The mathematical model of an induction machine in terms of the skin effect in the rotor and the saturation of magnetic circuits

2018 ◽  
Author(s):  
V. F. Syvokobylenko ◽  
S. N. Tkachenko
Keyword(s):  
Mathematical Model ◽  
Skin Effect ◽  
Induction Machine ◽  
Magnetic Circuits ◽  
The Mathematical Model

scholarly journals THE ANALYSIS OF THE THREE-PHASE INDUCTION MOTOR WITH DEEP ROTOR BARS THROUGH NUMERICAL SIMULATIONS UTILIZING A MODIFIED MATHEMATICAL MODEL

2021 ◽  
Vol 2020 (1) ◽  
pp. 1-11
Author(s):  
Mihai IORDACHE ◽  
Sorin DELEANU ◽  
Neculai GALAN
Keyword(s):  
Mathematical Model ◽  
Numerical Simulations ◽  
Induction Motor ◽  
Skin Effect ◽  
Induction Machine ◽  
Rotor Resistance ◽  
Three Phase ◽  
Space Phasor ◽  
Analytical Expressions ◽  
Circuit Resistance

The three-phase induction machine mathematical model presented in the paper, is adequate for applying to the deep rotor bars case. The rotor resistance R’r(r), respectively its leakage inductivity L’r(r), depend upon the rotor currents’ frequency fr because of the skin effect. Following the previous considerations, one developed slip dependent analytical expressions of the rotor circuit resistance R’r(s), respectively rotor circuit leakage reactance L’r (s). A modified space phasor based mathematical model of the deep bar induction motor is tested through simulations to assess the motor’s characteristics. The results are in accordance with the literature.

Francis Turbine Modeling for Hydrounit on the Bases of the Doubly Fed Induction Machine

2015 ◽  
Vol 792 ◽  
pp. 203-208
Author(s):  
Rustam Kh. Diyorov ◽  
M.V. Glazyrin
Keyword(s):  
Mathematical Model ◽  
Numerical Modeling ◽  
Induction Machine ◽  
Hydraulic Turbine ◽  
Francis Turbine ◽  
Variable Speed ◽  
Physical Representation ◽  
Doubly Fed Induction Machine ◽  
Doubly Fed ◽  
The Mathematical Model

The mathematical model of Francis turbine, operating at variable speed hydrounit, has created. The results of numerical modeling are fully consistent with the physical representation of the behavior of the hydraulic turbine in dynamic modes.

scholarly journals Sliding mode control of a Five-Phase Series- Connected Two-Motor Drive

2021 ◽  
Vol 1 (1) ◽  
pp. 59-68
Author(s):  
Lazhari NEZLI ◽  
Omar Zouaid
Keyword(s):  
Mathematical Model ◽  
Sliding Mode Control ◽  
Vector Control ◽  
Sliding Mode ◽  
Induction Machine ◽  
Voltage Inverter ◽  
Mode Control ◽  
Asynchronous Machines ◽  
Park Transformation ◽  
The Mathematical Model

In this work, we study vector control and sliding mode control of series-connected five-phase two asynchronous machines supplied with a three levels inverter. After presentation of multiphase machines, we worked out the mathematical model of five phase asynchronous machine supplied with voltage inverter. Application of Park transformation reduces considerably the mathematical model of machine. After, we applied vector control and sliding mode control to the five-phase induction machine. After that, we study a multi-machine system which comport five-phase two asynchronous machines supplied with a single voltage inverter. In the last, we had the independent vector control and the sliding mode control of series-connected five-phase two asynchronous machines. We observe that an appropriate transposition of phase’s order permits an independent control of two machines.

scholarly journals High-frequency periodic processes in two-winding power transformers

2021 ◽  
pp. 96-100
Author(s):  
M.S Seheda ◽  
P.F Gogolyuk ◽  
Y.V Blyznak
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
High Frequency ◽  
Structural Parameters ◽  
Power Transformers ◽  
Voltage Distribution ◽  
Magnetic Circuits ◽  
Periodic Processes ◽  
The Mathematical Model

Purpose. Mathematical modeling of high-frequency periodic processes in winding power transformers to improve the technology of their design and operation. Methodology. The methods of the formation of mathematical models for the research of high-frequency periodic processes in transformers and methods of solving systems of partial differential equations are applied. Findings. The mathematical model for the research of high-frequency periodic processes in two-winding transformers, with adequate considering of electromagnetic connections of windings and structural parameters of transformers, is created. Originality. To form a mathematical model for the research of high-frequency periodic processes, a substitute scheme of a two-windings transformer, taking into account the parameters of the electric and magnetic circuits of windings and electromagnetic connections between them, is proposed. Practical value. The mathematical model, which allows analyzing the voltage distribution in the transformer windings for high-frequency periodic processes in windings, and adjusting their insulating abilities, is created.

scholarly journals Mathematic model of three-phase induction machine connected to advanced inverter for traction system for electric trolley

2013 ◽  
Vol 85 (2) ◽  
pp. 849-858 ◽  
Author(s):  
LIVIU S. BOCII ◽  
VALENTIN MULLER
Keyword(s):  
Mathematical Model ◽  
Electric Motor ◽  
Induction Machine ◽  
Mathematic Model ◽  
Higher Order ◽  
Motor Drive ◽  
Operating Characteristics ◽  
Electric Motor Drive ◽  
The Mathematical Model ◽  
Frequency Inverter

This paper establishes a mathematical model of induction machine connected to a frequency inverter necessary to adjust the electric motor drive. The mathematical model based on the Park's theory allows the analysis of the whole spectrum (electric car – frequency inverter) to drive the electric trolley bus made on ASTRA Bus Arad (Romania). To remove higher order harmonics, the PWM waveform of supply voltage is used, set in the general case. Operating characteristics of electric motor drive are set to sub-nominal frequency (f < 50 Hz) and for different angles of the control switching elements in the construction of the inverter. Tensions in the stator of the equivalent machine are determined by three components: the fundamental component; the second component corresponding to the higher order harmonics, which rotate in direct connection; and the appropriate third component of higher order harmonics, which are rotated in reverse. The mathematical model developed will help to determine the harmonics which have a negative influence on the performance of the electric engine and also determines the control angle of the switching elements to remove these harmonics, (Bele 2007).

Determination of slot leakage inductance for three-phase induction motor winding using an analytical method

2013 ◽  
Vol 62 (4) ◽  
pp. 569-591 ◽  
Author(s):  
Jan Staszak
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Analytical Method ◽  
Induction Machine ◽  
Electrical Machines ◽  
Coordinate Frame ◽  
Leakage Inductance ◽  
Three Phase ◽  
The Mathematical Model

Abstract The article introduced some expressions for self- and mutual slot leakage inductance of phase windings for the mathematical model of an induction machine in the natural phase coordinate system and for dq0 model and in an arbitrary coordinate frame. Calculation of self- and mutual slot leakage inductance have been performed for threephase double-layer, delta and delta-modified winding connections. Introduced expressions may be useful in the design of windings and in the analysis of dynamic states of AC electrical machines.

scholarly journals Control with Sliding Mode of a Five-Phase Series-Connected Two-asynchronous Motor Drive

2018 ◽  
Vol 3 (1) ◽  
pp. 18
Author(s):  
Omar Zouaid ◽  
Lazhari Nezli
Keyword(s):  
Mathematical Model ◽  
Sliding Mode Control ◽  
Sliding Mode ◽  
Asynchronous Motor ◽  
Induction Machine ◽  
Mode Control ◽  
Asynchronous Machines ◽  
Park Transformation ◽  
The Mathematical Model ◽  
Two Machines

In this paper, we study sliding mode control of series-connected five-phase two asynchronous machines supplied with a three levels inverter. After presentation of multiphase machines, we worked out the mathematical model of five phase asynchronous machine supplied with voltage inverter. Application of Park transformation reduces considerably the mathematical model of machine. After, we applied vector control and sliding mode control to the five-phase induction machine. After that, we study a multi-machine system, which comport five-phase two asynchronous machines supplied with a single voltage inverter.In the last, we had the sliding mode control of series-connected five-phase two asynchronous machines. Simulations are presented to show the effectiveness of the control strategy. We observe that an appropriate transposition of phase’s order permits an independent control of two machines.

scholarly journals Mathematical Model and Characteristics of the Induction Motor with a Power Supply from a Current Source

2021 ◽  
Vol 64 (5) ◽  
pp. 421-434
Author(s):  
V. S. Malyar ◽  
A. V. Malyar
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Power Supply ◽  
Skin Effect ◽  
Jacobi Matrix ◽  
Current Source ◽  
Static Characteristics ◽  
Squirrel Cage ◽  
The Mathematical Model ◽  
Electrical Equilibrium

. Methods and mathematical models for studying the modes and characteristics of the three-phase squirrel-cage induction motor with the power supplied to the stator winding from the current source have been developed. The specific features of the algorithms for calculating transients, steady-state modes and static characteristics are discussed. The results of the calculation of the processes and characteristics of induction motors with the power supply from the current source and the voltage source are compared. Steady-state and dynamic modes cannot be studied with a sufficient adequacy based on the known equivalent circuits; this requires using dynamic parameters, which are the elements of the Jacobi matrix of the system of equations of the electromechanical equilibrium. In the mathematical model, the state equations of the stator and rotor circuits are written in the fixed two-phase coordinate system. The transients are described by the system of differential equations of electrical equilibrium of the transformed circuits of the motor and the equation of the rotor motion and the steady-state modes by the system of algebraic equation. The developed algorithms are based on the mathematical model of the motor in which the magnetic path saturation and skin effect in the squirrel-cage bars are taken into consideration. The magnetic path saturation is accounted for by using the real characteristics of magnetizing by the main magnetic flux and leakage fluxes of the stator and rotor windings. Based on them, the differential inductances are calculated, which are the elements of the Jacobi matrix of the system of equations describing the dynamic modes and static characteristic. In order to take into account the skin effect in the squirrel-cage rotor, each bar along with the squirrel-cage rings is divided height-wise into several elements. As a result, the mathematical model considers the equivalent circuits of the rotor with different parameters which are connected by mutual inductance. The non-linear system of algebraic equations of electrical equilibrium describing the steady-state modes is solved by the parameter continuation method. To calculate the static characteristics, the differential method combined with the Newton’s Iterative refinement is used.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

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