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equations</title> <meta name="description" content="Search results for: harmonic equations"> <meta name="keywords" content="harmonic equations"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="harmonic equations"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 2099</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: harmonic equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2099</span> Approximate Solution to Non-Linear Schrödinger Equation with Harmonic Oscillator by Elzaki Decomposition Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Emad%20K.%20Jaradat">Emad K. Jaradat</a>, <a href="https://publications.waset.org/abstracts/search?q=Ala%E2%80%99a%20Al-Faqih"> Ala’a Al-Faqih</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20Schrodinger%20equation" title="non-linear Schrodinger equation">non-linear Schrodinger equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Elzaki%20decomposition%20method" title=" Elzaki decomposition method"> Elzaki decomposition method</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20oscillator" title=" harmonic oscillator"> harmonic oscillator</a>, <a href="https://publications.waset.org/abstracts/search?q=one%20and%20two-dimensional%20Schrodinger%20equation" title=" one and two-dimensional Schrodinger equation"> one and two-dimensional Schrodinger equation</a> </p> <a href="https://publications.waset.org/abstracts/102537/approximate-solution-to-non-linear-schrodinger-equation-with-harmonic-oscillator-by-elzaki-decomposition-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/102537.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">187</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2098</span> Second Sub-Harmonic Resonance in Vortex-Induced Vibrations of a Marine Pipeline Close to the Seabed</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yiming%20Jin">Yiming Jin</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuanhao%20Gao"> Yuanhao Gao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vortex-induced%20vibrations" title="vortex-induced vibrations">vortex-induced vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=marine%20pipeline" title=" marine pipeline"> marine pipeline</a>, <a href="https://publications.waset.org/abstracts/search?q=seabed" title=" seabed"> seabed</a>, <a href="https://publications.waset.org/abstracts/search?q=sub-harmonic%20resonance" title=" sub-harmonic resonance"> sub-harmonic resonance</a> </p> <a href="https://publications.waset.org/abstracts/50829/second-sub-harmonic-resonance-in-vortex-induced-vibrations-of-a-marine-pipeline-close-to-the-seabed" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50829.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">332</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2097</span> Diagnosis of Static Eccentricity in 400 kW Induction Machine Based on the Analysis of Stator Currents</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saleh%20Elawgali">Saleh Elawgali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Current spectrums of a four pole-pair, 400 kW induction machine were calculated for the cases of full symmetry and static eccentricity. The calculations involve integration of 93 electrical plus four mechanical ordinary differential equations. Electrical equations account for variable inductances affected by slotting and eccentricities. The calculations were followed by Fourier analysis of the stator currents in steady state operation. Zooms of the current spectrums, around the 50 Hz fundamental harmonic as well as of the main slot harmonic zone, were included. The spectrums included refer to both calculated and measured currents. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diagnostic" title="diagnostic">diagnostic</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic" title=" harmonic"> harmonic</a>, <a href="https://publications.waset.org/abstracts/search?q=induction%20machine" title=" induction machine"> induction machine</a>, <a href="https://publications.waset.org/abstracts/search?q=spectrum" title=" spectrum"> spectrum</a> </p> <a href="https://publications.waset.org/abstracts/1932/diagnosis-of-static-eccentricity-in-400-kw-induction-machine-based-on-the-analysis-of-stator-currents" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1932.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">523</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2096</span> Reducing Total Harmonic Content of 9-Level Inverter by Use of Cuckoo Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mahmoud%20Enayati">Mahmoud Enayati</a>, <a href="https://publications.waset.org/abstracts/search?q=Sirous%20Mohammadi"> Sirous Mohammadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a novel procedure to find the firing angles of the multilevel inverters of supply voltage and, consequently, to decline the total harmonic distortion (THD), has been presented. In order to eliminate more harmonics in the multilevel inverters, its number of levels can be lessened or pulse width modulation waveform, in which more than one switching occur in each level, be used. Both cases complicate the non-algebraic equations and their solution cannot be performed by the conventional methods for the numerical solution of nonlinear equations such as Newton-Raphson method. In this paper, Cuckoo algorithm is used to compute the optimal firing angle of the pulse width modulation voltage waveform in the multilevel inverter. These angles should be calculated in such a way that the voltage amplitude of the fundamental frequency be generated while the total harmonic distortion of the output voltage be small. The simulation and theoretical results for the 9-levels inverter offer the high applicability of the proposed algorithm to identify the suitable firing angles for declining the low order harmonics and generate a waveform whose total harmonic distortion is very small and it is almost a sinusoidal waveform. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=evolutionary%20algorithms" title="evolutionary algorithms">evolutionary algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=multilevel%20inverters" title=" multilevel inverters"> multilevel inverters</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20harmonic%20content" title=" total harmonic content"> total harmonic content</a>, <a href="https://publications.waset.org/abstracts/search?q=Cuckoo%20Algorithm" title=" Cuckoo Algorithm"> Cuckoo Algorithm</a> </p> <a href="https://publications.waset.org/abstracts/24347/reducing-total-harmonic-content-of-9-level-inverter-by-use-of-cuckoo-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24347.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">532</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2095</span> Subclass of Close-To-Convex Harmonic Mappings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jugal%20K.%20Prajapat">Jugal K. Prajapat</a>, <a href="https://publications.waset.org/abstracts/search?q=Manivannan%20M."> Manivannan M.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article we have studied a class of sense preserving harmonic mappings in the unit disk D. Let B⁰H (α, β) denote the class of sense-preserving harmonic mappings f=h+g ̅ in the open unit disk D and satisfying the condition |z h״(z)+α (h׳(z)-1) | ≤ β - |z g″(z)+α g′(z)| (α > -1, β > 0). We have proved that B⁰H (α, β) is close-to-convex in D. We also prove that the functions in B⁰H (α, β) are stable harmonic univalent, stable harmonic starlike and stable harmonic convex in D for different values of its parameters. Further, the coefficient estimates, growth results, area theorem, boundary behavior, convolution and convex combination properties of the class B⁰H (α, β) of harmonic mapping are obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytic" title="analytic">analytic</a>, <a href="https://publications.waset.org/abstracts/search?q=univalent" title=" univalent"> univalent</a>, <a href="https://publications.waset.org/abstracts/search?q=starlike" title=" starlike"> starlike</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20and%20close-to-convex" title=" convex and close-to-convex"> convex and close-to-convex</a> </p> <a href="https://publications.waset.org/abstracts/109786/subclass-of-close-to-convex-harmonic-mappings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/109786.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">175</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2094</span> Investigation of Grid Supply Harmonic Effects in Wound Rotor Induction Machines</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nur%20Sarma">Nur Sarma</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20M.%20Tuohy"> Paul M. Tuohy</a>, <a href="https://publications.waset.org/abstracts/search?q=Sini%C5%A1a%20Djurovi%C4%87"> Siniša Djurović</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an in-depth investigation of the effects of several grid supply harmonic voltages on the stator currents of an example wound rotor induction machine. The observed effects of higher order grid supply harmonics are identified using a finite element time stepping transient model, as well as a time-stepping electromagnetic model. In addition, a number of analytical equations to calculate the spectral content of the stator currents are presented in the paper. The presented equations are validated through comparison with the obtained spectra predicted using the finite element and electromagnetic models. The presented study provides a better understanding of the origin of supply harmonic effects identified in the stator currents of the example wound rotor induction machine. Furthermore, the study helps to understand the effects of higher order supply harmonics on the harmonic emissions of the wound rotor induction machine.   <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=wound%20rotor%20induction%20machine" title="wound rotor induction machine">wound rotor induction machine</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20harmonics" title=" supply harmonics"> supply harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=current%20spectrum" title=" current spectrum"> current spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20spectrum" title=" power spectrum"> power spectrum</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20emmisions" title=" harmonic emmisions"> harmonic emmisions</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20analysis" title=" finite element analysis"> finite element analysis</a> </p> <a href="https://publications.waset.org/abstracts/87478/investigation-of-grid-supply-harmonic-effects-in-wound-rotor-induction-machines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/87478.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">177</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2093</span> Harmonic Distortion Caused by Electric Bus Battery Charger in Alexandria Distribution System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20Elhosieny%20Aly%20Ismail">Mohamed Elhosieny Aly Ismail</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper illustrates the total voltage and current harmonic distortion impact caused by fast-charging an electric bus and maintaining standard limit compliance. Measuring the current harmonic level in the range of 2 kHz-9 kHz. Also, the impact of the total demand distortions current caused by fast charger electric bus on the utility by measuring at the point of common coupling and comparing the measurement with IEEE519 -2014 standard. The results show that the total harmonic current distortion for the charger is within the limits of IEC 61000-3-12 and the fifth harmonic current was the most dominant frequency then the seventh harmonic current. The harmonic current in the range of 2 kHz- 9 kHz shows the frequency 5.1kHz is the most dominant frequency. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=electric%20vehicle" title="electric vehicle">electric vehicle</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20harmonic%20distortion" title=" total harmonic distortion"> total harmonic distortion</a>, <a href="https://publications.waset.org/abstracts/search?q=IEEE519-2014" title=" IEEE519-2014"> IEEE519-2014</a>, <a href="https://publications.waset.org/abstracts/search?q=IEC%2061000-3-12" title=" IEC 61000-3-12"> IEC 61000-3-12</a>, <a href="https://publications.waset.org/abstracts/search?q=super%20harmonic%20distortion" title=" super harmonic distortion"> super harmonic distortion</a> </p> <a href="https://publications.waset.org/abstracts/177738/harmonic-distortion-caused-by-electric-bus-battery-charger-in-alexandria-distribution-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/177738.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">101</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2092</span> Flexural Analysis of Symmetric Laminated Composite Timoshenko Beams under Harmonic Forces: An Analytical Solution</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Ali%20Hjaji">Mohammed Ali Hjaji</a>, <a href="https://publications.waset.org/abstracts/search?q=A.K.%20El-Senussi"> A.K. El-Senussi</a>, <a href="https://publications.waset.org/abstracts/search?q=Said%20H.%20Eshtewi"> Said H. Eshtewi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The flexural dynamic response of symmetric laminated composite beams subjected to general transverse harmonic forces is investigated. The dynamic equations of motion and associated boundary conditions based on the first order shear deformation are derived through the use of Hamilton’s principle. The influences of shear deformation, rotary inertia, Poisson’s ratio and fibre orientation are incorporated in the present formulation. The resulting governing flexural equations for symmetric composite Timoshenko beams are exactly solved and the closed form solutions for steady state flexural response are then obtained for cantilever and simply supported boundary conditions. The applicability of the analytical closed-form solution is demonstrated via several examples with various transverse harmonic loads and symmetric cross-ply and angle-ply laminates. Results based on the present solution are assessed and validated against other well established finite element solutions and exact solutions available in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title="analytical solution">analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=flexural%20response" title=" flexural response"> flexural response</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20forces" title=" harmonic forces"> harmonic forces</a>, <a href="https://publications.waset.org/abstracts/search?q=symmetric%20laminated%20beams" title=" symmetric laminated beams"> symmetric laminated beams</a>, <a href="https://publications.waset.org/abstracts/search?q=steady%20state%20response" title=" steady state response"> steady state response</a> </p> <a href="https://publications.waset.org/abstracts/18423/flexural-analysis-of-symmetric-laminated-composite-timoshenko-beams-under-harmonic-forces-an-analytical-solution" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/18423.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">487</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2091</span> New Coordinate System for Countries with Big Territories</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammed%20Sabri%20Ali%20Akresh">Mohammed Sabri Ali Akresh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The modern technologies and developments in computer and Global Positioning System (GPS) as well as Geographic Information System (GIS) and total station TS. This paper presents a new proposal for coordinates system by a harmonic equations “United projections”, which have five projections (Mercator, Lambert, Russell, Lagrange, and compound of projection) in one zone coordinate system width 14 degrees, also it has one degree for overlap between zones, as well as two standards parallels for zone from 10 S to 45 S. Also this paper presents two cases; first case is to compare distances between a new coordinate system and UTM, second case creating local coordinate system for the city of Sydney to measure the distances directly from rectangular coordinates using projection of Mercator, Lambert and UTM. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20equations" title="harmonic equations">harmonic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=coordinate%20system" title=" coordinate system"> coordinate system</a>, <a href="https://publications.waset.org/abstracts/search?q=projections" title=" projections"> projections</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithms" title=" algorithms"> algorithms</a>, <a href="https://publications.waset.org/abstracts/search?q=parallels" title=" parallels"> parallels</a> </p> <a href="https://publications.waset.org/abstracts/6986/new-coordinate-system-for-countries-with-big-territories" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6986.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">472</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2090</span> Study of Ultrasonic Waves in Unidirectional Fiber-Reinforced Composite Plates for the Aerospace Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=DucTho%20Le">DucTho Le</a>, <a href="https://publications.waset.org/abstracts/search?q=Duy%20Kien%20Dao"> Duy Kien Dao</a>, <a href="https://publications.waset.org/abstracts/search?q=Quoc%20Tinh%20Bui"> Quoc Tinh Bui</a>, <a href="https://publications.waset.org/abstracts/search?q=Haidang%20Phan"> Haidang Phan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article is concerned with the motion of ultrasonic guided waves in a unidirectional fiber-reinforced composite plate under acoustic sources. Such unidirectional composite material has orthotropic elastic properties as it is very stiff along the fibers and rather compliant across the fibers. The dispersion equations of free Lamb waves propagating in an orthotropic layer are derived that results in the dispersion curves. The connection of these equations to the Rayleigh-Lamb frequency relations of isotropic plates is discussed. By the use of reciprocity in elastodynamics, closed-form solutions of elastic wave motions subjected to time-harmonic loads in the layer are computed in a simple manner. We also consider the problem of Lamb waves generated by a set of time-harmonic sources. The obtained computations can be very useful for developing ultrasound-based methods for nondestructive evaluation of composite structures. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lamb%20waves" title="lamb waves">lamb waves</a>, <a href="https://publications.waset.org/abstracts/search?q=fiber-reinforced%20composite%20plates" title=" fiber-reinforced composite plates"> fiber-reinforced composite plates</a>, <a href="https://publications.waset.org/abstracts/search?q=dispersion%20equations" title=" dispersion equations"> dispersion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nondestructive%20evaluation" title=" nondestructive evaluation"> nondestructive evaluation</a>, <a href="https://publications.waset.org/abstracts/search?q=reciprocity%20theorems" title=" reciprocity theorems"> reciprocity theorems</a> </p> <a href="https://publications.waset.org/abstracts/110250/study-of-ultrasonic-waves-in-unidirectional-fiber-reinforced-composite-plates-for-the-aerospace-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/110250.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">149</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2089</span> Some Inequalities Related with Starlike Log-Harmonic Mappings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Melike%20Aydo%C4%9Fan">Melike Aydoğan</a>, <a href="https://publications.waset.org/abstracts/search?q=D%C3%BCrdane%20%C3%96zt%C3%BCrk"> Dürdane Öztürk</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let H(D) be the linear space of all analytic functions defined on the open unit disc. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential equation where w(z) ∈ H(D) is second dilatation such that |w(z)| < 1 for all z ∈ D. The aim of this paper is to define some inequalities of starlike logharmonic functions of order α(0 ≤ α ≤ 1). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=starlike%20log-harmonic%20functions" title="starlike log-harmonic functions">starlike log-harmonic functions</a>, <a href="https://publications.waset.org/abstracts/search?q=univalent%20functions" title=" univalent functions"> univalent functions</a>, <a href="https://publications.waset.org/abstracts/search?q=distortion%20theorem" title=" distortion theorem"> distortion theorem</a> </p> <a href="https://publications.waset.org/abstracts/22032/some-inequalities-related-with-starlike-log-harmonic-mappings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22032.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2088</span> Global Voltage Harmonic Index for Measuring Harmonic Situation of Power Grids: A Focus on Power Transformers</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Zabihi">Alireza Zabihi</a>, <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Peyghami"> Saeed Peyghami</a>, <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Mokhtari"> Hossein Mokhtari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> With the increasing deployment of renewable power plants, such as solar and wind, it is crucial to measure the harmonic situation of the grid. This paper proposes a global voltage harmonic index to measure the harmonic situation of the power grid with a focus on power transformers. The power electronics systems used to connect these plants to the network can introduce harmonics, leading to increased losses, reduced efficiency, false operation of protective relays, and equipment damage due to harmonic intensifications. The proposed index considers the losses caused by harmonics in power transformers which are of great importance and value to the network, providing a comprehensive measure of the harmonic situation of the grid. The effectiveness of the proposed index is evaluated on a real-world distribution network, and the results demonstrate its ability to identify the harmonic situation of the network, particularly in relation to power transformers. The proposed index provides a comprehensive measure of the harmonic situation of the grid, taking into account the losses caused by harmonics in power transformers. The proposed index has the potential to support power companies in optimizing their power systems and to guide researchers in developing effective mitigation strategies for harmonics in the power grid. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=global%20voltage%20harmonic%20index" title="global voltage harmonic index">global voltage harmonic index</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonics" title=" harmonics"> harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20grid" title=" power grid"> power grid</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20transformers" title=" power transformers"> power transformers</a>, <a href="https://publications.waset.org/abstracts/search?q=renewable%20energy" title=" renewable energy"> renewable energy</a> </p> <a href="https://publications.waset.org/abstracts/169470/global-voltage-harmonic-index-for-measuring-harmonic-situation-of-power-grids-a-focus-on-power-transformers" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/169470.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">127</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2087</span> Identification of Transformer Core Vibrations and the Effect of Third Harmonic in the Electricity Grid</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Setareh%20Gorji%20Ghalamestani">Setareh Gorji Ghalamestani</a>, <a href="https://publications.waset.org/abstracts/search?q=Lieven%20Vandevelde"> Lieven Vandevelde</a>, <a href="https://publications.waset.org/abstracts/search?q=Jan%20Melkebeek"> Jan Melkebeek</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, an experimental technique is applied for the measurements of the vibrations and deformation of a test transformer core. Since the grid voltage contains some higher harmonics, in addition to a purely sinusoidal magnetisation of the core the presence of third harmonic is also studied. The vibrations of the transformer core for points as well as the surface scan of the leg show more deformation in the corners of the leg than the middle of the leg. The influence of the higher harmonic of the magnetisation on the core deformation is also more significant in the corners of the leg. The core deformation shape under a sinusoidal magnetisation with a higher harmonic is more wavy and fluctuating than that under a purely sinusoidal magnetisation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=vibrations%20and%20noise" title="vibrations and noise">vibrations and noise</a>, <a href="https://publications.waset.org/abstracts/search?q=transformer" title=" transformer"> transformer</a>, <a href="https://publications.waset.org/abstracts/search?q=vibration%20measurements" title=" vibration measurements"> vibration measurements</a>, <a href="https://publications.waset.org/abstracts/search?q=laser%20vibrometer" title=" laser vibrometer"> laser vibrometer</a>, <a href="https://publications.waset.org/abstracts/search?q=higher%20harmonic" title=" higher harmonic "> higher harmonic </a> </p> <a href="https://publications.waset.org/abstracts/6336/identification-of-transformer-core-vibrations-and-the-effect-of-third-harmonic-in-the-electricity-grid" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/6336.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2086</span> Third Super-Harmonic Resonance in Vortex-Induced Vibration of a Pipeline Close to the Seabed</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yiming%20Jin">Yiming Jin</a>, <a href="https://publications.waset.org/abstracts/search?q=Ping%20Dong"> Ping Dong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The third super-harmonic resonance of a pipeline close to the seabed is investigated in this paper. To analyse the vortex-induced vibration (VIV) of the pipeline close to the seabed, the classic Van der Pol equation is extended with a nonlinear item. Then, on the base of the multi-scale method, the frequency-response curves of the pipeline with regard to the third super-harmonic resonance are studied with a series of parameters, such as the mass ratio, frequency, damp ratio and gap ratio. On the whole, the numerical results show that the characters of third super-harmonic resonance are quite from that of primary resonance, though with the same trend that the larger is the mass ratio, the smaller impact the gap ratio has on the frequency-response curves of the third super-harmonic resonance. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=the%20third%20super-harmonic%20resonance" title="the third super-harmonic resonance">the third super-harmonic resonance</a>, <a href="https://publications.waset.org/abstracts/search?q=gap%20ratio" title=" gap ratio"> gap ratio</a>, <a href="https://publications.waset.org/abstracts/search?q=vortex-induced%20vibration" title=" vortex-induced vibration"> vortex-induced vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=multi-scale%20method" title=" multi-scale method"> multi-scale method</a> </p> <a href="https://publications.waset.org/abstracts/42056/third-super-harmonic-resonance-in-vortex-induced-vibration-of-a-pipeline-close-to-the-seabed" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/42056.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2085</span> Harmonic Mitigation and Total Harmonic Distortion Reduction in Grid-Connected PV Systems: A Case Study Using Real-Time Data and Filtering Techniques</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Atena%20Tazikeh%20Lemeski">Atena Tazikeh Lemeski</a>, <a href="https://publications.waset.org/abstracts/search?q=Ismail%20Ozdamar"> Ismail Ozdamar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents a detailed analysis of harmonic distortion in a grid-connected photovoltaic (PV) system using real-time data captured from a solar power plant. Harmonics introduced by inverters in PV systems can degrade power quality and lead to increased Total Harmonic Distortion (THD), which poses challenges such as transformer overheating, increased power losses, and potential grid instability. This research addresses these issues by applying Fast Fourier Transform (FFT) to identify significant harmonic components and employing notch filters to target specific frequencies, particularly the 3rd harmonic (150 Hz), which was identified as the largest contributor to THD. Initial analysis of the unfiltered voltage signal revealed a THD of 21.15%, with prominent harmonic peaks at 150 Hz, 250 Hz and 350 Hz, corresponding to the 3rd, 5th, and 7th harmonics, respectively. After implementing the notch filters, the THD was reduced to 5.72%, demonstrating the effectiveness of this approach in mitigating harmonic distortion without affecting the fundamental frequency. This paper provides practical insights into the application of real-time filtering techniques in PV systems and their role in improving overall grid stability and power quality. The results indicate that targeted harmonic mitigation is crucial for the sustainable integration of renewable energy sources into modern electrical grids. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=grid-connected%20photovoltaic%20systems" title="grid-connected photovoltaic systems">grid-connected photovoltaic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=fast%20Fourier%20transform" title=" fast Fourier transform"> fast Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20filtering" title=" harmonic filtering"> harmonic filtering</a>, <a href="https://publications.waset.org/abstracts/search?q=inverter-induced%20harmonics" title=" inverter-induced harmonics"> inverter-induced harmonics</a> </p> <a href="https://publications.waset.org/abstracts/192300/harmonic-mitigation-and-total-harmonic-distortion-reduction-in-grid-connected-pv-systems-a-case-study-using-real-time-data-and-filtering-techniques" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/192300.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">34</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2084</span> Estimation of Harmonics in Three-Phase and Six-Phase-Phase (Multi-Phase) Load Circuits</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zakir%20Husain">Zakir Husain</a>, <a href="https://publications.waset.org/abstracts/search?q=Deepak%20Kumar"> Deepak Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The harmonics are very harmful within an electrical system and can have serious consequences such as reducing the life of apparatus, stress on cable and equipment etc. This paper cites extensive analytical study of harmonic characteristics of multiphase (six-phase) and three-phase system equipped with two and three level inverters for non-linear loads. Multilevel inverter has elevated voltage capability with voltage limited devices, low harmonic distortion, abridged switching losses. Multiphase technology also pays a promising role in harmonic reduction. Matlab simulation is carried out to compare the advantage of multi-phase over three phase systems equipped with two or three level inverters for non-linear load harmonic reduction. The extensive simulation results are presented based on case studies. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fast%20Fourier%20transform%20%28FFT%29" title="fast Fourier transform (FFT)">fast Fourier transform (FFT)</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonics" title=" harmonics"> harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=inverter" title=" inverter"> inverter</a>, <a href="https://publications.waset.org/abstracts/search?q=ripples" title=" ripples"> ripples</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20harmonic%20distortion%20%28THD%29" title=" total harmonic distortion (THD)"> total harmonic distortion (THD)</a> </p> <a href="https://publications.waset.org/abstracts/11824/estimation-of-harmonics-in-three-phase-and-six-phase-phase-multi-phase-load-circuits" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11824.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">552</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2083</span> Validation of Solar PV Inverter Harmonics Behaviour at Different Power Levels in a Test Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Wilfred%20Fritz">Wilfred Fritz </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonics" title="harmonics">harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=pulse%20width%20modulation" title=" pulse width modulation"> pulse width modulation</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20harmonic%20distortion" title=" total harmonic distortion"> total harmonic distortion</a> </p> <a href="https://publications.waset.org/abstracts/96827/validation-of-solar-pv-inverter-harmonics-behaviour-at-different-power-levels-in-a-test-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96827.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">239</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2082</span> Impact of Harmonic Resonance and V-THD in Sohar Industrial Port–C Substation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=R.%20S.%20Al%20Abri">R. S. Al Abri</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20H.%20Albadi"> M. H. Albadi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20H.%20Al%20Abri"> M. H. Al Abri</a>, <a href="https://publications.waset.org/abstracts/search?q=U.%20K.%20Al%20Rasbi"> U. K. Al Rasbi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20H.%20Al%20Hasni"> M. H. Al Hasni</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20M.%20Al%20Shidi"> S. M. Al Shidi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents an analysis study on the impacts of the changes of the capacitor banks, the loss of a transformer, and the installation of distributed generation on the voltage total harmonic distortion and harmonic resonance. The study is applied in a real system in Oman, Sohar Industrial Port–C Substation Network. Frequency scan method and Fourier series analysis method are used with the help of EDSA software. Moreover, the results are compared with limits specified by national Oman distribution code. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title="power quality">power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=capacitor%20bank" title=" capacitor bank"> capacitor bank</a>, <a href="https://publications.waset.org/abstracts/search?q=voltage%20total%20harmonics%20distortion" title=" voltage total harmonics distortion"> voltage total harmonics distortion</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20resonance" title=" harmonic resonance"> harmonic resonance</a>, <a href="https://publications.waset.org/abstracts/search?q=frequency%20scan" title=" frequency scan"> frequency scan</a> </p> <a href="https://publications.waset.org/abstracts/35249/impact-of-harmonic-resonance-and-v-thd-in-sohar-industrial-port-c-substation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35249.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">617</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2081</span> Optimal Harmonic Filters Design of Taiwan High Speed Rail Traction System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ying-Pin%20Chang">Ying-Pin Chang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a method for combining a particle swarm optimization with nonlinear time-varying evolution and orthogonal arrays (PSO-NTVEOA) in the planning of harmonic filters for the high speed railway traction system with specially connected transformers in unbalanced three-phase power systems. The objective is to minimize the cost of the filter, the filters loss, the total harmonic distortion of currents and voltages at each bus simultaneously. An orthogonal array is first conducted to obtain the initial solution set. The set is then treated as the initial training sample. Next, the PSO-NTVEOA method parameters are determined by using matrix experiments with an orthogonal array, in which a minimal number of experiments would have an effect that approximates the full factorial experiments. This PSO-NTVEOA method is then applied to design optimal harmonic filters in Taiwan High Speed Rail (THSR) traction system, where both rectifiers and inverters with IGBT are used. From the results of the illustrative examples, the feasibility of the PSO-NTVEOA to design an optimal passive harmonic filter of THSR system is verified and the design approach can greatly reduce the harmonic distortion. Three design schemes are compared that V-V connection suppressing the 3rd order harmonic, and Scott and Le Blanc connection for the harmonic improvement is better than the V-V connection. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20filters" title="harmonic filters">harmonic filters</a>, <a href="https://publications.waset.org/abstracts/search?q=particle%20swarm%20optimization" title=" particle swarm optimization"> particle swarm optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20time-varying%20evolution" title=" nonlinear time-varying evolution"> nonlinear time-varying evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=orthogonal%20arrays" title=" orthogonal arrays"> orthogonal arrays</a>, <a href="https://publications.waset.org/abstracts/search?q=specially%20connected%20transformers" title=" specially connected transformers"> specially connected transformers</a> </p> <a href="https://publications.waset.org/abstracts/3435/optimal-harmonic-filters-design-of-taiwan-high-speed-rail-traction-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3435.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">392</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2080</span> Classification of Equations of Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amritpal%20Singh%20Nafria">Amritpal Singh Nafria</a>, <a href="https://publications.waset.org/abstracts/search?q=Rohit%20Sharma"> Rohit Sharma</a>, <a href="https://publications.waset.org/abstracts/search?q=Md.%20Shami%20Ansari"> Md. Shami Ansari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=velocity-time%20graph" title="velocity-time graph">velocity-time graph</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental%20equations" title=" fundamental equations"> fundamental equations</a>, <a href="https://publications.waset.org/abstracts/search?q=additional%20equations" title=" additional equations"> additional equations</a>, <a href="https://publications.waset.org/abstracts/search?q=requisite%20conditions" title=" requisite conditions"> requisite conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=importance%20and%20educational%20benefits" title=" importance and educational benefits"> importance and educational benefits</a> </p> <a href="https://publications.waset.org/abstracts/15102/classification-of-equations-of-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15102.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">787</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2079</span> A Novel Idea to Benefit of the Load Side’s Harmonics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hussein%20Al-bayaty">Hussein Al-bayaty</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a novel idea to show the ability to benefit of the harmonic currents which are produced on the load side of the power grid. The proposed circuit contributes in reduction of the total harmonic distortion (THD) percentage through adding a high pass filter to draw harmonic currents with 150 Hz and multiple frequencies a and convert them to DC current and then reconvert it to AC current with 50 Hz frequency in order to feed different loads. The circuit has been designed, investigated and simulated in the MATLAB, Simulink program; the results will be assessed and compared the two cases: firstly, the system without adding the new circuit. Secondly, with adding the high pas filter circuit to the power system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonics%20elimination" title="harmonics elimination">harmonics elimination</a>, <a href="https://publications.waset.org/abstracts/search?q=passive%20filters" title=" passive filters"> passive filters</a>, <a href="https://publications.waset.org/abstracts/search?q=Total%20Harmonic%20Distortion%20%28THD%29" title=" Total Harmonic Distortion (THD)"> Total Harmonic Distortion (THD)</a>, <a href="https://publications.waset.org/abstracts/search?q=filter%20circuit" title=" filter circuit"> filter circuit</a> </p> <a href="https://publications.waset.org/abstracts/14148/a-novel-idea-to-benefit-of-the-load-sides-harmonics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/14148.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">413</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2078</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">209</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2077</span> Technical and Economic Evaluation of Harmonic Mitigation from Offshore Wind Power Plants by Transmission Owners</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Prajapati">A. Prajapati</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20L.%20Koo"> K. L. Koo</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Ghassemi"> F. Ghassemi</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Mulimakwenda"> M. Mulimakwenda</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the UK, as the volume of non-linear loads connected to transmission grid continues to rise steeply, the harmonic distortion levels on transmission network are becoming a serious concern for the network owners and system operators. This paper outlines the findings of the study conducted to verify the proposal that the harmonic mitigation could be optimized and can be managed economically and effectively at the transmission network level by the Transmission Owner (TO) instead of the individual polluter connected to the grid. Harmonic mitigation studies were conducted on selected regions of the transmission network in England for recently connected offshore wind power plants to strategize and optimize selected harmonic filter options. The results – filter volume and capacity – were then compared against the mitigation measures adopted by the individual connections. Estimation ratios were developed based on the actual installed and optimal proposed filters. These estimation ratios were then used to derive harmonic filter requirements for future contracted connections. The study has concluded that a saving of 37% in the filter volume/capacity could be achieved if the TO is to centrally manage the harmonic mitigation instead of individual polluter installing their own mitigation solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=C-type%20filter" title="C-type filter">C-type filter</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonics" title=" harmonics"> harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=offshore%20wind%20farms" title=" offshore wind farms"> offshore wind farms</a>, <a href="https://publications.waset.org/abstracts/search?q=interconnectors" title=" interconnectors"> interconnectors</a>, <a href="https://publications.waset.org/abstracts/search?q=HVDC" title=" HVDC"> HVDC</a>, <a href="https://publications.waset.org/abstracts/search?q=renewable%20energy" title=" renewable energy"> renewable energy</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20owner" title=" transmission owner"> transmission owner</a> </p> <a href="https://publications.waset.org/abstracts/98379/technical-and-economic-evaluation-of-harmonic-mitigation-from-offshore-wind-power-plants-by-transmission-owners" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/98379.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">157</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2076</span> Harmonic Data Preparation for Clustering and Classification</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Asheibi">Ali Asheibi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The rapid increase in the size of databases required to store power quality monitoring data has demanded new techniques for analysing and understanding the data. One suggested technique to assist in analysis is data mining. Preparing raw data to be ready for data mining exploration take up most of the effort and time spent in the whole data mining process. Clustering is an important technique in data mining and machine learning in which underlying and meaningful groups of data are discovered. Large amounts of harmonic data have been collected from an actual harmonic monitoring system in a distribution system in Australia for three years. This amount of acquired data makes it difficult to identify operational events that significantly impact the harmonics generated on the system. In this paper, harmonic data preparation processes to better understanding of the data have been presented. Underlying classes in this data has then been identified using clustering technique based on the Minimum Message Length (MML) method. The underlying operational information contained within the clusters can be rapidly visualised by the engineers. The C5.0 algorithm was used for classification and interpretation of the generated clusters. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=data%20mining" title="data mining">data mining</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20data" title=" harmonic data"> harmonic data</a>, <a href="https://publications.waset.org/abstracts/search?q=clustering" title=" clustering"> clustering</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a> </p> <a href="https://publications.waset.org/abstracts/80801/harmonic-data-preparation-for-clustering-and-classification" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80801.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">248</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2075</span> Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gulgassyl%20Nugmanova">Gulgassyl Nugmanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhanat%20Zhunussova"> Zhanat Zhunussova</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmakhanova"> Kuralay Yesmakhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Galya%20Mamyrbekova"> Galya Mamyrbekova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Heisenberg%20Ferromagnet%20equations" title="Heisenberg Ferromagnet equations">Heisenberg Ferromagnet equations</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20equations" title=" soliton equations"> soliton equations</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalence" title=" equivalence"> equivalence</a>, <a href="https://publications.waset.org/abstracts/search?q=Lax%20representation" title=" Lax representation"> Lax representation</a> </p> <a href="https://publications.waset.org/abstracts/27440/integrable-heisenberg-ferromagnet-equations-with-self-consistent-potentials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27440.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">457</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2074</span> Execution of Optimization Algorithm in Cascaded H-Bridge Multilevel Inverter</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Suresh%20Kumar">M. Suresh Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Ramani"> K. Ramani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper proposed the harmonic elimination of Cascaded H-Bridge Multi-Level Inverter by using Selective Harmonic Elimination-Pulse Width Modulation method programmed with Particle Swarm Optimization algorithm. PSO method determine proficiently the required switching angles to eliminate low order harmonics up to the 11th order from the inverter output voltage waveform while keeping the magnitude of the fundamental harmonics at the desired value. Results demonstrate that the proposed method does efficiently eliminate a great number of specific harmonics and the output voltage is resulted in minimum Total Harmonic Distortion. The results shown that the PSO algorithm attain successfully to the global solution faster than other algorithms. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-level%20inverter" title="multi-level inverter">multi-level inverter</a>, <a href="https://publications.waset.org/abstracts/search?q=Selective%20Harmonic%20Elimination%20Pulse%20Width%20Modulation%20%28SHEPWM%29" title=" Selective Harmonic Elimination Pulse Width Modulation (SHEPWM)"> Selective Harmonic Elimination Pulse Width Modulation (SHEPWM)</a>, <a href="https://publications.waset.org/abstracts/search?q=Particle%20Swarm%20Optimization%20%28PSO%29" title=" Particle Swarm Optimization (PSO)"> Particle Swarm Optimization (PSO)</a>, <a href="https://publications.waset.org/abstracts/search?q=Total%20Harmonic%20Distortion%20%28THD%29" title=" Total Harmonic Distortion (THD)"> Total Harmonic Distortion (THD)</a> </p> <a href="https://publications.waset.org/abstracts/20709/execution-of-optimization-algorithm-in-cascaded-h-bridge-multilevel-inverter" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20709.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">603</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2073</span> Harmonic Distortion Analysis in Low Voltage Grid with Grid-Connected Photovoltaic</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hedi%20Dghim">Hedi Dghim</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmed%20El-Naggar"> Ahmed El-Naggar</a>, <a href="https://publications.waset.org/abstracts/search?q=Istvan%20Erlich"> Istvan Erlich</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Power electronic converters are being introduced in low voltage (LV) grids at an increasingly rapid rate due to the growing adoption of power electronic-based home appliances in residential grid. Photovoltaic (PV) systems are considered one of the potential installed renewable energy sources in distribution power systems. This trend has led to high distortion in the supply voltage which consequently produces harmonic currents in the network and causes an inherent voltage unbalance. In order to investigate the effect of harmonic distortions, a case study of a typical LV grid configuration with high penetration of 3-phase and 1-phase rooftop mounted PV from southern Germany was first considered. Electromagnetic transient (EMT) simulations were then carried out under the MATLAB/Simulink environment which contain detailed models for power electronic-based loads, ohmic-based loads as well as 1- and 3-phase PV. Note that, the switching patterns of the power electronic circuits were considered in this study. Measurements were eventually performed to analyze the distortion levels when PV operating under different solar irradiance. The characteristics of the load-side harmonic impedances were analyzed, and their harmonic contributions were evaluated for different distortion levels. The effect of the high penetration of PV on the harmonic distortion of both positive and negative sequences was also investigated. The simulation results are presented based on case studies. The current distortion levels are in agreement with relevant standards, otherwise the Total Harmonic Distortion (THD) increases under low PV power generation due to its inverse relation with the fundamental current. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20distortion%20analysis" title="harmonic distortion analysis">harmonic distortion analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=PV%20systems" title=" PV systems"> PV systems</a>, <a href="https://publications.waset.org/abstracts/search?q=residential%20distribution%20system" title=" residential distribution system"> residential distribution system</a> </p> <a href="https://publications.waset.org/abstracts/96165/harmonic-distortion-analysis-in-low-voltage-grid-with-grid-connected-photovoltaic" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/96165.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">267</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2072</span> Mathematics Vision of the Companies' Growth with Educational Technologies</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Valencia%20P.%20L.%20Rodrigo">Valencia P. L. Rodrigo</a>, <a href="https://publications.waset.org/abstracts/search?q=Morita%20A.%20Adelina"> Morita A. Adelina</a>, <a href="https://publications.waset.org/abstracts/search?q=Vargas%20V.%20Martin"> Vargas V. Martin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This proposal consists of an analysis of macro concepts involved within an organization growth using educational technologies, which will relate each concept, in a mathematical way with a vision of harmonic work. Working collaboratively, competitively and cooperatively so that this growth is harmonious and homogenous, coining a new term, Harmonic Work. The Harmonic Work ensures that the organization grows in all business directions, allowing managers to project a much more accurate growth, making clear the contribution of each department, resulting in an algorithm that analyzes each of the variables both endogenous and exogenous, establishing different performance indicators in its process of growth. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=business%20projection" title="business projection">business projection</a>, <a href="https://publications.waset.org/abstracts/search?q=collaboration" title=" collaboration"> collaboration</a>, <a href="https://publications.waset.org/abstracts/search?q=competitiveness" title=" competitiveness"> competitiveness</a>, <a href="https://publications.waset.org/abstracts/search?q=educational%20technology" title=" educational technology"> educational technology</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonious%20growth" title=" harmonious growth"> harmonious growth</a> </p> <a href="https://publications.waset.org/abstracts/78593/mathematics-vision-of-the-companies-growth-with-educational-technologies" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78593.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">321</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2071</span> Application of Single Tuned Passive Filters in Distribution Networks at the Point of Common Coupling</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Almutairi">M. Almutairi</a>, <a href="https://publications.waset.org/abstracts/search?q=S.%20Hadjiloucas"> S. Hadjiloucas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The harmonic distortion of voltage is important in relation to power quality due to the interaction between the large diffusion of non-linear and time-varying single-phase and three-phase loads with power supply systems. However, harmonic distortion levels can be reduced by improving the design of polluting loads or by applying arrangements and adding filters. The application of passive filters is an effective solution that can be used to achieve harmonic mitigation mainly because filters offer high efficiency, simplicity, and are economical. Additionally, possible different frequency response characteristics can work to achieve certain required harmonic filtering targets. With these ideas in mind, the objective of this paper is to determine what size single tuned passive filters work in distribution networks best, in order to economically limit violations caused at a given point of common coupling (PCC). This article suggests that a single tuned passive filter could be employed in typical industrial power systems. Furthermore, constrained optimization can be used to find the optimal sizing of the passive filter in order to reduce both harmonic voltage and harmonic currents in the power system to an acceptable level, and, thus, improve the load power factor. The optimization technique works to minimize voltage total harmonic distortions (VTHD) and current total harmonic distortions (ITHD), where maintaining a given power factor at a specified range is desired. According to the IEEE Standard 519, both indices are viewed as constraints for the optimal passive filter design problem. The performance of this technique will be discussed using numerical examples taken from previous publications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonics" title="harmonics">harmonics</a>, <a href="https://publications.waset.org/abstracts/search?q=passive%20filter" title=" passive filter"> passive filter</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20factor" title=" power factor"> power factor</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a> </p> <a href="https://publications.waset.org/abstracts/65962/application-of-single-tuned-passive-filters-in-distribution-networks-at-the-point-of-common-coupling" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/65962.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">306</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">2070</span> Distribution System Modelling: A Holistic Approach for Harmonic Studies</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Stanislav%20Babaev">Stanislav Babaev</a>, <a href="https://publications.waset.org/abstracts/search?q=Vladimir%20Cuk"> Vladimir Cuk</a>, <a href="https://publications.waset.org/abstracts/search?q=Sjef%20Cobben"> Sjef Cobben</a>, <a href="https://publications.waset.org/abstracts/search?q=Jan%20Desmet"> Jan Desmet</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The procedures for performing harmonic studies for medium-voltage distribution feeders have become relatively mature topics since the early 1980s. The efforts of various electric power engineers and researchers were mainly focused on handling large harmonic non-linear loads connected scarcely at several buses of medium-voltage feeders. In order to assess the impact of these loads on the voltage quality of the distribution system, specific modeling and simulation strategies were proposed. These methodologies could deliver a reasonable estimation accuracy given the requirements of least computational efforts and reduced complexity. To uphold these requirements, certain analysis assumptions have been made, which became de facto standards for establishing guidelines for harmonic analysis. Among others, typical assumptions include balanced conditions of the study and the negligible impact of impedance frequency characteristics of various power system components. In latter, skin and proximity effects are usually omitted, and resistance and reactance values are modeled based on the theoretical equations. Further, the simplifications of the modelling routine have led to the commonly accepted practice of neglecting phase angle diversity effects. This is mainly associated with developed load models, which only in a handful of cases are representing the complete harmonic behavior of a certain device as well as accounting on the harmonic interaction between grid harmonic voltages and harmonic currents. While these modelling practices were proven to be reasonably effective for medium-voltage levels, similar approaches have been adopted for low-voltage distribution systems. Given modern conditions and massive increase in usage of residential electronic devices, recent and ongoing boom of electric vehicles, and large-scale installing of distributed solar power, the harmonics in current low-voltage grids are characterized by high degree of variability and demonstrate sufficient diversity leading to a certain level of cancellation effects. It is obvious, that new modelling algorithms overcoming previously made assumptions have to be accepted. In this work, a simulation approach aimed to deal with some of the typical assumptions is proposed. A practical low-voltage feeder is modeled in PowerFactory. In order to demonstrate the importance of diversity effect and harmonic interaction, previously developed measurement-based models of photovoltaic inverter and battery charger are used as loads. The Python-based script aiming to supply varying voltage background distortion profile and the associated current harmonic response of loads is used as the core of unbalanced simulation. Furthermore, the impact of uncertainty of feeder frequency-impedance characteristics on total harmonic distortion levels is shown along with scenarios involving linear resistive loads, which further alter the impedance of the system. The comparative analysis demonstrates sufficient differences with cases when all the assumptions are in place, and results indicate that new modelling and simulation procedures need to be adopted for low-voltage distribution systems with high penetration of non-linear loads and renewable generation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=electric%20power%20system" title="electric power system">electric power system</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20distortion" title=" harmonic distortion"> harmonic distortion</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20quality" title=" power quality"> power quality</a>, <a href="https://publications.waset.org/abstracts/search?q=public%20low-voltage%20network" title=" public low-voltage network"> public low-voltage network</a>, <a href="https://publications.waset.org/abstracts/search?q=harmonic%20modelling" title=" harmonic modelling"> harmonic modelling</a> </p> <a href="https://publications.waset.org/abstracts/115141/distribution-system-modelling-a-holistic-approach-for-harmonic-studies" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115141.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">159</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=harmonic%20equations&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=harmonic%20equations&page=3">3</a></li> <li class="page-item"><a class="page-link" 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