Odd Harmonics Research Articles

The Analysis of Odd Triple Harmonics to Detect Broken Rotor Bar in Delta-Connected Induction Motors

The Analysis of Odd Triple Harmonics to Detect Broken Rotor Bar in Delta-Connected Induction Motors

Numerical simulation of flow around a transversely oscillating square cylinder at Re=22000

The study utilized OpenFOAM software, combined with the k-ω shear stress transport (SST) turbulence model and Arbitrary Lagrangian-Eulerian (ALE) dynamic mesh method, to investigate the influence of the oscillation amplitude on the flow dynamics around a square cylinder at Re = 2.2 × 104. It was found that various oscillation amplitudes affect the non-Gaussian characteristics of fluctuating pressure differently along the cylinder's surface: diminishing at the leading edge while intensifying at the trailing-edge corner. Concurrently, secondary recirculation bubbles near the cylinder's leading and trailing edges gradually diminish and eventually disappear with increasing oscillation amplitudes. Analysis of the amplitude spectrum of transverse velocity indicates the exclusive presence of odd-order harmonics along the central axis, while both odd and even-order harmonics are observed on either side of the central axis. Additionally, heightened oscillation amplitudes result in increased energy transfer from the cylinder to the fluid, with the energy density function predominantly exhibiting negative values and periodic variations occurring at twice the frequency of cylinder displacement or lift coefficient. As the oscillation amplitude increases, the vortex in the wake region transitions from a single-row to a double-row configuration. The research results provide important theoretical guidance for deepening the understanding of the flow characteristics around the oscillating square cylinder.

An MTCA-based LLRF prototype system of LINAC in Hefei Advanced light facility

The linear accelerator (LINAC) system currently under construction at the Hefei Advanced Light Facility (HALF) employs acceleration tubes to accelerate the electron beam to 2.2 GeV. The RF field within the acceleration tube is controlled by an MTCA.4-based low-level radio frequency (LLRF) prototype system to meet stringent phase stability requirements. This paper introduces the structure of the LLRF system, encompassing both its hardware and software components. The LLRF system uses the non-IQ-sampling method to suppress odd harmonics through digital filters, achieving a signal-to-noise ratio (SNR) of approximately 73 dB. Given that the power sources of most acceleration tubes operate in a saturated state, the radio-frequency (RF) control algorithm within the software is based on a separate amplitude open-loop and phase close-loop to maintain stable phase control during amplitude disturbances. The design of the RF control logic, including digital filters, the REF phase tracking method, the close-loop feedback controller, and the output pulse mode control algorithm, is detailed. Offline pulse-to-pulse test results demonstrate that it achieves a phase stability of 0.0176° rms with a solid-state amplifier, meeting the facility's requirements.

Cubic nonlinearity and surface shock waves in soft tissue-like materials

The cubic nonlinearity of shear wave propagation plays a significant role in brain injury biomechanics. However, soft materials, like the brain, also support the propagation of surface waves, which produce a combination of longitudinal and transverse deformation. The order of the nonlinearity of surface waves in soft materials is still unknown. Here, we directly observe nonlinear Scholte waves propagating in an interface formed by an incompressible gelatin tissue-mimicking phantom and a water layer using ultrasound imaging operated as fast as 16667 frames per second. A two-dimensional correlation-based tracking algorithm was utilized to extract movies of the movement produced by the surface wave. Our results show that the initially nearly monochromatic wave becomes progressively distorted with the propagation due to nonlinearity. The distortion of the wave and its frequency spectrum indicate a high content of odd harmonics when compared with even harmonics. Additionally, by fitting our experimental data to a minimalist one-dimensional model based on the wave speed variation as a function of the perturbation amplitude, we found a cubic nonlinear parameter 46 times larger than the quadratic nonlinear parameter. Overall, the wave distortion, the harmonic development, and the dependence of the wave speed with the amplitude prove that cubic nonlinearity is essential to modeling nonlinear Scholte wave propagation.

M3D‐DPWM strategy for three‐phase four‐leg inverter with higher harmonic suppression capability

AbstractThree‐phase four‐leg inverters are widely used in power systems due to their inherent ability to handle unbalanced loads. However, with conventional 3D space vector pulse width modulation (3D‐SVPWM), high harmonics of large amplitude exist in the output voltage around the switching frequency and its integer multiples leading to noise in the load motor and limiting the application range of the inverter system. The passband amplification of conventional sinusoidal filters and their cutoff frequency vary with the load, so it is particularly important to investigate the regulation strategy with harmonic suppression. In this study, an improved 3D discontinuous pulse width modulation (M3D‐DPWM) strategy is proposed based on 3D‐SVPWM. By reducing the conventional 3D‐SVPWM switching segments and changing the vector synthesis sequence of the last half switching cycle, the output phase voltage period is reduced to half of the original one, which achieves the purpose of suppressing the output voltage at the switching frequency and its odd multiple high harmonics without changing the fundamental characteristics and adding additional circuits. In contrast, the conventional 3D‐SVPWM switching frequency is increased to 20 kHz to achieve similar performance. Finally, the effectiveness of the proposed strategy is verified by simulation and experiment.

MHD activity induced coherent mode excitation in the edge plasma region of ADITYA-U tokamak

In this paper, we report the excitation of coherent density and potential fluctuations induced by magnetohydrodynamic (MHD) activity in the edge plasma region of ADITYA-U tokamak. When the amplitude of the MHD mode, mainly the m/n = 2/1, increases beyond a threshold value, |B̃θ|/Bθ ∼ 0.3%–0.4%, coherent oscillations in the density and potential fluctuations are observed having the same frequency as that of the MHD mode. The mode numbers of these MHD induced density and potential fluctuations are obtained by Langmuir probes placed at different radial, poloidal, and toroidal locations in the edge plasma region. Detailed analyses of these Langmuir probe measurements reveal that the coherent mode in edge potential fluctuation has a mode structure of m/n = 2/1, whereas the edge density fluctuation has an m/n = 1/1 structure. It is further observed that beyond the threshold, the coupled power fraction scales almost linearly with the magnitude of B̃θ/Bθ fluctuations. Furthermore, the rise rates of the coupled power fraction for coherent modes in density and potential fluctuations are also found to be dependent on the growth rate of magnetic fluctuations. The disparate mode structures of the excited modes in density and plasma potential fluctuations suggest that the underlying mechanism for their existence is the coupling of even harmonics of potential to the odd harmonics of pressure due to 1/R dependence of the toroidal magnetic field.

Evaluation of the Nonlinear Response of KCl Solution to High-Amplitude Stimulation Using a Four-Point Cylindrical Gold Electrode.

A four-electrode system and high-voltage amplitude stimulation (with a voltage of more than 1 V) are always used for nonlinear spectroscopy of biological solutions like yeast suspension. Multiple studies indicate that yeast membrane activities are the primary source of the harmonics detected from yeast suspensions. However, other investigations have demonstrated that at least part of the harmonics are mainly due to the nonlinear impedance of the electrode-electrolyte interface. Here, we want to find a mathematical model to analyze the odd harmonics generated by the interface. The KCl solution is the basis of the essential medium used in yeast culture. No study models the nonlinear behavior of the KCl solution using four-electrode. We used a sinusoidal voltage with a low frequency and a high amplitude to test an ionic solution with 1, 30, and 130 mM of potassium chloride. The voltage had no direct current component. Here, we show that the relationship between the amplitude of the excitation voltage and the third harmonic of the current can be accurately represented using the Butler-Volmer equation. Additionally, we analyze the impact of potassium chloride (KCl) concentration on the behavior of the third harmonic. This paper presents a method and model that can be used for nonlinear spectroscopy studies of biological solutions using a four-electrode system with the aim of deriving information from cells without considering the interface effect.

Comparing different segments in shut-in pressure signals: new insights into frequency range and energy distribution

Water hammer diagnostics is an important fracturing diagnosis technique to evaluate fracture locations and other downhole events in fracturing. The evaluation results are obtained by analyzing shut-in water hammer pressure signal. The field-sampled water hammer signal is often disturbed by noise interference. Noise interference exists in various pumping stages during water hammer diagnostics, with significantly different frequency range and energy distribution. Clarifying the differences in frequency range and energy distribution between effective water hammer signals and noise is the basis of setting specific filtering parameters, including filtering frequency range and energy thresholds. Filtering specifically could separate the effective signal and noise, which is the key to ensuring the accuracy of water hammer diagnosis. As an emerging technique, there is a lack of research on the frequency range and energy distribution of effective signals in water hammer diagnostics. In this paper, the frequency range and energy distribution characteristics of field-sampled water hammer signals were clarified quantitatively and qualitatively for the first time by a newly proposed comprehensive water hammer segmentation-energy analysis method. The water hammer signals were preprocessed and divided into three segments, including pre-shut-in, water hammer oscillation, and leak-off segment. Then, the three segments were analyzed by energy analysis and correlation analysis. The results indicated that, one aspect, the frequency range of water hammer oscillation spans from 0 to 0.65 Hz, considered as effective water hammer signal. The pre-shut-in and leak-off segment ranges from 0 to 0.35 Hz and 0 to 0.2 Hz respectively. Meanwhile, odd harmonics were manifested in water hammer oscillation segment, with the harmonic frequencies ranging approximately from 0.07 to 0.75 Hz. Whereas integer harmonics were observed in pre-shut-in segment, ranging from 6 to 40 Hz. The other aspect, the energy distribution of water hammer signals was analyzed in different frequency ranges. In 0 − 1 Hz, an exponential decay was observed in all three segments. In 1 − 100 Hz, a periodical energy distribution was observed in pre-shut-in segment, an exponential decay was observed in water hammer oscillation, and an even energy distribution was observed in leak-off segment. In 100 − 500 Hz, an even energy distribution was observed in those three segments, yet the highest magnitude was noted in leak-off segment. In this study, the effective frequency range and energy distribution characteristics of the field-sampled water hammer signals in different segments were sufficiently elucidated quantitatively and qualitatively for the first time, laying the groundwork for optimizing the filtering parameters of the field filtering models and advancing the accuracy of identifying downhole event locations.

Modeling of Human-Induced Dynamic Bouncing Force Using a Self-Sustained Nonlinear Oscillator

This paper proposed a single-degree-of-freedom self-sustained nonlinear oscillator capable of precisely predicting the bouncing force induced by a person during bouncing activity on a flat and rigid surface. A bouncing person produces essential internal energy required to maintain its motion, so it can be modeled as a self-sustained oscillator that can generate (i) the stable limit cycle, (ii) the periodic bouncing force signal, and (iii) the self-sustained motion. A hybrid Van der Pol–Rayleigh oscillator added with two quadratic and one cubic nonlinear terms has been derived to yield desired softening and hardening effects as well as even and odd harmonics, as observed from the analysis of experimental bouncing force data. The force applied on the surface corresponds to its restoring force. The stability analysis of the oscillator has been performed using the energy balance and perturbation methods. The model parameters are extracted from the experimental bouncing force data resulting from a bouncing test on a group of seven subjects with shoe insoles at six different frequencies guided by a metronome. The bootstrapping method has been performed to examine the convergence of mean values of each model parameter by increasing the cardinality of the experimental set. The bouncing force signals produced by the proposed model and experimental results demonstrate an excellent agreement.

High‐Order Nonlinear Frequency Conversion in Transparent Conducting Oxide Thin Films

AbstractThe study of conductive oxides has gained momentum within the photonics community due to their unique linear and nonlinear optical properties. Despite recent experiments reporting on high harmonic generation from thin films, the optical/electronic behavior of these compounds at the nanoscale is still not fully understood due to the lack of a suitable theoretical model. In the present work, aluminum zinc oxide is excited near its epsilon‐near‐zero crossing point using incident femtosecond pulses having peak power densities in the 1 TW cm−2 range. A relatively efficient frequency up‐conversion including even and odd harmonics up to the seventh order is observed. A hydrodynamic‐Maxwell theoretical approach is adopted, capable of simultaneously taking into account linear and nonlinear dispersions, nonlocal effects, surface, magnetic, and bulk nonlinearities in a spectral region that spans over two and a half octaves from the UV to the NIR region. The study enables a deeper understanding of the fundamental material parameters regulating optical nonlinearities, providing important insights to engineer this class of materials for applications in sensing, ultra‐fast physics, and spectroscopy.

Next-to-eikonal corrections to dijet production in Deep Inelastic Scattering in the dilute limit of the Color Glass Condensate

We analyze the effects of next-to-eikonal corrections on dijet production in Deep Inelastic Scattering off nuclear targets in the framework of the Color Glass Condensate. They require the knowledge of correlators of fields in the target beyond those computed in the standard McLerran-Venugopalan model, specifically those between transverse and boost-enhanced components, and of the recoil of the fields. We neglect the latter, while for the former we develop a linear model valid for large nuclei. We considered the unpolarized cross sections for dijet production in the approximation of a homogenous dilute nucleus, obtaining simple analytic expressions for the cross sections at next-to-eikonal accuracy, valid in the limit of total dijet momentum and dijet momentum imbalance larger than the saturation scale of the nucleus. We perform a numerical study of the results at energies of the Electron Ion Collider, finding O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) effects in the cross sections at large total momentum. We also analyze the azimuthal asymmetries between total momentum and imbalance, finding that non-eikonal corrections induce odd azimuthal harmonics for the situation of jets with equal momentum fractions from the virtual photon, where they are absent in the eikonal approximation. Finally, in the eikonal approximation we have compared the results of our analytic expansion valid in the dilute limit of the target, and the full Color Glass Condensate results in the McLerran-Venugopalan model and their correlation limit. Our analytic expressions match the correlation limit ones in the region where both should be simultaneously valid and reproduce very well the full Color Glass Condensate results in its validity region.

First-principles simulations of high-order harmonics generation in thin films of wide bandgap materials [Invited

High-order harmonics generation (HHG) is the only process that enables tabletop-sized sources of extreme ultraviolet (XUV) light. The HHG process typically involves light interactions with gases or plasma––material phases that hinder wider adoption of such sources. This motivates the research in HHG from nanostructured solids. Here, we employ the time-dependent density function theory (TDDFT) to investigate material platforms for HHG at the nanoscale using first-principles supercomputer simulations. We reveal that wide bandgap semiconductors, aluminum nitride (AlN) and silicon nitride (Si3N4), are highly promising for XUV light generation when compared to silicon, one of the most common nonlinear nanophotonic materials. In our calculations, we assume excitation with a 100 fs pulse duration, 1×1013W/cm2 peak power, and 800 nm central wavelength. We demonstrate that in AlN material the interplay between the crystal symmetry and the incident light direction and polarization can enable the generation of both even and odd harmonics. Our results should advance the development of high-harmonics generation of XUV light from nanostructured solids.

Current Sensor Fault-Tolerant Control Strategy for Speed-Sensorless Control of Induction Motors Based on Sequential Probability Ratio Test

In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed estimation strategy based on the current sensor fault-tolerant control is proposed to improve the speed estimation accuracy under the current sensor faults. First, to detect the current sensor faults in real time, the sequential probability ratio test is introduced to the system by using the innovations of the extended Kalman filter (EKF). Second, to ensure speed estimation accuracy, a double-cascading second-order generalized integrator (DSOGI) is employed to reconstruct the faulty current information when a fault is identified. Finally, the reconstructed current information is fed back to the sequential probability extended Kalman filter (SPEKF), which estimates the rotor speed of the IM, and high-accuracy speed estimation under the condition of current sensor faults is achieved. The effectiveness of the proposed strategy is validated by a series of experiments, which were conducted on a 3 kW induction motor drive platform.

Harmonic Detection Methods and Optimization Strategies for Charger in Power Grid

The charger’s operation in the power grid will cause harmonic pollution, affecting the service life of the equipment and the quality of the power grid. The harmonic characteristics and detection during the charging process are studied. The simulation model of charger is established first using MATLAB, the results of the experiment show that odd harmonics are mainly generated during charging, and the distortion rate of the current harmonics remains between 0.231 and 0.443 during the charging process. A new wavelet neural network is proposed to detect the harmonic method. Experimental results indicate that, compared with previous detection methods, this network has better detection efficiency and accuracy for harmonics. But detection result of this network is unstable and does not even converge. A new adaptive bat algorithm with improved focusing distance is presented here to optimize the wavelet neural network, which effectively solves the defect of being sensitive to the node number of hidden layer, resulting in higher detection accuracy, faster detection speed, and stable convergence. The detection error range is reduced from −0.03 to 0.02, and the number of iterations is reduced to around 1000.

CLEMD, a circuit-level electrical measurements dataset for electrical energy management

Enhancing energy efficiency in commercial buildings is crucial for reducing energy consumption. Achieving this goal requires careful monitoring and analysis of the energy usage patterns exhibited by different devices. Nonetheless, gathering data from individual appliances in commercial buildings presents difficulties due to the large number of appliances, complex installations, and costs. This paper presents the Circuits-Level Electrical Measurements Dataset (CLEMD). The measurement was conducted at the main switchboard to a set of distribution boards instead of measuring at the individual loads. The data is gathered from an institutional setting. It consists of 42 records of vital electrical parameters including voltage, current, frequency, real power, reactive power, apparent power, power factor, and odd harmonics for electrical currents. The device deployed in the measurement were industry-grade and had a high sampling rate of 200 kHz. The measurements were done over a 40-day period, from September 16 2023 to October 25 2023. CLEMD is the first Malaysian public dataset on circuit-level electricity consumption and offers analysis opportunities in different research areas such as electricity load disaggregation at circuit level, circuit identification, load profile forecasting, and pattern recognition.

Modeling and Mitigating Output-Dependent Modulation in Current-Steering DAC Based on Differential-Quad Switching Scheme

This brief presents a comprehensive analysis of the output-dependent modulation (ODM) in a current-steering digital-to-analog converter (CS-DAC) based on the differential-quad switching (DQS) structure. A mathematical model is proposed to accurately describe ODM, which is categorized into two types: output transition errors and boundary effect errors. A novel approach of adding isolation devices is introduced and reinterpreted to mitigate the effect of ODM. The simulation results indicate that the inclusion of isolation devices efficiently suppresses the odd harmonics at mid-to-high frequency by a value that is 13 dB lower than before. Experimental validation is conducted on a 16-bit 250 MS/s CS-DAC fabricated in a 180 nm process.

LVRT Control Strategy for Three-Phase CHB PV Inverter Based on Coordinated Compensation of Fundamental-Frequency Adaptive Zero-Sequence Voltage and its Odd Harmonics

LVRT Control Strategy for Three-Phase CHB PV Inverter Based on Coordinated Compensation of Fundamental-Frequency Adaptive Zero-Sequence Voltage and its Odd Harmonics

Electric field and higher harmonics of RF plasma slit jet measured by antennas and VI probes

The cold atmospheric plasma jets change their character when interacting with the different surfaces. Since such interaction is the primary area of plasma jet applications, it is essential to monitor the process. The non-linearity of the RF plasma slit jet (PSJ) was analyzed using the VI probes and a novel method, the non-intrusive antenna measurements. Regardless of the experimental setup and gas mixture (Ar, Ar/O2, Ar/N2), the PSJ frequency spectrum consisted of the following main features: dominant fundamental frequency peak, relatively strong odd harmonics, and significantly weaker even harmonics. The lowest degree of non-linearity was recorded for the Ar PSJ ignited against a grounded target. Admixing a molecular gas increased the discharge non-linearity. It was attributed to the enhancement of secondary electron emission from the dielectric surfaces. In addition to the non-linearity analysis, the antenna spectra were for the first time used to determine the semi-quantitative values of the PSJ-radiated electric field. The electric fields decreased by a factor of 2 after the admixing of nitrogen and oxygen molecular gases. Out of the studied targets, the highest electric fields were observed when plasma impinged on the grounded targets, followed by the floating target (2× lower) and the PSJ ignited in the open space configuration (4× lower than in the grounded target configuration).

High‐Order Harmonics of Thermal Tides Observed in the Atmosphere of Mars by the Pressure Sensor on the InSight Lander

AbstractThermal tides are atmospheric planetary‐scale waves with periods that are harmonics of the solar day. In the Martian atmosphere thermal tides are known to be especially significant compared to any other known planet. Based on the data set of pressure timeseries produced by the InSight lander, which is unprecedented in terms of accuracy and temporal coverage, we investigate thermal tides on Mars and we find harmonics even beyond the number 24, which exceeds significantly the number of harmonics previously reported by other works. We explore comparatively the characteristics and seasonal evolution of tidal harmonics and find that even and odd harmonics exhibit some clearly differentiated trends that evolve seasonally and respond to dust events. High‐order tidal harmonics with small amplitudes could transiently interfere constructively to produce meteorologically relevant patterns.

Nearest Vector Control Method Applied to an MMC for PV Generation

This paper proposes a new and simplified Nearest Vector Control (NVC) modulation technique for a grid-connected photovoltaic (PV) system using a Modular Multilevel Converter (MMC). Compared to the Nearest Level Control (NLC) technique, which defines three independent states for the three phases of medium to large four-wire multilevel converters, NVC offers a more coordinated behavior for three-wire converters. The proposed scheme is easy to implement, and it simplifies the understanding of using vectors when detecting the vector of the converter nearest to a given reference. Because it uses natural coordinates, namely, ab, bc and ca, the proposed method is easier to understand and more useful for further developments. Compared with earlier NVC methods, this approach offers full independence of the number of levels at the converter and it can readily accommodate changes in the number of levels, with no need for lookup tables or artificial coordinate transformations. The proposed NVC method was implemented on a 16-cell MMC used for PV generation and then it was compared to NLC, leading to a smaller and more consistent low-order harmonic distortion, requiring about the same complexity of implementation. Furthermore, in comparison to NLC, when applying the proposed NVC modulation, a behavior more insensitive to changes in the grid voltage was found, the most hazardous odd harmonics from the 5th to the 19th were reduced, and a consistent reduction of about 25 dB was achieved on the 5th and 7th harmonics. The newly proposed method is supported by simulations and experimental results with constant and sharply changing solar irradiance, leaving or removing the 100 Hz component of the MMC circulating currents.