Nothing Special   »   [go: up one dir, main page]

You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Search Results (624)

Search Parameters:
Keywords = nonlinear distortion

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
28 pages, 3675 KiB  
Review
Machine Learning in Active Power Filters: Advantages, Limitations, and Future Directions
by Khaled Chahine
AI 2024, 5(4), 2433-2460; https://doi.org/10.3390/ai5040119 (registering DOI) - 15 Nov 2024
Viewed by 497
Abstract
Machine learning (ML) techniques have permeated various domains, offering intelligent solutions to complex problems. ML has been increasingly explored for applications in active power filters (APFs) due to its potential to enhance harmonic compensation, reference signal generation, filter control optimization, and fault detection [...] Read more.
Machine learning (ML) techniques have permeated various domains, offering intelligent solutions to complex problems. ML has been increasingly explored for applications in active power filters (APFs) due to its potential to enhance harmonic compensation, reference signal generation, filter control optimization, and fault detection and diagnosis. This paper reviews the most recent applications of ML in APFs, highlighting their abilities to adapt to nonlinear load conditions, improve fault detection and classification accuracy, and optimize system performance in real time. However, this paper also highlights several limitations of these methods, such as the high computational complexity, the need for extensive training data, and challenges with real-time deployment in distributed power systems. For example, the marginal improvements in total harmonic distortion (THD) achieved by ML-based methods often do not justify the increased computational overhead compared to traditional control methods. This review then suggests future research directions to overcome these limitations, including lightweight ML models for faster and more efficient control, federated learning for decentralized optimization, and digital twins for real-time system monitoring. While traditional methods remain effective, ML-based solutions have the potential to significantly enhance APF performance in future power systems. Full article
Show Figures

Figure 1

Figure 1
<p>The block diagram of a shunt APF [<a href="#B3-ai-05-00119" class="html-bibr">3</a>].</p>
Full article ">Figure 2
<p>Common active power filter faults.</p>
Full article ">Figure 3
<p>The steady increase in machine-learning publications related to active power filters from 2019 to 2024.</p>
Full article ">Figure 4
<p>Machine learning methods and applications in active power filters.</p>
Full article ">Figure 5
<p>Advantages and disadvantages of machine learning in active power filters.</p>
Full article ">Figure 6
<p>Future research on machine learning in active power filters and the expected outcomes.</p>
Full article ">Figure 7
<p>Advantages of lightweight machine learning in active power filters.</p>
Full article ">Figure 8
<p>Advantages of federated learning in active power filters.</p>
Full article ">Figure 9
<p>Advantages of digital twins in active power filters.</p>
Full article ">
21 pages, 14386 KiB  
Article
A High-Quality and Convenient Camera Calibration Method Using a Single Image
by Xufang Qin, Xiaohua Xia and Huatao Xiang
Electronics 2024, 13(22), 4361; https://doi.org/10.3390/electronics13224361 - 6 Nov 2024
Viewed by 345
Abstract
Existing camera calibration methods using a single image have exhibited some limitations. These limitations include relying on large datasets, using inconveniently prepared calibration objects instead of commonly used planar patterns such as checkerboards, and requiring further improvement in accuracy. To address these issues, [...] Read more.
Existing camera calibration methods using a single image have exhibited some limitations. These limitations include relying on large datasets, using inconveniently prepared calibration objects instead of commonly used planar patterns such as checkerboards, and requiring further improvement in accuracy. To address these issues, a high-quality and convenient camera calibration method is proposed, which only requires a single image of the commonly used planar checkerboard pattern. In the proposed method, a nonlinear objective function is derived by leveraging the linear distribution characteristics exhibited among corners. An algorithm based on enumeration theory is designed to minimize this function. It calibrates the first two radial distortion coefficients and principal points. The focal length and extrinsic parameters are linearly calibrated from the constraints provided by the linear projection model and the unit orthogonality of the rotation matrix. Additionally, a guideline is explored through theoretical analysis and numerical simulation to ensure calibration quality. The quality of the proposed method is evaluated by both simulated and real experiments, demonstrating its comparability with the well-known multi-image-based method and its superiority over advanced single-image-based methods. Full article
(This article belongs to the Special Issue Robot-Vision-Based Control Systems)
Show Figures

Figure 1

Figure 1
<p>Camera imaging model.</p>
Full article ">Figure 2
<p>The image of a checkboard without distortion.</p>
Full article ">Figure 3
<p>Lens distortion. The red dots represent undistorted points, and the blue dots represent distorted points. (<b>a</b>) Barrel distortion generated by <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mrow> <mn>1</mn> <mi>min</mi> </mrow> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mrow> <mn>2</mn> <mi>min</mi> </mrow> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) pillow distortion generated by <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mrow> <mn>1</mn> <mi>max</mi> </mrow> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>k</mi> </mrow> <mrow> <mrow> <mn>2</mn> <mi>max</mi> </mrow> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 4
<p>Simulated corners.</p>
Full article ">Figure 5
<p>The number of corners in the image.</p>
Full article ">Figure 6
<p>The relationship between the number of corners in the image and the calibration quality.</p>
Full article ">Figure 7
<p>The fullness level of corners in the image.</p>
Full article ">Figure 8
<p>The relationship between the fullness level of corners in the image and the calibration quality.</p>
Full article ">Figure 9
<p>The symmetry level of corners in the image.</p>
Full article ">Figure 10
<p>The relationship between the symmetry level of corners in the image and the calibration quality. (<b>a</b>) The horizontal symmetry level; (<b>b</b>) the vertical symmetry level.</p>
Full article ">Figure 11
<p>The distribution of corners in images with different inclination angles.</p>
Full article ">Figure 12
<p>The relationship between the inclination angle of the checkerboard in the image and the calibration quality. (<b>a</b>) The rotation angle of the planar pattern around <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>X</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math>; (<b>b</b>) the rotation angle of the planar pattern around <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Y</mi> </mrow> <mrow> <mi>c</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 13
<p>Simulated corners. The green plus sign represents the pixel coordinates of undistorted corners, and the red plus represents the pixel coordinates of distorted corners.</p>
Full article ">Figure 14
<p>The simulated results. (<b>a</b>) The effects of noise on intrinsic parameters by the proposed method; (<b>b</b>) the effects of noise on <span class="html-italic">Re</span>.</p>
Full article ">Figure 15
<p>Images used for calibration experiments. (<b>a</b>) A single image; (<b>b</b>) a set of images.</p>
Full article ">Figure 16
<p>Relative error of calibration results of different methods.</p>
Full article ">Figure 17
<p>Testing images.</p>
Full article ">Figure 18
<p>Experimental procedures.</p>
Full article ">Figure 19
<p>The comparison of the fitting error. (<b>a</b>) The fitting errors of the five images corrected by the proposed method and Wang’s, Zhang’s, Huang’s, and Genovese’s methods; (<b>b</b>) the fitting errors of the five images corrected by the proposed method and WM-Zhang’s method and those of the five uncorrected images.</p>
Full article ">Figure 20
<p>The distribution of the reprojection error of the corners. (<b>a</b>) Image 1, (<b>b</b>) image 2, (<b>c</b>) image 3, (<b>d</b>) image 4, (<b>e</b>) image 5, (<b>f</b>) statistical property.</p>
Full article ">
16 pages, 3143 KiB  
Article
A Low-Power 5-Bit Two-Step Flash Analog-to-Digital Converter with Double-Tail Dynamic Comparator in 90 nm Digital CMOS
by Reena George and Nagesh Ch
J. Low Power Electron. Appl. 2024, 14(4), 53; https://doi.org/10.3390/jlpea14040053 - 4 Nov 2024
Viewed by 561
Abstract
Low-power portable devices play a major role in IoT applications, where the analog-to-digital converters (ADCs) are very important components for the processing of analog signals. In this paper, a 5-bit two-step flash ADC with a low-power double-tail dynamic comparator (DTDC) using the control [...] Read more.
Low-power portable devices play a major role in IoT applications, where the analog-to-digital converters (ADCs) are very important components for the processing of analog signals. In this paper, a 5-bit two-step flash ADC with a low-power double-tail dynamic comparator (DTDC) using the control switching technique is presented. The most significant bit (MSB) in the proposed design is produced by only one low-power DTDC in the first stage, and the remaining bits are generated by the flash ADC in the second stage with the help of an auto-control circuit. A control circuit produced reference voltages with respect to the control input and mid-point voltage (Vk). The proposed design and simulations are carried out using 90 nm CMOS technology. The result shows that the peak differential non-linearity (DNL) and integral non-linearity (INL) are +0.60/−0.69 and +0.66/−0.40 LSB, respectively. The signal-to-noise and distortion ratio (SNDR) for an input signal having a frequency of 1.75 MHz is found to be 30.31 dB. The total power consumption of the proposed design is significantly reduced, which is 439.178 μW for a supply voltage of 1.2 V. The figure of merit (FOM) is about 0.054 pJ/conversion step at 250 MS/s. The present design provides low power consumption and occupies less area compared to the existing works. Full article
(This article belongs to the Special Issue Analog/Mixed-Signal Integrated Circuit Design)
Show Figures

Figure 1

Figure 1
<p>Block diagram of proposed N-bit two-step flash ADC.</p>
Full article ">Figure 2
<p>Schematic diagram of proposed 5-bit flash ADC.</p>
Full article ">Figure 3
<p>Schematic diagram of double tail dynamic comparator.</p>
Full article ">Figure 4
<p>Circuit diagram of control circuit.</p>
Full article ">Figure 5
<p>Circuit diagram of mux-based encoder.</p>
Full article ">Figure 6
<p>Transient simulation of low-power DTDC.</p>
Full article ">Figure 7
<p>Transient simulation of control circuit.</p>
Full article ">Figure 8
<p>DC simulation of control circuit.</p>
Full article ">Figure 9
<p>Post-layout simulation of 5-bit proposed two-step flash ADC.</p>
Full article ">Figure 10
<p>Spectral plot of low input frequency 1.75 MHz at 250 MS/s after post-layout simulation.</p>
Full article ">Figure 11
<p>Spectral plot of Nyquist frequency 121.09 MHz at 250 MS/s after post-layout simulation.</p>
Full article ">Figure 12
<p>Monte-Carlo simulation of (<b>a</b>) SNR and (<b>b</b>) SINAD for low input 1.75 MHz at 250 MS/s after post-layout simulation for 200 runs.</p>
Full article ">Figure 13
<p>Monte-Carlo simulation of (<b>a</b>) SFDR and (<b>b</b>) SNDR for input 1.75 MHz at 250 MS/s after post-layout simulation.</p>
Full article ">Figure 14
<p>Post-layout simulations: (<b>a</b>) DNL and (<b>b</b>) INL.</p>
Full article ">Figure 15
<p>Monte-Carlo simulation: (<b>a</b>) DNL and (<b>b</b>) INL after post-layout simulation for 200 runs.</p>
Full article ">Figure 16
<p>Post-layout of (<b>a</b>) control circuit and (<b>b</b>) double-tail dynamic comparator.</p>
Full article ">Figure 17
<p>Layout of proposed 5-bit two-step flash ADC.</p>
Full article ">Figure 18
<p>Monte-Carlo simulation of total power consumption with 200 runs.</p>
Full article ">Figure 19
<p>(<b>a</b>) SNDR and (<b>b</b>) SFDR of proposed ADC versus temperatures (T = −40 °C to 120 °C) with process corner variations (TT, SF, FS, SS, FF) after post-layout simulation.</p>
Full article ">Figure 20
<p>Average power of proposed ADC versus (<b>a</b>) temperatures (T = −40 °C to 120 °C) and (<b>b</b>) supply voltage (VDD = 1 V to 1.3 V) with process corner variations (TT, SF, FS, SS, FF) after post-layout simulation.</p>
Full article ">
18 pages, 1968 KiB  
Article
Lineshape of Amplitude-Modulated Stimulated Raman Spectra
by Marco Lamperti, Lucile Rutkowski, Guglielmo Vesco, Luca Moretti, Davide Gatti, Giulio Cerullo, Dario Polli and Marco Marangoni
Sensors 2024, 24(21), 6990; https://doi.org/10.3390/s24216990 - 30 Oct 2024
Viewed by 306
Abstract
The amplitude modulation of a pump field and the phase-sensitive detection of a pump-induced intensity change of a probe field encompass a common practice in nonlinear spectroscopies to enhance the detection sensitivity. A drawback of this approach arises when the modulation frequency is [...] Read more.
The amplitude modulation of a pump field and the phase-sensitive detection of a pump-induced intensity change of a probe field encompass a common practice in nonlinear spectroscopies to enhance the detection sensitivity. A drawback of this approach arises when the modulation frequency is comparable to the width of the spectral feature of interest, since the presence of sidebands in the amplitude-modulated pump field provides distortion to the observed spectral lineshape. This represents a problem when accurate measurements of spectral lineshapes and line positions are pursued, as recently happened in our group with the metrology of the Q(1) line in the 1-0 band of molecular hydrogen. The measurement was performed with a Stimulated Raman Scattering spectrometer that was calibrated, for the first time, against an optical frequency comb. In this work, we develop an analytical tool for nonlinear Stimulated Raman spectroscopies that allows us to precisely quantify spectral distortions arising from high-frequency amplitude modulation in one of the interacting fields. Once they are known, spectral distortions can be deconvolved from the measured spectra to retrieve unbiased data. The application of this tool to the measured spectra is discussed. Full article
(This article belongs to the Section Optical Sensors)
Show Figures

Figure 1

Figure 1
<p>Solid arrows refer to absorption (photon annihilation), dashed lines to emission processes (photon generation). Bold arrows refer to the excitation fields, namely pump and Stokes fields (and also probe field in the general scheme in the (<b>a</b>) panel), whereas the grey frame encompasses the fields that are responsible for the nonlinear polarization of the medium. Dashed horizontal lines refer to the virtual energy levels through which the third-order nonlinear interaction takes place. Panels (<b>b</b>,<b>c</b>) are the photon energy diagrams in the degenerate case of Stimulated Raman Scattering, for an SRL and an SRG measurement, respectively.</p>
Full article ">Figure 2
<p>Different combinations of sidebands for the field at <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> (experiencing stimulated emission from the virtual level after pump excitation) and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </mrow> </semantics></math> (read-out field from the vibrational level) lead to the same emitted frequency <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> </mrow> </semantics></math> (for example <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math> in the three different cases shown on the right of the figure); each combination corresponds to a different frequency detuning between <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math> and thus to a different <math display="inline"><semantics> <mrow> <msup> <mrow> <mi>χ</mi> </mrow> <mrow> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math> value. A case is also shown for an emitted field at frequency <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mn>4</mn> </mrow> </msub> <mo>=</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> <mo>+</mo> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>The curves shown in this figure refer to a 250-MHz Lorentzian Raman profile and to an intensity modulation waveform at 10 MHz that well fits that used in our experiments. Panels (<b>a</b>) and (<b>b</b>) report the normalized in-phase and quadrature SRL signals, respectively, when an optical demodulation phase (see text) is selected, while panels (<b>c</b>,<b>d</b>) report the same curves for a phase error of 0.05 rad (2.9°). Demodulation phase errors are responsible for the onset of a 1st order perturbation in the in-phase SRL signal (compare (<b>c</b>) vs. (<b>a</b>) panel) and for an evident change of the spectral response of the total quadrature signal, from a single- to a double-lobe curve (compare (<b>d</b>) vs. (<b>b</b>) panel). The lack of some orders in panels (<b>a</b>–<b>c</b>) is only apparent: depending on the case, either a given order is zero, or the total response is dominated by one order only. In the latter case, the total response (sum of all orders) is substantially identical to said order and the two curves are not distinguishable.</p>
Full article ">Figure 4
<p>(<b>a</b>) Measured SRS spectra of the Q(1) 1-0 line of H2 at different pressures. (<b>b</b>) Residuals obtained for the above spectra from a global fitting performed over 9 spectral datasets at different pressures, from 0.05 to 4 bar, using a beta-corrected Harmann Tran profile [<a href="#B49-sensors-24-06990" class="html-bibr">49</a>] (see [<a href="#B43-sensors-24-06990" class="html-bibr">43</a>] for details). (<b>c</b>) Residuals obtained by including in the fitting model the second order distortion computed in this paper through Equation (30).</p>
Full article ">Figure 5
<p>Quadrature signal adapted from [<a href="#B44-sensors-24-06990" class="html-bibr">44</a>]: this shape can be explained with a slightly wrong demodulation phase (see <a href="#sensors-24-06990-f003" class="html-fig">Figure 3</a>d).</p>
Full article ">
14 pages, 3887 KiB  
Article
A Low-Computational-Complexity Digital Predistortion Model for Wideband Power Amplifier
by Xu Lu, Qiang Zhou, Lei Zhu, Zhihu Wei, Yaqi Wu, Zunyan Liu and Zhang Chen
Sensors 2024, 24(21), 6941; https://doi.org/10.3390/s24216941 - 29 Oct 2024
Viewed by 387
Abstract
This paper proposes a Composition Piecewise Memory Polynomial (CPMP) digital predistortion model based on a Vector Switched (VS) behavioral model to address the challenges of severe nonlinearity and strong memory effects in wideband power amplifiers (PAs). To tackle this issue, two thresholds are [...] Read more.
This paper proposes a Composition Piecewise Memory Polynomial (CPMP) digital predistortion model based on a Vector Switched (VS) behavioral model to address the challenges of severe nonlinearity and strong memory effects in wideband power amplifiers (PAs). To tackle this issue, two thresholds are calculated and used to segment the envelope values of the input signal according to the nonlinear distortion characteristics of the PA. In this approach, a Generalized Memory Polynomial (GMP) model is employed for the lower segment, a Memory Polynomial (MP) model is employed for the middle segment, and a higher-order GMP model is employed for the upper segment. By sharing the fundamental MP among the proposed segmented models and leveraging a design methodology that configures different cross terms, memory depths, and polynomial orders for each segment, this model achieves superior linearization performance while simultaneously reducing the computational complexity associated with model extraction. The experimental results demonstrate that the adjacent channel power ratio (ACPR) of the predistorted PA output signal using the proposed model improves from −36 dBc to −54 dBc, matching the performance of the GMP model. Furthermore, this performance is 0.5 dBc better than the Piecewise Dynamic Deviation Reduction (PDDR) and Decomposed Vector Rotation (DVR) models. Notably, the complexity of the proposed parameter extraction process is 28.8% of the DVR model, 21.79% of the GMP model, and 12.83% of the PDDR model. Full article
Show Figures

Figure 1

Figure 1
<p>VS model structure diagram.</p>
Full article ">Figure 2
<p>Signal decomposition and recombination.</p>
Full article ">Figure 3
<p>The structure of CPMP.</p>
Full article ">Figure 4
<p>The CPMP model parameter extraction process.</p>
Full article ">Figure 5
<p>Extraction complexity of different threshold parameters.</p>
Full article ">Figure 6
<p>Different threshold power amplifier output signal ACPR value.</p>
Full article ">Figure 7
<p>Different threshold power amplifier output signal EVM value.</p>
Full article ">Figure 8
<p>Measurement setup for the DPD scheme.</p>
Full article ">Figure 9
<p>Constellation.</p>
Full article ">Figure 10
<p>The spectral comparison of the amplifier output signals before and after predistortion.</p>
Full article ">
17 pages, 26224 KiB  
Article
Parametric Analytical Modulation Transfer Function Model in Turbid Atmosphere with Application to Image Restoration
by Mengxing Guo, Pengfei Wu, Zizhao Fan, Hao Lu and Ruizhong Rao
Remote Sens. 2024, 16(21), 3998; https://doi.org/10.3390/rs16213998 - 28 Oct 2024
Viewed by 457
Abstract
To address the issues of image blurring and color distortion in hazy conditions, an image restoration method based on a parametric analytical modulation transfer function model is proposed under turbid atmospheric conditions. A source database is established using a numerical radiative transfer method [...] Read more.
To address the issues of image blurring and color distortion in hazy conditions, an image restoration method based on a parametric analytical modulation transfer function model is proposed under turbid atmospheric conditions. A source database is established using a numerical radiative transfer method based on discrete ordinate. Through multivariate nonlinear fitting and linear interpolation, the quantitative relationships among critical spatial frequency, turbid atmospheric MTF, and key atmospheric optical parameters—such as optical thickness, single scattering albedo, and asymmetry factor—are examined. A fast and efficient parametric analytical MTF model for turbid atmospheres is developed and applied to restore images affected by fog. The results demonstrate that, within the applicable range of the model, the model’s maximum mean relative error and the root mean square error are 7.16% and 0.0454, respectively. The computational speed is nearly a thousand times faster than that of the numerical radiative transfer method, achieving high accuracy and ease of application. Images restored using this model exhibit enhanced clarity and quality, effectively compensating for the degradation in image quality caused by turbid atmospheres. This approach represents a novel solution to the challenges of image processing in complex atmospheric environments. Full article
Show Figures

Figure 1

Figure 1
<p>MTF of a homogenous turbid medium with different <math display="inline"><semantics> <mi>τ</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 2
<p>MTF of a homogenous turbid medium with different <math display="inline"><semantics> <mi>ω</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 2 Cont.
<p>MTF of a homogenous turbid medium with different <math display="inline"><semantics> <mi>ω</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>g</mi> <mo>=</mo> <mn>0.95</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 3
<p>MTF for different scattering phase functions.</p>
Full article ">Figure 4
<p>MTF of a homogenous turbid medium with different <math display="inline"><semantics> <mi mathvariant="normal">g</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 4 Cont.
<p>MTF of a homogenous turbid medium with different <math display="inline"><semantics> <mi mathvariant="normal">g</mi> </semantics></math>: (<b>a</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>b</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>; (<b>c</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>; (<b>d</b>) <math display="inline"><semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mn>2.0</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>ω</mi> <mo>=</mo> <mn>1.0</mn> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>MTF with different integration nodes in DISORT simulations.</p>
Full article ">Figure 6
<p>Comparison of experimental results. (<b>a</b>) Foggy image; (<b>b</b>) He’s method; (<b>c</b>) Equivalence principle method; (<b>d</b>) Method proposed in this paper.</p>
Full article ">
14 pages, 4157 KiB  
Article
D-Band 4.6 km 2 × 2 MIMO Photonic-Assisted Terahertz Wireless Communication Utilizing Iterative Pruning Deep Neural Network-Based Nonlinear Equalization
by Jingwen Lin, Sicong Xu, Qihang Wang, Jie Zhang, Jingtao Ge, Siqi Wang, Zhihang Ou, Yuan Ma, Wen Zhou and Jianjun Yu
Photonics 2024, 11(11), 1009; https://doi.org/10.3390/photonics11111009 - 26 Oct 2024
Viewed by 494
Abstract
In this paper, we explore the enhancement of a 4.6 km dual-polarization 2 × 2 MIMO D-band photonic-assisted terahertz communication system using iterative pruning-based deep neural network (DNN) nonlinear equalization techniques. The system employs advanced digital signal processing (DSP) methods, including down-conversion, resampling, [...] Read more.
In this paper, we explore the enhancement of a 4.6 km dual-polarization 2 × 2 MIMO D-band photonic-assisted terahertz communication system using iterative pruning-based deep neural network (DNN) nonlinear equalization techniques. The system employs advanced digital signal processing (DSP) methods, including down-conversion, resampling, matched filtering, and various equalization algorithms to combat signal distortions. We demonstrate the effectiveness of DNN and iterative pruning techniques in significantly reducing bit error rates (BERs) across a range of symbol rates (10 Gbaud to 30 Gbaud) and polarization states (vertical and horizontal). Before pruning, at 10 GBaud transmission, the lowest BER was 0.0362, and at 30 GBaud transmission, the lowest BER was 0.1826, both of which did not meet the 20% soft-decision forward error correction (SD-FEC) threshold. After pruning, the BER at different transmission rates was reduced to below the hard decision forward error correction (HD-FEC) threshold, indicating a substantial improvement in signal quality. Additionally, the pruning process contributed to a decrease in network complexity, with a maximum reduction of 85.9% for 10 GBaud signals and 63.0% for 30 GBaud signals. These findings indicate the potential of DNN and pruning techniques to enhance the performance and efficiency of terahertz communication systems, providing valuable insights for future high-capacity, long-distance wireless networks. Full article
(This article belongs to the Special Issue New Advances in Optical Wireless Communication)
Show Figures

Figure 1

Figure 1
<p>Photonics-assisted terahertz technology based on heterodyne beat frequency.</p>
Full article ">Figure 2
<p>Schematic diagrams of 2 × 2 MIMO wireless transmission systems. (<b>a</b>) Traditional 2 × 2 MIMO. (<b>b</b>) Polarization multiplexed 2 × 2 MIMO.</p>
Full article ">Figure 3
<p>(<b>a</b>) Schematic diagram of the iterative pruning process. (<b>b</b>) Weight matrix diagram of pruning in the fully connected layer.</p>
Full article ">Figure 4
<p>(<b>a</b>) Schematic diagram of a 4.6 km 2 × 2 MIMO photonic-assisted terahertz communication system architecture in the D-band; (<b>b</b>) flowchart of the digital signal processing at the receiving end; and (<b>c</b>) the 4.6 km 2 × 2 MIMO photonic-assisted terahertz experimental setup. (I) Transmitter, before single-mode fiber, (II) transmitter, after single-mode fiber, (III) receiver, signal processing, and (IV) receiver, lens.</p>
Full article ">Figure 5
<p>Signal spectra: (<b>a</b>) V-pol-10 Gbaud, (<b>b</b>) V-pol-20 Gbaud, (<b>c</b>) V-pol-30 Gbaud, (<b>d</b>) H-pol-10 Gbaud, (<b>e</b>) H-pol-20 Gbaud, and (<b>f</b>) H-pol-30 Gbaud.</p>
Full article ">Figure 6
<p>Neural network training epochs vs. average loss. (<b>a</b>) V-pol and (<b>b</b>) H-pol.</p>
Full article ">Figure 7
<p>V-pol neural network pruning rounds vs. sparsity: (<b>a</b>) 10 GBaud-I, (<b>b</b>) 10 GBaud-Q, (<b>c</b>) 20 GBaud-I, (<b>d</b>) 20 GBaud-Q, (<b>e</b>) 30 GBaud-I, and (<b>f</b>) 30 Gbaud-Q.</p>
Full article ">Figure 8
<p>Neural network pruning threshold ratio vs. sparsity: (<b>a</b>) 10 GBaud, (<b>b</b>) 20 GBaud, and (<b>c</b>) 30 GBaud.</p>
Full article ">Figure 9
<p>Neural network pruning threshold ratio vs. BER: (<b>a</b>) V-pol-10 GBaud, (<b>b</b>) V-pol-20 GBaud, (<b>c</b>) V-pol-30 GBaud, (<b>d</b>) H-pol-10 GBaud, (<b>e</b>) H-pol-20 GBaud, and (<b>f</b>) H-pol-30 GBaud.</p>
Full article ">Figure 10
<p>Different equalization methods vs. BER.</p>
Full article ">
17 pages, 1709 KiB  
Article
Point of Common Connection Voltage Modulated Direct Power Control with Disturbance Observer to Increase in Renewable Energy Acceptance in Power System
by Yong Woo Jeong and Woo Young Choi
Energies 2024, 17(21), 5319; https://doi.org/10.3390/en17215319 - 25 Oct 2024
Viewed by 491
Abstract
In this paper, we present a disturbance observer-based point of common connection voltage-modulated direct power control (PCCVM-DPC) system, which increases the robustness of the PCCVM-DPC system. First, the mathematical analysis of the disturbances for the step-up transformer’s nonlinearity, the grid voltage harmonics, and [...] Read more.
In this paper, we present a disturbance observer-based point of common connection voltage-modulated direct power control (PCCVM-DPC) system, which increases the robustness of the PCCVM-DPC system. First, the mathematical analysis of the disturbances for the step-up transformer’s nonlinearity, the grid voltage harmonics, and the parameter uncertainties is presented. By analyzing the disturbance terms of the PCCVM-DPC system, we present the disturbance observer (DOB) for the PCCVM-DPC system. To assess the efficacy of our approach, we perform comparative studies of the PCCVM-DPC without DOB and PCCVM-DPC with DOB by constructing the simulation environment based on the commercial step-up transformer and ESS inverter datasheet. We have validated that the active and reactive power control performance of the PCCVM-DPC with DOB outperforms the PCCVM-DPC without DOB from the observation that the current total harmonic distortion reduced by more than 40% compared to the PCCVM-DPC without the DOB. Full article
(This article belongs to the Special Issue Energy, Electrical and Power Engineering: 3rd Edition)
Show Figures

Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Schematic of the grid-connected voltage source inverter with the step-up transformer and the proposed PCCVM-DPC and proposed DOB.</p>
Full article ">Figure 2
<p>Schematic of the Simulink/MATLAB simulation environments.</p>
Full article ">Figure 3
<p>Closed-loop bode plot of PCCVM-DOC with PI and PI + DOB.</p>
Full article ">Figure 4
<p>Fast Fourier Transform (FFT) result of <math display="inline"><semantics> <msub> <mi>v</mi> <mrow> <mi>p</mi> <mi>c</mi> <mi>c</mi> <mo>,</mo> <mi>a</mi> </mrow> </msub> </semantics></math>.</p>
Full article ">Figure 5
<p>Validation results of the estimated disturbances of PI + DOB.</p>
Full article ">Figure 6
<p>Validation results of the active power for PCCVM-DPC with PI and PI + DOB.</p>
Full article ">Figure 7
<p>Validation results of the reactive power for PCCVM-DPC with PI and proposed PI+DOB.</p>
Full article ">Figure 8
<p>Validation results of the current harmonics for PCCVM-DPC with PI and proposed PI + DOB.</p>
Full article ">Figure 9
<p>Validation results of the power control performance during the transient region.</p>
Full article ">Figure 10
<p>Validation results of the current harmonics for PCCVM-DPC with PI and the proposed PI + DOB, considering the parameter uncertainties (THD of grid voltage: 2.9%).</p>
Full article ">
13 pages, 2194 KiB  
Article
MSSI System Combined with Dispersion-Managed Link Configured with Random-Based RDPS Differently Controlled by Fiber Length
by Jae-Pil Chung and Seong-Real Lee
Appl. Sci. 2024, 14(21), 9722; https://doi.org/10.3390/app14219722 - 24 Oct 2024
Viewed by 404
Abstract
We numerically demonstrate the dispersion map configured by random-based residual dispersion per span (RDPS) applied into the mid-span spectral inversion (MSSI) system to mitigate the impact of chromatic dispersion and the fiber nonlinearity in wavelength division multiplexed (WDM) signals. The dispersion map proposed [...] Read more.
We numerically demonstrate the dispersion map configured by random-based residual dispersion per span (RDPS) applied into the mid-span spectral inversion (MSSI) system to mitigate the impact of chromatic dispersion and the fiber nonlinearity in wavelength division multiplexed (WDM) signals. The dispersion map proposed was a scheme in which the RDPS of all optical fiber spans in the front section of the midway optical phase conjugator (OPC) are randomly selected, and the arrangement order of the RDPS in the rear section is inverted from that of the front section. Numerical simulations were performed by evaluating the compensation of the distorted 960 Gb/s WDM signal as a function of the variation of the DCF length and the SMF length, which are involved in determining RDPS. It was confirmed that the compensation effect of the proposed dispersion maps has improved compared to the conventional dispersion map since the dispersion maps examined in this paper have antipodal symmetry around the midway OPC. In particular, it was confirmed that the method of randomly determining the RDPSs by varying the DCF length slightly improved system performance compared to the variation of SMF lengths. We also found that the feature of the RDPS random distribution patterns can achieve excellent compensation for the distorted WDM signal through 50 iterations. Full article
Show Figures

Figure 1

Figure 1
<p>The 960 Gbps WDM transmission system through the dispersion-managed link and the midway-OPC.</p>
Full article ">Figure 2
<p>The eye diagrams. (<b>a</b>) random pattern number 24; varied DCF length, (<b>b</b>) random pattern number 24; varied SMF length, (<b>c</b>) random pattern number 39; varied DCF length and (<b>d</b>) random pattern number 39; varied SMF length.</p>
Full article ">Figure 3
<p>The maximum launch power of the worst channel. (<b>a</b>) resulting 1-dB EOP and (<b>b</b>) resulting 2 ps TJ.</p>
Full article ">Figure 4
<p>The product of the effective NRD and launch power. (<b>a</b>) resulting 1-dB EOP, and (<b>b</b>) resulting 2 ps TJ.</p>
Full article ">Figure 5
<p>Five dispersion maps with the best/worst compensation based on EOP evaluation. (<b>a</b>) the best compensation cases for varying DCF length, (<b>b</b>) the best compensation cases for varying SMF length, (<b>c</b>) the worst compensation cases for varying DCF length, and (<b>d</b>) the worst compensation cases for varying SMF length.</p>
Full article ">Figure 6
<p>Five dispersion maps with the best/worst compensation based on TJ evaluation. (<b>a</b>) the best compensation cases for varying DCF length, (<b>b</b>) the best compensation cases for varying SMF length, (<b>c</b>) the worst compensation cases for varying DCF length, and (<b>d</b>) the worst compensation cases for varying SMF length.</p>
Full article ">
15 pages, 5687 KiB  
Article
Synergistic Control of Active Filter and Grid Forming Inverter for Power Quality Improvement
by Khaliqur Rahman, Jun Hashimoto, Kunio Koseki, Taha Selim Ustun, Dai Orihara and Hiroshi Kikusato
Sustainability 2024, 16(20), 9068; https://doi.org/10.3390/su16209068 - 19 Oct 2024
Viewed by 655
Abstract
This paper addresses the challenges and opportunities associated with integrating grid-forming inverters (GFMs) into modern power systems, particularly in the presence of nonlinear loads. Nonlinear loads introduce significant harmonic distortions in the source voltage and current, leading to reduced power factor, increased losses, [...] Read more.
This paper addresses the challenges and opportunities associated with integrating grid-forming inverters (GFMs) into modern power systems, particularly in the presence of nonlinear loads. Nonlinear loads introduce significant harmonic distortions in the source voltage and current, leading to reduced power factor, increased losses, and an overall reduction in system performance. To mitigate these adverse effects, active filters are employed. The objective of this study is to investigate a synergistic approach to modeling and control in integrated power systems with GFMs, focusing on enhancing power quality and grid stability by reducing harmonic distortions through the use of voltage-source active filters. This research contributes to sustainability by supporting the reliable and efficient integration of renewable energy sources, thereby reducing dependency on fossil fuels and minimizing greenhouse gas emissions. Additionally, improving power quality and system efficiency helps reduce energy waste, which is crucial for achieving sustainable energy goals. Simulations are conducted on a 1000 kW GFM connected to a grid with a nonlinear variable load, demonstrating the system’s effectiveness in adapting to dynamic conditions, reducing harmonics, and promoting a stable, resilient, and sustainable power grid. Full article
Show Figures

Figure 1

Figure 1
<p>Integrated power system network [<a href="#B16-sustainability-16-09068" class="html-bibr">16</a>].</p>
Full article ">Figure 2
<p>Droop control of grid-forming inverter [<a href="#B3-sustainability-16-09068" class="html-bibr">3</a>,<a href="#B16-sustainability-16-09068" class="html-bibr">16</a>].</p>
Full article ">Figure 3
<p>Harmonic current control of shunt active filter [<a href="#B21-sustainability-16-09068" class="html-bibr">21</a>].</p>
Full article ">Figure 4
<p>Active and reactive power at different components of the system. (<b>a</b>) Active and reactive power in the network; (<b>b</b>) Active filter power loss.</p>
Full article ">Figure 5
<p>System frequency and filter voltage and current characteristics. (<b>a</b>) SAF DC link voltage and current; (<b>b</b>) Inverter and grid frequency.</p>
Full article ">Figure 6
<p>Voltage at PCC in different operating conditions.</p>
Full article ">Figure 7
<p>(<b>a</b>) Grid current with harmonic spectrum without and with SAF; (<b>b</b>) Inverter current with harmonic spectrum without and with SAF.</p>
Full article ">Figure 8
<p>Total harmonics distortion (THD) at different operating conditions.</p>
Full article ">Figure 9
<p>(<b>a</b>) Power system network currents with and without shunt active filter. (<b>b</b>–<b>e</b>) Zommed-in view of power system network currents at different time.</p>
Full article ">Figure 10
<p>Characteristics under drastic load change and high harmonic environments. (<b>a</b>) Inverter and grid frequency; (<b>b</b>) Voltage at PCC.</p>
Full article ">
21 pages, 3096 KiB  
Article
Efficient Estimation of Synthetic Indicators for the Assessment of Nonlinear Systems Quality
by Pietro Burrascano, Andrea Di Schino and Mario Versaci
Appl. Sci. 2024, 14(20), 9259; https://doi.org/10.3390/app14209259 - 11 Oct 2024
Viewed by 481
Abstract
The availability of synthetic indicators of the degree and type of nonlinearity in systems is used in various fields to assess system quality or to highlight possible malfunctions. Different distortion or damage indexes are synthetic measures designed (and standardized) to evaluate the frequency [...] Read more.
The availability of synthetic indicators of the degree and type of nonlinearity in systems is used in various fields to assess system quality or to highlight possible malfunctions. Different distortion or damage indexes are synthetic measures designed (and standardized) to evaluate the frequency trend of specific aspects resulting from the nonlinear behavior of the system under consideration. The different measures of deviation from linear behavior quantitatively consider the system and its nonlinearity characteristics; they were defined according to practically feasible measurement methodologies and the various aspects of the system’s nonlinearity that needed to be highlighted. In parallel, techniques for representing and modeling nonlinear systems have been defined, capable of describing the system in a more general way, attempting to capture its input–output characteristics by varying the level of stress to which the system is subjected. Numerous modeling techniques have been proposed, aimed at representing the nonlinear behavior of physical devices. In this paper, after an extensive description of the Hammerstein model identification technique based on swept sinusoidal signals, we show how the nonlinear model of the system can be used to obtain accurate estimates of the parameter aimed at describing the nonlinearity characteristics of the system. This extensive description makes it possible to point out that the same Hammerstein model can be obtained not only from a single type of excitation, but it is shown that the identification technique can be extended to input signals of different types. The description of the method also makes clear the motivation behind the introduction of the proposed original technique for estimating, from a single measurement, the model parameters of the nonlinear system—and from these the synthetic estimators—relative to multiple values of the input signal amplitude, thus enabling a considerable increase in the estimation efficiency of these parameters. The proposed technique is verified with both synthetic and laboratory experiments, demonstrating the effectiveness of the method in evaluating nonlinear system parameters, distortion estimates, and parameters defined for an early detection of defects of the structure. Full article
(This article belongs to the Section Acoustics and Vibrations)
Show Figures

Figure 1

Figure 1
<p>The Hammerstein model.</p>
Full article ">Figure 2
<p>PuC estimates of <span class="html-italic">THD</span>, <span class="html-italic">HD</span><sub>2</sub> and <span class="html-italic">HD</span><sub>3</sub> for the synthetic experiment. (<b>a</b>) Estimates related to the excitation signal amplitude R = 1 obtained from the measurements made for R = 1; (<b>b</b>) estimates related to the excitation signal R = 0.5 obtained by extrapolation from the measurements made for R = 1.</p>
Full article ">Figure 3
<p>PuC estimate of <math display="inline"><semantics> <mrow> <mo> </mo> <mi>I</mi> <mi>M</mi> <msub> <mi>D</mi> <mrow> <msub> <mi>f</mi> <mn>2</mn> </msub> <mo>−</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> </mrow> </msub> </mrow> </semantics></math> for the synthetic experiment.</p>
Full article ">Figure 4
<p>The one degree of freedom system spring-mass-damper.</p>
Full article ">Figure 5
<p>Damage index HI for different SNR values as a function of the value of <span class="html-italic">α</span>. (<b>a</b>) HI trends for two different values of input signal amplitude: amplitude R1 which guarantees SNR = 5 and amplitude R2 which guarantees SNR = 10 dB. (<b>b</b>) Comparison between the experimental HI curve for amplitude R1 (SNR = 5) and the curve obtained by applying the extrapolation procedure from R2 (SNR = 10) to R1 (SNR = 5).</p>
Full article ">Figure 6
<p>Schematic representation: (<b>a</b>) the stressed bar; (<b>b</b>) the measuring bench.</p>
Full article ">Figure 7
<p>Trend of the signal energy ratio for different input signal amplitudes; in both panels the dotted lines represent linear interpolations on the first group of points (from 1 to 5) and on the remaining 15 points: (<b>a</b>) estimates obtained from 20 independent measures. (<b>b</b>) blue dots represent four estimates obtained from 20 independent measures; red dots are estimates obtained from each of the four measured values by extrapolating for lower signal amplitudes.</p>
Full article ">
30 pages, 12819 KiB  
Article
Hybrid Deep Neural Network Approaches for Power Quality Analysis in Electric Arc Furnaces
by Manuela Panoiu and Caius Panoiu
Mathematics 2024, 12(19), 3071; https://doi.org/10.3390/math12193071 - 30 Sep 2024
Viewed by 641
Abstract
In this research, we investigate the power quality of the grid where an Electric Arc Furnace (EAF) with a very high load operates. An Electric Arc Furnace (EAF) is a highly nonlinear load that uses very high and variable currents, causing major power [...] Read more.
In this research, we investigate the power quality of the grid where an Electric Arc Furnace (EAF) with a very high load operates. An Electric Arc Furnace (EAF) is a highly nonlinear load that uses very high and variable currents, causing major power quality issues such as voltage sags, flickers, and harmonic distortions. These disturbances produce electrical grid instability, affect the operation of other equipment, and require strong mitigation measures to reduce their impact. To investigate these issues, data are collected from the Point of Common Coupling where the Electric Arc Furnace is fed. The following three main factors are identified for evaluating power quality: apparent power, active and reactive power, and distorted power. Along with these powers, Total Harmonic Distortion, an important indicator of power quality, is calculated. These data are collected during the full process of producing a complete steel batch. To create a Deep Neural Network that can model and forecast power quality parameters, a network is developed using LSTM layers, Convolutional Layers, and GRU Layers, all of which demonstrate good prediction performance. The results of the prediction models are examined, as well as the primary metrics characterizing the prediction, using the following: MAE, RMSE, R-squared, and sMAPE. Predicting active and reactive power and Total Harmonic Distortion (THD) proves useful for anticipating power quality problems in an Electric Arc Furnace (EAF). By reducing the EAF’s impact on the power system, accurate predictions will anticipate and minimize disturbances, optimize energy consumption, and improve grid stability. This research’s principal scientific contribution is the development of a hybrid deep neural network that integrates Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM), and Gated Recurrent Unit (GRU) layers. This deep neural network was designed to predict power quality metrics, including active power, reactive power, distortion power, and Total Harmonic Distortion (THD). The proposed methodology indicates an important step in improving the accuracy of power quality forecasting for Electric Arc Furnaces (EAFs). The hybrid model’s ability for analyzing both time-series data and complex nonlinear patterns improves its predictive accuracy compared to traditional methods. Full article
(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)
Show Figures

Figure 1

Figure 1
<p>The measurement scheme from the secondary of the furnace transformer.</p>
Full article ">Figure 2
<p>The currents and voltages on the EAF’s power supply line during the melting phase: (<b>a</b>) Arc voltage in the melting stage; (<b>b</b>) Arc current in the melting stage.</p>
Full article ">Figure 3
<p>The currents and voltages on the EAF’s power supply line during the refining phase: (<b>a</b>) Arc voltage in the refining stage; (<b>b</b>) Arc current in the refining stage.</p>
Full article ">Figure 4
<p>The harmonic spectrum of the voltage and current during the melting stage: (<b>a</b>) the harmonic spectrum of voltage; (<b>b</b>) the harmonic spectrum of current.</p>
Full article ">Figure 5
<p>The harmonic spectrum of the voltage and current during the refining stage: (<b>a</b>) the harmonic spectrum of voltage; (<b>b</b>) the harmonic spectrum of current.</p>
Full article ">Figure 6
<p>The three phase voltage amplitudes for harmonics during the melting stage: (<b>a</b>) voltage harmonics for phase 1; (<b>b</b>) voltage harmonics for phase 2; (<b>c</b>) voltage harmonics for phase 3.</p>
Full article ">Figure 7
<p>The three phase voltage amplitudes for harmonics during the refining stage: (<b>a</b>) voltage harmonics for phase 1; (<b>b</b>) voltage harmonics for phase 2; (<b>c</b>) voltage harmonics for phase 3.</p>
Full article ">Figure 8
<p>The three phase current amplitudes for harmonics during the melting stage: (<b>a</b>) current harmonics for phase 1; (<b>b</b>) current harmonics for phase 2; (<b>c</b>) current harmonics for phase 3.</p>
Full article ">Figure 9
<p>The three phase current amplitudes for harmonics during the refining stage: (<b>a</b>) current harmonics for phase 1; (<b>b</b>) current harmonics for phase 2; (<b>c</b>) current harmonics for phase 3.</p>
Full article ">Figure 10
<p>The variation of the apparent power throughout the entire process.</p>
Full article ">Figure 11
<p>The variation of the active power throughout the entire process.</p>
Full article ">Figure 12
<p>The variation of the reactive power throughout the entire process.</p>
Full article ">Figure 13
<p>The variation of the distorted power throughout the entire process.</p>
Full article ">Figure 14
<p>The variation of the THD throughout the entire process.</p>
Full article ">Figure 15
<p>The relative transformation ratio: (<b>a</b>) Relative transformation ratio for voltage transformers; (<b>b</b>) Relative transformation ratio for current transformers.</p>
Full article ">Figure 16
<p>The hybrid CNN network architecture.</p>
Full article ">Figure 17
<p>Recursive single-step and multi-step prediction.</p>
Full article ">Figure 18
<p>Details about the single-step prediction.</p>
Full article ">Figure 19
<p>The steps used for analyzing the power quality using deep neural network.</p>
Full article ">Figure 20
<p>The full sequence of the measured values of active power used to train the hybrid deep neural network.</p>
Full article ">Figure 21
<p>The result of training using the following parameters: learning rate 0.006, previous samples: 400, 65% data used for training and 35% data used for testing.</p>
Full article ">Figure 22
<p>The measured and predicted values for the test sequence: (<b>a</b>) the curve variation for measured and predicted values; (<b>b</b>) scatter plot of predicted versus measured (target) values for the active power.</p>
Full article ">Figure 23
<p>The measured and predicted values for the multi-step prediction: (<b>a</b>) the curve variation for measured and predicted values; (<b>b</b>) scatter plot of predicted versus measured (target) values for the active power.</p>
Full article ">Figure 24
<p>Multi-step prediction for a value of “horizon” 820.</p>
Full article ">Figure 25
<p>The full sequence of the measured values of the reactive power used to train the hybrid deep neural network.</p>
Full article ">Figure 26
<p>The result of training using the following parameters: learning rate 0.006, previous samples: 400, 65% data used for training and 35% data used for testing. sMAPE = 0.0091.</p>
Full article ">Figure 27
<p>The measured and predicted values for the test sequence: (<b>a</b>) the curve variation for measured and predicted values; (<b>b</b>) scatter plot of predicted versus measured (target) values for the reactive power.</p>
Full article ">Figure 28
<p>The measured and predicted values for the multi-step prediction: (<b>a</b>) the curve variation for measured and predicted values; (<b>b</b>) scatter plot of predicted versus measured (target) values for the reactive power.</p>
Full article ">
21 pages, 3979 KiB  
Article
Modeling, Design, and Application of Analog Pre-Distortion for the Linearity and Efficiency Enhancement of a K-Band Power Amplifier
by Tommaso Cappello, Sarmad Ozan, Andy Tucker, Peter Krier, Tudor Williams and Kevin Morris
Electronics 2024, 13(19), 3818; https://doi.org/10.3390/electronics13193818 - 27 Sep 2024
Viewed by 544
Abstract
This paper presents the theory, design, and application of a dual-branch series-diode analog pre-distortion (APD) linearizer to improve the linearity and efficiency of a K-band high-power amplifier (HPA). A first-of-its-kind, frequency-dependent large-signal APD model is presented. This model is used to evaluate different [...] Read more.
This paper presents the theory, design, and application of a dual-branch series-diode analog pre-distortion (APD) linearizer to improve the linearity and efficiency of a K-band high-power amplifier (HPA). A first-of-its-kind, frequency-dependent large-signal APD model is presented. This model is used to evaluate different phase relationships between the linear and nonlinear branches, suggesting independent gain and phase expansion characteristics with this topology. This model is used to assess the impact of diode resistance, capacitance, and ideality factors on the APD characteristics. This feature is showcased with two similar GaAs diodes to find the best fit for the considered HPA. The selected diode is characterized and modeled between 1 and 26.5 GHz. A comprehensive APD design and simulation workflow is reported. Before fabrication, the simulated APD is evaluated with the measured HPA to verify linearity improvements. The APD prototype achieves a large-signal bandwidth of 6 GHz with 3 dB gain expansion and 8° phase rotation. This linearizer is demonstrated with a 17–21 GHz GaN HPA with 41 dBm output power and 35% efficiency. Using a wideband 750 MHz signal, this APD improves the noise–power ratio (NPR) by 6.5–8.2 dB over the whole HPA bandwidth. Next, the HPA output power is swept to compare APD vs. power backoff for the same NPR. APD improves the HPA output power by 1–2 W and efficiency by approximately 5–9% at 19 GHz. This efficiency improvement decreases by only 1–2% when including the APD post-amplifier consumption, thus suggesting overall efficiency and output power improvements with APD at K-band frequencies. Full article
Show Figures

Figure 1

Figure 1
<p>Schematic of the dual-branch APD with series diode, phase delay lines, bias-Ts (ideal RF choke <math display="inline"><semantics> <msub> <mi>L</mi> <mo>∞</mo> </msub> </semantics></math> and an ideal DC block <math display="inline"><semantics> <msub> <mi>C</mi> <mo>∞</mo> </msub> </semantics></math>), and 3 dB splitters and combiners.</p>
Full article ">Figure 2
<p>AC equivalent circuit of the nonlinearity in the APD circuit. Highlighted on the circuit are the diode series impedance <math display="inline"><semantics> <msub> <mi>Z</mi> <mi>S</mi> </msub> </semantics></math> and total capacitance <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math> between the A-K terminals.</p>
Full article ">Figure 3
<p>Ideal APD gain (<b>a</b>) and phase (<b>b</b>) vs. input power. Highlighted on the characteristics are the small-signal gain and phase (<math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> </semantics></math>), the large-signal gain and phase (<math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>L</mi> <mi>S</mi> </mrow> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>L</mi> <mi>S</mi> </mrow> </msub> </semantics></math>), maximum gain and phase variations (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>G</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mo>Φ</mo> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </mrow> </semantics></math>) at the maximum input power <math display="inline"><semantics> <msub> <mi>P</mi> <mrow> <mi>I</mi> <mi>N</mi> <mo>,</mo> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </semantics></math>.</p>
Full article ">Figure 4
<p>(<b>Left</b>) Small-signal gain <math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> </semantics></math>, large-signal gain <math display="inline"><semantics> <msub> <mi>G</mi> <mrow> <mi>L</mi> <mi>S</mi> </mrow> </msub> </semantics></math>, and gain variation <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mi>G</mi> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </mrow> </semantics></math> vs. phase difference <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ϕ</mi> </mrow> </semantics></math>. (<b>Right</b>) Small-signal phase <math display="inline"><semantics> <msub> <mo>Φ</mo> <mrow> <mi>S</mi> <mi>S</mi> </mrow> </msub> </semantics></math>, large-signal phase <math display="inline"><semantics> <msub> <mo>Φ</mo> <mrow> <mi>L</mi> <mi>S</mi> </mrow> </msub> </semantics></math>, and maximum phase variation <math display="inline"><semantics> <mrow> <mo>Δ</mo> <msub> <mo>Φ</mo> <mrow> <mi>M</mi> <mi>A</mi> <mi>X</mi> </mrow> </msub> </mrow> </semantics></math> vs. linear branch phase <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>L</mi> <mi>I</mi> <mi>N</mi> </mrow> </msub> </semantics></math> for a set <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ϕ</mi> <mo>=</mo> <msup> <mn>84</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
Full article ">Figure 5
<p>APD gain and phase for a fixed <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>ϕ</mi> </mrow> </semantics></math> setting the amplitude variation. Depending on the <math display="inline"><semantics> <msub> <mi>ϕ</mi> <mrow> <mi>L</mi> <mi>I</mi> <mi>N</mi> </mrow> </msub> </semantics></math> choice, this APD can realize a negative (<b>a</b>), neutral (<b>b</b>), and positive (<b>c</b>) phase variation.</p>
Full article ">Figure 6
<p>(<b>Left</b>) Gain variation vs. <math display="inline"><semantics> <msub> <mi>P</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </semantics></math> for different total capacitances <math display="inline"><semantics> <msub> <mi>C</mi> <mi>T</mi> </msub> </semantics></math>. (<b>Right</b>) Gain variation vs. <math display="inline"><semantics> <msub> <mi>P</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </semantics></math> for different series resistance <math display="inline"><semantics> <msub> <mi>R</mi> <mi>S</mi> </msub> </semantics></math>.</p>
Full article ">Figure 7
<p>Gain variation vs. <math display="inline"><semantics> <msub> <mi>P</mi> <mrow> <mi>I</mi> <mi>N</mi> </mrow> </msub> </semantics></math> for different ideality factor <span class="html-italic">n</span>. Lower ideality factors have the effect of shifting the APD amplitude turn-on “knee”.</p>
Full article ">Figure 8
<p>Measured (blue) vs. modeled (dashed) APD gain at 15 GHz (<b>a</b>) and 21 GHz (<b>b</b>) for different diode biases. The APD model fits the measured data on a broad frequency range for different diode biases and input powers.</p>
Full article ">Figure 9
<p>Inverted gain (<b>a</b>) and phase (<b>b</b>) of the HPA at 19 GHz. Superposed is the APD model response for Diodes 1 and 2. Diode 1 approximates the HPA characteristics on a wider range than Diode 2, thus suggesting higher linearity and efficiency improvements with this diode.</p>
Full article ">Figure 10
<p>(<b>a</b>) Diode fixture mounted on the test jig with bias-Ts. (<b>b</b>) Two-line TRL calibration kit. (<b>c</b>) Photo of the setup to characterize the diode and APD.</p>
Full article ">Figure 11
<p>Measured (solid) and modeled (dashed) I/V of two Diode 1 samples.</p>
Full article ">Figure 12
<p>(<b>a</b>) Diode layout [<a href="#B19-electronics-13-03818" class="html-bibr">19</a>] with reference planes. (<b>b</b>) Diode equivalent circuit with parasitic network realized with lumped and distributed elements.</p>
Full article ">Figure 13
<p>Measured (solid) and modeled (dashed) diode <math display="inline"><semantics> <msub> <mi>S</mi> <mn>11</mn> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>S</mi> <mn>22</mn> </msub> </semantics></math>, and <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>S</mi> <mn>21</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> between 1 GHz and 26.5 GHz and for 0, 1, 25 mA bias current.</p>
Full article ">Figure 14
<p>Layout (<b>left</b>) and photo (<b>right</b>) of the APD prototype.</p>
Full article ">Figure 15
<p>(<b>Left</b>) Simulation between 10 and 26 GHz of the APD circuit for varying input powers and <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>D</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> V. The HPA and APD bandwidths are indicated on the plot. (<b>Right</b>) Simulated APD gain vs. input power for varying <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>D</mi> <mn>0</mn> </mrow> </msub> </semantics></math>. Superposed are the inverted HPA characteristics and diode DC current.</p>
Full article ">Figure 16
<p>Simulated AC voltage across the diode at 17 GHz (<b>Left</b>) and 20 GHz (<b>Right</b>) for varying input powers. The voltage peaks are below the 7 V diode breakdown voltage.</p>
Full article ">Figure 17
<p>(<b>a</b>) Simulated APD input and output signal. (<b>b</b>) Measured HPA output signal without and with simulated APD. (<b>c</b>) Measured HPA gain with simulated APD for different bias voltages. An optimal bias voltage that ensures maximum gain flatness is found before fabricating the APD circuit.</p>
Full article ">Figure 18
<p>Measured <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>S</mi> <mn>11</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> (<b>a</b>) and <math display="inline"><semantics> <mrow> <mrow> <mo>|</mo> </mrow> <msub> <mi>S</mi> <mn>21</mn> </msub> <mrow> <mo>|</mo> </mrow> </mrow> </semantics></math> (<b>b</b>) for varying <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>D</mi> <mn>0</mn> </mrow> </msub> </semantics></math> (to simulate the expanding APD characteristic caused by the RF power).</p>
Full article ">Figure 19
<p>Measured large-signal APD gain (<b>left</b>) and phase (<b>right</b>) between 15 and 21 GHz. For these measurements, the diode bias is <math display="inline"><semantics> <mrow> <msub> <mi>V</mi> <mrow> <mi>D</mi> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> V.</p>
Full article ">Figure 20
<p>(<b>Left</b>) Block diagram of the wideband setup. (<b>Right</b>) Photo of the setup.</p>
Full article ">Figure 21
<p>Pulsed gain and phase at 19 GHz for different diode biases.</p>
Full article ">Figure 22
<p>Measured HPA output spectrum for the same 750 MHz signal without APD (brown), with APD (blue), and ideal response (black). NPR improves between 6.5 and 8.2 dB over the 4 GHz HPA bandwidth while maintaining the same average output power.</p>
Full article ">Figure 23
<p>Measured NPR, average output power, and average efficiency for the same 750 MHz signal at different backoff powers. For the same NPR, APD improves the HPA average output power by 1-2 W and the average efficiency by 5–9%.</p>
Full article ">
17 pages, 7222 KiB  
Article
Breaking Queer Silences, Building Queer Archives, and Claiming Queer Indigenous P’urhépecha Methodologies
by Mario A. Gómez Zamora
Genealogy 2024, 8(4), 123; https://doi.org/10.3390/genealogy8040123 - 26 Sep 2024
Viewed by 1151
Abstract
In this essay, I recover queer Indigenous P’urhépecha histories in Michoacán, México, by claiming queer P’urhépecha research methods. To do so, I introduce the Indigenous methodology of talking-while-walking, which refers to how I learned to connect with P’urhépecha knowledge and traditions through the [...] Read more.
In this essay, I recover queer Indigenous P’urhépecha histories in Michoacán, México, by claiming queer P’urhépecha research methods. To do so, I introduce the Indigenous methodology of talking-while-walking, which refers to how I learned to connect with P’urhépecha knowledge and traditions through the voice of my P’urhépecha grandfather. Since the colonial system eradicated queer histories from my land, I seek historical narratives about queer people in Michoacán from any source available to me, including oral histories, archives, information in the media, and interviews. I argue that queer P’urhépecha histories are unstable and non-linear, and that P’urhépecha bodies have been hunted and their histories distorted, provoking fear and false speculations about queerness among the collective. I also examine the attachment of P’urhépecha people to gender binary traditions and heteronormativity and how the narratives behind these practices relate to colonial violence and the persecution of queer P’urhépechas. Thus, I demonstrate how P’urhépecha queerness has been marginalized and simultaneously displaced from the archival records while I claim queer P’urhépecha histories and build queer P’urhépecha archives. Finally, I propose a sensitive and personal approach to queer histories guided by the voices of my queer P’urhépecha interlocutors and the histories that my P’urhépecha abuelo passed to me. Full article
(This article belongs to the Section Family History)
Show Figures

Figure 1

Figure 1
<p>Map of the Michoacán territory painted by my father, Miguel A. Gómez Estrada, based on the colors of the P’urhépecha flag used in Santa Fe de la Laguna in the 1980s. He highlighted with four different colors the current P’urhépecha regions and he followed the municipality division proposed by the National Institute of Statistics and Geography in México (2024).</p>
Full article ">Figure 2
<p>Papá Quique and the author in Cocucho, Michoacán. On our way to visit <span class="html-italic">tía</span> Elpidia Montelongo in Nurio. Photo by <span class="html-italic">tía</span> Sarita Gómez Estrada. 2017.</p>
Full article ">Figure 3
<p>A drawing made by my father, Miguel A. Gómez Estrada, based on how he imagined Pedro and Simpliciano looked when they met in Valladolid, Michoacán, in 1604. January 2024.</p>
Full article ">Figure 4
<p>Colonial records of criminalization against Simpliciano, Pedro Quini, Joaquín Sisiqui, Francisco Capiche, and Juan Indio for “committing sins against nature”. AHMM, Fondo Colonial, III. 2.1.4. Sodomia, c.30, e.20, 1604.</p>
Full article ">
36 pages, 25510 KiB  
Article
Synchronized Measurement of the Fundamental Voltage and Harmonic, Interharmonic, and Subharmonic Components of the Electrical Grid Using an Adaptive Kalman Filter
by Germán Martínez-Navarro, Salvador Orts-Grau, José Carlos Alfonso-Gil and Pedro Balaguer-Herrero
Appl. Sci. 2024, 14(19), 8669; https://doi.org/10.3390/app14198669 - 26 Sep 2024
Viewed by 526
Abstract
The effects of harmonics, interharmonics, and subharmonics on low-voltage distribution networks, leading to a deterioration in electrical power quality, have become more evident in recent years. The main harmonic sources are power electronic devices due to their implicit nonlinearity. Interharmonic and subharmonic components [...] Read more.
The effects of harmonics, interharmonics, and subharmonics on low-voltage distribution networks, leading to a deterioration in electrical power quality, have become more evident in recent years. The main harmonic sources are power electronic devices due to their implicit nonlinearity. Interharmonic and subharmonic components are mainly caused by a lack of synchronization between the grid frequency and the switching frequency of the power converters. This can be caused by asynchronous modulated devices, or more commonly by fluctuations in the fundamental grid frequency. Interharmonic currents cause interharmonic voltage distortions that affect grid-synchronized or frequency-dependent systems. The IEC-61000-4-7 proposes a general guide on harmonics, interharmonic measurements, and instrumentation in current supply systems. However, the techniques proposed in the standard are intended for measurement and do not enable a precise identification of the interharmonic components in a signal. This work proposes new definitions for the spectral energy aggrupation to improve signal component detection for the IEC standard. Furthermore, an adaptive Kalman filter algorithm is developed that enables the exact identification in real time of the frequency, amplitude, and phase of these components. The proposed system will become the basis for the implementation of a new range of measurement systems that provide improved accuracy and real-time operation. The work is supported by simulated results analysing various scenarios (including transients after changes in harmonic content in the grid voltage) that demonstrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Electric Power Applications II)
Show Figures

Figure 1

Figure 1
<p>Spectral components obtained with the DFT for a 50 Hz network.</p>
Full article ">Figure 2
<p>Harmonic and interharmonic groups.</p>
Full article ">Figure 3
<p>Harmonic and interharmonic subgroups.</p>
Full article ">Figure 4
<p>Flow diagram of the evolution of Kalman filter calculations.</p>
Full article ">Figure 5
<p>Description of the state of the harmonic subgroups with the new method.</p>
Full article ">Figure 6
<p>Spectral components filtering process flowchart: (<b>a</b>) first part of the algorithm (<b>b</b>) second part of the algorithm.</p>
Full article ">Figure 7
<p>Spectral components grouping process.</p>
Full article ">Figure 8
<p>Structure of the developed method.</p>
Full article ">Figure 9
<p>Research methodology flowchart.</p>
Full article ">Figure 10
<p>Input signal of the measurement system.</p>
Full article ">Figure 11
<p>(<b>a</b>) Harmonic spectrum of the input signal; (<b>b</b>) detail of the harmonic spectrum.</p>
Full article ">Figure 12
<p>LKF estimated signal (red) versus input signal (blue).</p>
Full article ">Figure 13
<p>LKF estimated signal error.</p>
Full article ">Figure 14
<p>Evolution of the input signal during the component change at t = 0.8 s.</p>
Full article ">Figure 15
<p>LKF estimated signal (red) versus input signal (blue).</p>
Full article ">Figure 16
<p>LKF estimated signal error.</p>
Full article ">Figure 17
<p>Evolution of the estimation of the spectral component at 22 Hz (red) and the real component (blue).</p>
Full article ">Figure 18
<p>Evolution of the estimation of the spectral component at 149.7 Hz (red) and the real component (blue).</p>
Full article ">Figure 19
<p>Evolution of the estimation of the spectral component at 449.1 Hz (red) and the real component (blue).</p>
Full article ">Figure 20
<p>Estimation of the LKF signal (red) versus input signal during the change in the number of spectral components (blue).</p>
Full article ">Figure 21
<p>LKF estimated signal error.</p>
Full article ">Figure 22
<p>Detail of the error made in the signal estimation.</p>
Full article ">Figure 23
<p>The evolution of the estimation of the subharmonic spectral component at 22 Hz (red) versus the real component (blue).</p>
Full article ">Figure 24
<p>Temporal evolution of the estimation of the frequency value (rad/s) of all spectral components within the input signal.</p>
Full article ">Figure 25
<p>Waveform of the input signal for the second simulation.</p>
Full article ">Figure 26
<p>Input signal (blue) versus LKF estimation (red).</p>
Full article ">Figure 27
<p>Error signal between the input signal and the LKF estimation.</p>
Full article ">Figure 28
<p>Detail of the temporal evolution of the error signal.</p>
Full article ">Figure 29
<p>Evolution of the input subharmonic component at 33.9 Hz (blue) and the LKF prediction (red).</p>
Full article ">Figure 30
<p>Temporal evolution of the estimation of the value of the frequency of all spectral components inside the input signal.</p>
Full article ">Figure 31
<p>Evolution of the input signal during the modification of the number of spectral components.</p>
Full article ">Figure 32
<p>LKF estimated signal error.</p>
Full article ">Figure 33
<p>LKF estimated signal (red) versus input signal (blue).</p>
Full article ">Figure 34
<p>LKF estimated signal (red) versus input signal (blue).</p>
Full article ">Figure 35
<p>LKF estimated signal error.</p>
Full article ">Figure 36
<p>LKF estimated signal error detail.</p>
Full article ">Figure 37
<p>Estimation of the interharmonic spectral component at 214.3 Hz (red) versus real component (blue).</p>
Full article ">Figure 38
<p>Estimation detail of the interharmonic spectral component at 214.3 Hz (red) versus real component (blue).</p>
Full article ">Figure 39
<p>Estimation of the interharmonic spectral component at 229 Hz (red) versus real component (blue).</p>
Full article ">Figure 40
<p>Estimation detail of the interharmonic spectral component at 229 Hz (red) versus real component (blue).</p>
Full article ">Figure 41
<p>Estimation of the frequency values of the spectral components at 214.3 Hz (green), 229 Hz (red), and 250.3 Hz (blue).</p>
Full article ">Figure 42
<p>White noise signal used in the simulation.</p>
Full article ">Figure 43
<p>Input signal generated for the noise analysis.</p>
Full article ">Figure 44
<p>Input signal (blue) versus Kalman filter estimated signal (red).</p>
Full article ">Figure 45
<p>Error signal obtained as the difference between input and estimated signals.</p>
Full article ">Figure 46
<p>Subharmonic estimation comparison. LKF estimation (red) versus 33.9 Hz component of the input signal (blue).</p>
Full article ">Figure 47
<p>Subharmonic frequency estimation.</p>
Full article ">Figure 48
<p>Frequency estimation of the five components that form the input signal.</p>
Full article ">Figure 49
<p>Estimated rms value of the subharmonic (33.9 Hz).</p>
Full article ">Figure 50
<p>Estimated rms value of the five spectral components, 1 (blue), 2 (red), 3 (green), 4 (dark blue), and 5 (cyan).</p>
Full article ">
Back to TopTop