Improvement of modeling techniques of transients in transformers based on magnetoelectric equivalent schemes

Abstract

Purpose. Use of an improved numerical method of calculating transient processes in electrical circuits for modeling electromagnetic processes in nonlinear magneto-electric circuits, and also development of a circuit model based on this method, which leads to the convenience of calculation. Methodology. Approximation of functions by Chebyshevs polynomials, numerical methods of differential equations integrating, matrix methods, spline interpolation, programming, theory of electric and magnetic circuits. Findings. On the base of the well-known method of transient process analysis in linear electric circuits, the method of numerical calculation of transient processes in nonlinear magneto-electric equivalent circuits of transformer has been developed. By the help of the proposed method it is possible to reduce processing time for modeling electromagnetic processes in transformers. The example of using the developed method is shown. The computer program for modeling of electromagnetic transient in a single-phase transformer based on the described method has been developed. This example shows reduction of processor time by more than four times compared to examples of calculations based on other known methods. Originality. The method in which the solution of state differential equations is presented in the form of decomposition into a series along orthogonal Chebyshevs polynomials is used in this work. The polynomial approximation applied in this work is not corresponding to the solution function itself, but its derivative, which significantly reduces the error of integration of differential equations. Differential equations of state are transformed into linear algebraic equations for special images of solution functions. A principle is developed of constructing magneto-electric substitution circuits in which images of solution functions appear. Images of true dynamic currents and magnetic fluxes in the proposed equivalent scheme are interpreted as direct currents and direct magnetic fluxes. The used method has shown advantages in accuracy and time of simulation of electromagnetic transient over other known methods based on application of magneto-electric substitution circuits. Practical value. The developed method opens up the possibility of using the apparatus of the theory of electric and magnetic circuits to work with images of currents and magnetic fluxes. Based on this, a universal software complex is being developed to calculate transients in transformers of various constructions.