Analysis of three-phases matrix reactance frequency converter with two pulsations of control signal

2012 ◽  
Vol 61 (3) ◽  
pp. 359-371
Author(s):  
Igor Korotyeye ◽  
Beata Zięba
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Control Signal ◽  
Periodic Coefficients ◽  
Method Of Calculation ◽  
Frequency Converters ◽  
Control Signals ◽  
Three Phases

Analysis of three-phases matrix reactance frequency converter with two pulsations of control signalThis paper presents a method of calculation of steady-state processes in three-phases matrix-reactance frequency converters (MRFC's), in which voltages and currents are transformed by control signals with two pulsations. A solution of nonstationary differential equations with periodic coefficients that describe this system is obtained by using Galerkin's method and an extension of equations of one variable of time to equations of two variables of time. The results of calculations are presented in an example of three-phases MRFC with buck-boost topology and compared with a numerical method embedded in the program Mathematica.

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 NUMERICAL METHOD OF CALCULATION OF ROUND PLATES IN A GEOMETRICALLY NONLINEAR STATEMENT

Vestnik MGSU ◽  
2017 ◽  
pp. 631-635
Author(s):  
Radek Fatykhovich Gabbasov ◽  
Natalia Borisovna Uvarova
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Geometrically Nonlinear ◽  
Method Of Calculation ◽  
First Order ◽  
Nonlinear Statement ◽  
Minimum Number ◽  
Dead Loading ◽  
The Right ◽  
The Given

The article considers the axisymmetric problem about the calculation of round plates with dead loading in a geometrically nonlinear system. To solve the problem some generalized equations of finite difference method (FMD) are needed that allow to solve tasks within intergrable scope taking into account discontinuities of the required function, its first-order derivative and the right-hand side of the primitive differential equation. Resolvent differential equations of the question comprised fractionally the required function of the inflection and stresses are reduced to four differential equations, two of which are linear of the first-order and two are nonlinear of the second order. The obtained system of differential equations is solved numerically. The proposed method is shown with the example of calculation of a round plate; the given data are taken from work [1]. The calculation data with the minimum number of partitions are compared to the known solution of A.S. Vol’mir [1] and they indicate the possibility of using a numerical method for handling the problem in nonlinear statement.

scholarly journals An efficient numerical procedure for calculating periodic vibrations of elastic mechanisms

2016 ◽  
Vol 38 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Nguyen Van Khang ◽  
Nguyen Phong Dien ◽  
Nguyen Sy Nam
Keyword(s):  
Periodic Solution ◽  
Steady State ◽  
Differential Equations ◽  
Integration Method ◽  
Initial Conditions ◽  
Numerical Procedure ◽  
Periodic Coefficients ◽  
Linear Differential ◽  
Time Periodic ◽  
Elastic Elements

This paper proposes a numerical procedure based on the well-known Newmark integration method to determine initial conditions for the periodic solution of a system of linear differential equations with time-periodic coefficients. Based on this, steady-state periodic vibrations of mechanisms with elastic elements governed by linearized differential equations with time-periodic coefficients can be conveniently calculated. The proposed procedure is demonstrated by a dynamic model of a planar four-bar mechanism with the flexible coupler.

Critical Speeds of a Rotor With Unequal Shaft Flexibilities, Mounted in Bearings of Unequal Flexibility—I

1943 ◽  
Vol 10 (2) ◽  
pp. A77-A84
Author(s):  
W. R. Foote ◽  
H. Poritsky ◽  
J. J. Slade
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Infinite Number ◽  
Critical Speed ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Rotation Period ◽  
Rotor Speed ◽  
Periodic Coefficients ◽  
Linear Differential

Abstract This paper contains a study of the motion of a rotor possessing unequal flexibilities in two mutually perpendicular directions and mounted in bearings which likewise possess different stiffnesses in two mutually perpendicular directions, say, the horizontal and vertical directions. A two-pole turbogenerator is an example of such a rotor. As known, the effect of ρ, the fractional inequality in rotor flexibilities, by itself, that is, without unequal bearing flexibilities, consists in giving rise to an unstable range of speed near the critical whose width depends upon ρ; the larger ρ is, the wider is the unstable range. If neither ρ nor σ vanishes (σ = fractional inequality of bearing flexibilities), the investigation becomes more difficult due to the fact that the principal flexibility directions are fixed for the bearings but rotate for the rotor. The differential equations of motion now acquire periodic coefficients whose period is half the rotation period. Their solution shows that near the main critical speed, for small ρ the unstable range splits up into three parts, which coalesce into one range for large ρ. The separation of three unstable ranges increases with σ. A further slight instability also occurs when the rotor speed is near half of the main critical speed. If one attempts to revolve such a rotor at a constant speed inside an unstable range, it may, even if in perfect balance, whirl with an exponentially increasing amplitude. With friction the amount of instability decreases and the size of the unstable regions decreases too, and with sufficient friction complete stability is restored. The friction necessary to restore stability is computed and the effect of unbalance on the steady-state amplitudes is studied. The solution of linear differential equations with periodic coefficients leads to an infinite number of algebraic linear equations in an infinite number of coefficients. Various ways of solving these equations and of speeding up the convergence of the solution are discussed in detail.

scholarly journals Insulation Life Span of Low-Voltage Electric Motors—A Survey

Energies ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1738
Author(s):  
Vanessa Neves Höpner ◽  
Volmir Eugênio Wilhelm
Keyword(s):  
Life Span ◽  
Electric Motor ◽  
Low Voltage ◽  
Frequency Converter ◽  
Rate Of Change ◽  
High Rate ◽  
Switching Frequency ◽  
Electric Motors ◽  
Frequency Converters ◽  
High Switching Frequency

The use of static frequency converters, which have a high switching frequency, generates voltage pulses with a high rate of change over time. In combination with cable and motor impedance, this generates repetitive overvoltage at the motor terminals, influencing the occurrence of partial discharges between conductors, causing degradation of the insulation of electric motors. Understanding the effects resulting from the frequency converter–electric motor interaction is essential for developing and implementing insulation systems with characteristics that support the most diverse applications, have an operating life under economically viable conditions, and promote energy efficiency. With this objective, a search was carried out in three recognized databases. Duplicate articles were eliminated, resulting in 1069 articles, which were systematically categorized and reviewed, resulting in 481 articles discussing the causes of degradation in the insulation of electric motors powered by frequency converters. A bibliographic portfolio was built and evaluated, with 230 articles that present results on the factors that can be used in estimating the life span of electric motor insulation. In this structure, the historical evolution of the collected information, the authors who conducted the most research on the theme, and the relevance of the knowledge presented in the works were considered.

An implicit multistep numerical method for real-time simulation of stiff systems

SIMULATION ◽  
2021 ◽  
pp. 003754972110216
Author(s):  
Zhang Lei ◽  
Li Jie ◽  
Wang Menglu ◽  
Liu Mengya
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Real Time ◽  
Physical System ◽  
Physical Models ◽  
Stiff Systems ◽  
Real Time Simulation ◽  
Stiff Ordinary Differential Equations ◽  
Root Finding ◽  
Time Simulation

Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.

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