Harmonic Estimation Research Articles

Astrophysics-based transit search optimization heuristics for parameter estimation of multi-frequency sinusoidal signals

This study investigates an astrophysics-based Transit search optimization algorithm (TSOA) for solving a challenging engineering problem. This innovative strategy uses the fundamentals of physics to improve the accuracy and efficacy of problem solving techniques. Harmonic distortions in power systems have become a massive challenge because of the nonlinear loads associated with the electrical power distribution system. Overheating of the equipment, motor failure, capacitor failure, and improper power metering are all issues caused by harmonic distortion. A new examination of the causes and consequences of these issues, as well as the status of hardware and software available for harmonic evaluation, is necessary in light of the unprecedented advancements in power electronic devices and their integration at all levels in the power and energy system. In order to estimate phase and amplitude simultaneously with a specified frequency, an objective function of power system harmonics is created. Keeping in mind the adverse effects of harmonics, parameter estimation is carried out under various conditions by taking different particle sizes and signal-to-noise ratios. TSOA proved its efficacy for both phase and amplitude parameters under different situations and precisely estimated the harmonics signal up to an accuracy of 1.1648E–15. Two harmonic signals were taken in this research work, and the best MSE values achieved are 9.748E–4, 8.287E–07, 6.157E–10, and 1.165E–15 for 30, 60, 90, and 150 dB noise, respectively, under case study 1 while varying the particle size from 50 to 450. The results for case study 2 proved to be best up to 7.373E–16, and no significant change occurred by increasing the generations above 500. The proposed study would be a step further in developing a more accurate and robust computing platform for robust estimation of harmonics arising in power and energy systems.

Multiple Discrete Adaptive Filter Based Position Error Reduction for Sensorless IPMSM Drives

The inverter nonlinearity and the flux spatial harmonics will lead to noticeable (6κ±1) harmonics in the observed back electromotive force (EMF), causing (6κ) pulsations in the rotor position estimation error and deteriorating the performance of sensorless interior permanent magnet synchronous motor (IPMSM) drives. To improve the sensorless IPMSM control accuracy, a multiple discrete adaptive filter (MDAF) embedded between sliding mode observer (SMO) and normalized quadrature phase-locked loop (PLL) is adopted to solve the above problem in this paper. The MDAF consists of a fundamental extraction block and a harmonic cancellation block. Harmonic cancellation works similarly to fundamental extraction, simply by removing the dominant 5th and 7th harmonics from the distorted back-EMF in a frequency multiplicative manner. The proposed algorithm is designed directly in the discrete domain, avoiding the complex discretization process. The open-loop amplitude-frequency characteristic curves show that the method is able to achieve infinite gain exactly at the expected frequency, thus allowing closed-loop zero steady-state error tracking of the back-EMF and providing higher precision for harmonic estimation. The excellent performance of the suggested method is validated based on a 1.5kW sensorless IPMSM control system.

Multi-source data driven harmonic spectrum estimation of substation feeder current

With the proliferation of non-linear loads and distributed power resources that connect through power electronic equipment, decentralized harmonic pollution in three-phase symmetric power system becomes increasingly serious. Despite this, monitoring the current harmonic of all substation feeders regardless of cost is unrealistic. To this end, a multi-source data driven method is proposed in this paper, utilizing data from the power quality monitoring system, dispatching system, and market business system, to estimate the harmonic spectrum of substation feeder currents and estimate the harmonic current components of each feeder with monitoring data of bus voltage harmonics and line harmonic currents. The objective function of the harmonic spectrum estimation model is constructed based on the analysis of current harmonic phasor and power relationship on the feeders. An improved particle swarm optimization (PSO) algorithm is proposed to solve the proposed estimation model thereby obtaining the current harmonic content of each feeder and the phase angle difference between the current harmonics of the feeders. The performance of the proposed model and algorithm is validated by numerical simulation with a test system and an actual system.

Moving harmonic source depth estimation by MDFMD-v in a weakly range-depend waveguide

To estimate the depth of a non-cooperative moving sound source in a range-depend waveguide, a passive depth estimation method combining depth-polarity search for a harmonic moving source is proposed in this paper. Firstly, the method obtains each mode parameters at the source and horizontal linear array (HLA) locations by utilizing the modal depth function constrained modal Doppler velocity estimation (MDFMD-v) and matrix pencil (MP) methods, respectively. Subsequently, mode amplitudes are calculated by compressive sensing. To determine the polarity of each mode amplitude, a depth-polarity search method is given in this paper. Finally, a depth ambiguity function with mode amplitude polarity is used to obtain the depth estimation results. Simulation results verify the effectiveness of the method.

Knacks of Evolutionary Mating Heuristics for Renewable Energy Source–Based Power Systems Signal Harmonics Estimation

Renewable energy sources–based power systems are increasing rapidly every year with higher chances of destabilization and low power quality due to harmonics, subharmonics, and interharmonics. The elimination of the root causes of these harmonics is difficult because harmonics are generated at different levels due to various electronic components. However, the accurate estimation of power signal harmonic can be done and eliminated with a counter signal. Therefore, in this paper, the evolutionary mating heuristic is implied to accurately estimate the parameters of power signal harmonics. The proposed heuristic was tested under multiple scenarios to accurately estimate the phase and amplitude parameters of power signal harmonics at various noise levels. The tuning of the evolutionary mating heuristic is carried out for encountering predator probability and crossover probability Epp <0.8, Cp <0.9. The simulation analysis depicts that the best fitness achieved by the proposed heuristic for noise levels (no) 104, 78, 52, 26, and 13 dB are 2.8169e−11, 9.6969e−09, 3.7703e−06, 1.3501e−03, and 2.8624e−02, respectively, for iteration I = 1249. The comparative analysis shows that the proposed heuristic performance is significantly better than other heuristics.

Analysis of Water Level Monitoring using GNSS Interferometric Reflectometry in River Waters

GNSS Interferometric Reflectometry (GNSS-IR) is one of the newest explorations of Global Navigation Satellite System (GNSS) signals which utilizes multipath signals to calculate the vertical distance from the reflecting surface to the geodetic antenna/receiver. However, scientific-grade or geodetic GNSS instruments are expensive, which is a limiting factor for their prompt and more widespread deployment as a dedicated environmental sensor. Hence, in this study, low-cost GNSS receiver devices were used to monitor the surface level of PT Garam River in Pamekasan Regency using the GNSS-IR method. The study location of PT Garam River which is quite close to the sea causes the water level to vary following the tides at the sea. This is because there are needs for advanced methodologies to limit GNSS observations in a much narrower area. The river in this case is a more challenging study location in terms of monitoring the water level. Calculation of river water level height with GNSS-IR observations is based on determining the peak frequency on the periodogram resulting from signal-to-noise ratio (SNR) data extraction. The two-weeks GNSS-IR observation in this study were applied by installing sideway orientation of GNSS antenna towards the river. This will be done to see how effective the strength of the reflected signal received by the low-cost GNSS devices are in narrow footprint area. Conventional tide gauge near the GNSS-IR site was used to evaluate the accuracy of GNSS-IR in river water level monitoring. Tide analysis is carried out to obtain tidal constituents and tide predictions using least square harmonics estimation (LSE). The resulting accuracy of the validation data is at an RMSE of 15.35 cm, with the correlation value of 0.94. The type of river tides in the study location based on the calculation results is mixed tide prevailing semidiurnal. Tide prediction for 20 days gives promising results with an RMSE of 16 cm. These results indicate that low-cost GNSS device has a promising capability for water level monitoring using GNSS-IR method in a narrow reflector area.

Harmonic state estimation and localization based on broad-band measurement

Harmonic state estimation and localization based on broad-band measurement

PLL-based Enhanced Control of Boost PFC Converter for Smart Farming Lighting Application

Controlled environment farming has become an attractive solution to increase the food production with limited use of resources. LED lights are often used in this type of farming to increase plant yield. LED lights are dc load, whereas the grid provides ac power. This necessitates the use of power factor correction (PFC) converter as an interface between the grid and the lights. This paper proposes an innovative control method for the boost PFC converter, where an advanced phase-locked loop scheme is developed that can eliminate measurement dc offset and provide harmonic robust estimation of the grid voltage fundamental component. The applied nonlinear control uses the existing two-loop control architecture. Based on a baseline PI controller, a nonlinear function is added to make the controller react faster when it is far from the reference and vice-versa. Comprehensive simulation studies are conducted to assess the performance of the proposed method under various challenging test scenarios. Compared to the baseline method, the proposed technique achieved 42%∼65% reduction in total harmonic distortion depending on the test cases, which makes the technique a suitable candidate for improving the operational efficiency and, consequently, the running cost of a smart farming lighting system on an industrial scale. Results show the effectiveness of the proposed method over the conventional counterpart.

An efficient iterative optimization-based algorithm for the real-time estimation of harmonics under power system frequency deviations

In current electrical power industry, a great number of power electronic devices produce harmonics. Moreover, the fundamental system frequency of a power line can deviate in the cases of fluctuating and periodically varying loads and transients. This frequency deviation introduces further undesirable frequency components in the spectrum. Correct measurement of harmonics under such system frequency deviations has prominent importance for the protection of power electronics devices. For this goal, this paper proposes a new iterative optimization-based algorithm for the estimation of harmonics in these circumstances. The method is based on time-domain Gauss-Newton optimization of distorted power line signal which attains its parameters directly from the spectrum of the signal by employing local extrema of the corresponding spectrum. In the first phase of the algorithm, the deviated system frequency is estimated. In the second phase, the harmonic components are estimated and fine-tuned correspondingly. Case studies show that the proposed method is robust and precisely estimates deviations in the system’s fundamental frequency and measure the amplitudes of harmonic components very accurately. It requires just a stoppage criterion. The computational assessment of the method also shows its time efficiency in identifying harmonics. Thus, it is a very good candidate for real-time harmonic measurements.

Sideband Harmonic Model Considering Sampling Delay Effect in the PMSM Drives With Regular Sampled SVPWM Technique under the Low Carrier Frequency Ratio

Regular sampled space vector pulse-width modulation (SVPWM) is a widely implemented technique in permanent magnet synchronous machine (PMSM) drives with the voltage-source inverter (VSI). The modulation technique would generate the sideband harmonics and increase electromagnetic loss, vibration, and acoustic noise. Therefore, a fast and accurate evaluation of sideband harmonics is particularly important. However, the carrier frequency ratio could be relatively low in some applications, which means it would cause sampling delay and influence the sideband harmonics. This paper analyzes the sampling delay effect in PMSM drives, and proposes a modified sideband harmonic model using Lagrange expansion and complex coordinate transformation for both symmetric and asymmetric regular sampling methods. Furthermore, the amplitudes and phases of whole sideband harmonic components are derived. Experiment results are carried out to validate the accuracy improvement of the modified model, which reveals that it could give a superior estimation of the sideband harmonics in the PMSM drives under the low carrier frequency ratio.

Tidal harmonics retrieval using GNSS-R dual-frequency complex observations

Tidal analysis and methods for estimation and prediction of ocean tidal constitutes are essential in a large area of scientific disciplines, for example, navigation, onshore and offshore engineering, and production of green energy. Ground-based Global Navigation Satellite System-Reflectometry (GNSS-R) has been proposed as an alternative method for measuring sea surface height. We use 6 years of GNSS-R observations at In-phase and Quadrature levels from July 2015 to May 2021 obtained from a dedicated receiver and sea-looking left hand circular polarization antenna for estimating sea level (SL). In the first step, the multivariate least-square harmonic estimation (LS-HE) method is applied for SL estimation. Then, final SL time series are generated by combining estimated SL from all satellites at L1 and L2 frequencies in the averaging step. The 6-year root-mean-square error between GNSS-R L12 sea surface heights and a collocated tide gauge (TG) is 5.8 cm with a correlation of 0.948 for a high temporal resolution of 5 min with 15 min averaging window. Afterward, using the univariate LS-HE, we detect tidal harmonics with periods between 30 min to 1 year. The detection results highlight a good match between GNSS-R and TG. Higher harmonics, i.e., the periods shorter than 3 h, show stronger signatures in GNSS-R data. Finally, we estimate the amplitude and phase of standard tidal harmonics from the two datasets. The results show an overall good agreement between the datasets with a few exceptions.

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.

A Hybrid Algorithm for Acceleration Harmonic Estimation and Elimination in Shake Table

A Hybrid Algorithm for Acceleration Harmonic Estimation and Elimination in Shake Table

A generalized admittance criterion for dominant harmonic source determination without synchronous phasor measurements

The widespread integration of various nonlinear power electronic devices in modern power systems has made harmonic distortion more serious than ever before. Given the urgent need to improve power quality, the harmonic contribution evaluation (HCE) is of great importance since it can provide a strong basis for harmonic mitigation measures. However, the conventional HCE methods are not effective due to the lack of synchronous voltage and current phasor information in real-field practice. To overcome the phasor limitation, an HCE method based on a generalized admittance criterion (GAC) is proposed in this paper. The proposed GAC aims to determine the dominant harmonic source at the point of common coupling (PCC) from the utility side and customer side. Compared to the conventional method, the developed method only needs the RMS values of the PCC voltage, current, and phase angle difference. Therefore, the synchronous phasor information of voltage and current is no longer required. Meanwhile, a threshold to determine the dominant harmonic source is established by using the equivalent admittance ratio on both sides of PCC. The evaluation process of the proposed method is significantly simplified by comparing the generalized admittance limit with the proposed threshold, which also greatly improves the method evaluation accuracy. Moreover, the interference of background harmonic fluctuation is excluded by using the linear calibration-based harmonic admittance estimation method. Finally, multiple scenarios with various admittance characteristics were simulated to verify the performance of the proposed criterion, and the real-field measurement is also used to demonstrate the accuracy and validity of the proposed method.

Non-Intrusive Efficiency Estimation of Inverter-Fed Induction Motors

The use of inverter supplies over sinusoidal supplies for induction motors is growing considerably. Inverter supplies enable effective and robust control of induction motors in many automated systems. However, this benefit features at the expense of additional harmonic motor losses due to pulse-width modulated (PWM) voltages and currents produced by inverter supplies. The quantification of these additional harmonic losses and the estimation of efficiency in a non-intrusive manner can be quite challenging. This paper proposes a non-intrusive efficiency estimation technique for inverter–fed induction motors that is based on harmonic regression analysis, harmonic equivalent circuit parameter estimation and harmonic loss analysis using limited measured data. The efficiency results from the proposed technique are comparable to those obtained using the IEC 60034-2-3 Standard up to 1% accuracy when tested on three different inverter-fed motors at different loads.

Harmonic-Based MIMO Transceiver With Time-Modulated Arrays

A simple harmonic-based multiple-input multiple-output (MIMO) transceiver based on the time-modulated array (TMA) is proposed and verified, including detailed performance analysis, comparisons with state-of-the-art works and experiment verification. The essential concept is utilizing the time modulation technique to linearly map the actual multipath channels between multiple users and the antenna elements of the TMA to the equivalent virtual channels between users and harmonics with different frequencies. Models of the received and transmitted signals in both uplink and downlink transmissions based on the multi-user single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenario are analyzed and derived, followed by the proposed harmonic channel estimation, detection and beamforming methods. Simulations on the performance of the proposed harmonic-based MIMO transceiver are provided and compared to the also TMA-based space division multiple access (SDMA) scheme, showing that the latter is more like a special case of the proposed scheme. An experimental 2-user wireless communication prototype based on a 4-element TMA is fabricated and tested to verify the feasibility and effectiveness of uplink signal transmission.

Harmonic State Estimation for Distribution Networks Based on Multi-Measurement Data

Accurate harmonic state estimation (HSE) is necessary to mitigate harmonic issues in power distribution networks. However, existing HSE methods face difficulties in solution of state equation that the measured data is insufficient with limited monitors. Therefore, this study proposes a HSE algorithm for distribution networks based on multi-measurement data. Firstly, a harmonic source location method based on mutual information and distribution network partition is proposed to reduce the number of state variables and to solve the state equation. Thus, HSE with low resolution (15 min) is realized. Secondly, a HSE method with enhanced resolution is developed. This method establishes maximum entropy principle models for harmonic currents injected into buses, calculates the probability density function (PDF) of the harmonic current, and realizes optimal interpolation of the harmonic data to enhance the resolution of the HSE (3 min) according to the PDF. Finally, the applicability and effectiveness of the proposed method are verified using an IEEE-33 test system simulation and a real power system in South China.

Harmonic Estimation and Comparative Analysis of Ultra-High Speed Flip-Flop and Latch Topologies for Low Power and High Performance Future Generation Micro-/Nano Electronic Systems

This paper presents estimation and analysis of the higher order harmonics, power features, and real performance of flip-flop and master-slave latch topologies. This research article outlines the impact of transistor model quality and input signal selection on the estimate of higher order harmonic contents of switching waveform emitted by the digital integrated circuits. Highly integrated systems require accurate estimation of higher order harmonics to control noise. This work presents simulations of 12 kinds of flip-flop and latch topologies on different process technologies i.e., 28 nm, 45 nm, 65 nm, and 130 nm. It is implied that the steeper the spectrum roll-off, the fewer the contents of higher order harmonics. Results of 28 nm process design kit are improved compared to 45 nm, 65 nm, and 130 nm process design kits. Furthermore, the results of the comparison of representative flip-flop and latch topologies illustrate the advantage of the approach and the suitability for high performance and low power consumption.

Computational Methods for Estimating the Evidence and Bayes Factor in SEIR Stochastic Infectious Diseases Models Featuring Asymmetrical Dynamics of Transmission

Stochastic epidemic models may offer a vitally essential public health tool for comprehending and regulating disease progression. The best illustration of their importance and usefulness is perhaps the substantial influence that these models have had on the global COVID-19 epidemic. Nonetheless, these models are of limited practical use unless they provide an adequate fit to real-life epidemic outbreaks. In this work, we consider the problem of model selection for epidemic models given temporal observation of a disease outbreak through time. The epidemic models are stochastic individual-based transmission models of the Susceptible–Exposed–Infective–Removed (SEIR) type. The main focus is on the use of model evidence (or marginal likelihood), and hence the Bayes factor is a gold-standard measure of merit for comparing the fits of models to data. Even though the Bayes factor has been discussed in the epidemic modeling literature, little focus has been given to the fundamental issues surrounding its utility and computation. Based on various asymmetrical infection mechanism assumptions, we derive analytical expressions for Bayes factors which offer helpful suggestions for model selection problems. We also explore theoretical aspects that highlight the need for caution when utilizing the Bayes factor as a model selection technique, such as when the within-model prior distributions become more asymmetrical (diffuse or informative). Three computational methods for estimating the marginal likelihood and hence Bayes factor are discussed, which are the arithmetic mean estimator, the harmonic mean estimator, and the power posterior estimator. The theory and methods are illustrated using artificial data.

A SVD-Based Dynamic Harmonic Phasor Estimator With Improved Suppression of Out-of-Band Interference

The diffusion of nonlinear loads and power electronic devices in power systems deteriorates the signal environment, and increases the difficulty of measuring harmonic phasors. Considering accurate harmonic phasor information is necessary to deal with harmonic related issues, this paper focuses on realizing accurate dynamic harmonic phasor estimation when the signal is contaminated by certain interharmonic tones, i.e. the out-of-band interference (OBI). Specifically, this work introduces the singular value decomposition into the Taylor-Fourier transform algorithm, deriving a general decomposition form for harmonic phasor filters, and yielding a set of adjustable parameters. Then these parameters are configured to minimize the negative influence of OBI on the dynamic harmonic phasor filters. Based on the recommended parameter values, the optimized harmonic estimator is obtained, and then tested under signals distorted by OBI, harmonic, noise, and in worse cases, frequency deviation, and some dynamic conditions. Test results show the proposal achieves good harmonic phasor estimation even under multiple interferences and dynamic scenarios, and has a much weaker dependence on OBI tones compared to conventional approaches.