Harmonic Contributions Research Articles

Experimental decomposition of nonlinear hydrodynamic loads and hydroelastic responses in wave–structure interactions of monopile wind turbines

This study explores the nonlinear effects of hydrodynamic loads and hydroelastic responses in monopile-supported offshore wind turbines, with a focus on their harmonic structures. High-quality experimental data were collected in a shallow water basin across various irregular waves. Their harmonic components up to the fourth order were successfully isolated using a novel four-phase decomposition technique, which effectively extracts harmonics from random time series. The results highlight significant contributions of higher-order harmonics across various sea states. Specifically, two physical models were employed: a flexible monopile to capture structural hydroelastic deformations during large wave events and a rigid monopile to accurately estimate hydrodynamic loads without hydroelastic effects. Additionally, numerical results from fully nonlinear potential-flow calculations were compared, revealing that while the potential-flow solver underestimates total wave loading, especially for higher harmonics. In terms of the free-surface elevations and hydrodynamic forces, this study confirms that their higher-order harmonics align well with the scaling of their corresponding linear components in both amplitude and phase. This enables the prediction of higher-order profiles based solely on their linear components. However, this efficient model is inadequate for accurately estimating the higher-order harmonics of monopile's hydroelastic responses during these extreme wave events, highlighting the need for further refinement.

РЕГИСТРАЦИЯ МАГНИТОМОДУЛЯЦИОННЫМ ДАТЧИКОМ НИЗКОЧАСТОТНОГО ЭЛЕКТРОМАГНИТНОГО ИЗЛУЧЕНИЯ В ЛАБОРАТОРНЫХ ЭКСПЕРИМЕНТАХ ПО РАЗРУШЕНИЮ ОБРАЗЦОВ ГОРНЫХ ПОРОД

The article presents the results of observations of variations in magnetic induction using magnetomodulation sensors, which made it possible to register the signals of electromagnetic (EM) emission in the range of 0.01–200 Hz generated by rock samples under fast and slow uniaxial loading in laboratory experiments. The description of the equipment and measurement techniques used in the experiments is given. At two modes of loading rock samples differences in EM emission signals reflecting the peculiarities of the development of their destruction processes are found. It is shown that during the destruction of rock samples, the amplitude-frequency spectrum of magnetic field components clearly reveals the contribution of low-frequency harmonics, which is mainly concentrated in the frequency range below 15 Hz. It is established that magnetomodulation sensors have sufficient sensitivity and resolution to observe and register EM emission signals in the frequency range of 0.01–200 Hz, manifested during the destruction of rock samples in the process of their loading.

Strong coupling yields abrupt synchronization transitions in coupled oscillators

Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions—such as synchrony and rotating wave solutions—following perturbation or parameter variation. In the limit of weak coupling, these transitions can be understood in terms of commonly studied phase approximations. As the coupling strength increases, however, predicting the location and criticality of transition, whether continuous or discontinuous, from the phase dynamics may depend on the order of the phase approximation—or a phase description of the network dynamics that neglects amplitudes may become impossible altogether. Here we analyze synchronization transitions and their criticality systematically for varying coupling strength in theory and experiments with coupled electrochemical oscillators. First, we analyze bifurcations analysis of synchrony and splay states in an abstract phase model and discuss conditions under which synchronization transitions with different criticalities are possible. In particular, we show that such conditions can be understood by considering the relative contributions of higher harmonics to the phase dynamics. Second, we illustrate that transitions with different criticality indeed occur in experimental systems. Third, we highlight that the amplitude dynamics observed in the experiments can be captured in a numerical bifurcation analysis of delay-coupled oscillators. Our results showcase that reduced order phase models may miss important features that one would expect in the dynamics of the full system. Published by the American Physical Society 2024

Experimental jet control with Bayesian optimization and persistent data topology

This study experimentally optimizes the mixing of a turbulent jet at Reynolds number 10 000 with the surrounding air by targeted shear layer actuation. The forcing is composed of superposed harmonic signals of different azimuthal wavenumber m generated by eight loudspeakers circumferentially distributed around the nozzle lip. Amplitudes and frequencies of the individual harmonic contributions serve as optimization parameters, and the time-averaged centerline velocity downstream of the potential core is used as a metric for mixing optimization. The actuation is optimized through Bayesian optimization. Three search spaces are explored—axisymmetric forcing, m = 0, superposed axisymmetric and helical forcing, m∈{0,1}, and axisymmetric actuation combined with two counter-rotating helical modes, m∈{−1,0,1}. High-speed particle image velocimetry (PIV) is employed to analyze the jet response to the optimized forcing. The optimization processes are analyzed by persistent data topology. In the search space of axisymmetric excitation, the routine identifies an actuation at the natural frequency of the flow to be most efficient, with the centerline velocity being decreased by 15%. The optimal solutions in both the two-mode and three-mode search space converge to a similar forcing with one axial and one helical mode combined at a frequency ratio of around 2.3. Spectral analysis of the PIV images reveals that for the identified optimal forcing frequencies, a non-linear interaction between forced and natural structures in the jet flow is triggered, leading to a reduction in centerline velocity of around 35%. The topology of the most complex search space from the discrete data reveals four basins of attractions, classified into three forcing patterns including axisymmetric, axisymmetric-helical, and axisymmetric-flapping. Two deep basins are related to the optimal pattern found as axisymmetric-helical, and the others are shallower.

A new dual-thickness semi-transparent beamstop for small-angle X-ray scattering.

An innovative dual-thickness semi-transparent beamstop designed to enhance the performance of small-angle X-ray scattering (SAXS) experiments is introduced. This design integrates two absorbers of differing thicknesses side by side into a single attenuator, known as a beamstop. Instead of completely stopping the direct beam, it attenuates it, allowing the SAXS detector to measure the transmitted beam through the sample. This approach achieves true synchronization in measuring both scattered and transmitted signals and effectively eliminates higher-order harmonic contributions when determining the transmission light intensity through the sample. This facilitates and optimizes signal detection and background subtraction. This contribution details the theoretical basis and practical implementation of this solution at the SAXS station on the 1W2A beamline at the Beijing Synchrotron Radiation Facility. It also anticipates its application at other SAXS stations, including that at the forthcoming High Energy Photon Source, providing an effective solution for high-precision SAXS experiments.

Method for determining the harmonic contribution of consumer installations based on the application of passive filters

AbstractThe paper presents a new method for estimating the contribution of distortion sources based on the application of passive harmonic filters. The method does not require the measurement of harmonic network impedance and is based on the measurement of harmonic currents of the grid, consumers and passive harmonic filters. Evaluation of the consumer contribution using a passive harmonic filter is necessary to select the parameters and connection points for harmonic reduction devices. A feature of the method is the correct determination of share contributions, regardless of background harmonic distortions. Based on this method, a single consumer can evaluate both the harmonic contributions of its own loads, even in the presence of background distortions, and the harmonic voltage distortions in the case of installing harmonic reduction devices. The research results are confirmed in laboratory conditions with various combinations of electrical loads connected both at the grid side and at the consumer side. For such conditions, the proposed method was compared with existing methods, among which are methods based on the measurement of harmonic voltage vectors, harmonic current vectors and active harmonic power. The application of the developed method was demonstrated using the example of a gas production field.

Observation of multiple attractors and diffusive transport in a periodically driven Klein-Gordon chain.

We consider a Klein-Gordon chain that is periodically driven at one end and has dissipation at one or both boundaries. An interesting numerical observation in a recent study [Prem et al., Phys. Rev. B 107, 104304 (2023)2469-995010.1103/PhysRevB.107.104304] was that for driving frequency in the phonon band, there is a range of values of the driving amplitude F_{d}∈(F_{1},F_{2}) over which the energy current remains constant. In this range the system exhibits a traveling wave solution termed a "resonant nonlinear wave" (RNW). It was noted that the RNW mode occurs over a range (F_{1},F_{2}) and shrinks with increasing system size, N. Remarkably, we find that the RNW mode is in fact a stable solution even for F_{d}>F_{2}, and that in this regime there exist two attractors, both with finite basins of attraction. We improve the perturbative treatment for the RNW mode, presented in the earlier work, by including the contributions of third harmonics. We also consider the effect of thermal noise at the boundaries and find that the RNW mode is stable for small temperatures. Corresponding to the two attractors for large F_{d} at zero temperature, the system can now be in two nonequilibrium steady states. Finally, we present results for a different driving protocol [Komorowski et al., Commun. Math. Phys. 400, 2181 (2023)10.1007/s00220-023-04654-4] where F_{d} is taken to scale with system size as N^{-1/2} and dissipation is only at the nondriven end. We find that the steady state for this case can be characterized by Fourier's law. We point out interesting differences that occur because of our dynamics being nonlinear and Hamiltonian. Our results suggest the intriguing possibility of observing the high-current-carrying RNW phase in experiments by careful preparation of initial conditions.

Harmonics Assessment of Distribution Transformer with Photovoltaic Integration and Unbalanced Loads

Harmonic distortion is one of the monumental power quality problems in an electrical power system. It frequently originated from non-linear loads generating non-sinusoidal steady state waveforms, which may lead to various undesirable effects on distribution transformers such as increased losses, overheating and lifetime reduction. In previous works, the harmonic current contributions from non-linear loads from consumers have been appointed as the main contributor of harmonic issues in the distribution transformers. However, since the integrations of renewable energy as a distributed generation (DG) have exponentially increasing in recent years, the impact of solar photovoltaic (PV) system implementation into distribution system on amplifying additional harmonic contents also needs to be addressed. Therefore, this paper conducts a comparative analysis of voltage and current harmonic profiles within the distribution transformer in three-phase distribution network and three-phase grid-connected photovoltaic (GCPV) system, with both subjected to supply unbalanced non-linear loads. The simulation is carried out using MATLAB Simulink 2021a software and the results are compared according to standards. As a result, the distribution transformer in the GCPV system is proven to contain higher levels of voltage and current harmonic distortion compared to a normal distribution grid.

Nonlinear theory of the modulational instability at the ion–ion hybrid frequency and collapse of ion–ion hybrid waves in two-ion plasmas

We study the dynamics of two-dimensional (2D) nonlinear ion–ion hybrid waves propagating perpendicular to an external magnetic field in plasmas with two ion species. We derive nonlinear equations for the envelope of electrostatic potential at the ion–ion hybrid frequency to describe the interaction of ion–ion hybrid waves with low-frequency acoustic-type disturbances. The resulting nonlinear equations also take into account the contribution of the second harmonics of the ion–ion hybrid frequency. A nonlinear dispersion relation is obtained, and, for a number of particular cases, modulational instability growth rates are found. By neglecting the contribution of second harmonics, the phenomenon of the collapse of ion–ion hybrid waves is predicted. It is shown that taking into account the interaction with the second harmonic results in the existence of a stable two-dimensional soliton.

Primary and secondary resonance phenomenon for two-layer liquid sloshing in a rectangular container under horizontal excitation

Laboratory experiments were conducted to study primary and secondary resonant sloshing in a laterally excited rectangular container containing two-layer stratified liquids. The findings revealed that primary resonance of the free surface or the separation surface occurs when the forcing frequency closely matches the corresponding natural frequency. Some intriguing phenomena, such as the sudden wave amplitude increase and the downward shift in resonant peaks, can be observed due to the soft-spring effect. Secondary resonance arises when superharmonic or sub-harmonic frequencies associated with liquid sloshing closely align with the natural frequencies of the system. For the free surface, the secondary resonances of the first five modes occur at forcing frequencies closely related to a third of the first mode, half of the second mode, a third of the third mode, a quarter of the fourth mode, and a fifth of the fifth mode natural frequency of the free surface, respectively. Furthermore, secondary resonance can also manifest under other forcing conditions, such as when the harmonic at a fractional multiple is near the second mode natural frequency of the free surface. Regarding the separation surface, it is worth noting that secondary resonance occurs due to the dominant contribution of fractional harmonics of the forcing frequency. To the best of the authors' knowledge, this is the first systematic investigation of primary and secondary resonance behaviors in a two-layer liquid system.

Analytical Torque Ripple Reduction Strategy for Flux Modulated Doubly-Salient Reluctance Motor Drives Based on ZSC Harmonic Regulation

Compared to the conventional doubly-salient reluctance motor (DRM) drives, the novel flux modulated DRM (FMDRM) drives can achieve a better overall torque performance due to the dc-biased sinusoidal current excitation. However, previous investigations only focus on the dc-biased and fundamental current components, and the contributions of current harmonics to the torque production are not clear. This paper proposes an analytical torque ripple reduction strategy for open-winding FMDRM drives based on zero-sequence current (ZSC) harmonic regulation. Firstly, the contribution of third-order ZSC harmonic to the electromagnetic torque is investigated together with the dc-biased sinusoidal current components. Secondly, an alternative torque component cancellation method is put forward, where the additional third-order ZSC is utilized to counteract the dominating part of the alternative torque generated by the dc-biased sinusoidal current for torque ripple reduction. Both the amplitude and initial phase angle of the additional third-order ZSC are calculated by the analytical equation of electromagnetic torque. Moreover, the corresponding three-dimensional current distribution is investigated to achieve the desired ZSC regulation. With the proposed scheme, the torque ripple can be effectively suppressed while maintaining high output torque capability and efficiency. Furthermore, experimental results are presented on a three-phase FMDRM prototype to verify the proposed strategy. <fn fn-type="other" id="fn3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> </fn>

Assessment of Harmonic Contribution of a Photovoltaic Installation Based on Field Measurements

Quantifying harmonic contribution of customer installations to the voltage distortion in the network is still one of the main challenges of utilities with respect to power quality, particularly when integrating large number of renewable energy sources. This paper discusses different aspect of evaluating the low-order harmonic emission of a 100 kW photovoltaic (PV) installation consisting of 16 single-phase inverters. Based on field measurements of one week the harmonic currents of the installation are analyzed with respect to different operating conditions. The measured harmonic currents are compared with emission values provided by the manufacturer as well as emission limits specified in standards. Finally, different methods for the determination of the contribution of the PV installation to the voltage distortion in the network are compared.

A novel method for calculating harmonic contribution based on difference recurrence estimation

AbstractDetermining the harmonic contribution of each harmonic source is conducive to improving the harmonic management of the power system. The main problem with harmonic contribution calculation is determining the equivalent system harmonic impedance. The previous harmonic impedance calculation method can only calculate the impedance value when the harmonic fluctuation is significant, and the calculation fails when the harmonic fluctuation is small. Therefore, a new method called difference recurrence estimation is proposed to construct the objective function from impedance parameters. The advantages of the proposed method are low data requirement, high estimation accuracy, and excellent tracking performance. An improved genetic algorithm (GA) is presented by integrating an adaptive crossover operator and population intervention into the standard GA to improve the global searching impedance parameter ability. Based on these parameters, harmonic impedance and harmonic contribution are calculated accurately. The superiority of the proposed model is verified through simulation and field cases.

A Method for Determining Harmonic Contribution and Harmonic Source Current Based on Minimum Mutual Information and Bayesian Optimization

A Method for Determining Harmonic Contribution and Harmonic Source Current Based on Minimum Mutual Information and Bayesian Optimization

Three-Phase Distortion Analysis based on Space-Vector Locus Diagrams

This work deals with the use of the space vector concept to characterize the harmonic content of a three-phase voltage/current. It is shown that the shape of the trajectory of the space vector on the complex plane (i.e., the locus diagram) provides information about its harmonic content. In particular, it is shown that each harmonic contributes to the locus diagram with a number of lobes depending on the relative angular frequency between the harmonic and the fundamental component. To this aim, the different contributions of positive-sequence and negative-sequence harmonics is explained and put into evidence with specific examples. The expressions for the magnitude and phase of the space vector as functions of the harmonics are derived analytically. Numerical examples are provided to show how the locus diagram can represent a three-phase quantity with positive-sequence and negative-sequence harmonics.

Multi-harmonic sources identification and evaluation method based on cloud-edge-end collaboration

With the increase of power electronic devices such as distributed renewable energies, energy storage, and flexible loads, the disturbance sources are rapidly raised and distributed in multiple voltage levels in the distributed network. The harmonics they produce are random and uncertain, and the massive amounts of data propose high demands on server computing capability, which restrict harmonic sources evaluation and significantly influence the judgments of the power quality in the distribution network. In order to improve the power quality and the harmonic source evaluation function of the distribution network, in this paper, a framework for multi-harmonic source identification and evaluation based on cloud-edge-end collaboration is proposed. Firstly, based on the analysis of the functional requirements harmonic sources evaluation in multiple voltage levels, a novel framework of cloud-edge-end collaboration is proposed. Secondly, the cloud-edge-end collaborative harmonic sources evaluation method which executes different service strategies according to voltage levels and grid operation based on the multi-level interaction of edge computing is proposed. Further, the working principle of the proposed novel framework with multiple evaluation methods including the dominant harmonic source identification, concentrated multiple harmonic sources evaluation (CMHSE) and hierarchical harmonic sources evaluation (HHSE) is described in detail in order to show the completed work processes of the proposed framework. Finally, the performance of the proposed method is verified based on the real data measured from different realistic urban power grids in China. The proposed method can effectively evaluate harmonic contributions in distribution systems and in turn provide a basis for harmonic mitigation measures.

Determination of acoustic phonon anharmonicities via second-order Raman scattering in CuI

We demonstrate the determination of anharmonic acoustic phonon properties via second-order Raman scattering exemplarily on copper iodide single crystals. The origin of multi-phonon features from the second-order Raman spectra was assigned by the support of the calculated 2-phonon density of states. In this way, the temperature dependence of acoustic phonons was determined down to 10 K. To determine independently the harmonic contributions of respective acoustic phonons, density functional theory in quasi-harmonic approximation was used. Finally, the anharmonic contributions were determined. The results are in agreement with earlier publications and extend CuI’s determined acoustic phonon properties to lower temperatures with higher accuracy. This approach demonstrates that it is possible to characterize the acoustic anharmonicities via Raman scattering down to zero-temperature renormalization constants of at least 0.1 cm−1.

Interaction among Multiple Electric Vehicle Chargers: Measurements on Harmonics and Power Quality Issues

The electric vehicle (EV) market is growing rapidly due to the necessity of shifting from fossil fuel-based mobility to a more sustainable one. Smart charging paradigms (such as vehicle-to-grid (V2G), vehicle-to-building (V2B), and vehicle-to-home (V2H)) are currently under development, and the existing implementations already enable a bidirectional energy flow between the vehicles and the other systems (grid, buildings, or home appliances, respectively). With regard to grid connection, the increasingly higher penetration of electric vehicles must be carefully analyzed in terms of negative impacts on the power quality; and hence, the effects of electric vehicle charging stations (EVCSs) must be considered. In this work, the interactions of multiple electric vehicle charging stations have been studied through laboratory experiments. Two identical bidirectional DC chargers, with a rated power of 11 kW each, have been supplied by the same voltage source, and the summation phenomenon of the current harmonics of the two chargers (which leads to an amplification of their values) has been analyzed. The experiment consisted of 100 trials, which considered four different combinations of power set-points in order to identify the distribution of values and to find suitable indicators for understanding the trend of the harmonic interaction. By studying the statistical distribution of the Harmonic Summation Index, defined in the paper, the impact of the harmonic distortion caused by the simultaneous charging of multiple electric vehicles has been explored. Based on this study, it can be concluded that the harmonic contributions of the electric vehicle charging stations tend to add up with increasing degrees of similarity of the power set-points, while they tend to cancel out the more the power set-points differ among the chargers.

Refined convolution‐based measures for real‐time harmonic distortions estimation in power system dominated by inverter‐based resources

AbstractReal‐time estimating harmonic distortion levels near the Point of Interconnections of grid‐connected inverter‐based resources (IBRs) is critical for maintaining the operational reliability and security of the power grid, particularly during transients when IBRs generate excessive harmonics. Traditional methods like Total Harmonic Distortion (THD) are unsuitable for time‐varying waveforms as they suffer from aliasing, spectral leakage, and picket‐fence effects. This paper proposes a novel approach that utilizes convolution‐based measures for estimating harmonic distortion, which offers a more suitable way for ongoing real‐time applications. The first measure uses a 60 Hz sinusoidal function as the convolution kernel, while an enhanced measure employs the Gaussian function as the kernel. Two convolution‐based measures are proposed and compared with THD. The comparison criteria are based on the two significant features describing the variation of harmonics: min/max values and variation curvature of harmonics showing the accurate performance of proposed measures. Moreover, short‐term estimations of harmonic distortion are used to validate the effectiveness of the proposed measures, while long‐term estimations are used to determine the ability of the proposed measures to determine harmonic distortion contributions among power network components. The proposed technique's intrinsic characteristics provide a sampling window with low sensitivity to deviations in the fundamental frequency and signal's stationary condition to prevent aliasing and spectral leakage and rule out the impact of the picket‐fence effect on the harmonic distortion level estimation.

Efficiency-enhanced DC-excited Vernier reluctance machine with reduced excitation coils for electric vehicles

Due to its good mechanical robustness and field control capacity, the DC-excited Vernier reluctance machine (DC-VRM) is a promising candidate for electrical vehicle propulsion. However, the conventional design of this machine suffers from large excitation copper loss and leading to low efficiency, due to an identical distribution of DC excitation coils at the stator side. This paper proposes a novel efficiency-enhanced DC-VRM. The key technology is based on the flux modulation mechanism to reduce DC field coils and mitigate DC copper loss while keeping the excitation ability and power density not sacrificed. In this paper, the machine configuration and operation principle are introduced. A combination of the magneto-static finite element and the analytical method is used to quantitatively analyze the contribution of different harmonics on the phase EMF under two different DC layouts. The feasibility of the proposed topology is further verified by a transient finite element analysis, which proves that, with the same design parameters, the proposed design achieves higher back EMF and output torque per DC copper loss. Therefore, this new topology enhances efficiency and can be a more promising non-PM machine for EVs.