Harmonic Estimation Research Articles

A Modified Least Square Harmonics Estimation Method and Comparative Analysis of Established Full Periodicity Models

AbstractUnmodelled periodicities of GNSS coordinate time series lead to colored noise and therefore, unreal estimations of uncertainties and misinterpretation of geophysical phenomena. This paper firstly conducted Least Square Harmonics Estimation (LSHE) and Lomb‐Scargle periodogram method respectively on 25 CMONOC GNSS time series in Yunnan Province, China to establish the corresponding function models for each station. However, several prominent problems emerge: (1) design matrix singularity occurs when too close alternative frequencies are introduced; (2) low frequencies would be missed due to the cutoff of alternative frequencies. Consequently, periodic variations of a station would be depicted in an incorrect way. In order to solve these problems, this paper proposes a method that takes advantages of both LSHE and Lomb‐Scargle periodogram, that is, (1) to conduct an examination on the reciprocal of condition number of design matrix to avoid singularity problem, (2) to introduce the frequency results from the periodogram as a priori candidate frequencies to include low frequencies and improve accuracy of alternative frequencies. Compared with LSHE method and Lomb‐Scargle periodogram, the modified LSHE method reduces Root Mean Square (RMS) value of residuals by 0.83 mm and 0.43 mm, and reduces absolute spectrum indices of residuals by 0.11 and 0.04. Spectrum analysis and auto‐correlation function of residuals indicates corresponding residuals are closer to white noise, indicating modified LSHE method of this paper is valid to reduce colored noise through establishing a full periodicity model.

Optimal Dynamic Harmonic Extraction and Suppression in Power Conditioning Applications

Power quality in electrical systems is a basic requirement that should be guaranteed. Nonetheless, the increase of power-electronics-based applications and other nonlinear loads have induced harmonic distortion degrading the power quality; therefore, effective methods to measure and suppress such distortion need to be developed. The main contributions of this article are the following: the development of a novel fast-converging optimal estimator to determine online the harmonic components of a time-varying signal, which can be used for analysis and control purposes; the usage of the estimator to generate reference signals for an optimal control system in order to suppress the harmonics components; and the experimental validation of the proposed methodology as a feasible solution for industrial applications. The proposal considers practical assumptions such as the signal to be analyzed is corrupted with noise and contains time-varying harmonics (i.e., no steady-state condition is assumed). As an application of the harmonic estimator, the following two experimental tests are carried out: first, the optimal determination of the harmonic components of the current waveform in a nonlinear load, and second, the usage of harmonics information to mitigate them through of an active power filter, which is controlled by using an optimal trajectory tracking control scheme.

Reduction of harmonic monitors and estimation of voltage harmonics in distribution networks using wavelet analysis and NARX

The use of power quality monitors is necessitated for optimizing power systems to improve efficiency and decrease power system-related failures. These monitors are expensive and their installation at all buses is not economic. With regard to optimum allocation approaches, power quality monitors should be installed for the assessment of the power quality of sensitive loads. Monitoring of sensitive loads is eliminated in this paper, and an estimator is used for virtually monitoring voltage harmonics. This paper presents an intelligent system based on the nonlinear autoregressive model with exogenous input (NARX) and wavelet analysis. The wavelet transform is utilized for extracting the feature of waveforms, and NARX is employed to detect the voltage harmonic distortion waveforms (VHDWs) at non-monitored sensitive loads in distribution networks using the information gained through the nearest monitoring data. The proposed estimator can be considered as a virtual monitor, eliminating the monitor of sensitive load such that the optimum number of power quality monitors and monitoring cost of the distribution network would be reduced. The estimator is examined on the IEEE test system and the performance of the intelligent system has been verified in many different ways.

Ultrathin initiated chemical vapor deposition polymer interfacial energy control for directed self-assembly hole-shrink applications

Integrated circuit layouts consist of patterned lines and holes, where holes define the electrical contacts between adjacent layers. Block copolymer directed self-assembly (DSA) successfully shrinks the critical dimension (CD) of these contacts beyond the resolution of conventional lithography. DSA also radically improves the CD uniformity. One particularly difficult step of the DSA hole-shrink process involves establishing the correct interfacial energy throughout a lithographically templated hole to ensure good assembly. Initiated chemical vapor deposition (iCVD) is a uniform, ultrathin, ultraconformal, all-organic deposition technique that allows for precise control of the interfacial energy. In this work, the authors use iCVD of polydivinylbenzene at film thicknesses below 5 nm to blend the interfacial energy of the coated film with that of the silicon/spin-on carbon template. They fully characterize the iCVD surface by means of two liquid surface energy measurements. They further identify the interfacial energies presented by these functionalized templates through qualitative hole-island tests as well as quantitative harmonic mean estimations. In parallel, the authors run theoretically informed coarse grained simulations with the determined interaction parameters and DSA experiments and find good agreement across the range of chemistries created. Through careful control of iCVD conditions, especially filament temperature, they achieve a strong polystyrene-preferential sidewall with a nonpreferential bottom which they then demonstrate, both in the simulation and in the experiment, allows for a successful hole-shrink process across a wide range of template hole diameters.

Orbit propagation around small bodies using spherical harmonic coefficients obtained from polyhedron shape models

AbstractMissions to asteroids have been the trend in space exploration for the last years. They provide information about the formation and evolution of the Solar System, contribute to direct planetary defense tasks, and could be potentially exploited for resource mining. Be their purpose as it may, the factor that all these mission types have in common is the challenging dynamical environment they have to deal with. The gravitational environment of a certain asteroid is most of the times not accurately known until very late mission phases when the spacecraft has already orbited the body for some time.Shape models help to estimate the gravitational potential with a density distribution assumption (usually constant value) and some optical measurements of the body. These measurements, unlike the ones needed for harmonic coefficient estimation, can be taken from well before arriving at the asteroid’s sphere of influence, which allows to obtain a better approximation of the gravitational dynamics much sooner. The disadvantage they pose is that obtaining acceleration values from these models implies a heavy computational burden on the on-board processing unit, which is very often too time-consuming for the mission profile.In this paper, the technique developed on [1] is used to create a validated Python-based tool that obtains spherical harmonic coefficients from the shape model of an asteroid or comet, given a certain density for the body. This validated software suite, called AstroHarm, is used to analyse the accuracy of the models obtained and the improvements in computational efficiency in a simulated spacecraft orbiting a small body.The results obtained are shown offering a qualitative comparison between different order spherical harmonic models and the original shape model. Finally, the creation of a catalogue for harmonics is proposed together with some thoughts on complex modelling using this tool.

Bayesian Learning-Based Harmonic State Estimation in Distribution Systems With Smart Meter and DPMU Data

This paper studies the problem of locating harmonic sources and estimating the distribution of harmonic voltages in unbalanced three-phase power distribution systems. We develop an approach for harmonic state estimation utilizing two types of measurements from smart meters and distribution-level phasor measurement units (DPMUs). It involves regression analysis for power flow calculation, prediction of demands using recurrent neural networks, and sparse Bayesian learning for state estimation. The proposed approach requires fewer DPMUs than nodes, making it more applicable to existing distribution grids. We show the effectiveness of the proposed estimator through extensive numerical simulations on an IEEE test feeder. We also investigate how the increased penetration of distributed energy resources could affect the performance of our state estimator.

Frequency‐scaled optimized time‐frequency transform for harmonic estimation in photovoltaic‐based microgrid

Frequency‐scaled optimized time‐frequency transform for harmonic estimation in photovoltaic‐based microgrid

Dynamic Harmonic Synchrophasor Estimator Based on Sinc Interpolation Functions

This paper introduces a new dynamic harmonic synchrophasor estimator (DHSE) based on the Shannon sampling theorem. Each dynamic harmonic phasor is modeled as a weighted sum of a series of sinc interpolation functions. Based on this, a bank of finite impulse response filters is designed. They are used to estimate not only the dynamic harmonic synchrophasor but also the harmonic frequency and rate of change of frequency (ROCOF). A model parameter is properly selected to adapt filters’ passband and stopband performances for different order harmonics. Frequency responses and simulation tests are used to compare the performance of the DHSE and the Taylor–Fourier transform (TFT). The results show that the DHSE has lower passband ripples and higher stopband attenuation than the TFT. Moreover, under frequency deviation, harmonic oscillation, and frequency ramp conditions, the DHSE is more accurate than the TFT in dynamic harmonic synchrophasor, frequency, and ROCOF estimations.

Harmonic estimation in power systems using an optimised adaptive Kalman filter based on PSO‐GA

A hybrid particle swarm optimisation (PSO) and genetic algorithm (GA) aided Kalman filter (PSO-GA-KF) method for dynamic harmonic state estimation in the power system is investigated. The initial choice of states and KF's parameters, such as process and measurement error covariance matrices significantly affects the estimation precision. Aiming at this problem, a combination of PSO and GA (PSO-GA) is proposed to optimise KF's parameters. In this hybrid algorithm, by replacing the gene mutation operator of GA, the PS algorithm mutation operator is constructed, which can adjust the evolution direction and range based on historical records and swarm records, leading to avoiding the blindness of GA mutation and reducing the probability of devious mutation and enhancing the velocity of evolution. Thus, the global search ability of the hybrid PSO-GA can ensure KF has more accurate estimation of harmonics. To test the effectiveness of the algorithm, several time-varying signals are simulated with harmonics and decaying DC components in the presence of amplitude drift and white noise. Simulation results show that the proposed hybrid algorithm has more accurate estimation, faster convergence and better robustness against noise in comparison with the conventional Kalman filter (KF), KF based on the maximum likelihood and PSO aided KF (PSO-KF).

Active damping method based self‐adjust notch filter for current source converter

Inductor–capacitor (LC) filter in current source converter (CSC) exits resonance peak, which result in reducing control stability and amplifying harmonic component near resonance frequency. This study proposed a simply self-adjust notch filter active damping method for CSC. A notch filter is inserted into control loop to damp the control gain at resonance frequency, no need of additional sensor. The grid inductance varies as power system operating conditions change, which deteriorates notch filter damping performance because of resonance frequency changing. The harmonic impedance estimation method is used in the paper to estimate grid inductance and actively adjust notch filter centre frequency. Both simulation and experimental results verified the effectiveness and robustness of the proposed method.

Multiple Nonlinear Harmonic Oscillator-Based Frequency Estimation for Distorted Grid Voltage

In the presence of nonlinear loads and various disturbances, harmonics and dc bias may corrupt the grid voltage signal leading to distorted grid. Frequency estimation of distorted grid signal is a challenging issue. In this paper, multiresonant nonlinear harmonic oscillators-based frequency estimation technique is reported for the distorted power grid. The proposed approach has also been applied for detecting the sequences of the unbalanced grid. In the proposed approach, a nonlinear harmonic oscillator is used as the proxy of the grid signal. Then, using the frequency-locked loop, an adaptive approach is proposed to estimate the frequency and other parameters (sequences) in the presence of harmonics and dc component. Local stability analysis and parameter tuning are provided. Comparative experimental results are provided with two other nonlinear state-of-the-art techniques. Experimental results demonstrated the suitability of the proposed technique.

Robust Bayesian Pitch Tracking Based on the Harmonic Model

Fundamental frequency is one of the most important characteristics of speech and audio signals. Harmonic model-based fundamental frequency estimators offer a higher estimation accuracy and robustness against noise than the widely used autocorrelation-based methods. However, the traditional harmonic model-based estimators do not take the temporal smoothness of the fundamental frequency, the model order, and the voicing into account as they process each data segment independently. In this paper, a fully Bayesian fundamental frequency tracking algorithm based on the harmonic model and a first-order Markov process model is proposed. Smoothness priors are imposed on the fundamental frequencies, model orders, and voicing using first-order Markov process models. Using these Markov models, fundamental frequency estimation and voicing detection errors can be reduced. Using the harmonic model, the proposed fundamental frequency tracker has an improved robustness to noise. An analytical form of the likelihood function, which can be computed efficiently, is derived. Compared to the state-of-the-art neural network and nonparametric approaches, the proposed fundamental frequency tracking algorithm has superior performance in almost all investigated scenarios, especially in noisy conditions. For example, under 0 dB white Gaussian noise, the proposed algorithm reduces the mean absolute errors and gross errors by 15% and 20% on the Keele pitch database and 36% and 26% on sustained /a/ sounds from a database of Parkinson's disease voices. A MATLAB version of the proposed algorithm is made freely available for reproduction of the results.11An implementation of the proposed algorithm using MATLAB may be found in https://tinyurl.com/yxn4a543.

SHORE‐based detection and imputation of dropout in diffusion MRI

In diffusion MRI, dropout refers to a strong attenuation of the measured signal that is caused by bulk motion during the diffusion encoding. When left uncorrected, dropout will be erroneously interpreted as high diffusivity in the affected direction. We present a method to automatically detect dropout, and to replace the affected measurements with imputed values. Signal dropout is detected by deriving an outlier score from a simple harmonic oscillator-based reconstruction and estimation (SHORE) fit of all measurements. The outlier score is defined to detect measurements that are substantially lower than predicted by SHORE in a relative sense, while being less sensitive to measurement noise in cases of weak baseline signal. A second SHORE fit is based on detected inliers only, and its predictions are used to replace outliers. Our method is shown to reliably detect and accurately impute dropout in simulated data, and to achieve plausible results in corrupted in vivo dMRI measurements. Computational effort is much lower than with previously proposed alternatives. Deriving a suitable outlier score from SHORE results in a fast and accurate method for detection and imputation of dropout in diffusion MRI. It requires measurements with multiple b values (such as multi-shell or DSI), but is independent from the models used for analysis (such as DKI, NODDI, deconvolution, etc.).

Robust estimation of voltage harmonics in a single‐phase system

A frequency adaptive technique relying on a linear Kalman filter (KF) is presented here for robust estimation of voltage harmonics under variable frequency conditions in a single-phase system. A relatively simple frequency-locked loop (FLL) is combined with the linear KF (LKF-FLL) to achieve frequency adaptive ability and avoid the use of a non-linear KF. In contrast to the non-linear extended KF (EKF), the LKF-FLL technique has several advantages such as robustness, linearity, simple tuning, having fewer states, requiring no derivative actions, while offering low complexity, excellent convergence, and computational efficiency. When compared to the non-linear extended real KF, it can generate a faster dynamic response and more accurate steady-state estimation of the harmonics under frequency variations. It can also provide an improved estimation for off-nominal frequency conditions when compared to the discrete Fourier transform (DFT) method. The effectiveness of the technique is verified by various simulated and real-time experimental case studies.

Analysis of Power System Harmonic Subgroups of the Electric Arc Furnace Currents Based on a Hybrid Time-Frequency Analysis Method

In this paper, a hybrid time-frequency analysis method, specially developed to decompose harmonic subgroups and interharmonics of the electric arc furnace (EAF) currents, which are highly time varying due to the operation principles of the EAFs, is presented. The main objective is accurate perception of harmonics and interharmonics in cases of rapid changes or power quality (PQ) events in power system voltages and currents. Harmonic and interharmonics detection has been achieved using discrete wavelet transform (DWT), which provides time-localization in cases of highly time-varying signals. Although DWT elicits accurate spectral decomposition at low frequencies, and especially at the baseband, bandwidths of the band-pass filters increase which results in loss of accuracy at higher frequencies. In order to avoid this problem, power signals are modulated by complex exponential waveforms, which corresponds to shifting the required harmonic sub-band contents to the baseband, where the accuracy of the DWT is the best. Using the proposed hybrid combination of DWT and complex exponential modulation, time domain waveform of each harmonic sub-band of the EAF currents can be estimated close to ideal values. The method also enables to focus on any required interharmonic sub-band in addition to the harmonics. To optimize the performance of the DWT in cases of PQ events, various windowing approaches are discussed. The proposed harmonic and interharmonic estimation method has been verified on both synthetic data and EAF currents collected from the electricity transmission system. Estimated harmonic and interharmonic waveforms can serve as a good reference in many areas including active power filtering operations, limit violation determinations, etc., in the power system.

Development of a steepest-descent control solution for Multi-Input Multi-Output swept sine testing in avirtual shaker environment

Multiple-Input Multiple-Output (MIMO) sine sweep is nowadays acknowledged to be one of the best excitation techniques for the modal testing of large aerospace structures, being an optimal solution in the tradeoff between high-quality FRFs testing time. Due to the test levels that can be reached during the sine sweeps and the increasing complexity and cost of the test articles, monitoring the recordings of multiple transducers translates in the actual need of guaranteeing that the responses are controlled on-line to a (safe) reference level. The development of a dedicated MIMO control strategy is very challenging, especially as a consequence of the transient behavior of the sweeps. This work proposes to investigate a solution for the on-line control of a MIMO continuous swept sine test combining the harmonic estimator with a steepest descent feedback control, typically adopted for the cancellation of tonal disturbances. The controller is developed in a virtual shaker testing environment, in order to tackle, already in the development stage, the effects that can be encountered during an actual test and that cannot be modeled with a linear system identification.

Harmonic Phasor Estimation With Flat-Top FIR Filter

The IEEE Std C37.118.1(a) describes synchrophasor measurement by a phasor measurement unit (PMU) for the system fundamental frequency. Harmonic synchrophasor, i.e., synchrophasor measured for harmonic frequencies, is not considered in the standard. Harmonic synchrophasor is useful for harmonic state estimation, power quality (PQ) monitoring, and harmonic power flow analysis. In this paper, we investigate the usability of the standard basic synchrophasor estimation model for the estimation of harmonic phasor (HP) up to the 50th harmonic as advised by the IEC Std 61000-4-7. For the estimation of HPs, an application of the flat-top (FT) finite-impulse-response (FIR) filter is proposed. Results for the maximally flat differentiator and the interpolated discrete Fourier transform (DFT) are also presented, confirming the superior performance of the proposed FT filter approach. HP estimation is verified with extended tests of the IEEE Std C37.118.1(a), including steady-state and dynamic conditions with additive 60-dB noise.

Harmonic Phasor Estimator for P-Class Phasor Measurement Units

Fast harmonic phasor measurements are very useful in power system protection applications, e.g., high-impedance fault location and intelligent method-based islanding detection. To address this problem, a novel harmonic phasor estimator is proposed in this paper, especially for P-class phasor measurement units (PMUs). The exponential functions are used to model the decaying dc (ddc) component, and the optimal time constant (TC) set for the ddc model is searched based on an enumeration method. In addition, the dynamic harmonic phasors are modeled based on the Shannon sampling theorem. As a result, a filter bank is designed for harmonic phasor and frequency estimations. The rate of change of frequency (ROCOF) of the harmonic is estimated based on a second-order fitting method. The response time of the proposed method for harmonic phasor estimation is always no longer than 40 ms. Simulation test results indicate that the proposed method is more accurate than the Taylor–Fourier transform (TFT) under ddc offset and frequency deviation conditions. In particular, the proposed method is more robust to ddc’s TC variations. An experimental test is implemented to demonstrate the advantages of the proposed method.

Sensorless Vibration Harmonic Estimation of Servo System Based on the Disturbance Torque Observer

This paper proposes a sensorless vibration harmonic frequency estimation for a servo system driven by a permanent magnet (PM) synchronous machine. Traditional vibration harmonic estimation relies on the measurement using external sensors. An accelerometer is typically installed in the servo system to measure the vibration harmonic signal. Because the accelerometer must be attached on the visibly vibrational location inside the system, this vibration detection results in both issues about installation and reliability. To overcome this drawback, this paper proposes a disturbance observer to estimate the vibration harmonic by using current and position signal. A real-time signal process is developed to identify the vibration frequency from estimated harmonic. A servo system with a 400-W PM machine is built to verify the proposed vibration harmonic and frequency estimation. This paper includes the comparative evaluation between the accelerometer-based vibration harmonic measurement and the sensorless estimation.

Analysis of Fault Harmonic in Electrical Power System Based on Improved Particle Swarm Optimization Algorithm

To estimate the parameters of fault harmonics in electrical power system more accurately and control the harmonic pollution, an improved Particle Swarm Optimization (PSO) algorithm is proposed. The traditional PSO algorithm has been improved, the problem of harmonic estimation is transformed into a minimum optimization problem, and the harmonic parameter optimization algorithm based on improved PSO and least square method is proposed, and corresponding simulation examples and measured data are created in matrix laboratory (MATLAB). The results show that the algorithm is not only accurate, but also has the advantages of anti-gaussian white noise and processing interharmonic. The proposed algorithm has potential application in harmonic fault analysis of electrical power system.