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

. 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.

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Analysis of the synchronous motors behavior in the transients for backup power supply. Purpose.

Journal of Electrical and power engineering ◽

10.31474/2074-2630-2020-2-28-37 ◽

2020 ◽

Vol 23 (2) ◽

pp. 28-37

Author(s):

V. F. SYVOKOBYLENKO ◽

◽

V.A. LYSENKO ◽

Keyword(s):

Mathematical Model ◽

Steady State ◽

Power Supply ◽

Optimization Methods ◽

Synchronous Motor ◽

Magnetic Core ◽

Synchronous Motors ◽

Salient Pole ◽

Passport Data ◽

The Mathematical Model

Simulation of transient and steady state modes of synchronous motors for the analysis of switching to backup power using mathematical model. Method. The methods of linear algebra, numerical optimization methods, methods of modeling and analysis of established and transient modes are used. Results. The mathematical model of the salient pole rotor and non-salient or cylindrical pole rotor synchronous motor is presented, which is presented in the form of a alternate scheme, which allows to take into account the effect of displacement of current and saturation of the non-salient pole rotor motor's magnetic core. A method for determining the parameters of the synchronous motor based on passport data is proposed, which allows to improve the accuracy of modeling in steady state and transient modes. The mathematical model is reduced to a three-phase coordinate system a, b, c of the stator winding. The rotor windings are modeled in the coordinates d, q. The results of mathematical modeling allow us to determine the magnitude of the shock currents and mechanical moments of the synchronous motor. It is shown that non-synchronous switching on of the synchronous motor, which occurs in case of automatic transfer switch, can lead to engine damage. Shock currents can also be dangerous to other power supply equipment. Thus, synchronous motors, if transfer switch is used, require synchronization before being connected to the network. Scientific novelty. The mathematical model of the synchronous motor was improved taking into account the displacement of current and saturation of the magnetic conduit, the method of determining the parameters of the mathematical model based on the passport data of the engine was improved, which allowed to increase the accuracy of the simulation and the reliability of the simulation results. The modes of power transfer switch are simulated and the values of shock current and shock mechanical moment of the engine are obtained. Practical meaning. The mathematical model of the synchronous motor allows to analyze the behavior of synchronous motors in interaction in the power supply system and to identify the dangerous states of synchronous motors that may occur during the transfer switching. The proposed model improves the accuracy of determination of the limits of dangerous states and improves the reliability of synchronous motors and power supply systems.

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Spectral and integral methods of determining parameters in selected electric arc models with a forced sinusoid current circuit

Archives of Electrical Engineering ◽

10.1515/aee-2016-0007 ◽

2016 ◽

Vol 65 (1) ◽

pp. 87-103 ◽

Cited By ~ 3

Author(s):

Antoni Sawicki ◽

Maciej Haltof

Keyword(s):

Mathematical Model ◽

Mathematical Models ◽

Power Supply ◽

Electric Arc ◽

Dynamic Processes ◽

Model Parameters ◽

Static Characteristics ◽

Integral Methods ◽

The Mathematical Model ◽

Linear Shape

Abstract The paper discusses problems arising in attempts to accurately represent dynamic processes of an electric arc by means of simple mathematical models. It describes the properties of the universal Pentegov model, employing any shape of static voltagecurrent characteristics of an arc. Next, it presents spectral and integral measuring methods for determining arc parameters in the Mayr, Cassie and Pentegov models of the electric arc with a forced sinusoid current circuit, with the raising static characteristics of hyperbolic-flat and hyperbolic-linear shape. The influence is discussed of the random power supply disturbances on errors of determining the mathematical model parameters.

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Analysis of mathematical models of transmission lines.

Journal of Electrical and power engineering ◽

10.31474/2074-2630-2020-2-16-19 ◽

2020 ◽

Vol 23 (2) ◽

pp. 16-19

Author(s):

G. SHEINA ◽

Keyword(s):

Mathematical Model ◽

Power Systems ◽

Transmission Lines ◽

Power Supply ◽

Power Supply System ◽

Power Transmission ◽

Supply System ◽

Power Lines ◽

Power Transmission Lines ◽

The Mathematical Model

This paper investigates a mathematical model of one elements of the power supply system - power transmission lines. The type of models depends on the initial simplifications, which in turn are determined by the complexity of the physics of processes. The task of improving the accuracy of modeling of emergency processes in the power system is due to the significant complexity of modern power systems and their equipment, high-speed relay protection, automation of emergency management and the introduction of higher-speed switching equipment. One of the reasons for a significant number of serious emergencies in the system is the lack of complete and reliable information for modeling modes in the design and operation of power systems. The development of a mathematical model of a three-phase power line, which provides adequate reflection of both normal and emergency processes, is relevant. The advanced mathematical model of power transmission lines allows to investigate various operational modes of electric networks. The improved mathematical model of the power transmission line reflects all the features of physical processes at state modes and transient process and provides sufficient accuracy of the results. The type of mathematical model of power transmission lines depends on the accepted simplifications, depending on the task of research. The purpose of this work is to analyze the mathematical model of the power transmission line to study the modes of operation of the power supply system, with the possibility of its application to take into account all the design features of overhead and cable power lines. The mathematical model of the power line for the study of the modes of operation of the power supply system is analyzed. It is used to take into account the design features of overhead and cable power lines, skin effect.

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New “Full-Bridge Buck Inverter–DC Motor” System: Steady-State and Dynamic Analysis and Experimental Validation

Electronics ◽

10.3390/electronics8111216 ◽

2019 ◽

Vol 8 (11) ◽

pp. 1216 ◽

Cited By ~ 2

Author(s):

Eduardo Hernández-Márquez ◽

Carlos Alejandro Avila-Rea ◽

José Rafael García-Sánchez ◽

Ramón Silva-Ortigoza ◽

Magdalena Marciano-Melchor ◽

...

Keyword(s):

Mathematical Model ◽

Steady State ◽

Motor System ◽

Circuit Simulation ◽

Dc Motor ◽

Matlab Simulink ◽

Duty Cycles ◽

System Variables ◽

The Mathematical Model ◽

Steady State Stability

A mathematical model of a new “full-bridge Buck inverter–DC motor” system is developed and experimentally validated. First, using circuit theory and the mathematical model of a DC motor, the dynamic behavior of the system under study is deduced. Later, the steady-state, stability, controllability, and flatness properties of the deduced model are described. The flatness property, associated with the mathematical model, is then exploited so that all system variables and the input can be differentially parameterized in terms of the flat output, which is determined by the angular velocity. Then, when a desired trajectory is proposed for the flat output, the input signal is calculated offline and is introduced into the system. In consequence, the validation of the mathematical model for constant and time-varying duty cycles is possible. Such a validation of this mathematical model is tackled from two directions: (1) by circuit simulation through the SimPowerSystems toolbox of Matlab-Simulink and (2) via a prototype of the system built by using Matlab-Simulink and a DS1104 board. The good similarities between the circuit simulation and the experimental results allow satisfactorily validating the mathematical model.

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Determination of squirrel cage induction machine parameters including skin effect in steady-state operation

2008 IEEE International Conference on Industrial Technology ◽

10.1109/icit.2008.4608700 ◽

2008 ◽

Author(s):

O. Touhami ◽

M. Mehenoun ◽

M.O. Mahmoudi ◽

N. Benakba

Keyword(s):

Steady State ◽

Skin Effect ◽

Induction Machine ◽

Squirrel Cage ◽

Steady State Operation

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The Effect of Leakage on Railroad Brake Pipe Steady State Behavior

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.3152690 ◽

1988 ◽

Vol 110 (3) ◽

pp. 329-335 ◽

Cited By ~ 1

Author(s):

K. Abdol-Hamid ◽

D. E. Limbert ◽

G. A. Chapman

Keyword(s):

Mathematical Model ◽

Steady State ◽

Transmission Lines ◽

Computation Time ◽

State Behavior ◽

Implicit Finite Difference Scheme ◽

Inlet Flow Rate ◽

Model Equations ◽

The Mathematical Model ◽

Steady State Behavior

A mathematical model for pneumatic transmission lines containing leakage is developed. This model is used to show the effect of leakage size and distribution on the steady state behavior of the brake pipe on a train brake system. The model equations are solved using the implicit finite difference scheme without neglecting any terms. The model is presented in a nonlinear continuous network form, consisting of N sections. Each of the network sections represents one car and may contain one leakage. A computer program was developed to solve the model equations. This program is capable of simulating a train with cars of various lengths and takes a minimum amount of computation time as compared with previous methods. Through analysis and experimentation, the authors have demonstrated that pressure gradient and inlet flow rate are very sensitive to leakage locations as compared with leakage size. The results, generated by the mathematical model, are compared with the experimental data of two different brake pipe set-ups having different dimensions.

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Mass transfer during electrodeposition of metals at a periodically changing rate

Journal of the Serbian Chemical Society ◽

10.2298/jsc9906317m ◽

1999 ◽

Vol 64 (5-6) ◽

pp. 317-340 ◽

Cited By ~ 3

Author(s):

Miodrag Maksimovic ◽

Konstantin Popov

Keyword(s):

Mathematical Model ◽

Mass Transfer ◽

Steady State ◽

Layer 4 ◽

Millisecond Range ◽

The Mathematical Model ◽

Pulsating Current ◽

Pulsating Overpotential ◽

Changing Rate ◽

Electrodeposition Of Metals

1. Introduction 2. Mass transfer in the steady state periodic condition 2.1. Reversing current 2.2. Pulsating current 2.3. Alternating current superimposed on direct current 3. The influence of the charge and discharge of the electrical double layer 4. The validity of the mathematical model 4.1. Reversing current in the millisecond range 4.2. Reversing current in the second range 4.3. Pulsating current 4.4. Pulsating overpotential 5. Conclusion

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On the global attractors in one mathematical model of antiviral immunity

10.1101/2020.10.16.343145 ◽

2020 ◽

Author(s):

Alexei Tsygvintsev

Keyword(s):

Mathematical Model ◽

Steady State ◽

Immune System ◽

Asymptotic Stability ◽

Global Asymptotic Stability ◽

Antiviral Immunity ◽

Global Attractors ◽

Viral Pathogens ◽

Basic Reproductive Ratio ◽

The Mathematical Model

AbstractWe consider the mathematical model introduced by Batholdy et al. [1] describing the interaction between viral pathogens and immune system. We prove the global asymptotic stability of the infection steady-state if the basic reproductive ratio R0 is greater than unity. That solves the conjecture announced in [7].

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Optimization of the power supply system for connection of the end user to electric grids according to the scheme of the third category of reliability

E3S Web of Conferences ◽

10.1051/e3sconf/20185802011 ◽

2018 ◽

Vol 58 ◽

pp. 02011

Author(s):

Ivan Bandurin ◽

Alexey Khaimin

Keyword(s):

Mathematical Model ◽

Power System ◽

Power Supply ◽

Power Supply System ◽

Supply System ◽

End User ◽

The Third ◽

Electric Grids ◽

The Mathematical Model ◽

Optimal Type

The article first developed a mathematical model of optimization of the power supply system for connection of the end user to electric grids according to the scheme of the third category of reliability. The mathematical model allows to choose the optimal type and brand power system equipment.

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