ANALYSIS OF THE M/N WINDING ASYNCHRONOUS MACHINE WITH SPACE HARMONICS USING SYMMETRICAL COMPONENTS

ABSTRACT

This paper is concerned with the analysis of the asynchronous. machines with m symmetrical stator windings and a rotor of cage type which consists of n symmetrically distributed bars. The analysis is performed in the presence of space harmonics. Considering the relation between any sequence of symmetrical components related to unbalanced voltage supply, the possibly established space harmonics can be assigned. The m/n wielding machine voltage equations are presented in phase coordinate form in order to apply a transformation by symmetrical components. Sufficient conditions are presented in order to express these equations in the form of linear differential equations with constant coefficients. The suggested method is able to include large numbers of space harmonics. The transformation with the help of symmetrical components here will divide the complete set into n separate subsets when it is applied to the rotor quantities. The equivalent symmetrical component model of the m/n winding machine will make the stator/rotor space harmonics interactions more understandable.

It is also possible to discuss the problem of obtaining linear voltage differential equations by simpler method.     

GENERALIZED THEORY FOR THE PERFORMANCE OF THREE-PHASE INDUCTION MOTOR WITH STAR-DELTA WINDING

Abstract

A theory has been developed for the performance of three-phase induction motor with star-delta stator winding. Space harmonics of delta and star components of the winding and their space-phase displacements have been taken into account in the analysis. A general computer program has been developed incorporating the new theory for evaluation of performance. Predictions of performance have been verified by tests on a few three-phase squirrel-cage induction motors with star-delta stator connections.     

Transient and steady-state operation of induction motors with stator asymmetries

Contents Steady-state analysis of three-phase induction motors with asymmetrical stator external impedances is presented by the application of the symmetrical components theory. New and general equivalent circuits are derived, and it is shown how they can be extended for constant-speed transients, too. State-variable equations are given for the case of asymmetrical stator voltages and external resistances. — By the application of a new two-phase symmetrical component transformation, steady-state equations of an asymmetrical two-phase machine with nonquadrature windings are set up; a new equivalent circuit is also derived. Transient equations are also given.

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Übersicht Das stationäre Verhalten von Asynchronmaschinen mit Unsymmetrien im Statorkreis wird mit Hilfe symmetrischer Komponenten behandelt. Neue und allgemeine Ersatzstromkreise werden abgeleitet und ferner wird gezeigt, wie die Ersatzschaltbilder für den transienten Betrieb bei konstanter Drehzahl erweitert werden können. Für die Berechnung des transienten Verhaltens werden allgemeine Zustandsgleichungen angegeben, wenn unsymmetrische Statorspannungen und äußerliche Widerstände existieren. Bei Anwendung einer neuen Zweiphasen symmetrischen Komponentenumstellung werden stationäre Betriebsgleichungen einer unsymmetrischen Zweiphasenmaschine mit nichtrechtwinkligen Wicklungen aufgestellt, und man findet einen neuen Ersatzstromkreis. Transiente Gleichungen werden auch gegeben.

     

Equivalent circuits of unbalanced loads supplied with symmetrical and asymmetrical voltage and their identification

Contents A concept of equivalent circuits of three-phase unbalanced loads supplied with symmetrical and with asymmetrical voltage is discussed in the paper. In particular, it is shown that there is an infinite number of equivalent circuits of unbalanced loads supplied with a symmetrical voltage but there is only one equivalent circuit if the voltage is asymmetrical. Also, a method of dynamic identification of the equivalent parameters of unbalanced loads with asymmetrical supply voltage is discussed in the paper.

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Ersatzchaltbilder und identifikation von Schieflasten bei symmetrischer und unsymmetrischer Spannungsversorgung

Übersicht In dem Beitrag wird ein Konzept für Ersatzschaltbilder dreiphasiger Schaltungen mit unsymmetrischer Belastung erörtert. Insbesondere wird gezeigt, daß es für solche Belastungen bei symmetrischer Spannungsversorgung eine unbeschränkte Anzahl von Ersatzschaltungen gibt, jedoch nur eine, wenn eine unsymmetrische Spannungsversorgung vorliegt. Weiterhin wird ein Verfahren zur Identifikation der Parameter unsymmetrischer Belastungen mit unsymmetrischer Versorgung diskutiert.

     

定子为不对称绕组的排列及谐波分析

三相不对称分数槽绕组与对称分数槽绕组相比,没有比较系统的排列方法,只有通过研究分析不对称分数槽绕组的排列特点提出每极每相槽数q的分母为3时绕组排列的新方法,并对q分母为6时绕组排列问题进行了简单的分析.另外,针对不对称绕组中通有不对称电流运行时的磁势谐波问题进行了探讨,编制了Matlab通用程序,并利用程序和新的绕组排...     

ANALYSIS OF SELF-EXCITED INDUCTION GENERATORS UNDER UNBALANCED CONDITIONS

ABSTRACT

This paper presents general mathematical models for various generator-load configurations that accurately determine the conditions for self-excitation and performance characteristics of an isolated, three-phase, self excited induction generator operating under balanced or unbalanced excitation and/or load conditions. The models are derived using symmetrical components theory along with the generator sequence equivalent circuits. The theoretical predictions obtained from the proposed models have been verified experimentally for several balanced and unbalanced configurations.     

PERFORMANCE ANALYSIS OF A HIGH STARTING TORQUE SINGLE-PHASE INDUCTION MOTOR

ABSTRACT

The objective of the work described is to make an assessment of the possible use of three-phase induction motor working as a single-phase motor. The analysis is performed on the proposed winding arrangement, introduced previously by same authors. The analysis includes all motor windings, whereas the conventional analysis is performed on the running winding only. The motor windings are analyzed through the stationary direct and quadrature axes. The magnetic field and E.M.F's of the motor are studied at starting, run-up and running operation. Hence, d-q axis equivalent circuits are deduced to represent the motor at different modes of operation, taking into consideration the core losses and sturation effects. Prediction of the run-up and running characteristics of the motor under investigation is achieved by solving the equations of equivalnet circuits in a simple manner. The predicted results are compared with the releavant experimental results. Good agreement has been achieved, and this confirms the validity of proposed analysis.     

A Contribution to the Frequency Analysis and Transient Response of Power Transformer Windings

Abstract—This article proposes a new approach to study the frequency response and the transient analysis of power transformer windings. For improved accuracy, the suggested model includes, among other equivalent circuit elements, the mutual magnetic couplings between any winding turn and all others. This implies that the equivalent inductance of any considered turn will be a location-dependent parameter. Accordingly, the winding will be analyzed as a non-uniform transmission line. Through the application of a recursive circuit reduction technique, a closed-form Laplace s-domain analytical expression for the winding's input impedance can be obtained for any neutral treatment. The resulting expression can be used to determine the winding's series and parallel resonance frequencies. The s-domain expression for the input impedance, in connection with the numerical inverse Laplace transform, will be utilized for determination of the winding's time-domain transient response for any input voltage or current time waveform. Accuracy increases with the assumed number of winding sections, which can be even increased to the actual number of turns, limited only by the available computation resources. The results of case studies are in good agreement with those available in the literature using the time-domain solution of the simultaneous differential equations in the state variables.     

NON-TRANSFORMATIONAL MATRIX ANALYSIS OF ELECTRICAL MACHINERY

ABSTRACT

The general theory of electrical machines based on space phasor representation of space waves is explained. Harmonics of both the winding distribution and air-gap irregularities are taken into account for any winding asymmetry. Complex winding factors, symmetrical components of instantaneous values, and the winding inductances referring to the air-gap field are obtained during derivation of equation without the use of transformations. All quantities involved are physically defined. The method represents a common basis for analysis and design.     

REVOLVING-FIELD ANALYSIS OF TWO-SPEED SHUNTED CAPACITOR MOTORS WITH NONQUADRATURE WINDINGS

ABSTRACT

The main purpose of this paper is to extend the well-known revolving-field theory for the general development of the so-called analysis equations to predict the performance of two-speed shunted capacitor motors with arbitrary arrangements of their primary windings. It has been found that sometimes by arranging the auxiliary winding at an unconventional location, the motor efficiency can be considerably improved especially at low-speed setting. The accuracy of the present mathematical development has been confirmed by actual measurements on such motors with windings both in quadrature and nonquadrature     

Analysis of Space Harmonic Interactions in Squirrel Cage Induction Machines—Part I: Modeling and the Equivalent Circuit

ABSTRACT

By means of the transition from the symmetrical components to the α, β components regarding the rotor variables it is possible to obtain a linear model of the voltage equations representation. It is shown that, even in this linear formulation the harmonic interactions are not separated. The equivalent circuit which expresses the harmonic interactions and accounts for the stator additional harmonic currents is presented. In the light of this equivalent circuit, the suitable choice of the cage bars number can be performed. It is possible also to make a good base regarding the assessment of the differential leakage.     

CONTROL OF SINGLE PHASE INDUCTION MOTOR USING FORCED-COMMUTATED ELECTRONIC SWITCHES

ABSTRACT

Single phase induction motors require assistant methods for starting, speed-control and reversing direction of rotation. The available methods suffer from many drawbacks. Most of these drawbacks are due to use of mechanical switches in addition to other expensive electrical equipment. This paper suggests a nonconventional versatile method which realizes all the motor requirements. The method uses two forced-commutated electronic switches to feed a single-phase motor which has two symmetrical stator windings. By this circuit, the motor could produce a high starting torque. Also the speed could be controlled and the direction could be reversed. A state space mathematical model has been developed for the motor and its solid state feeding converter. With the aid of the model, the system has been simulated by a developed computer program. Transient starting characteristics have been computed. Also, steady state speed control characteristics have been obtained for different control strategies. The performance of the motor has been compared with other conventional control methods, and with a method which uses naturally commutated electronic switches.     

A MATHEMATICAL MODEL OF THREE-PHASE INDUCTION MACHINES

ABSTRACT

A technique for studying the behaviour of three-phase, wound-rotor induction machines under both transient and steady-state conditions is described. It is arranged to cope with both non-sinusoidal winding distributions and non-linear operation of the magnetic paths. Because such conditions prevent simple expressions from being obtained when transformations are made to produce a two-axis equivalent model, the present analysis is based on the actual machine windings. The basic equation. |v| = |z| |i| is solved for each time step after the appropriate values of the elements in the impedance matrix have been determined by examining the magnetic conditions around the air gap periphery.

The results of particular studies are given.     

3/3相双绕组发电机系统的等效电路模型

整流桥的存在使3／3相双绕组发电机系统成为非线性系统，发电机始终处于非对称运行状态，为了对此进行解析分析，将3／3相双绕组发电机的d,q轴变量分解为低频分量和高频分量分别加以处理，忽略转子回路电阻对高频电流和阻尼绕组对低频分量的作用，在d,q轴超瞬变电抗近似相等的条件下，分别建立了3／3相双绕组发电机系统从整流绕组侧和交流绕组观察的等效电路模型，给出了模型中等效发电机的Park程，稳态运行矢量图及相应稳态量的计算方法，该模型可用于系统稳态和似稳态过程的分析计算。     

一种分析两相不对称绕组电机的新方法

通过不对称绕组磁势的分析,将结构和电气均不对称的两相不对称绕组问题转化为单纯的电气不对称问题,从而将这类绕组的分析问题转化为对称绕组问题。进一步分析了此对称等效绕组的阻抗、等效电路、电磁性能,最终使不对称绕组电机的分析与普通的三相异步电机统一。     

Modeling the saturation processes of a power-transformer core under simultaneous direct and alternating current passing through the winding

A mathematical model of a three-phase two-winding step-up power transformer with the winding circuit Δ/Yo with simultaneous ac and dc currents passed through the grounded winding has been developed. The proposed model is represented by a system of differential equations, which are nonlinear because of the nonlinearity of the inductive resistances of the magnetization curve. The calculation results for a TDTs-400000/242/20 shell–core transformer are given. The model takes into account the effect of dc on the saturation of the power-transformer core, which is especially important under asymmetrical modes that can occur during thunderstorms, seismic activities, or space-weather disturbances.     

Sequence networks to the calculation of two-simultaneous faults at the same location

The system of symmetrical components (012-system) can be used to simulate symmetrical and asymmetrical operation of power systems. However, the classical literature of Power Systems Analysis does not present one equivalent circuit in 012-system to two-simultaneous faults where there are a single-line-to-ground fault and a bolted line-to-line fault. This paper presents the equations and the new equivalent circuit mentioned. In addition, we present a comparison of results between the proposed approach and the output of the commercial software ANAFAS, which validates the methodology. We find evidence that the new equivalent circuit developed can substitute the equivalent circuits used to calculate a single line-to-ground fault and a bolted line-to-line fault.     

不对称六相分数槽绕组磁势分析

针对不对称六相分数槽绕组合成磁势的对称性问题,采用槽号相位图法及单元电机理论,对三种典型的不对称六相绕组磁势进行分析.通过与对称三相及六相绕组比较,得出其合成磁势的性质与分数槽绕组每极每相槽数表达式的整数及小数部分取值有关,其变化规律是:在设计允许范围内,整数部分值选取的越大,其特性就越接近对称绕组;当整数部分值一定,...     

Modeling of the Saturated Leakage Reactance of Induction Motors as a Time Varying Parameter for Transient Computations

ABSTRACT

A procedure has been developed for incorporating the saturated leakage reactance of induction motors into starting transient performance evaluation. An empirical formula has been provided for simulating the envelope of the transient current in terms of time. This faciliated to express the transient rmg stator winding current in terms of time. Then saturated leakage reactance is expressed in terms of the transient rms stator winding current, which in turn, made it possible to express the leakage reactance as a time varying parameter. All types of slot openings, i.e., closed slots, semi closed slots and open slots are considered separately. Transient performance of a machine having closed slots on the rotor and semi closed slots on the stator is evaluated using the approach described in this article and the effect of leakage path saturation is demonstrated.     

Electrodynamics of distributed-parameter induction devices

Contents The search for a self-consistent field theory for linear induction motors entails analysis of the excitation winding of the primary member. Two models for this winding, lending themselves to a relatively simple analysis with the aid of Maxwell's field equations, have been considered in a previous communication. In the present paper, the entire energy conversion process between the stator and the rotor is investigated according to these two models.

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Beitrag zur Theorie linearer Induktionsmaschinen

Übersicht Der Ausbau einer befriedigenden Theorie linearer Induktionsmaschinen erzwingt die Untersuchung der Feldwicklungen des Erregerkreises. Zwei Modelle der Erregerwicklungen wurden in einem früheren Aufsatz untersucht; der gegenwärtige Aufsatz untersucht den vollständigen Energie-Austausch zwischen dem Stator und dem Rotor an Hand der vorgeschlagenen Modelle.