Fundamental Frequency Component Research Articles

Improving protection reliability of series‐compensated transmission lines by a fault detection method through an ML‐based model

AbstractThis article addresses the distance protection challenges associated with the series‐compensated transmission lines and the impact of fault resistance by employing a machine‐learning model. In the proposed model, stacked layers of bidirectional long short‐term memory (Bi‐LSTM) cells are fed by voltage and current signals to distinguish between different fault scenarios. This method takes advantage of only local bus measurements to prevent information leakage in communication channels. Moreover, to make the proposed method harmonics‐robust and improve the correlation interpretation between the features for the Bi‐LSTM model, the 3‐phase raw measurement signals are passed through a discrete Fourier transform (DFT) which extracts their fundamental frequency component magnitudes and angles. Then, an extensive amount of fault scenarios including different compensation levels, fault resistances, and fault locations in normal and power‐swing operational conditions are simulated to train the model. Finally, to validate the performance of the proposed protection method in the series‐compensated transmission lines, distinctive studies are also carried out based on electromagnetic transient simulations. The obtained results confirm the remarkable performance of the proposed method in discriminating fault types, faulty phases, internal or external faults, and normal or power‐swing conditions of the power system.

A Novel Wiener‐Type Dynamic Neural Network Method for Large Signal Modeling of Power Amplifiers

ABSTRACTA novel Wiener‐type dynamic neural network (Wiener‐type DNN) method for large signal modeling of power amplifiers (PAs) is proposed in this paper. In this method, the proposed model structure for the PA contains two Wiener‐type DNNs to describe the input impedance and the amplification efficiency, respectively. The Wiener‐type DNN includes a simplified linear dynamic equation module and a nonlinear static equation module. For the simplification process of the linear dynamic equation, it is proposed to process fundamental frequency components of the large signal harmonic data of the PA by vector fitting. The neural network is used to implement the static equation in the Wiener‐type DNN. The formulas for training the proposed Wiener‐type DNN model of the PA using large signal data are derived. The training algorithm of the PA model is proposed to improve the training efficiency. A Motorola MOSFET PA example and a Freescale lateral double‐diffused MOSFET PA example are present to validate the proposed Wiener‐type DNN method. For the Motorola MOSFET PA, a dynamic neural network (DNN) model and a time‐delay deep neural network (TDDNN) are established for comparison. For the Freescale PA, the DNN model is used for comparison experiment. The comparison figures show that the Wiener‐type DNN model has better convergence properties than the DNN model in the nonlinear region of the PA. The established accurate PA model is conducive to the design of subsequent communication circuits.

A gear fault diagnosis method based on reactive power and semi-supervised learning

Abstract In gearbox gear fault diagnosis based on motor current signals, the gear fault characteristic frequency component is often overshadowed by the fundamental frequency component of the current. In addition, the complex working conditions during actual production and use make it difficult to collect gear operation monitoring data containing labeled feature information. To address the above problems, a semi-supervised learning method based on reactive power signals is proposed for gear fault diagnosis of gearboxes. First, the method utilizes the Hilbert transform to process the current signal of the drive motor in the mechanical system, from which the reactive power is constructed. Then, the reactive power signal is analyzed by spectral analysis as a basis for gear fault diagnosis. Subsequently, the GAF-CNN-MTDL(Gramian angular field—convolutional neural network-mean teacher deep learning) fault diagnosis model is proposed to convert the reactive power signal into a two-dimensional image by using the GAF, and the semi-supervised training method of the average teacher is applied to input the fault dataset into the gear fault diagnosis model which is based on the CNN as the main backbone after the fault dataset has been divided into the labeled and the unlabeled dataset in accordance with a certain ratio. Finally, the gear fault dataset is used for method validation. The experimental outcomes demonstrate the method’s proficiency in effectively emphasizing the fault feature information pertaining to the gear part, and the introduced GAF-CNN-MTDL fault diagnosis model enables the utilization of a minimal number of labeled samples to achieve highly accurate gear fault diagnosis.

Converter-based multi-frequency power transfer system for efficient energy packet transmission in the energy internet

The energy internet concept involves the transmission of energy in discrete packets, akin to the information internet's principle. The energy internet must adopt a decentralized configuration and enable bidirectional and simultaneous power transfer. This raises the problem of congestions during the energy packet dispatching process. To address potential congestion issues, we propose a three-phase multi-frequency power transfer system (MFPTS) where the positive-sequence fundamental frequency component is supplemented with the zero-sequence third and the negative-sequence fifth harmonic components. By using such signals with proper amplitudes, the harmonics are added to the voltage without changing the peak amplitude but increasing the rms value. To exert complete control over the different frequencies employed within the MFPTS, a decoupling method is necessary to separate these frequencies in the control system. This leads to creating three independent channels of power transfer by three frequencies without changing the existing infrastructure as these powers can be transferred within the same lines. This paper explores the feasibility of three-phase three-frequency power transfer by using three parallel power transfer channels, achieved through the utilization of three-phase grid-forming and grid-feeding converters. Using power converters provides the advantage of bidirectional power transfer and facilitates decentralization by serving as an interface between distributed power generation systems and the utility grid. These properties are essential for achieving optimal energy internet performance. The simulation and practical results prove that the proposed MFPTS could solve the energy packet dispatching congestion problem to have a reliable energy internet for the future.

A rotor open-phase imbalance protection for variable speed pumped storage unit based on rotation transformation fault component ratio

Doubly-fed variable speed pumped storage unit (VSPSU) adopts slip ring injection AC excitation mode, and its rotor side structure is complex and prone to open-phase faults. It is very important to configure specific open-phase imbalance protection to ensure its safe operation. Traditional doubly-fed motors only stay in the state monitoring stage for rotor electrical imbalance, which cannot meet the requirements of large-capacity VSPSU for fast, real-time, and high-reliability protection. Therefore, this paper proposes a VSPSU rotor open-phase imbalance protection method based on the rotation transformation fault component ratio (FCR). The fundamental frequency component and fault characteristic component of the stator current space vector are extracted by rotation transformation and FCR is calculated, and then different protection action modes are divided according to the amplitude of FCR. To realize the engineering application, a microcomputer protection algorithm suitable for the proposed protection method is further proposed, and then a complete microcomputer protection scheme is formed. Simulation and experiment results show that the proposed protection scheme has high sensitivity and fast action speed. At the same time, the proposed algorithm can be directly embedded in the existing microcomputer protection device to meet the needs of engineering applications.

A Master-Slave-Structure Position Observer for Multiharmonics Suppression in Sensorless PMSM Drives

Due to the influence of inverter nonlinearity and nonideal spatial flux, it inevitably exists the back electromotive force (BEMF) harmonics in permanent magnet synchronous motor (PMSM) drives, affecting the accuracy of model-based position-sensorless control. Although different schemes have been studied to suppress the BEMF harmonics, it is still challenging to alleviate the contradiction between harmonics suppression effect and structure complexity. To address this problem, a master-slave-structure position observer is proposed for multi-harmonics suppression in this paper. With the help of the master-slave structure, the fundamental frequency component of the BEMF is extracted as the output of the studied observer, realizing the separation from the harmonic components. The number of the integrators can be reduced by half with the complex-coefficient resonators instead of the real-coefficient resonators. Thus, the design degree of freedom is fully exploited to realize the desired frequency-domain characteristics of band-pass and specific frequency band-stop. The studied method is verified by the experiments on a 2.2-kW PMSM platform.

A Novel Method for Removal of Dual Decaying DC Offsets to Enhance Discrete Fourier Transform-Based Phasor Estimation

This paper presents a novel method for the removal of dual decaying DC offsets (DDCOs) to enhance discrete Fourier transform-based phasor estimation. The method proposed in this paper uses the sum of even samples and the sum of odd samples from the input signal to remove the AC components, thereby precisely estimating the primary and secondary DDCOs. The fluctuations induced by DCCOs present in the output of traditional DFT methods are eliminated by using the estimated DCCOs. The performance of the method was evaluated in terms of both mathematical-generated signals and fault current signals from a 154 kV Korean overhead transmission system. PSCAD/EMTDC was used to generate fault current signals at various fault distances and angles. The results show that the proposed method can estimate the phasor of the fundamental frequency component accurately regardless of the primary and secondary DCCOs. The paper concludes by describing the hardware implementation in a prototype unit that considers the real-world requirements of power system protection.

Noncontact Cardiac Activity Detection Based on Single-Channel ISM Band FMCW Radar.

The heart is an important organ that maintains human life activities, and its movement reflects its health status. Utilizing electromagnetic waves as a sensing tool, radar sensors enable noncontact measurement of cardiac motion, offering advantages over conventional contact-based methods in terms of comfort, hygiene, and efficiency. In this study, the high-precision displacement detection algorithm of radar is applied to measure cardiac motion. Experimental is conducted using a single out-channel frequency modulated continuous wave (FMCW) radar operating in the ISM frequency band with a center frequency of 24 GHz and a bandwidth of 150 MHz. Since the detection signal is influenced by both respiratory and heartbeat movements, it is necessary to eliminate the respiratory signal from the measurement signal. Firstly, the harmonic composition of the respiratory signal is analyzed, and a method is proposed to calculate the parameters of the respiratory waveform by comparing the respiratory waveform coverage area with the area of the circumscribed rectangle. This allows for determining the number of respiratory harmonics, assisting in determining whether respiratory harmonics overlap with the frequency range of the heartbeat signal. Subsequently, a more accurate cardiac motion waveform is extracted. A reference basis is provided for extracting cardiac health information from radar measurement waveforms by analyzing the corresponding relationship between certain extreme points of the waveform and characteristic positions of the electrocardiogram (ECG) signal. This is achieved by eliminating the fundamental frequency component of the heartbeat waveform to emphasize other spectral components present in the heartbeat signal and comparing the heartbeat waveform, the heartbeat waveform with the fundamental frequency removed, and the heartbeat velocity waveform with synchronized ECG signals.

Transmission Perspective on the Mechanism of Coarse and Fine Crackle Sounds

The possibility of a normal distribution indicates that few particles are in the same phase during a breath and their reflections can be observed on the chest wall, then a few explosive waves with relatively large power occurr occasionally. Therefore, the one-cycle sine wave which is simulated as a single burst of the explosive effect phenomenon penetrates through the chest wall and was analysed to explore the reason of the crackle sounds. The results explain the differences between the definitions of crackle proposed by Sovijarvi et al. (2000a). The crackles in the lungs were synthesised by a computer simulation. When the coarse crackles occur, the results indicate that higher burst frequency carriers (greater than 100 Hz) directly penetrate the bandpass filter to simulate the chest wall. The simulated coarse crackle sounds were low pitched, with a high amplitude and long duration. The total duration was greater than 10 ms. However, for a lower frequency carrier (approximately 50 Hz), the fundamental frequency component was filtered out. Therefore, the second harmonic component of the lower frequency carrier, i.e., the fine crackle, penetrated the chest wall. Consequently, it is very possible that the normal lung sounds may contain many crackle-shaped waves with very small amplitudes because of the filtering effects of the chest wall, environment noises, electric devices, stethoscopes, and human ears, the small crackles disappear in the auscultations. In addition, our study pointed out that some unknown crackles of the very low frequency under the bandwidth of the human ears cannot penetrate the airways and be detected by medical doctors. Therefore, it might be necessary to focus advanced electronic instrumentation on them in order to analyse their possible characteristics for diagnosis and treatment of the respiration system.

A Tacholess Order Tracking Method Based on the STFTSC Algorithm for Rotor Unbalance Fault Diagnosis Under Variable-Speed Conditions

Abstract Due to the fact that rotors usually operate in a non-stationary mode with changing speeds, the conventional rotor unbalance detection method based on the stationary signal will produce a major “spectrum ambiguity issue” and affect the accuracy of rotor unbalance detection. To this end, a tacholess order tracking method based on the STFTSC algorithm is suggested in this study, where the STFTSC algorithm is developed by combining the short-time Fourier transform and the seam carving algorithm. First, the STFTSC algorithm is utilized to accurately extract the instantaneous frequency (IF) of the rotor and calculate the instantaneous phase under variable-speed conditions. Subsequently, the original signal is resampled in the angular domain to transform the non-stationary time domain signal into a stable angle domain signal, eliminating the effect of the speed variations. Finally, the angular domain signal is transformed into the order domain signal, which uses the discrete Fourier transform and the discrete spectrum correction method to identify the amplitude and phase corresponding to the fundamental frequency component of the signal. The simulation results show that the IF extracted by the STFTSC algorithm has higher extraction accuracy compared with the traditional STFT spectral peak detection method and effectively eliminates the effect of speed fluctuations. A rotor dynamic-balancing experiment shows that the unbalance correction effect based on the STFTSC algorithm is remarkable, with the average unbalance amount decrease rate on the left and right sides being 90.02% and 92.56%, respectively, after a single correction.

Output current harmonic analysis and suppression method for PMSM drive system with modular multilevel converter

AbstractAiming at the output current distortion problem in the low frequency operation of permanent magnet synchronous motor (PMSM) drive system of modular multilevel converter (MMC), the essential relationship between the output current distortion and the injected components is analyzed in this paper. A current harmonic suppression method combining feedforward and feedback compensation is proposed. Firstly, the feedback control method is applied to transform the MMC three‐phase output current into the dq rotating coordinate system at fundamental frequency ω. The harmonics of the AC terms to be suppressed are filtered out. The dominant fundamental frequency component turned into the DC term is retained. Then combined with feedforward control, the control performance of the system is improved. Secondly, the deadbeat predictive current control is improved by introducing an integral link in it. System disturbances caused by parameter changes can be compensated in real time. The design of the control system is simplified and the static error is reduced. Meanwhile, the system has the advantages of small torque pulsation and fast speed response. Finally, the PMSM drive system model of the 11‐level MMC is built in MATLAB/Simulink. The correctness and effectiveness of the proposed suppression method are verified.

Sagnac Magnetic Field Sensor Based on Sinusoidal Modulation and Empirical Mode Decomposition

A direct current (DC) Sagnac magnetic field sensor is a kind of fiber sensor based on alternate current magnetic field (ACMF) demodulation and empirical mode decomposition (EMD) to detect the magnetic field by measuring the phase variety caused by direct current magnetic field (DCMF). Commonly, Sagnac DCMF sensors can improve the magnetic detection sensitivity by using high Verdet constant (HVC) medium, which is expensive to prepare, or optical resonant cavity. However, the polarization diffraction in cavity restricts the performance of these devices. Meanwhile, none of them can suppress the electrical noise of the system such as 1/f noise. In this paper, we use ACMF modulation to couple the phase containing the DCMF information into the amplitude of the fundamental frequency component of the interference signal. Then we demodulate the signal by EMD to extract the fundamental frequency component. The designed sensor demonstrates a sensitivity of 4.651 mV/μT with an accuracy of 1.649 nT in the magnetic field range of 0-40 mT. It has the advantages of high stability, anti-electromagnetic interference and miniaturization.

Inverter Controller with Synthetic Inertia and Adaptive Harmonic Damping Based on Fourier Linear Combiners

This paper proposes an inverter control strategy that combines virtual synchronous generator control with harmonic detection based on Fourier linear combiners with adaptive gain. In the proposed strategy, the virtual synchronous generator control calculates the current in the fundamental frequency component, responsible for the control inertial characteristic, and harmonic voltage detector based on Fourier linear combiners selectively detects the harmonic voltages to be damped. The 5th harmonic order adaptive gain is calculated from voltage and current measurements on a bus of interest in the system. Real-time simulation results were developed in a hardware-in-the-loop test-bench to show that the proposed control can simultaneously mitigate the grid voltage and current harmonics and reduce the peaks of frequency oscillations after transients.

Second-harmonic generation in the system with fractional diffraction

We construct a family of bright optical solitons composed of fundamental-frequency (FF) and second-harmonic (SH) components in the one-dimensional (planar) waveguide with the quadratic (second-harmonic-generating) nonlinearity and effective fractional diffraction, characterized by the Lévy index α, taking values between 2 and 0.5, which correspond to the non-fractional diffraction and critical collapse, respectively. The existence domain and stability boundary for the solitons are delineated in the space of α, FF-SH mismatch parameter, and propagation constant. The stability boundary is tantamount to that predicted by the Vakhitov–Kolokolov criterion, while unstable solitons spontaneously evolve into localized breathers. A sufficiently weak transverse kick applied to the stable solitons excite small internal vibrations in the stable solitons, without setting them in motion. A stronger kick makes the solitons’ trajectories tilted, simultaneously destabilizing the solitons.

Vibrations of porous functionally graded CNT reinforced viscoelastic beams connected via a viscoelastic layer

This work analyses the vibrational response of porous viscoelastic functionally graded (FG) carbon nanotube (CNT) reinforced double beams. The beams are simply supported, connected through a viscoelastic layer, where four functionally graded patterns of CNT in the thickness directions (uniformly distributed (UD), FG-V, FG-O, and FG-X) are considered. The porosity models considered are UD, PO-V and PO-X. After formulating the coupled equations of motion via an energy-based method, and incorporating the effects of the viscoelastic beams and viscoelastic layers, the equations are solved using an assumed series expansion technique. The equations and solution methodology are verified utilising simplified models from existing literature and also through development of a finite element method (FEM) based simplified model; very good agreement has been achieved. Effects of the stiffness and viscous coefficients of the viscoelastic layer, the structural viscosity parameter of the porous CNT reinforced double beams, the porosity coefficient, and porosity models are examined. Overall, the results indicate that the stiffness and viscous coefficients of the viscoelastic layer have increasing effects on the real and imaginary components of second series fundamental transverse natural frequency of the double beam system, respectively. An increase in the structural viscosity parameter of the porous CNT reinforced double beams leads to an increase in the imaginary components of the fundamental frequencies of both the series. Moreover, a range of different effects on the real and imaginary components of the natural frequencies were noted while varying the porosity coefficient and models. The FG-X CNT porous reinforced viscoelastic double beams with a viscoelastic layer have the highest natural frequencies of all the cases. The study demonstrates the importance of the porosity, viscoelastic layer and viscoelastic material properties on the dynamics of the system.

Weakly nonlinear focused ultrasound in viscoelastic media containing multiple bubbles

To facilitate practical medical applications such as cancer treatment utilizing focused ultrasound and bubbles, a mathematical model that can describe the soft viscoelasticity of human body, the nonlinear propagation of focused ultrasound, and the nonlinear oscillations of multiple bubbles is theoretically derived and numerically solved. The Zener viscoelastic model and Keller–Miksis bubble equation, which have been used for analyses of single or few bubbles in viscoelastic liquid, are used to model the liquid containing multiple bubbles. From the theoretical analysis based on the perturbation expansion with the multiple-scales method, the Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation, which has been used as a mathematical model of weakly nonlinear propagation in single phase liquid, is extended to viscoelastic liquid containing multiple bubbles. The results show that liquid elasticity decreases the magnitudes of the nonlinearity, dissipation, and dispersion of ultrasound and increases the phase velocity of the ultrasound and linear natural frequency of the bubble oscillation. From the numerical calculation of resultant KZK equation, the spatial distribution of the liquid pressure fluctuation for the focused ultrasound is obtained for cases in which the liquid is water or liver tissue. In addition, frequency analysis is carried out using the fast Fourier transform, and the generation of higher harmonic components is compared for water and liver tissue. The elasticity suppresses the generation of higher harmonic components and promotes the remnant of the fundamental frequency components. This indicates that the elasticity of liquid suppresses shock wave formation in practical applications.

Submodule Capacitor Voltage Ripple Reduction of Full-Bridge Submodule-Based MMC (FBSM-MMC) with Non-Sinusoidal Voltage Injection

The full-bridge submodule (FBSM)-based modular multilevel converter (FBSM-MMC) offers promising performance due to its ability to output negative FBSM voltage. This paper studies this ability of the FBSM-MMC under zero-sequence voltage injection (ZSVI) and second-order harmonic current injection (SHCI). The focus of the research is to redistribute the FBSM powers by injecting an additional power degree of freedom, resulting in a smaller FBSM capacitor voltage ripple, while keeping the maximum AC output voltage for a given fundamental frequency component of the arm voltage reference. Accordingly, a control strategy was developed, based on non-sinusoidal ZSVI, and SHCI is proposed for further improving the performance of the FBSM-MMC. The proposed non-sinusoidal ZSVI contains a higher sinusoidal third-order harmonic component than that of pure sinusoidal third-order voltage injection (THVI) when operating under the same maximum AC output voltage. By implementing this solution, a smaller amplitude of the injected second-order harmonic current can be achieved, producing a lower power loss in the FBSM-MMC. Considering the proposed solution, the relationship of the arm powers and FBSM capacitor voltages are also discussed. Finally, the simulation results and experimental results are presented to verify the effectiveness of the theoretical analysis of the proposed method.

Effective Frequency Lock-In Changes of a Ring Laser Gyroscope Due to Harmonic Components of Dithering Signal

The frequency lock-in phenomenon is the most important error factor that degrades the performance of a ring laser gyroscope by causing a non-linear output to the rotational angular velocity input. To solve the problem of frequency lock-in, a mechanical dithering technique has been proposed and most successfully and widely applied to date. In addition, in the case of dithering with a sinusoidal signal of a single-frequency component, the theoretical background is well established. However, in actual applications, it is almost impossible to implement a perfect single sinusoidal signal owing to various electrical and mechanical constraints. In general, although the occupied portion is smaller than the fundamental frequency component, the dithering signal inevitably includes harmonics. Therefore, it is essential to analyze the influence of the corresponding harmonic component to accurately predict the frequency lock-in characteristics of a ring laser gyroscope. In this study, it is assumed that the dithering signal has odd harmonics, and through numerical experiments, the frequency lock-in widths of the ring laser gyroscope according to the dithering amplitude change and the effectiveness of improving the related characteristics according to the application of random dithering are analyzed. The analysis confirmed that the resonance condition, including the higher harmonics of mechanical dithering, can be a major variable that determines the frequency lock-in characteristics of the ring laser gyroscope. To improve the relevant performance of the ring laser gyroscope, in-depth research from that point of view is necessary.

Reduction of Motor Drive System Loss by 5th Harmonic Superimposition PWM Control

Herein, the loss reduction of a motor drive system is experimentally studied by means of the 5th harmonic superimposition in the reference signal of a sinusoidal PWM inverter from the perspective of nonlinear magnetic characteristics. The measured data of the motor drive system loss exhibits a reduction of 1.5% in the condition when the superimposition rate is -0.15. More specifically, the motor core, copper and inverter losses are reduced. The results confirm the feasibility and efficacy of the proposed method. According to the fundamental research of a ring test with the same electrical steel as the motor, the magnetic characteristics of the B-H curve changes in the case of the 5th harmonic superimposition, which decreases the fundamental component of the current. Accordingly, the loss is considered to be reduced due to the decline in the fundamental current component and carrier frequency components.

Deadbeat Voltage Control for a Grid-Forming Power Converter With LCL Filter

Grid-forming power converters are controlled as voltage sources to regulate the grid voltage and frequency. These converters can increase power system strength if they impose a voltage waveform resilient to grid transients. For this reason, in this paper, we propose a deadbeat control strategy of the capacitor voltage for high power converters with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> filter. To damp the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LCL</i> resonant poles, an active damping strategy is developed, based on a modification of the deadbeat control law. With this purpose, a notch filter is applied to the electrical variables allowing to emulate different damping resistances for the fundamental component and the harmonics. As a result, the active damping does not introduce tracking errors of the fundamental frequency component, while it provides damping to the filter resonance. The proposed strategy does not require knowledge of the grid impedance, an interesting feature in grid-connected power converters because the grid impedance is generally unknown. Experimental results validate the proposed strategy.