Model of implicit pole electric machine based on mathematical formulation of magnetic field in air gap

When modeling transient processes in electric power systems, the issue of designing reliable models of electrical machines is of great interest. The most difficult task is to design the models of synchronous and asynchronous machines. The purpose of the project is to develop mathematical models of synchronous and asynchronous machines based on a generalized model of an implicit-pole machine that considers the change of rotor speed, geometric shapes, and the type of rotor and stator windings. Methods of mathematical modeling of electromagnetic fields in the air gap based on Maxwell equations and methods of the theory of electrical circuits are applied. A system of nonlinear differential equations is considered as a mathematical model of a generalized implicit-pole machine. The key assumption made is the high magnetic permeability of the stator and rotor cores. Technical data of real electric machines have been used for verification. Mathematical models of an implicit pole synchronous machine and an asynchronous machine with a phase rotor have been developed. These models can be used to analyze transient processes in the aggregate without dividing them into electromagnetic and electromechanical ones. The novelty of the models is the fact of non-sinusoidal distribution of the magnetic field in the air gap, various types of multiphase AC windings and rejecting the principle of constant rotation frequency at the time step of the simulation. The proposed mathematical models can be used to solve design problems, to analyze the modes of electric power systems, the operation of relay protection and automation of electric power facilities, and emergency automation. In the future, the equations that consider the influence of the damper circuits and the peculiarities of the windings will be added to the developed mathematical models. The purpose of further research is to develop models of salient-pole synchronous machines and asynchronous machines with a squirrel-cage rotor.

EXPERIMENTAL STUDY OF STATIC CHARACTERISTICS ASYNCHRONOUS MACHINE IN DYNAMIC BRAKING MODE WITH INDUCTION RESISTANCE IN THE ROTOR WINDING

The article discusses the results of a study of the static electromechanical characteristics of an asynchronous machine (AM) when prototypes of induction resistances (IR) with improved parameters are included in its rotor circuits. The dynamic braking (DB) of asynchronous machines, which is widespread in practice, provides for the dissipation of the kinetic energy of the rotating parts in the resistance boxes included in the rotor winding. In the process of stopping, to maintain a constant average braking torque AM, a bulky relay-contactor circuit for shunting rotor resistances is used. However, it is not possible to eliminate significant fluctuations in the electromagnetic torque in this way. To optimize the DB AM process, it is proposed to include a three-phase IR in the rotor winding instead of resistance boxes, the value of which automatically decreases along with the rotor current frequency. This approach allows you to abandon contact equipment and ensure smooth braking of the machine with fluctuations in the electromagnetic moment in narrower limits. The known IR designs are designed for starting modes of induction motors with a wound rotor, but they cannot ensure the constancy of the torque on the AM shaft in the DB mode. Therefore, the purpose of the study is to develop and experimentally confirm the effectiveness of simple control circuits of an induction machine in the specified mode with improved contactless induction rheostats in the rotor. The paper presents a diagram of a pilot plant and a figure explaining the design features of the IR. The studies were carried out for an asynchronous machine of the MTB-412-8 type, equipped with a thyristor exciter and a tachogenerator. The three phases of the AM rotor included ICs connected by a "star". The experiments were carried out in the direction of obtaining the necessary braking characteristics of the AM by varying the switching circuit of the stator phases and the value of the current supplying them. The figures show the mechanical characteristics of AM, obtained in the process of studying the influence on them of three typical circuits for switching on the phases of the stator winding and two values ​​of the fixed supply current. The research results show that the desired form of the mentioned AM characteristics is achieved only when using the stator phase switching in a function of the rotor speed and a constant supply current value.

PROPERTIES OF THE REACTIVE POWER OF THE ASYNCHRONOUS MACHINE AS A LOAD OF THE ELECTRIC NETWORK

It is known that the voltage mode of the electrical network is associated with the balance of reactive power and directly affects the operation of production equipment. A typical static characteristic of a power supply unit in terms of reactive power, obtained for a load composition characteristic of electrical networks, is an extreme function with a minimum point. It is the presence of a minimum point in the dependence of reactive power on voltage that makes it possible to develop this type of instability as a voltage avalanche. This mode is especially dangerous for industrial units with abruptly variable loads, which can create significant fluctuations in the supply voltage, which significantly affects the operation of powerful asynchronous motors. Therefore, the issues of the relationship between the parameters mode of the electrical network and the properties of electrical loads are always important, especially asynchronous machines as the main consumer of electricity, which largely determines the properties of the generalized reactive power curve of the entire load unit. Literary sources do not explain in detail why the curve of the dependence of the reactive power of the power supply unit on voltage has a minimum. The article sets out this issue in sufficient detail for asynchronous machines as the main consumer of reactive power in electrical networks. The task is to obtain the dependence of the reactive power of an induction machine with a squirrel-cage rotor on the voltage of the supply network, as well as to determine the criteria for controlling reactive power flows in order to inadmissibly reduce the voltage in the load unit. As a result, based on the system of equations of an asynchronous machine, the dependence of its reactive power on the supply voltage of the network was derived. The mathematical properties of this function are investigated with a physical justification of its unimodality and the presence of a minimum point. The obtained expressions make it possible to determine the magnitude of the control action on the high-speed reactive power compensation devices to stabilize the voltage level in the power supply unit.

Stepper induction motors for electric drive

Aim: The goal is to present a new asynchronous principle of operation of stepper motors, based on the use of counter-rotating (or traveling) magnetic fields. Method: A change in the degree of symmetry of one of these magnetic fields leads to the fact that the armature (rotor or secondary element) makes a precise discrete movement. Result: The force moving the armature of a stepper induction motor is created as a result of the interaction of eddy currents in the armature with a rotating or traveling magnetic field. Stepper induction motors can rotate the rotor at a certain angle and discretely move flat or cylindrical electrically conductive armatures, which can be smooth and non-magnetic. A separate group of motors for a discrete electric drive is made up of two-coordinate linear stepping asynchronous machines, which also operate using the same counter-running magnetic fields both in the longitudinal and transverse directions. Conclusion: The features of the design of such electric machines are presented, the values of the magnetic induction in different zones of a two-coordinate stepper motor are determined, the relations for calculating the steps of the armature in both the longitudinal and transverse directions are given.

Prospects for Increasing the Dynamic Efficiency of Asynchronous Double-Feed Machines and Wind Power Generators Using Structural Methods and Solutions

The chapter proposes to consider the problems of control of asynchronous machines with dual power supply, as a nonlinear structure, the transfer functions of which depend on the frequency of the stator voltage and the relative slip. The authors cite the results of research confirming the high efficiency of control of asynchronous electric motors, using cross-dynamic connections on the developed torque or a signal close to it (active component of the motor stator current). The proposed correction operates in a wide range of changes in the rotation and sliding speeds of the asynchronous electric generator. This is especially important for wind turbines that need to remain efficient at different speeds. As a justification, the results of experiments, modeling and industrial application of control algorithms with positive torque coupling are presented. Research results suggest that such algorithms will improve the efficiency of wind power by 5–10%.

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

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.

Features of autonomous and parallel operation of an asynchronous generator with a network of endless power in the current stage of EPS development

The article describes the use of asynchronous machines in generator mode to provide power to threephase consumers, as well as the features of autonomous and parallel operation of an asynchronous generator with an infinite power network. The use of static sources of reactive power allows widespread introduction of an asynchronous generator in the electric power system as a reliable source of active power.

STUDY OF PHYSICAL PROCESSES IN THE DIRECT CURRENT LINK OF THE LOADING-BACK SCHEME OF ASYNCHRONOUS MACHINES

The article notes the tendency of introducing asynchronous engines, entailing the necessity to introduce the equipment which is intended to carry out maintenance, repair and acceptance check-outs. The general part of test circuits for asynchronous motors by the loading-back method with two controlled inverters is emphasized. The mathematical model of similar schemes’ functioning is shown. The article gives the results obtained by mathematic simulation of physical processes in the direct current link in the loading-back scheme for asynchronous machines Significant ripple voltage of constant voltage and DC in these circuits is noted. The issue of measuring power in the DC link passing through one inverter to the test engine and through another inverter from the load generator is considered. The authors carried out calculation of the capacities mentioned in the steady state modes for asynchronous machines with nominal power of 0.37 kW, 5.5 kW and 250 kW at different values of capacitor capacitance included in the DC link. Basing on the results of calculations, the authors found the dependence between the relative value of the procedural error in determining power in the DC link by the product of the current values of pulsed voltages and current. The current value from the product of instantaneous values of voltage and current at some time interval was taken as the true value of power. It is shown that at the capacitor capacity above some critical value this procedural error does not exceed 0.9% at the nominal power of the test engines 0.37 kW; 0.3% – at the power of 5.5 kW; 0.2% – at the power of 250 kW. This error increases dramatically when capacitor capacitance decreases. It is shown that the value of the capacitance corresponding to the inflection of the considered dependence approximately corresponds to the value necessary for limiting ripple voltage in the DC link of up to 600 V.