The analysis of operating conditions of induction traction motors as part of traction electric drives of electric locomotives reported here has revealed that they are powered by autonomous voltage inverters with asymmetric non-sinusoidal voltage. It was established that the induction motor operation may be accompanied by defects caused by the asymmetrical modes of the motor stator. A model of the induction motor has been proposed that takes into consideration changes in the values of mutual inductance of phases and complete inductance of the magnetization circuit due to changes in the geometric dimensions of the winding caused by a certain defect. An algorithm that considers the saturation of the magnetic circuit of the electric motor has been proposed. This approach to modeling an induction motor is important because if one of the stator's windings is damaged, its geometry changes. This leads to a change in the mutual inductance of phases and the complete inductance of the magnetization circuit. Existing approaches to modeling an induction motor do not make it possible to fully take into consideration these changes. The result of modeling is the determined starting characteristics for an intact and damaged engine. The comparison of modeling results for an intact engine with specifications has shown that the error in determining the controlled parameters did not exceed 5 %. The modeling results for the damaged engine demonstrated that the nature of change in the controlled parameters did not contradict the results reported by other authors. The discrepancy in determining the degree of change in the controlled parameters did not exceed 10 %. That indicates a high reliability of the modeling results. The proposed model of an induction electric motor could be used to investigate electromagnetic processes occurring in an electric motor during its operation as part of the traction drive of electric locomotives
This article is devoted to development of a method for calculating the parameters of an asynchronous motor of an electric locomotive with asymmetrical windings of stator and rotor. A method for determining self and mutual inductances of the stator and rotor phases of an asynchronous motor with asymmetric windings and their relations to mechanical variables is proposed. It is based on comparing two equations of stored magnetic energy, one equation calculated through induction, magnetic field strength and geometrical dimensions and another equation calculated through the parameters of the motor circuits. It is shown that the obtained solutions correspond to the previously existing methods, but they give the additional possibilities in mathematical modeling. The proposed technical solution allows higher accuracy developing of a mathematical model of a drive with an asynchronous motor having asymmetrical stator and rotor windings for studying dynamic processes during the operation of the specified drive, in particular, the drive of auxiliary machines for electric locomotive, where an asynchronous motor with asymmetrical stator windings is used as a phase release.
A method is proposed for determining the number of damaged stator windings in the presence of an asymmetric power supply system for an induction electric motor based on the Park vector hodograph. As a result of the experiments on the simulation model, it was found that with the symmetry of the system of supply voltages and stator windings, the hodograph of the Park vector describes a circle; in all other cases it is an ellipse. It has been established that the presence of asymmetry in the supply voltage system is indicated by the angle of inclination of the ellipse, and the indicator of the presence of the asymmetry of the stator windings is the angle of ellipticity. In order to identify the presence of asymmetry of the stator windings in the conditions of asymmetry of the supply voltage system, an algorithm for recalculating the ellipse parameters for the condition of the symmetry of the supply voltage system was proposed. Recalculation errors did not exceed 6%. It has been established that the dependence of the increment of the amplitudes of the phase and angles of the phase currents of the stator on the number of damaged turns of the stator winding is linear. Based on this fact, an algorithm for determining the number of damaged turns was proposed. The results of this work can be used to build systems for diagnosing the interturn short circuit of the stator of an induction electric motor built into the drive.
Запропоновано для моделювання асинхронного двигуна транспортних засобів скористатися системою диферен ційних рівнянь, записаною в «загальмованих координатах». З метою підвищення стійкості алгоритму скорочено кіль кість рівнянь системи шляхом вираження фазних стру мів через фазні потокозчеплення. Розраховано параметри двигунапрототипу за класичною методикою. Розроблено алгоритм врахування механічних втрат та втрат потуж ності в сталі двигуна. Реалізовано в програмному середови щі MATLab імітаційне моделювання асинхронного двигуна з симетричними обмотками. Визначено основні техніч ні параметри двигуна за допомогою імітаційної моделі. Виконано порівняння результатів моделювання з резуль татами класичних розрахунків. Похибка при визначен ні параметрів на моделі і виконаних розрахунковим шля хом не перевищила 7 %. Це свідчить про високу збіжність результатів моделювання з результатами розрахунків. Запропоновано для дослідження асинхронного двигуна з несиметричними обмотками статора алгоритм, який полягає у врахуванні зміни взаємної індуктивності при зміні комплексного опору однієї, або декількох фаз обмо ток двигуна. Запропонований алгоритм організації неси метричного режиму обмоток статора дозволить без зміни структури моделі дослідити динамічні процеси в асин хронному двигуні при несиметрії фаз обмоток статора при їх пошкодженні. Врахування втрат потужності в сталі та механічних втрат підвищить достовірність отриманих результатів. Похибка визначення параметрів асинхронно го двигуна при несиметричних обмотках статора, отрима них при моделюванні, і знятих експериментально не пере вищила 3 %, що свідчить про адекватність моделі. Це дозволить застосувати запропоновану імітаційну модель асинхронного двигуна при дослідженні динаміч них процесів в двигунах транспортної інфраструктури при виникненні такого дефекту, як міжвиткове замикання в обмотках статору Ключові слова: оптимальне управління перевезеннями, параметри інфраструктури залізниці, математичне моде лювання, асинхронний двигун, несиметрія обмоток
This paper has proposed and substantiated the application of an additional diagnostic parameter for assessing the state of stator windings of induction motors during operation. The dependences of the values of phase shifts between phase currents and phase voltages have been obtained. These dependences showed that when an inter-turn short circuit occurs in the stator windings, the phase shifts are the same for all phases of the motor. That has made it possible to obtain the dependence of the change in phase shift on the change in the engine shaft rotation frequency. This study's result has established the dependence of the rates of change of the phase angle on the engine shaft rotation frequency for both one and two damaged phases with varying degrees of damage. When analyzing these dependences, it was found that with an increase in the number of damaged phases of the electric motor, the linear section of the dependences decreases. In addition, with an increase in the degree of phase damage, the angle of inclination of the linear sections of the characteristics decreases. That has made it possible to determine an additional parameter for diagnosing the place and degree of an inter-turn short circuit of the windings in an induction motor with a squirrel-cage rotor. The values of the additional parameter, termed by this paper's authors as a "phase criterion" can be used to assess the condition and degree of damage to the stator winding of induction motors. The values of the phase criteria for various types of damage were: when phase A is damaged by 90 %, ξ=0.634, (deg)2/(rpm)2; when phase A is damaged by 80 %, ξ=0.393, (deg)2/(rpm)2; when phase A is damaged by 80 % and phase B is damaged by 90 %, ξ=0.25, (deg)2/(rpm)2; when phase A is damaged by 80 % and phase B is damaged by 90 %, ξ=0.173, (deg)2/(rpm)2. The results of this research could be used to select an effective method for diagnosing an inter-turn short circuit in the stator winding when building a diagnostic system for induction motors as part of drives of transport equipment
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