![]() ![]() The fundamentals of the spectral method using the Chebyshev polynomials for integrating differential equations are given, and the advantages of this method over the finite difference method are shown in. The author considers the terms “interpolation” and “collocation” to be identical, but the term “interpolation” is used to represent a known function, and the term “collocation” is used for expansion into the series of a function resulting from solving a differential equation. The investigation of the convergence speed of the series is presented in this paper. This is due to the analogy of the function’s expansion into Fourier series of trigonometric functions, where the set of expansion coefficients is the frequency spectrum. The method of decomposing functions into a series of orthogonal polynomials is called the spectral method in this work. The set of orthogonal functions constitutes the basis over which an arbitrary continuous function can be decomposed. ![]() Orthogonal functions are a set of functions for which the scalar product of each pair is zero. The perspective of using orthogonal polynomials for integrating differential equations is shown in. Therefore, the actual scientific task is the development of improved numerical methods for calculating electromagnetic transients that are faster than existing methods. Modern requests of design engineers are required to increase the speed of calculations for realizing a real-time simulation. As a result, the simulation time of such processes can be long, which is undesirable. The duration of transients in complex circuits can be large. The investigated electrical circuits of real devices usually contain a great number of elements. These equations are integro-differential algebraic equations. The equations of state in these software systems are compiled automatically based on the circuit diagram. A number of well-known commercial software systems, such as EMTP, PSpice, Simulink, and others are currently used for modeling transients in electrical circuits. Until now, the development and improvement of methods for studying transients have not lost their relevance. This leads to dangerous current surges and overvoltages, which pose a significant danger to equipment, and also reduce the reliability of used protection. This leads to dangerous current surges and overvoltages representing a significant danger to the equipment, and also reduces the reliability of the protection system. The calculation of the process in the circuit over a long time interval showed a decrease and stabilization of errors, which indicates the prospects for using research methods for calculating complex electrical circuits.Įlectromagnetic transients occur in electrical systems because of switching and impulse actions. The advantages of the presented method over other known methods are to reduce the simulation time of electromagnetic transients (for the considered examples by more than 6 times) while ensuring the required accuracy. The performed comparison of methods made it possible to choose the best method and a way to use it. A computer program for simulating the transient process in an electrical circuit was developed on the basis of the described methods. The images of true current functions are interpreted as direct currents in the proposed equivalent circuit. The developed circuit model simplifies the calculation method. The proposed method made it possible to convert integro-differential equations of state into linear algebraic equations for images of time-dependent functions. Methods for calculating transients in electrical circuits based on the approximation of solution functions by series in algebraic polynomials as well as in the Chebyshev, Hermite and Legendre polynomials, have been developed and investigated. Approximation of functions by orthogonal polynomials, numerical methods for integrating differential equations, matrix methods, programming and theory of electrical circuits. The purpose of the work is to offer electrical engineers a method that can significantly reduce the time for modeling transients in electrical circuits. This work is devoted to the development of a unified spectral method for calculating electromagnetic transients in electrical circuits based on the representation of solution functions by series in algebraic and orthogonal polynomials. Modern requests of design engineers require an increase in the speed of calculations for realizing a real-time simulation. Simulation time is significantly increased if the circuit in the study is complex, and also if this circuit is described by a rigid system of state equations. Long electromagnetic transients occur in electrical systems because of switching and impulse actions As a result, the simulation time of such processes can be long, which is undesirable. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |