Harmonic Estimation Research Articles

Novelty method for the utility harmonic impedance estimation based on Gaussian mixed model

The accurate estimation of harmonic impedance on the utility side of a point of common coupling (PCC) is much important to harmonic control, harmonic emission level, and harmonic responsibility analysis. In this study, a novel estimation method for the utility harmonic impedance is proposed, which employs the Gaussian mixed model (GMM) to fit the measured data at a PCC, because the authors find that the statistical distribution of the measured data at a PCC is close to the Gaussian distribution. Also, in theory, GMM can approach the probability distribution of any data. In this method, the Norton equivalent circuit model at a PCC is first expressed as a GMM, and the utility harmonic impedance in the GMM is estimated by expectation maximisation iterative method. Compared to the existing estimation methods, an outstanding advantage of this method is that it is less affected by background harmonics; therefore, higher accuracy can be acquired in this method. The effectiveness and accuracy of this method are verified by simulation experiments and field data.

Analysis of the Coriolis perturbed rovibrational spectrum of the C[sbnd]O asymmetric stretch and C[sbnd]C symmetric stretch of trimethylene oxide

Rotationally-resolved vibrational spectra of trimethylene oxide (c-C3H6O) were recorded using synchrotron radiation from the Canadian Light Source between 400 and 1200 cm−1 with a resolution of 0.000959 cm−1. The dense spectra are composed of transitions arising from excitation of several fundamental vibrations as well as hotbands and combination bands involving the very low frequency ring puckering (ν18) vibration at ~53 cm−1. To date, 3452 transitions have been assigned corresponding to the CO asymmetric stretch (ν23) at ~1008 cm−1 and the CC symmetric stretch (ν6) at ~1033 cm−1 which are coupled via second order c-type Coriolis interaction. An additional perturbation from a lower energy state was observed and attributed to a first order b-type interaction with a state that is likely the combination of the CC asymmetric stretching (ν24) at ~937 cm−1 and ring puckering motions. An additional 916 transitions involving the CO stretching mode were assigned to two hotbands that originate in the first and second excited ring puckering states of trimethylene oxide. Accurate band centers for the ν6, ν23, ν23 + ν18, ν23 + 2ν18 and ν24 + ν18 vibrational states were determined and are compared with harmonic and anharmonic frequency estimates at the MP2 and DFT B3LYP levels using the 6-311++G(d,p) basis set. The analysis of additional features at lower frequency is in progress and will be reported in a subsequent article.

Active disturbance rejection control of torsional plant with unknown frequency harmonic disturbance

In this work, a new robust control algorithm is introduced for uncertain systems with harmonic disturbances of unknown frequencies. The proposed solution works under the active disturbance rejection control (ADRC) framework and utilizes a specialized observer for sinusoidal uncertainties, aided with an on-line harmonic disturbance frequency estimator. The entire governing structure is derived in a convenient error-based domain, easily deployable in various industrial control software. The idea behind the introduced approach is general, but is conveyed here using solely a three degrees-of-freedom torsional system, which is considered a benchmark for vibration phenomenon in many mechanical systems. The efficacy of the proposed control scheme is validated with a set of experiments on a laboratory testbed and a theoretical analysis based on theory of singular perturbation.

A General Time-Domain Method for Harmonic Distortion Estimation in CMOS Circuits

This article presents a general, time-domain harmonic distortion estimation method, applicable to linear CMOS circuits characterized by weakly nonlinear behavior, ranging from amplifiers, and transconductors to filters, with any number of stages. It offers a compact, fast, and systematic way to model circuits as a structure of interconnected G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> -stages, and estimates the harmonic distortion at every circuit node, providing insight into the distortion contribution of every stage. The method uses a more involved model for each G <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sub> -stage that also accounts for the dependence of its output current on cross-products of its input and output voltages, improving significantly the distortion estimation accuracy. The proposed method is easily implemented in MATLAB, and intends to be integrated as a tool in EDA suites to speed-up distortion estimation. A number of examples are presented, illustrating the application of the method and validating its accuracy via comparison with Cadence Spectre simulation.

Modeling and Prediction of Regular Ionospheric Variations and Deterministic Anomalies

Knowledge on the ionospheric total electron content (TEC) and its prediction are of great practical importance and engineering relevance in many scientific disciplines. We investigate regular ionospheric anomalies and TEC prediction by applying the least squares harmonic estimation (LS-HE) technique to a 15 year time series of the vertical TEC (VTEC) from 1998 to 2014. We first detected a few new regular and modulated signals in the TEC time series. The multivariate analysis of the time series indicates that there are diurnal, annual, 11 year, and 27 day periodic signals, as well as their higher harmonics. We also found periods matching with the global positioning system (GPS) draconitic year in the TEC time series. The results from the modulated harmonic analysis indicate that there exists a set of peaks with periods of 1 ± 0.0027 j ( j = 1 , … , 5 ) and 1 ± 0.00025 j ( j = 1 , 2 , 3 ) days. The same situation holds also true for the harmonics higher than the diurnal signal. A model is then adopted based on the discovered periods. This model, which consists of pure and modulated harmonic functions, is shown to be appropriate for assessing the regular variations and ionospheric anomalies. There is a clear maximum TEC at around 22:00 h, which we called the “evening anomaly”. The evening anomaly occurs in the winter and autumn, and is dependent on the solar activities. Also, the Semiannual, Winter, and Equatorial anomalies were investigated. Finally, to investigate the performance of the derived model, the TEC values have been predicted monthly, and the results show that the modulated signals can significantly contribute to obtaining superior prediction results. Compared with the pure signals, the modulated signals can improve a yearly average root mean squared error (RMSE) value in the lower and higher solar activities by 20% and 15%, respectively.

Anharmonic calculations of vibrational spectra for molecular adsorbates: A divide-and-conquer semiclassical molecular dynamics approach.

The vibrational spectroscopy of adsorbates is becoming an important investigation tool for catalysis and material science. This paper presents a semiclassical molecular dynamics method able to reproduce the vibrational energy levels of systems composed by molecules adsorbed on solid surfaces. Specifically, we extend our divide-and-conquer semiclassical method for power spectra calculations to gas-surface systems and interface it with plane-wave electronic structure codes. The Born-Oppenheimer classical dynamics underlying the semiclassical calculation is full dimensional, and our method includes not only the motion of the adsorbate but also those of the surface and the bulk. The vibrational spectroscopic peaks related to the adsorbate are accounted together with the most coupled phonon modes to obtain spectra amenable to physical interpretations. We apply the method to the adsorption of CO, NO, and H2O on the anatase-TiO2 (101) surface. We compare our semiclassical results with the single-point harmonic estimates and the classical power spectra obtained from the same trajectory employed in the semiclassical calculation. We find that CO and NO anharmonic effects of fundamental vibrations are similarly reproduced by the classical and semiclassical dynamics and that H2O adsorption is fully and properly described in its overtone and combination band relevant components only by the semiclassical approach.

Adaptive current harmonic estimation under fault conditions for smart grid systems

This paper presents an adaptive harmonic disturbances detection under fault conditions in a smart grid (SG) system. Monitoring and controlling SG networks require real-time measuring. This measuring demands high-speed, fully integrated, and two-way communication technologies.On a fault condition, the online accurate monitoring becomes difficult due to the transient current occurrences requiring adaptive methods to achieve SG requirements. In this work an adaptive technique to reliable monitoring harmonic distortion in the power network has been proposed. Harmonic estimation is implemented by utilizing the least square (LS), Kalman filter (KF), Maximum Likelihood estimation (MLE), and Goertzel Algorithm to obtain the amplitude of the harmonics in the network and its variation under dynamic fault conditions. The tested smart micro-grid (SmG) includes wind turbines (WT) and photovoltaic (PV) panels with time-variable loads at a medium voltage level. Consequently, the total demand distortion (TDD) estimations using the filtering estimators are also compared with the predictions obtained by the conservative power theory (Tenti) accordingly. Finally, a performance-complexity tradeoff analysis demonstrated the (dis)advantages of each filtering method.

Algorithm for phasor estimation during current transformer saturation and/or DC component presence: definition and application in arc detection on overhead lines

During the current transformer (CT) saturation, the secondary current waveform of a CT is notably different from the primary current's waveform. When the discrete Fourier transform (DFT) is applied to such a distorted secondary current of a CT, the obtained root mean square (RMS) value is significantly lower than it actually is, which can lead to the malfunctioning of the relay protection devices. The operation of some relay protection algorithms (such as certain algorithms for electric arc detection on overhead lines) is conditioned by higher fault current harmonics. Obviously, due to the secondary current's distortion, the higher current harmonics cannot be accurately estimated. On the other hand, even when there is no CT saturation, the RMS value can be incorrectly estimated under DFT due to the fault current's direct component. This study presents a new algorithm which enables an accurate RMS value estimation regardless of the CT saturation and/or presence of the direct fault current component. What is more, the algorithm also enables the estimation of higher fault current harmonics under CT saturation. Various tests have indicated a high precision and robustness of the proposed algorithm and the possibility of combining this algorithm with the algorithm for electric arc detection on overhead lines.

Genetic Algorithm Methodology for the Estimation of Generated Power and Harmonic Content in Photovoltaic Generation

Renewable generation sources like photovoltaic plants are weather dependent and it is hard to predict their behavior. This work proposes a methodology for obtaining a parameterized model that estimates the generated power in a photovoltaic generation system. The proposed methodology uses a genetic algorithm to obtain the mathematical model that best fits the behavior of the generated power through the day. Additionally, using the same methodology, a mathematical model is developed for harmonic distortion estimation that allows one to predict the produced power and its quality. Experimentation is performed using real signals from a photovoltaic system. Eight days from different seasons of the year are selected considering different irradiance conditions to assess the performance of the methodology under different environmental and electrical conditions. The proposed methodology is compared with an artificial neural network, with the results showing an improved performance when using the genetic algorithm methodology.

Adaptive Harmonic and Disturbance Estimators for Rotary Machines with applications to Engines

In this article, we present a new method for estimation of the nonperiodic (mean) value and harmonics of unknown disturbance inputs with parametrically varying harmonic frequencies. The proposed methods shall be studied for mean value and harmonic estimation of internal combustion torque of an engine. The internal torque refers to the oscillatory torque resulting from the combustion process. Its estimation uses an unknown input observer approach with a proportional structure, modeling the combustion torque as disturbance. An adaptive harmonic estimator is developed to filter the nonperiodic mean value and the harmonic components using linear parameter-varying techniques. The developed estimation methods feature phase-free estimation, minimal model assumption, tunable noise attenuation, and efficient time-triggered implementation. Misfire event detection using harmonic filtering of generated torque is demonstrated using simulations. Experimental validation is performed on a dynamical engine test bench with a series-production four-cylinder diesel engine estimating the combustion torque and its mean value during engine start and transient operation. The generic nature of the proposed technique is demonstrated by applying it to estimate nonperiodic speed values of an electric machine operated in tandem with a two-cylinder gasoline engine.

Study on Harmonic Impedance Estimation and Harmonic Contribution Evaluation Index

Harmonic impedance estimation and suitable evaluation index selection are the key steps of harmonic contribution evaluation. Most of the traditional harmonic impedance estimation methods are only applicable to the scenario, where the background harmonic is stable and the utility impedance is constant. However, this scenario will change in many cases due to the fluctuation of harmonic, the change of system operation mode and so on. In order to improve the estimation accuracy for harmonic impedance, a harmonic impedance estimation method is proposed in this paper based on similarity measure and ordering points to identify the clustering structure (OPTICS). The total harmonic contribution index and harmonic comprehensive contribution index are proposed based on subjective analytic hierarchy process to simplify the evaluation results. Simulation analysis and their comparison with the traditional methods reveal that the proposed harmonic impedance estimation method can reduce the influence of background harmonic voltage fluctuation and utility impedance change, making the harmonic impedance estimation result more accurate. Besides, the proposed total harmonic contribution index and harmonic comprehensive contribution index can effectively simplify contribution evaluation results, which provide a new methodology for the evaluation of harmonic contribution.

A Fast Time-Domain Current Harmonic Extraction Algorithm for Power Quality Improvement Using Three-Phase Active Power Filter

Harmonic current estimation is the key aspect of Active Power Filter (APF) control algorithms to generate a reference current for harmonic compensation. This paper proposes a novel structure for harmonic current estimation scheme based on Trigonometric Orthogonal Principle (TOP) and Self Tuning Filter (STF). The key advantages of the proposed method are its simplicity, low computational burden and faster execution time in comparison to the conventional harmonic current estimation approaches. The TOP method provides a simple and fast approach to extract the reference current, while STF provides a simplified structure to generate the required synchronization signal that eliminates the need of a Phase Locked Loop (PLL) algorithm for synchronization. As a result, it exhibits less complexity in implementation and less consumption of microcontroller`s resources; thus, the proposed method can be implemented using a low-cost microcontroller. It is shown in the paper that the proposed method provides 10 times gain in processing speed as compared to the conventional DQ method. The proposed approach is analyzed in detail, and its effectiveness and superior performance are verified using simulation and experimental results.

Signal parameter estimation and classification using mixed supervised and unsupervised machine learning approaches

The increasing use of modern power electronics raises the issue of harmonics in power systems which ultimately deteriorate its optimal performance in terms of: increased power loss, breaker failure and mal-operation of equipment. It has been found that the most severe harmonics in the system are odd ones due to their unsymmetrical nature. This work presents the new framework for estimation and classification of harmonics using machine learning approaches. Initially, a shallow neural network and fuzzy logic systems are used to estimate the harmonics contents in the voltage and currents signals. Based on the sequence components and IHD level of source signals, the estimation of harmonic content is achieved. The obtained results are compared with the analytically computed data for validating the performance of designed networks. The results from neural and fuzzy systems are then used to train the explainable convolutional neural network (xCNN) for harmonics classification. The xCNN consists of pertained ALEXNET network which trains the standard binary support vector machine (SVM) for classification of harmonics. The dictionary-based approach is used to add the explanations to the SVM classifier output as a prototype. The performance of proposed framework is measured in-terms of accuracy and loss function and evaluated on the basis of its scalability and computability. The proposed approach is called a Human with Machine-In-Loop (HMIL).

Study on the Verification of the Calculated Harmonic Impedance

The verifications of the calculated harmonic impedances are necessary for harmonic impedance estimation. Among the existing methods of the verifications, the method, by matching the calculated background harmonic voltage with the measured voltage when the customer is out of operation, is widely used. The background harmonics can be calculated based on IEC61000-3-6 (named as the IEC method) or the superposition index. However, some researchers ignore the fact that these two methods cannot be chosen arbitrarily, otherwise, the misjudgments may occur. In our study, the nonlinear customers are classified into two categories according to the ways how they are out of operation: 1) only the harmonic source is cut off, and 2) the harmonic source and the impedance of the customer side are both cut off. Then, the differences in using the IEC method and the superposition index to match the calculated and measured background harmonic voltage are investigated. Finally, based on the properties of the two methods and the categories of the customers, a framework is proposed to accurately validate the calculated harmonic impedance. The effectiveness and reliability of the proposed framework are verified through simulation and field case studies.

3D Motion Estimation of Left Ventricular Dynamics Using MRI and Track-to-Track Fusion.

Objective: This study investigates the estimation of three dimensional (3D) left ventricular (LV) motion using the fusion of different two dimensional (2D) cine magnetic resonance (CMR) sequences acquired during routine imaging sessions. Although standard clinical cine CMR data is inherently 2D, the actual underlying LV dynamics lies in 3D space and cannot be captured entirely using single 2D CMR image sequences. By utilizing the image information from various short-axis and long-axis image sequences, the proposed method intends to estimate the dynamic state vectors consisting of the position and velocity information of the myocardial borders in 3D space. Method: The proposed method comprises two main components: tracking myocardial points in 2D CMR sequences and fusion of multiple trajectories correspond to the tracked points. The tracking which yields the set of corresponding temporal points representing the myocardial points is performed using a diffeomorphic nonrigid image registration approach. The trajectories obtained from each cine CMR sequence is then fused with the corresponding trajectories from other CMR views using an unscented Kalman smoother (UKS) and a track-to-track fusion algorithm. Results: We evaluated the proposed method by comparing the results against CMR imaging with myocardial tagging. We report a quantitative performance analysis by projecting the state vector estimates we obtained onto 2D tagged CMR images acquired from the same subjects and comparing them against harmonic phase estimates. The proposed algorithm yielded a competitive performance with a mean root mean square error of 1.3±0.5 pixels (1.8±0.6 mm) evaluated over 118 image sequences acquired from 30 subjects. Conclusion: This study demonstrates that fusing the information from short and long-axis views of CMR improves the accuracy of cardiac tissue motion estimation. Clinical Impact: The proposed method demonstrates that the fusion of tissue tracking information from long and short-axis views improves the binary classification of the automated regional function assessment.

A Novel Fundamental and Harmonics Detection Method Based on State-Space Model for Power Electronics System

Harmonic current estimation is the key technology of power electronics systems to generate a harmonics reference current for harmonic control. In this paper, a novel fundamental and harmonic current detection method based on the state-space model (SSM) is introduced. The proposed SSM harmonics detection method has the ability to detect the positive sequence component (PSC), negative sequence component (NSC), and zero-sequence component (ZSC) of both fundamental and each order harmonics current with fast response and high accuracy separately, including the fundamental component, which is appealing for harmonics control in power electronic applications, such as active power filter (APF), unified power quality conditioner (UPQC), virtual synchronous generator (VSG), and so on. The correctness of the proposed SSM based harmonics detection method has been verified by simulation and experiment result, and it shows that the PSC, NSC, and ZCS of the grid fundamental and high order harmonic current can be detected q uickly and accurately, which is important for harmonics analysis and control in the power electronics system.

A High-Speed Master-Slave ADALINE for Accurate Power System Harmonic and Inter-Harmonic Estimation

This paper presents a unique two-fold adaptive linear neural network (ADALINE) for fast and accurate measurement of fundamental, harmonics, sub-harmonics, inter-harmonics and decaying DC components of a distorted current signal with additive noise. The preceding parallel approach is termed as Master-Slave ADALINE (MS ADALINE). The Slave-ADALINE adopts least mean square (LMS) algorithm with a fixed and large step-size for weight vector adjustment. During the training interval or transients, this filter performs a significant role. On the other hand, the Master-ADALINE uses a variable step-size LMS algorithm for achieving a small steady-state error. At the end of each iteration, the local averages of the squared errors of both the ADALINE's are calculated and weights of the Master-ADALINE are updated accordingly. The amplitudes and phases of desired frequency components can be worked out from Master-ADALINE's weights. The proposed architecture improves the convergence speed by establishing an independent control action between the steady-state error and the speed of convergence. The simulation results of this method under various operating situations are analyzed and compared with single fold ADALINE structure that obeys dynamic step-size LMS (DSSLMS) adaptation rule. Eventually, a scaled laboratory prototype has been developed for the validation of the proposed technique in real-time utilization. This innovative research finding makes the power system smart and precise.

Optimization of harmonics with active power filter based on ADALINE neural network

Mostly the power quality issues in the distribution line system happen due to the presence of harmonics. Especially, the nonlinear loads such as power electronic converters, high-speed semi-conducting switches, and solid state drives were the major causes for harmonics in distorted power system signals. Moreover, the estimation of magnitude and the phase of this harmful harmonic interference are necessary. By taking in to consideration of all the above factors, this paper develops an efficient technique for harmonic estimation and detection of the renewable wind energy resources and elimination of these harmonics will also be done accordingly for getting desired output from wind energy. 8 bit inputs (4 + 4) are collected and used to generate the intended input set for ANN training. The proposed work develops an Adaptive Linear Neural Network (ADALINE) for the estimation of harmonics which is the novelty of this work. For making the harmonics content more negligible and to enhance the load power quality, an Active Power Filter (APF) is used. The novel control design is developed with a Pulse Width Modulation (PWM) control. In addition, feed forward networks (trained by back propagation algorithm) works like a hysteresis band comparator. An APF control design is developed with ADALINE network in which the load and current along with voltage will be analyzed and then the controller will be calculating the control signal by considering the reference compensation current. Afterwards, the power system is injected with compensating current. The simulation is carried out with Matlab-Simulink laboratory prototype is developed with Xilinux 3E Spartan FPGA board to verify the proposed control designs. The proposed work is compared with exiting method comprising Shunt Active Power Filters (SAPF) with ADALINE for the performance perspectives. This method was found to be effective in terms of many parameters such as load voltage, load current, voltage, reactive power, real power and especially THD value than those of the existing works which are considered.

A harmonic estimator design with evolutionary operators equipped grey wolf optimizer

Harmonic estimation is a challenging design problem in power networks. Accurate estimation of the inter, power and sub harmonics in networks can be a helpful aspect for designing potential solutions for elimination of these harmonics. Harmonic estimation design problem has been considered as an optimization problem with the amalgamation of least square algorithm in past. In this paper, we first propose an Evolutionary Operators Equipped Grey Wolf Optimizer (E-GWO). In this proposal a sinusoidal function enabled bridging is proposed and along with this tournament selection operator and crossover and mutation operation are incorporated at position updation phase. The variant is first benchmarked on latest CEC-2017 functions and then this design problem is addressed. After a meaningful comparison with the previously published approaches, we arrive at the conclusion that proposed modifications have positive implications on the performance of GWO. Proposed harmonic designs are robust when tested with different operating conditions.

An Open-Loop Fundamental and Harmonic Phasor Estimator for Single-Phase Voltage Signals

This article proposes a novel technique for fundamental and selective harmonic phasor estimation of a single-phase voltage signal based on open-loop voltage signal processing approach, under adverse distorted conditions. At heart, a modified fast discrete Stockwell transform (FDST) is used for the phasor estimation. The performance of the FDST is improved by incorporating a new frequency-dependent Gaussian window for capturing the time-localized variations of individual frequency component. The modified window has four parameters, which are selected based on the statistical properties of the given input voltage signal. Furthermore, under off-nominal frequency conditions the spectral leakage problem, faced by the S-transform, is avoided by proposing a modified sample value adjustment based preprocessing stage. Various static and dynamic tests were considered according to the IEEE Standard 1159, IEEE Standard C37.118.1a-2014, and EN-50160 standards under harmonics and interharmonics scenarios. The performance of the proposed method is validated using synthetic voltage signals, simulated voltage signals on 6-bus microgrid model developed in power system computer aided design (PSCAD), and hardware implementation on dSPACE 1103. The rigorous test cases reveal that the proposed phasor measurement unit has a good adaptability to grid frequency drifts, a good harmonic and dc-offset rejection capability, and a very good steady state as well as dynamic response.