Transients In Electrical Circuits Research Articles

NEURAL NETWORK SIGNAL PROCESSING: THE TASKS WITHOUT “DEEP LEARNING”

The purpose of the study is to evaluate the possibility of using artificial neural networks for electrical signals processing.
 
 Methods. The application of a multilayer perceptron for these purposes as the simplest neural feed forward network is considered. Its difference as the basis of neural network algorithms is that when analyzing dynamic processes, signal processing should be carried out in a “sliding time window”.
 
 Results. It is shown that neural network processing makes it possible to approximate the shape of the signal with high accuracy and determine its parameters in real time. Using the example of periodic signals and transients in electrical circuits, accuracy assessments are made and the features of neural network processing are analyzed. The necessary sizes of the training sample of signals and the level of errors that occur when testing a neural network are discussed. Estimates of the required signal sampling frequency, the “sliding window” duration and the variation range of signal parameters when creating a training sample are given.
 
 Conclusions. It is shown that the proposed approach does not require “deep learning” of neural networks with complex architecture. It enables to create a signals training sample based on simple analytical formulas and to control the neural network algorithm quality at intermediate stages of calculations.

ANALYSIS OF PROCESSES IN CONVERTER WITH TWENTY-ZONE VOLTAGE REGULATION ANDACTIVE-INDUCTIVE LOAD

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for fifteen zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

Development and Research of Method in the Calculation of Transients in Electrical Circuits Based on Polynomials

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. 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. Modern requests of design engineers require an increase in the speed of calculations for realizing a real-time simulation. 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. The purpose of the work is to offer electrical engineers a method that can significantly reduce the time for modeling transients in electrical circuits. Research methods. Approximation of functions by orthogonal polynomials, numerical methods for integrating differential equations, matrix methods, programming and theory of electrical circuits. Obtained results. 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. The proposed method made it possible to convert integro-differential equations of state into linear algebraic equations for images of time-dependent functions. The developed circuit model simplifies the calculation method. The images of true current functions are interpreted as direct currents in the proposed equivalent circuit. A computer program for simulating the transient process in an electrical circuit was developed on the basis of the described methods. The performed comparison of methods made it possible to choose the best method and a way to use it. 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 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.

Using customizable simulation models of high voltage electrical circuits in educational process

In the modern world, the issue of the use of digital technologies in the framework of teaching students in technical specialties is relevant. For a number of reasons, the solution of this issue is particularly important when preparing for training areas related to the electric power industry and high-voltage equipment. Software products that allow to carry out simulation modeling of technical systems are among the most accessible types of digital technologies used in higher educational institutions of Russia. When conducting classes on the study of transients in electrical circuits or electric drive control systems, students can use specialized software and build simulation models in the absence of real physical equipment. The paper assesses the need for training in the creation and use of simulation models of devices used in conducting high-voltage tests (using the example of a generator capable of realizing a high voltage of a given shape), as well as models of control systems of electric drives. An additional advantage contributing to the use of such schemes in teaching students is that the result of their work are the values of physical parameters presented in numerical form, which allows the developed models to be used as blocks or libraries for the implementation of larger-scale projects. A team of authors from the branch of the federal state budgetary educational institution of higher education “Murmansk Arctic State University”, Russia and the federal state autonomous educational institution of higher education “Murmansk State Technical University”, Russia process.

INVERTER MATHEMATICAL MODEL THREE-PHASE VOLTAGE TO DC WITH SIXTEEN ZONE REGULATION VOLTAGE

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for fifteen zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

Research of processes in a converter with four-zone voltage regulation and electromechanical load

The new mathematical models of the electromagnetic processes is designed in three-phase electric circuit of the semiconductor converters with many-server zoned regulation phases voltages disregarding losses in semiconductor commutator for quick estimation of the influence parameter loads on level and form of the output voltage. mathematical model of the semiconductor converter is also used for study of the connecting processes in semiconductor converter with actively-inductive load. Will develop the method multivariable function, what fall into algorithmic equations of the analysis formed and connecting processes in furcated electric circuit with semiconductor commutator and reactive element, toward account of the particularities of the use phase and linear voltages to network of the power supply. Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for eleven zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created.

MATHEMATICAL MODEL OF A TWELVE-PULSE CONVERTER WITH SIXTEEN ZONE CONTROL OF THE OUTPUT VOLTAGE AND ACTIVE-INDUCTIVE LOADS

Analysis of the electromagnetic processes is organized in this article in electric circuit with semiconductor commutator. Mathematical model twelve pulses of the converter is created for analysis of the electromagnetic processes in semiconductor converter with width-pulse regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method multivariable function was used when performing calculation. The mathematical model of the converter is created for five zoned regulations of the output voltage. Using method multivariable function was found current and voltage of the load, as well as input currents of the converter. The load of the converter has actively inductive nature. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

STUDY OF CONVERTER WITH FIFTEEN ZONE REGULATION VOLTAGEAND ACTIVE-INDUCTIVE LOADS

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for fifteen zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub- system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

Analysis of processes in converter with eleven zone regulation output voltage


 
 
 Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator . Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for eleven zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub- system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width- pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.
 
 

Skin Effect in Coaxial Conductors of Pulse Facilities

The article presents the results of the study of the skin effect in coaxial conductors of pulsed facilities. The analytical expressions for skin parameters of the coaxial conductors are deduced, and the methods for measurement of these parameters are described by the example of coaxial cables. Transients in electrical circuits with coaxial conductors are researched, and the methods for computation of these transients are described. The measurements of pulse and high-frequency signals in the coaxial cables confirm the correctness of the proposed mathematical models and the computation methods.

АНАЛІЗ ПРОЦЕСІВ У КОЛАХ ІЗ ПЕРЕТВОРЮВАЧАМИ ТРИФАЗНОЇ НАПРУГИ В ПОСТІЙНУ З ДВАНАДЦЯТИЗОННИМ РЕГУЛЮВАННЯМ НАПРУГИ

Urgency of the research. Due to the widespread use of semiconductor switches in the electrical circuits of modern converters of electricity parameters, the tasks of analysis of electromagnetic processes are significantly complicated. The greatest complications arise when it is necessary to model steady-state and transient processes in branched circuits of variable structure, in which links with reactive elements sinusoidal, constant and pulse voltages occur. Target setting. The mathematical model of the converter can be built using the method of multiparameter modulating functions in the direction of developing new mathematical models of electromagnetic processes in circuits with semiconductor switches and links of sinusoidal, direct and pulsed currents. Actual scientific researches and issues analysis. In the publications of M. Makarenko, V. Senko, N. Yurchenko, А. Scherba and other scientists have developed a method of multiparameter functions that simplifies the evaluation of electromagnetic processes in sinusoidal current circuits with semiconductor switches. Uninvestigated parts of general matters defining. There is a need to develop a multiparameter method for the analysis of transients in electrical circuits with links not only sinusoidal, but also direct and pulsed currents required for the implementation of electromechanical and discharge-pulse technologies. The research objective. Creation of a mathematical model for the analysis of electromagnetic processes in a semiconductor converter with multiband regulation of the output voltage when connecting the phase voltages of the power supply network. The statement of basic materials. The article analyzes the electromagnetic processes in electrical circuits with semiconductor switches. A mathematical model for the analysis of electromagnetic processes in semiconductor converters with pulsewidth regulation of the output voltage is created. Conclusions. A new mathematical model for the analysis of electromagnetic processes in electric circuits of semiconductor converters of modulation type with multichannel band use of phase voltages of three-phase power supply network without taking into account power losses in switches is developed.

MODIFICATION OF NUMERAL CALCULATION OF TRANSIENTS IN ELECTRIC CIRCUITS ON BASIS OF TCHEBYSHEV’S POLYNOMIALS

Purpose. Modification of the numerical calculation method of transients in linear electric circuits, as well as the development of a schematic model of the method, leading to ease the calculation and to increase the speed of calculation on a computer..Methodology. Polynomials approximation of functions, numeral methods of solution of integro-differential equations, matrix methods, computer programming and methods of electric circuits theory are used.Findings The improved method of transient calculation is worked out as the modification of the known one. It allows to reduce the computer modeling time of dynamic electric processes in linear electric circuits. The example of the application of the proposed method is shown. Based on the developed method, the computer program was compiled for calculating the transient in the model circuit. This example showed the reduction in CPU time of 45% compared with the use of known methodsOriginality. The approximation of the functions of currents with time by series in the Chebyshev orthogonal polynomials is used. Chebyshev polynomials possess the property of the approximation error uniformity of functions in the entire range of the argument, which distinguishes them from a number of other orthogonal functions. It is proposed to use a polynomial approximation not of the solution functions themselves, but of its derivative. This significantly reduces the approximation error of both the solution function and the derivative of the solution, which appears in the calculation method.. It is shown how, in the proposed method, integro-differential equations of state are transformed into linear algebraic equations. The schematic model of the proposed numerical calculation method is developed. The schematic model allows you to move from an electrical circuit in which processes are described by integro-differential equations to an equivalent circuit with images of currents. Images of true currents in the equivalent circuit are interpreted as direct currents. It is shown that the Kirchhoff laws are valid for current images in the equivalent circuit, which leads to the calculation of a system of algebraic equations. Such a circuit model creates convenience for an engineer performing transient calculations.Practical value. The developed method opens up the possibility of using the entire diverse apparatus of the theory of electric circuits for working with current images. Based on this, a universal software package is developed for calculating transients in electrical circuits of arbitrary

STUDY OF THE ELECTROMAGNETIC PROCESSES IN CONVERTER WITH ELEVEN ZONE REGULATION VOLTAGE

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for twenty zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

Дослідження електромагнітних процесів у перетворювачі з тризонним регулюванням напруги

The article focuses on electromagnetic processes in electric circuits with semiconductor switches. A mathematical model of a semiconductor converter with three-zone output voltage control has been created so as to analyse electromagnetic processes in semiconductor converters with pulsewidth control. The graphs showing electromagnetic processes in electric circuits are given. The mathematical model of the semiconductor converter is also used to study transients in semiconductor converters with actively-inductive load. The method of multiparameter functions, which are included in the algorithmic equations to analyse steady-state and transient processes in branchy circuits with semiconductor switches and reactive elements, has been improved by using the peculiarities of phase and linear voltages in the power supply grid. We have developed a new mathematical model of steadystate and transient processes in electric circuits of semiconductor converters of modulation type with multichannel zone usage of phase voltages of a three-phase power supply system without considering power losses in switches to quickly evaluate the influence of load parameters on the regulated sine and constant voltages. The results of this work can be used to develop the method of multiparameter modulating functions to simplify the analysis of transients in electrical circuits without taking into account the losses in key elements.Ref. 4, pic. 3

Analysis of electromagnetic processes in a converter with a decondon voltage regulation and electromechanical load

The new mathematical models of the electromagnetic processes is designed in three-phase electric circuit of the semiconductor converters with many-server zoned regulation phases voltages disregarding losses in semiconductor commutator for quick estimation of the influence parameter loads on level and form of the output voltage. mathematical model of the semiconductor converter is also used for study of the connecting processes in semiconductor converter with actively-inductive load. Will develop the method multivariable function, what fall into algorithmic equations of the analysis formed and connecting processes in furcated electric circuit with semiconductor commutator and reactive element, toward account of the particularities of the use phase and linear voltages to network of the power supply. Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for twenty zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

Skin Parameter of Massive Conductors and Transients in Electrical Circuits of Pulsed Power Facilities

For massive conductors with the characteristic sizes exceeding the penetration depth of variable or pulse magnetic field, it is possible to define the skin parameter, which affects transients in electrical circuits with massive conductors and does not depend on time and frequency. This paper describes the peculiarities of transients in circuits with massive conductors, defines and justifies the skin parameter, presents the methods of its calculation and measurement, as well as the results of calculation of transients in electrical circuits with massive conductors.

ANALYSIS OF THE ELECTROMAGNETIC PROCESSES IN CONVERTER WITH TWENTY ZONE REGULATION OUTPUT VOLTAGE

Analysis of the electromagnetic processes is organized beside this article in electric circuit with semiconductor commutator. Mathematical model is created for analysis electro-magnetic processes in semiconductor converter with width pulsed regulation of the output voltage. The broughted graphs, which reflect the electromagnetic processes in electric circuit. Method much parametric functions was used when performing calculation. The mathematical model of the converter is created for twenty zoned regulations of the output voltage. Article is devoted to the development of a method of multi-parametric modulating functions by means of working out of new mathematical models and definition of functions and the algorithmic equations for the analysis on sub-system components of electromagnetic processes in electric circuits of variable structure with sinusoidal, direct and pulsing voltage. Introduction of functions with discrete parameters in the algorithmic equations for analysis of processes in circuits with semiconductor commutators simplifies modeling on subsystem components. The mathematical model of steady-state processes and transients in electric circuits of semiconductor converters of modulation type with multi-channel zonal use of phase and line voltages of a three-phase network of power supplies is developed. The mathematical model of electric circuits of thyristor shapers of electro-discharge pulses for the analysis and the matching of capacitors charging modes with decrease several times of electric resistance of technological load is also created. The obtained results have a great value for development theoretical electrical engineering in a direction of simplification of calculations of electromagnetic processes in electric circuits with semi-conductor converters of the electric power. The Electromagnetic processes in electric circuit under width-pulse regulation possible to analyse with use the algorithmic equations multivariable function, which argument are a system parameters semiconductor commutator, signal of control, phases to network of the power supply and time. Introduction multivariable function with discrete parameter in algorithmic equations of the analysis formed and connecting processes in electric circuit of the variable structure allows to reflect change of this structure under system components, simplifying modeling and analysis of such processes to account of the generalization of the got equations. Except specified correlations and diagrams designed model allows to analyse forms of the output voltages and current of the separate power modules.

METHOD OF ACCELERATED NUMERICAL CALCULATION OF TRANSIENTS IN ELECTRICAL CIRCUITS BASED ON SOLUTION APPROXIMATION BY ALGEBRAIC POLYNOMIALS

The work purpose is modification of numerical calculation of transients in electric circuits that reduces the CPU time of calculation, and also development of circuit model method, that creates the convenience in its practical use. The circuit model of the modified numerical calculation of transients in electric circuits is developed. The circuit model created for the electric circuit, in which processes are described with the help of integro-differential equations, turn into the circuit with current images, for which Kirchhoff’s rules, reducing to the algebraic equations, are valid. Time-varying current image is vector, containing the polynomial approximation coefficients. Practical importance. The developed method uncloses the possibility of use of the whole manifold of the circuit theory to work on current images. On the basis of that the universal software package for transient analysis in the complex electric circuits could be designed. Research methods. Polynomial approximation of solution and matrix calculations is used

Calculation of transient processes in electrical circuits using Chebyshev polynomials

Transient electromagnetic processes in electrical systems present a significant risk to machines and influence the reliability of relay protection; therefore, the investigation of these processes is important. Transient modeling in transformers is presently done by construction and solution of state equations for magnetoelectrical equivalent schemes that bring together the electric and magnetic circuits of these devices, taking into account the interaction with each other. Modeling of these processes can be quite long when using modern software. An aim of the given work is development of more fast-acting method of calculation of electromagnetic transients, using a polynomial approximation of the solution, and also development of scheme model of method that creates convenience for engineers in modeling. A method of calculation of transients in electric circuits is developed on the basis of expansion of the solution of state equations in series of orthogonal Chebyshev polynomials. A scheme interpretation of the developed method is offered. It is shown that, in the special equivalent scheme, Kirchhoff’s laws apply to images of currents and magnetic fluxes as vectors containing the values of coefficients of decomposition of these values by Chebyshev polynomials. The given method allows replacement of operations with instantaneous values of currents by operations with direct currents in the presented equivalent scheme. Transient calculation via the suggested method in a single-phase transformer processor is twice as fast as with well-known methods. The presented method is especially appropriate for transient calculation in magnetoelectrical circuits, since it allows the use of voltage sources controlled by the current derivative for easy calculation of the integrals of solutions.

Расчет переходных процессов в магнитоэлектрических цепях при использовании полиномиальной аппроксимации решения

Calculation of transients in electrical circuits and its scheme interpretation is developed. It is proposed circuit interpretation of the developed method. To the original scheme, in which the originals of the currents are featured, corresponds special circuit, in which images of currents in the form of the vectors containing the factors values of Chebyshev’s polynoms are flowing. It is shown that Kirchhoff’s rules for images of currents are fair in proposed equivalent scheme. As result the state integro-differential equations are reduced to algebraic equations for the image currents. The advantages of the proposed calculation of transients in magnetoelectric equivalent circuits of electromagnetic devices are demonstrated. The computer programs developed on the basis of the proposed method have better quick-action as compared with programs developed on the basis of traditional methods. The example of transient calculation in single-phase transformer is presented.