Harmonic Frequency Components Research Articles

A novel parallel multi-harmonic global multi-channel control algorithm for helicopter active vibration control

The vibrations of the helicopter fuselage are mainly induced by the rotor with blade pass frequency and the high order harmonics. The conventional filtered-x least mean square (FxLMS) control algorithm usually used a uniform convergence factor for all the harmonics which leads poor effect in controlling multi-harmonic vibration. In this paper, a novel parallel multi-harmonic global multi-channel (MHGMC) control method is proposed to suppress the multi-harmonic vibration components transmitted from the main rotor to the fuselage. Bandpass filters are used to separate multiple frequency components of the error signals, the control channel models are identified for the corresponding frequency range to independently control each frequency component, and the reconstruction of the reference input signals can be obtained from the separated error signal, effectively improving the performance of tracking interference signals. In addition, the coupling of the control channels is considered, and the global vibration optimization is taken as the control objective to update the weight coefficient of the controller. An active vibration control system of the helicopter main gearbox eight-strut installation configuration has been established. The simulation and experiment results show that the proposed controller has faster control convergence speed and better control effect of multiple harmonics than the conventional filtered-x least mean square algorithm, and the attenuations of the disturbing frequency harmonic components at all measurement points in the experiment are over 38dB. The experimental results of variable excitation also verify that the proposed control algorithm has excellent adaptability and strong robustness.

Dynamic response of a pump-turbine runner during turbine's mode starting up

With an increase in head and rotational speed, pumped storage units, particularly the runner, experience higher pressure and centrifugal force. In this study, a combination of the 1D method of characteristics (MOC), 3D computational fluid dynamics (CFD) as well as computational structure dynamics (CSD) was employed to examine the dynamic response of a pump turbine runner during turbine's mode starting up. A detailed analysis of the transient characteristics during this process was conducted. Initially, the high-pressure zone concentrated on the pressure surface of the runner's inlet side. However, this zone gradually expanded over time and shifted to the suction surface. The time-frequency of pressure pulsation showed significant low-frequency and second harmonic frequency components. Different monitoring points exhibited different sensitivities to rotational speed and torque. It can be assumed that runner's blade stress is proportional to the square of the rotational speed. The sensitivity of blade stress related to runner speed and torque provides important results and analysis. P2 is the most sensitive to changes in rotational speed, while P1 is the most sensitive to changes in torque. These findings enhance our understanding of the dynamic behavior of the RPT runner and contribute to potential improvements in design and operation.

Lumped model for the calculation of harmonic eddy current losses in permanent magnets for homogeneous flux distributions considering eddy current reaction flux

This is the first of a series of papers on novel methods for the calculation of eddy current losses in permanent magnets (PMs) and the shortcomings of previously conducted analyses. Eddy current losses in PMs and their mitigation are significant factors when designing inverter-fed electric drives. Especially with the need for drives with high power density, a trend toward increased rotational speeds and, therefore, higher fundamental frequencies and inverter switching frequencies are observable. Higher harmonic frequency components of concentrated windings and fractional slot windings are widely taken into account when designing rare sintered earth magnets for permanent magnet synchronous machines (PMSMs). However, inverter-related losses are rarely simulated in Finite Element Method (FEM) co-simulations and can contribute as a major factor to the power losses in PMSMs. In the worst case, this neglection can lead to the thermal demagnetization of the permanent magnets. Segmentation provides an effective measure to limit eddy current losses. However, not every kind of segmentation proves effective in a drive application. Depending on the frequency behavior of the magnetic flux in a permanent magnet, segmentation can increase eddy current losses within the magnet compared to a non-segmented magnet. This behavior is due to the reaction to the flux caused by the eddy currents within the magnet. The reaction of the eddy currents is often neglected [1, 2], and, in other cases, the vicinity of ferromagnetic material is neglected in analytical calculations [3] but proves crucial for the exact calculation of higher frequency losses [4, 5]. In this paper, an analytical solution to calculate harmonic eddy current losses in permanent magnets, including the reaction flux with homogeneous excitation, is given.

Dynamic modeling and vibration analysis for the gear-rotor-bearing system with localized failures

Accurate identification of faults in gearbox requires a clear understanding of its vibration response. In this study, through establishing dynamic model and experimental observation, the vibration characteristics of gear-rotor-bearing systems with localized failures are investigated and discussed. Firstly, the models of the gear pair, rotor and bearing are integrated, a comprehensive model for gear-rotor-bearing systems is developed. Then the model for describing localized failures is established and supplemented to the system equations. By using the model, the influence of the spalling defect and bearing raceway failures on the dynamic response are analyzed. Moreover, multiple sets of experiments are conducted for verifying the model and analysis results. The paper explains that periodic shock will be generated due to the presence of localized failures, the vibration intensity of the faulty part at specific frequencies is greatly enhanced, and a series of harmonic frequency components will be generated. Additionally, due to the pulse force transmission, the operation state of other components is also seriously affected, and frequency modulation phenomenon between different components can be observed. The defect frequency of bearing outer raceway is commonly modulated with meshing frequency and cage frequency, while the inner raceway defect frequency and meshing frequency are modulated with shaft frequency, and the amplitude of harmonics caused by modulation is obviously increased under the excitation of localized failure.

Fiber-Optik Haberleşme Sistemlerinin Bant Genişliğinin Artırılması için Yeni Bir Yaklaşım

In this study, a theoretical systematic approach is introduced as a solution of the bandwidth problem of multi-tone network systems. This systematic approach proposes the use of unused harmonic components of non-linear harmonic distortion produced by the semiconductor laser diode, which is used as a source in the infrastructure of the fiber optic communication system. In order to separate these unused harmonic distortion frequency components from the others, it is possible to add a protocol to each harmonic distortion difference frequency signal, or by intermodulation distortion (IMD) phase modulation, or to use both protocol and IMD phase modulation together. Thus, all harmonic distortion frequency components can be separated theoretically. Thus, it is recommended to use IMD difference frequency components in multi-tone-input subcarrier fiber optic or similar communication systems in the same transmission medium. We think that if this technique is used, it will make a great contribution to increasing the bandwidth of fiber optic communication and network systems.

Study on partial discharge and charge accumulation characteristics of oil‐pressboard insulation under DC superimposed harmonic voltage

AbstractThe oil‐pressboard insulation on the valve side of the converter transformer withstands pulsating square wave voltage. The voltage contains lots of DC components and high‐order harmonics, which is likely to cause insulation failures. The partial discharge and space charge experiments of oil‐impregnated pressboard under DC superimposed harmonic voltage are conducted to study the effects of harmonic frequency and DC components on the discharge and charge accumulation and to explore the correlation mechanism of charge dynamic behaviour and discharge. Firstly, it is found that high‐order harmonic voltage promotes the partial discharge generation, but DC component suppresses the discharge. Moreover, the charge inside the pressboard is mainly injected in the same polarity and accumulates over time. The space charge density near the electrode increases with the increase of harmonic frequency, and the large amount of charge injection leads to electric field distortion. Meanwhile, the electric field direction changes faster, and the frequent charge injection and extraction behaviours make the charge recombination intensify, which promotes the discharge. Through the above analysis, the influence law of harmonic voltage on the failure of oil‐pressboard insulation is obtained, providing a theoretical basis for the structural optimisation and condition assessment of the converter transformer insulation.

PROPORTIONAL INTEGRAL QUASI RESONANT CONTROLLER FOR ZERO-SEQUENCE CIRCULATING CURRENT AND RIPPLES SUPPRESSION IN PARALLEL THREE-PHASE PWM RECTIFIERS

Parallel three-phase pulse with modulation (PWM) rectifiers with common sc and ac buses are widely used in power systems due to their many advantages such as flexibility, sinusoidal grid currents, lower switching frequency, and good reliability. However, this topology suffers from zero-sequence circulating current (ZSCC) generated by numerous reasons including filters inductors unbalanced, unequal dead time, and losses of synchronism between the control of each rectifier, which will distort the ac-side currents and increase power losses. This paper proposes both an adjusted space vector pulse width modulated (ASVPWM) method and proportional integral quasi resonant controller (PIQRC) method not only to force the ZSCC to be zero but also to reduce its ripples, which results in low frequency harmonic components in the ac side currents. This twofold objective can be achieved by adjusting the zero-vector duty ratios of ASVPWM to suppress the ZSCC and by using PIQRC to mitigate its predominant harmonics. Finally, the superiority and efficiency of the proposed control method in terms of ZSCC suppression and current ripple reduction are verified through comparative analysis with the conventional ZSCC-PI controller.

Setup of a Broadband High-Current Measuring System for the Traceable Calibration of Current Transducers

In this work, we show the development of a broadband high-current measuring system for the traceable calibration of current transducers up to 2000 A. The system can generate a measurement current with frequencies up to 10 kHz and achieves a minimum uncertainty of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$77~\mu \text{A}$ </tex-math></inline-formula> /A up to a frequency of 1 kHz with a reference current of 20 A. In addition to this, nonsinusoidal current waveforms with harmonic frequency components up to 2 kHz can be provided by the measurement system. To the best of our knowledge, this is the first measurement system demonstrated, which is capable of broadband signals up to 2000 A in such a large bandwidth.

Design Voltage Controller of Bipolar SPWM Voltage Source Inverter

This paper presents single phased VSI (Voltage Source Inverter) type bipolar SPWM. The main purpose of this system is generating a constant sinusoidal output waveform without affected by load (resistive) demand. Its concept is to get reference voltage from PI control and compare it with modulated triangular carrier for controlling inverter’s switches. The system is also represented by a LCL output filter. The LCL filter is employed to reduce the high frequency harmonic components in current waveform due to PWM switching and to reduce the output current THD. Simulation result and analysis are bravely presented to verify the effectiveness of proposed approach.

Условия полной компенсации токов однофазного замыкания на землю в кабельных сетях напряжением 610 кВ с заземлением нейтрали через дугогасящий реактор

To improve the reliability of power supply of consumers, a significant part of 6–10 kV cable networks (in Russia about 20 %) operate with resonant neutral grounding via arc suppression coil (ASC) (single-phase earth fault capacitive current compensation). This neutral grounding mode provides suppression of arcing earth faults accompanied by dangerous overvoltage and reduction of current at the point of fault by compensating the capacitive component of the elementary frequency. Field experience of operation of 6–10 kV compensated cable networks has shown that the reason of the decrease of the efficiency of the neutral grounding mode is an increase of the residual current at the point of fault. It happens due to the active component of the elementary frequency and higher harmonic components that are not compensated via ASC up to the values when long time arc duration and transition of the earth fault to the short circuit become possible. The existing solutions of the problem of full compensation of the current of a single-phase earth fault are not sufficiently developed and substantiated. Thus, the solution of the problem to increase the efficiency of grounding the neutral of the network via ASC can be achieved by developing and implementing methods and devices of the full compensation of the earth fault current, including the active component of the elementary frequency and higher harmonic components. To achieve the terms and conditions of full compensation of the current components of a single-phase earth fault, the classical theory of electrical circuits has been used. To verify the validity of the results obtained, simulation modeling in the Matlab software package has been carried out. For an electrical network with neutral grounding via ASC, the authors have obtained a general mathematical description of the terms and conditions of full current compensation at the point of earth fault, including higher harmonic components and transient components. The authors have defined the requirements for accuracy to determine the moment of a single-phase earth fault and the voltage value of the damaged phase when insulation fault occurs. Possible options of algorithms to compensate higher harmonics in the current of stable earth fault are proposed. The obtained general mathematical description of the terms and conditions of full current compensation at the point of a single-phase earth fault in 6–10 kV compensated cable networks allows us to substantiate existing methods and develop new ones to compensate both the total current at the point of fault and its components.

Nonlinear Ultrasonic Inspection of the Effect of Contaminants on Material Properties of Epoxy-Adhesive

Adhesive joints have been an effective alternative to conventional mechanical fasteners for joining materials in the aerospace and automotive industries. Although adhesive joints have various advantages, including uniform stress distribution, lower weight, improved corrosion tolerance, and design flexibility, there can be various defects in adhesive joints, which have limited wider application. This paper investigates the effect of a contaminant on the chemical and mechanical properties of the epoxy-adhesive and seeks to determine if a second harmonic generation method can reliably detect and characterize the degree of contamination in the epoxy-adhesive. A contact based ultrasonic through-transmission method was used to measure nonlinearity and then the nonlinearity parameter was calculated using the measured fundamental and second harmonic frequency components in the signals. It was found that there is higher sensitivity to contaminant concentration, up to 1.5%, of the nonlinearity parameter than that for the sound velocity. These data were also found to correlate with changes in the mechanical hardness, which was measured by the Rockwell hardness testing, with different four levels of contamination. Differential scanning calorimetry (DSC) and the thermogravimetric analysis (TGA) were also conducted to assess the effect of the contaminant on thermal properties of the epoxy-adhesive. The DSC and TGA techniques were used to evaluate the curing reaction and the thermal stability of the epoxy-adhesive respectively.

Harmonic suppression and uniformity improvement of plasma density in capacitively coupled plasma

A method for improving plasma uniformity in capacitively coupled plasma (CCP) is developed. Plasma contains harmonics due to the nonlinear characteristics of the sheath. Because high-frequency harmonic components in the plasma have short wavelengths, high-frequency harmonics components have a bad influence on plasma uniformity. This is because the electromagnetic standing wave effect (SWE) is severe at high frequencies. To improve plasma uniformity, a CCP using a parallel capacitor that is connected to the powered electrode is developed. By adjusting the capacitance of the parallel capacitor, a parallel resonance between the parallel capacitor and the reactor, which is net inductive, is generated. As the parallel loop approaches the parallel resonance, the currents of other harmonic frequency components in the plasma are greatly reduced. Therefore, the waveform of the plasma bulk current also becomes sinusoidal, and the amplitude of the plasma current becomes almost constant, regardless of the radial position at the parallel resonance condition. Moreover, the voltage applied across the plasma is greatly increased. Consequently, plasma uniformity and the voltage applied to the plasma along the electrode are significantly improved under the parallel resonance condition due to a greatly reduced SWE.

Multi-harmonic analysis in a floating harmonic probe method for diagnostics of electron energy and ion density in low-temperature plasmas

A floating harmonic probe (FHP) is used to measure the electron energy and ion density in plasmas. It applies an AC voltage to an electrically floated probe and measures harmonic frequency components in the probe current which contains information about the parameters. In this study, we have quantitatively investigated the effects of stray impedances in an FHP measurement system on the calculated parameters. We also discuss the influence of the electron energy distribution function (EEDF) when it deviates from a Maxwellian shape on the FHP measurement. A new approach of multi-harmonic analysis of FHP data (MHA-FHP) is proposed to analyze the electron energy in plasmas with non-Maxwellian EEDFs. The MHA-FHP method has been compared with the conventional FHP and Langmuir probe methods through the measurement of low-temperature argon plasmas. Experimental results indicated that the MHA-FHP method can provide the shape of the EEDFs, effective electron temperature, and ion density.

A Rotor Winding Internal Short-Circuit Fault Protection Method for Variable-Speed Pumped Storage Units

In electrical machinery, the rotor windings’ internal short-circuit faults are addressed by the instantaneous over-current protection of the power electronic excitation device, which has low sensitivity and has difficulty meeting the safety requirements. In this paper, a rotor windings’ internal short-circuit fault protection method is proposed based on the harmonic characteristics of the circulating current between stator branches. The magnetomotive force distribution of the short-circuit coils in the rotor windings is theoretically deduced, and the characteristic frequencies of the circulating current between stator branches are analyzed. On this basis, the protection criterion of the rotor windings’ internal short-circuit fault is constructed by using the harmonic component of the circulating current. Then, an analytic model of the variable-speed pumped storage unit is established based on the multi-loop method, and the finite element method is used to verify the correctness of the proposed modeling method. An actual large variable-speed pumped storage unit is taken as an example, and the possible faults under different slip ratios are simulated. In the simulation results, the stator branch circulation has the obvious characteristic frequency harmonic components, which is consistent with the theoretical analysis. It verifies the effectiveness of the proposed protection method. Finally, it is analyzed and verified that the proposed protection has a strong maloperation prevention ability under other kinds of faults.

In-Place Evaluation of Powering and Signaling Within Fan-Out Multiple IC Chip Packaging

This article confirms the advantage of fan-out (FO) packaging in the electrical performance of power delivery among integrated circuit (IC) chips with the best use of land side capacitors (LSCs). On-chip in-place waveform measurements quantitatively evaluate the integrity of powering and signaling within FO wafer level packaging (FOWLP) multiple chip module (MCM) demonstrators, where a pair of IC chips are assembled with LSCs with different sizes and structures. The IC chip incorporates an array of 12 digital cores and on-chip waveform monitor (OCM) circuits. Each digital core consists of a low-voltage differential signaling (LVDS) transceiver channel that is backed by a static random access memory (SRAM)-based built-in self test (BIST) module and supplied by an on-chip voltage regulator module (VRM). The LSCs are placed on the bottom side of an FO interposer and inserted between the output of VRM and the ground plane almost ideally with the shortest length of physical traces. A Si membrane capacitor of 10 nF sustains the lowest power line impedance over the frequency range of 2.0 GHz more constantly than a multilayer ceramic counterpart, and attenuates the high-order harmonic frequency components to the clocking frequency at 750 MHz. The leverage of LSCs in powering also improves signaling and helps achieve the wider eye openings in LVDS channels. The implications are elaborated for the capacitor selections with respect to the physical types of capacitors, the size of capacitances, and the level of shares in power delivery among digital cores, all toward the higher level of integrity in powering and signaling in FOWLP MCMs.

Analytical Prediction of the MCSA Signatures Under Dynamic Eccentricity in PM Machines With Concentrated Non-Overlapping Windings

This paper proposes a novel algorithm which made it feasible to predict the harmonic fault signatures under dynamic eccentricity in Permanent-Magnet synchronous machines with concentrated non-overlapping winding for any slot-pole combination. In the literature, only the appearance of the fractional harmonic components related with the pole number has been proposed but there are no studies to predict which exact components will rise in each topology. Initially, a mathematical equation is derived for the machine <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">EMF</i> under dynamic eccentricity based on the air gap permeance model. Later on, the terms of this equation are inserted in a Fault Signature Block Binary Array in which the position of each cell expresses a specific harmonic frequency component. After substitution of the machines parameters, the array results with zero and nonzero terms. The positions of the nonzero terms express the frequency components excited by this particular fault. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3-D</i> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FEA</i> and experimental results of a Permanent-Magnet Axial-Flux Machine are used to validate the proposed algorithm.

Aerodynamic interference and unsteady loads for a hovering intermeshing rotor

Synchropters are increasingly applied for precision work in placing suspended loads due to their unique flying characteristics. However, the special intermeshing rotor structural helicopter easily introduces rotor-and-rotor interference, leading to unsteady aerodynamic loads on the rotor blades in mission flight. Hence, we use the unsteady vortex lattice method to validate and analyze the aerodynamic characteristics of the intermeshing rotor in hover. In this method, a circulation suppression technique on the blade root is introduced to enhance the stability of the rotor wake in the steady-state hover. Results show that the meniscus truncated regions on the intermeshing rotor disks formed by the blade–vortex impact are nearly unchanged to collective pitches. The low-order frequency harmonic components and phase lag phenomenon universally found in dual rotor loads and additional oscillating roll moment become inherent characteristics of the intermeshing rotor in hover, especially for kΩ caused by interference of rotor downwash flow and 2 kΩ produced by the blade–vortex interaction at 10° and 190° azimuth. Finally, the left/right rotor loads exist harmonic components of 1, 2, and 3 kΩ. In contrast, the total thrust of the intermeshing rotor system eliminates the odd-order harmonic components but aggravates the even-order harmonic components.

Numerical and Experimental Analysis for the Dynamics of Flawed–Machining Rod–Disk Rotor with Inner Misalignment

The nonlinear dynamic effects of the misalignment between inner disks in a flawed–machining rod–disk rotor is studied. Non–uniform stress distribution due to inner misalignment is obtained based on 3D static solution. The concomitant unbalances, including constant mass eccentricity and speed–variant rotor bending, are taken into account in the nonlinear dynamics. The dynamic results show that rotor bending leads to stability reduction and vibration growth. There is a distinctive feature in that the rotor’s vibration goes up again after critical speed. The maximum allowable inner misalignment is obtained according to its stability boundaries. An uneven tightening method is also presented to reduce adverse effects when the inner misalignment exists. Moreover, an experiment is designed to measure the vibration characteristics for the rod–disk rotor bearing system with inner misalignment. The results show that the theoretical result of vibration amplitude of the flawed rod–rotor bearing system is basically consistent with the experimental value. It is also found that the precise rotor performs the periodic motion, but the flawed rod–disk rotor exhibits the period–doubling orbit. This phenomenon proves that the flawed rod–disk rotor loses stability more easily than the precise rotor due to inner misalignment. However, the amplitude of harmonic frequency components for the precise rod–disk rotor system is obviously larger than the flawed rod–disk rotor system with inner misalignment. The peak value of the vibration amplitude increases when the inner misalignment becomes larger. On the whole, this work presents numerical and experimental analysis to study the dynamics of flawed-machining rod–disk rotor with inner misalignment. It also establishes the relationship between centration precision and dynamic features.

Effects of Long-Term Vibration on Cellulose Degradation in an Oil-Impregnated Pressboard under Simultaneous Thermal–Electrical–Mechanical Stress Aging

Due to the complex operation conditions in a power transformer, an oil-impregnated pressboard (OIP) simultaneously suffers from thermal, electrical, and mechanical stress. Since most research studies have paid much attention to thermal or electrical aging of OIPs, this paper analyzes the effects of long-term mechanical vibrations on cellulose degradation in OIPs under simultaneous multi-stress. The aging experiments were firstly conducted at 130 °C, with a DC electric voltage of +6 kV, vibration amplitude of 10–50 μm, and vibration frequency of 100–300 Hz. The finite element analysis (FEA) of the pressboard vibration model was then performed on Abaqus to investigate the time–frequency domain characteristic parameters of compressive stress on the pressboard under varied vibration frequencies and amplitudes. The FEA results reveal that compressive stress on the pressboard in a multi-stress aging experiment coincided with the axial compressive stress on the insulation spacers in an SZ-50000/110 transformer. Moreover, combined with the degree of polymerization (DP) of cellulose, the effects of long-term vibration on cellulose degradation are reflected in two ways: the increase in compressive stress on the pressboard generates more links available for degradation, while more high frequency harmonic components in compressive stress accelerate the reaction rate in cellulose degradation.

A novel detection method for diagnosis of rotor eccentricity in three-phase induction motor

In this paper, a novel method to diagnose eccentricity fault in rotor of three-phase induction motor based on the current signal, is proposed along with experimental validation. It utilizes three-phase current in time series into Clarks two phase α–β 90° apart vectors assimilating into 0° measuring reference frame starting point with the aid of key-phasor averaging method. α–β sinusoidal waves are applied to an interpolation method which gives an improved Fast Fourier transform of amplitude and phase angle of α–β components. These transformed two-phase current signals are again measured to get amplitude and phase. Finally, the amplitude and phase of α–β are used to generate holo-spectrum with an ellipse of the first order. Since unbalance fault occur at peak fundamental 1X harmonic frequency component, so its amplitude and phase angle are utilized for orbit construction. A comparison is made on rotor orbit and its eccentricity values, constructed from vibration signals and three-phase current signals, both measured simultaneously. This leads to a direct relationship in terms of orbit eccentricity and its longitudinal major axis inclination. The results show that at low frequency the eccentricity values of vibration and current signals orbits coincide hence the unbalance fault is detectable in induction motor by only utilizing the current signals. This method represents rotor non-linear dynamic behavior and is immune to unsymmetrical and anisotropic surface properties of the rotor and can measure rotor condition representing an accurate severity level of air gap eccentricity or, in mechanical terms, rotor unbalance fault. The new technique is a progressive development in induction motor air gap eccentricity fault detection and is applicable to harsh running conditions due to its simplified and non-invasive approach.