ICE system is 56.07 %, which is 3 percentage points higher than the SOFC-GT system but 3–4 percentage points lower than the SOFC-ICE system with pre-reforming. Increasing fuel utilization rate, operation temperature, and excess air ratio is beneficial to the performance of the SOFC, and raising current density helps improve the system's power density. Load-sharing strategy research demonstrates that in a scenario where the power ratio between SOFC and the ICE is 35:65, compared to a methanol engine, the efficiency of the SOFC-ICE hybrid power system increases by 4.3 %. Despite a 1.4-fold increase in weight and a 1.66-fold increase in cost, the fuel consumption rate and carbon emissions decrease by 8.8 %. Therefore, the strategy of combining a high-power engine with a low-power SOFC is currently a suitable load-sharing strategy for ship applications.

Conceptual design and multi-objective optimization of a hybrid system based on direct ammonia protonic ceramic fuel cell and alkali metal thermal electric converter

As a power generation device, direct ammonia protonic ceramic fuel cells (NH3–PCFCs) also produce a significant amount waste heat, which not only results in energy wastage but also abnormal operation if the waste heat is not removed. To address these concerns and enhance generation electricity capacity, a novel waste heat recovery system based upon NH3-PCFC and alkali metal thermal electric converter (AMTEC) is first proposed, wherein the AMTEC converts the high-grade exhaust heat produced by the NH3-PCFC to extra electricity. Considering ammonia decomposition sluggish kinetics, various irreversible overpotential losses of NH3-PCFC as well as thermodynamic losses within the integrated system, the energetic/exergetic performance parameters evaluating the NH3-PCFC, AMTEC and the hybrid system are formulated. The general performance characteristics of the proposed system are revealed, along with a sensitive analysis conducted under specific operational conditions or structural parameters. Numerical calculation exhibited that the maximum attainable power density of the hybrid system has been promoted 20.5 % than that of stand-alone NH3-PCFC system. The multi-objective genetic algorithm is utilized to optimize the hybrid system performance for trade-off the power output and efficiency. Optimized results show the power density and corresponding efficiency of proposed system can respectively reach 6762.3 W m−2 and 49.8 % in the corresponding optimization conditions.

A Sinusoidal Doubly Salient Electromagnetic Machine Drive Fed by Third-Harmonic Injection Two-Stage Matrix Converter With Integrated Injection Inductor

This manuscript studies a sinusoidal doubly salient electromagnetic machine (SDSEM) drive fed by third-harmonic injection two-stage matrix converter (3TSMC) with integrated injection inductor to improve the power density of the whole system. First, compared with the conventional matrix converter (MC), the 3TSMC suffers from larger volume due to the inductor in the harmonic current injection circuit. In the proposed system, the harmonic injection current is synthesized by the field current of SDSEM and the injection inductor is removed. Then, the control strategy is proposed to decouple the current injection control and field current control, which means that the harmonic current and the field current can be regulated flexibly. Finally, a prototype is built to evaluate the proposed system and control strategy. Furthermore, the proposed 3TSMC-fed drive with the corresponding control strategy is also suitable for the other DC-excited three-phase sinusoidal AC machines, such as wound rotor synchronous machines.

Modeling, thermodynamic performance analysis, and parameter optimization of a hybrid power generation system coupling thermogalvanic cells with alkaline fuel cells

During the operation of alkaline fuel cells (AFCs), a significant amount of waste heat is generated, which has negative impacts on energy utilization and the environment. To improve energy efficiency, cost savings, environmental sustainability, and industrial practices, an effective approach is proposed to employ thermogalvanic cells (TGCs) for electric power generation by harvesting low-grade exhaust heat produced in AFCs. A mathematical model of the AFC-TGC hybrid system is established, taking into account the three overpotential losses in AFCs and the irreversible heat losses in TGCs. Based on this thermal-electric coupled model, we investigate the hybrid system’s output performance characteristics and optimal parameter design. The calculated results indicate that the hybrid system achieves a considerable increase of 19.72% in maximum power density from 247.07 W m−2 to 295.80 W m−2 and 5.71% in conversion efficiency from 10.16% to 10.74% compared to a single AFC, respectively. In addition, the output performance of the hybrid system can be further improved by adjusting system parameters such as the AFC’s operating temperature, the length of each TGC cell, the heat sink temperature, and the thermal convection coefficient. More importantly, a comparative study of the maximum power density of AFC-based cogeneration systems reveals that the TGC demonstrates a remarkable ability to economically recover waste heat from the AFC, surpassing previously reported thermal energy utilization devices. This study provides important theoretical guidance for the optimal design and parametric analysis of AFC-TGC hybrid systems, thereby facilitating the development of high-performance energy cascade utilization systems based on AFC devices.

Thermodynamic modeling and optimization of a novel hybrid system consisting of high-temperature PEMFC and spray flash desalination

The current study proposes a novel hybrid system consisting of the high-temperature proton exchange membrane fuel cell (HTPEMFC) and spray flash desalination (SFD) system to harvest the waste heat from HTPEMFC. The output power density and energy efficiency are analyzed to evaluate the system performance. Comparing the hybrid system with the stand-alone HTPEMFC system reveals that the maximum power density and energy efficiency of the proposed system are 69% and 40% higher than those of the stand-alone HTPEMFC system. Moreover, many parametric studies are conducted to determine how the performance of the hybrid system depends on its design and operating conditions. The cell working temperature exhibits contrary effects on the HTPEMFC and SFD system. The doping level should be less than 30 considering the stability of the membrane and the improvement of thermodynamic performance. A lower flow rate of feed water or a higher flow rate of cooling water is conducive to the proposed system. Finally, the multi-objective optimization is performed based on the genetic algorithm.

Linearized Minimum Current Stress Modulation Scheme of Single-Phase Bidirectional DAB AC–DC Converters

In this paper, the detailed steps for the derivation of linearized minimum current stress (LMCS) modulation scheme for single-phase bidirectional and isolated dual active bridge (DAB) ac-dc converters is presented. In order to reduce the current stress of the converter, a Lagrange multiplier method (LMM) scheme is designed to obtain the control coordinates constraint on the minimum value of the current stress. Compared with the conventional minimum current stress (MCS) control scheme, the proposed scheme realizes the linearization of power control, which significantly reduces the complexity of the controller algorithm. Moreover, the synchronous inverter control applied to the back-stage full-bridge is designed. Thus, the single stage power conversion is realized and the converter topology is electrolytic capacitorless, which promote the improvement of system reliability and power density. The impact of the ZVS scheme is analyzed in detail, and the adaptive-ZVS scheme for less system loss is selected. Finally, experimental results confirm the validity and feasibility of the proposed control scheme.

Research on dual‐winding permanent magnet generator system with integrated dual‐channel controller

AbstractThis article presents a dual‐winding permanent magnet generator (PMG) system with integrated dual‐channel controller to meet the requirements of high power density, high reliability, and high output performance of aircraft electric power system. The dual‐winding of the PMG are designed to have the same phase spatially, with which the same rotor position can be applied in independent vector control. In addition, a dual‐channel controller is applied to control the two sets of windings, which achieves high‐performance control under normal state and fault‐tolerant control under fault state. The integrated dual‐channel controller integrates two sets of main power circuits into one controller and uses a main control unit, which simplifies the PMG system leading to reduction in the overall volume and weight. Reliability analysis of dual‐winding PMG system is proposed to be compared with that of the single‐winding PMG system. A dual‐winding cooperative control strategy and a fault‐tolerant control strategy are proposed to achieve high‐performance control of DC‐link voltage under normal condition and redundant functions under fault condition. As a result, the reliability of the PMG system is improved. The experimental results validate the effectiveness of the proposed PMG system and the control strategy.

Efficient and geometry-matching two-stage annular thermoelectric generator for tubular solid oxide fuel cell waste heat recovery

Tubular solid oxide fuel cell (TSOFC) converts a great part of chemical energy within fuel into high-grade waste heat, leading to a decrease in overall fuel efficiency. In this paper, a steady-state hybrid system model based on TSOFC and two-stage annular thermoelectric generator (TATEG) is proposed. Considering various kinds of irreversible effects, mathematical model for the hybrid system is explicitly formulated and verified to guarantee the accuracy. Energetic and exergetic performance indexes of the hybrid system and subsystems are obtained, and the corresponding performance characteristics are revealed. Calculation results display that the power density, energetic and exergetic efficiencies of TSOFC-TATEG hybrid system can be 15.29 %, 11.25 % and 11.25 % higher than that of stand-alone TSOFC, respectively. The power density, energetic efficiency and exergetic efficiency of TSOFC-TATEG hybrid system are all increased by 5.65 % compared to that of TSOFC-ATEG hybrid system. Furthermore, this study reveals that enhancing the performance of the hybrid system is attainable through regulating variables, such as elevated operating temperatures, optimal quantities of thermoelectric elements, appropriate ratios between thermoelectric element numbers, well-considered thermocouple thickness, suitable thermocouple radial width, and the judicious selection of parameters like annular shape or height ratio.

Core–shell structure selective emitter doped with rare earth elements for solar thermophotovoltaic system

Aiming at the low utilization of radiation photons in the solar thermophotovoltaic system, a rare earth core–shell (REC) structure selective thermal emitter is designed to achieve selective emission. The 3D symmetrical opal core–shell structure and rare earth elements play an important role in the selective emission characteristic of the REC emitter. The opal core–shell structure of the REC emitter is optimized by finite difference time domain simulation and numerical calculation, and the optimal size is determined. The REC emitter can adjust the characteristic peak of rare earth elements to produce a narrow–band radiation peak with an emissivity approaching 1 at a wavelength just before the cutoff wavelength, and maintain low emissivity in the long and short–wave bands. The conversion efficiency of the solar thermophotovoltaic system based on the REC emitter and InGaAs cell is 17.29 % at 1400 K, and the power density can reach 428.3 mW/cm2. The mechanism of the selective emission characteristic of the REC emitter is revealed, and its emissivity is insensitive to polarization and incidence angle. The REC emitter further improves the selective emission characteristic and makes the radiation spectrum better match the thermophotovoltaic cell. The power density and conversion efficiency of the solar thermophotovoltaic system are increased by improving the utilization of the thermophotovoltaic cell to the radiation photon.

A New Current Ripple Suppression Strategy for DC Link Inductance of Three-Phase Current Source Converter

In this paper, a new modulation method is proposed to reduce the dc link inductor current ripple of a three-phase current source converter. The excessive current ripple of the dc link inductor of the current source converter will bring a series of hidden dangers to the system: the total harmonic distortion of current increases, the system stability decreases, and the electromagnetic interference increases. The traditional method to reduce the inductor current ripple is to increase the inductance value or increase the switching frequency of the system. Using this method reduces the system efficiency and power density and increases the cost. Compared with the above methods, the optimized modulation strategy appears more attractive. This paper first analyzes the mechanism of reducing current ripple by traditional methods, and then proposes a new vector action sequence and vector action time algorithm. Finally, an experimental platform is built to compare the new scheme with the traditional scheme. The experimental results prove the correctness of the new modulation strategy.