scholarly journals The numerical method of inverse Laplace transform for calculation of overvoltages in power transformers and test results

2014 ◽  
Vol 11 (2) ◽  
pp. 243-256 ◽  
Author(s):  
Jovan Mikulovic ◽  
Tomislav Sekara
Keyword(s):  
Laplace Transform ◽  
Numerical Method ◽  
Power Transformer ◽  
Neutral Point ◽  
Inverse Laplace Transform ◽  
Method Of Calculation ◽  
Distributed Parameters ◽  
Three Phase ◽  
Calculation Results ◽  
Isolated Neutral

A methodology for calculation of overvoltages in transformer windings, based on a numerical method of inverse Laplace transform, is presented. Mathematical model of transformer windings is described by partial differential equations corresponding to distributed parameters electrical circuits. The procedure of calculating overvoltages is applied to windings having either isolated neutral point, or grounded neutral point, or neutral point grounded through impedance. A comparative analysis of the calculation results obtained by the proposed numerical method and by analytical method of calculation of overvoltages in transformer windings is presented. The results computed by the proposed method and measured voltage distributions, when a voltage surge is applied to a three-phase 30 kVA power transformer, are compared.

scholarly journals Optimalisasi Material Utama Pada Auto Transformator 100 MVA

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Asep Saepudin
Keyword(s):  
Power Transformer ◽  
Power Transformers ◽  
Three Phase ◽  
Actual Use ◽  
Calculation Results ◽  
Ordinary Power ◽  
The Difference ◽  
Transformer Core ◽  
Secondary Winding ◽  
Main Material

Autotransformator is a transformer that has primary and secondary winding with the same common winding, so that it has a lighter weight compared to ordinary power transformers. The purpose of this study is to optimize the main material used in the three-phase Auto transformer in order to get the most optimum value approaching the calculation results and to know the comparison between the calculation results and the actual use of the main material in the Auto transformer and three-phase power transformer. The main material in power transformers is copper for winding and silicon steel for cores (transformer cores). Based on this research, it can be concluded that the use of main material in Auto three-phase power transformer is less than the three-phase power transformer for the same voltage and power, the magnitude of the difference in the range of 12.5% ​​for Copper and core (transformer core) range of 47.3% of the main material in the power transformer can.

scholarly journals Solusi Persamaan Transport dengan Menggunakan Metode Dekomposisi Adomian Laplace

2020 ◽  
Vol 2 (2) ◽  
pp. 173
Author(s):  
Wahidah Sanusi ◽  
Syafruddin Side ◽  
Beby Fitriani
Keyword(s):  
Differential Equation ◽  
Laplace Transform ◽  
Transport Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Inverse Laplace Transform ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Calculation Results

Abstrak. Penelitian ini mengkaji terbentuknya persamaan Transport dan menerapkan metode Dekomposisi Adomian Laplace dalam menentukan solusi persamaan Transport. Persamaan transport merupakan salah satu bentuk dari persamaan diferensial parsial. Bentuk umum persamaan Transport yaitu: Metode Dekomposisi Adomian Laplace merupakan kombinasi antara dua metode yaitu  metode dekomposisi adomian dan transformasi laplace. Penyelesaian persamaan Transport dengan metode Dekomposisi Adomian Laplace dilakukan dengan cara menggunakan tranformasi Laplace, mensubstitusi nilai awal, menyatakan solusi dalam bentuk deret tak hingga dan menggunakan invers transformasi laplace . Metode ini juga merupakan metode semi analitik untuk menyelesaikan persamaan diferensial nonlinier. Berdasarkan hasil perhitungan, metode dekomposisi Adomian Laplace dapat menghampiri penyelesaian persamaan diferensial biasa nonlinear.Kata Kunci: Metode Dekomposisi Adomian Laplace, Persamaan Diferensial Parsial, Persamaan Transport.This research discusses the solving of Transport equation applying Laplace Adomian Decomposition Method. Transport equation is one form of partial differential equations. General form of Transport equation is: Laplace Adomian Decomposition Method that combine between Laplace transform and Adomian Decomposition Method. The steps used to solve Transport equation are applying Laplace transform, initial value substitution, defining a solution as infinite series, then using the inverse Laplace transform. This method is a semi analytical method to solve for nonlinear ordinary differential equation. Based on the calculation results, the Laplace Adomian decomposition method can solve the solution of nonlinear ordinary differential equation.Keywords: Laplace Adomian Decomposition Method, Partial Differential Equation, Transport Equation.

scholarly journals Numerical Method for Inverse Laplace Transform with Haar Wavelet Operational Matrix

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Suazlan Mt Aznam ◽  
Amran Hussin
Keyword(s):  
Laplace Transform ◽  
Numerical Method ◽  
Operational Matrix ◽  
Haar Wavelet ◽  
Wavelet Function ◽  
Inverse Laplace Transform ◽  
Orthogonal Wavelet ◽  
Transform Method ◽  
Operational Matrix Method ◽  
Made In

Wavelets have been applied successfully in signal and image processing. Many attempts have been made in mathematics to use orthogonal wavelet function as numerical computational tool. In this work, an orthogonal wavelet function namely Haar wavelet function is considered. We present a numerical method for inversion of Laplace transform using the method of Haar wavelet operational matrix for integration. We proved the method for the cases of the irrational transfer function using the extension of Riemenn-Liouville fractional integral. The proposed method extends the work of J.L.Wu et al. (2001) to cover the whole of time domain. Moreover, this work gives an alternative way to find the solution for inversion of Laplace transform in a faster way. The use of numerical Haar operational matrix method is much simpler than the conventional contour integration method and it can be easily coded. Additionally, few benefits come from its great features such as faster computation and attractiveness. Numerical results demonstrate good performance of the method in term of accuracy and competitiveness compare to analytical solution. Examples on solving differential equation by Laplace transform method are also given.

STUDY OF ELECTROCUTION HAZARDS IN THREE-PHASE ELECTRICAL NETWORKS WITH GROUND-ISOLATED NEUTRAL POINT

2012 ◽  
Vol 11 (7) ◽  
pp. 1267-1271 ◽  
Author(s):  
Vlad Pasculescu ◽  
Dragos Pasculescu ◽  
Leonard Lupu ◽  
Ioan Inisconi ◽  
Marius Suvar
Keyword(s):  
Neutral Point ◽  
Electrical Networks ◽  
Three Phase ◽  
Isolated Neutral

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

scholarly journals Approximation of linear one dimensional partial differential equations including fractional derivative with non-singular kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Raheel Kamal ◽  
Kamran ◽  
Gul Rahmat ◽  
Ali Ahmadian ◽  
Noreen Izza Arshad ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Meshless Method ◽  
Inverse Laplace Transform ◽  
Contour Integral ◽  
Partial Differential ◽  
One Dimensional ◽  
The Laplace Transform

AbstractIn this article we propose a hybrid method based on a local meshless method and the Laplace transform for approximating the solution of linear one dimensional partial differential equations in the sense of the Caputo–Fabrizio fractional derivative. In our numerical scheme the Laplace transform is used to avoid the time stepping procedure, and the local meshless method is used to produce sparse differentiation matrices and avoid the ill conditioning issues resulting in global meshless methods. Our numerical method comprises three steps. In the first step we transform the given equation to an equivalent time independent equation. Secondly the reduced equation is solved via a local meshless method. Finally, the solution of the original equation is obtained via the inverse Laplace transform by representing it as a contour integral in the complex left half plane. The contour integral is then approximated using the trapezoidal rule. The stability and convergence of the method are discussed. The efficiency, efficacy, and accuracy of the proposed method are assessed using four different problems. Numerical approximations of these problems are obtained and validated against exact solutions. The obtained results show that the proposed method can solve such types of problems efficiently.

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