On a mathematical model of squirrel-cage induction motors

Contents This paper presents a mathematical model of 3-phase squirrel-cage induction motor accounting for a very high number of space harmonics in which, due to application of a special transformation of voltages and currents, a differential equation system with constant coefficients is obtained. The number of space harmonics is so high that it is possible to perform a direct computation of the alternating component of the electromagnetic torque which decides on the parasitic synchronous torque.An application example of this model for the analysis of steady and dynamic states of a concrete squirrel-cage motor is given.

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Über ein mathematisches Modell des Käfigläufermotors

Übersicht Im Artikel wird ein mathematisches Modell dreiphasiger Käfigläufermotoren mit Berücksichtigung einer großen Zahl räumlicher Harmonischer vorgestellt. Unter Anwendung einer speziellen Transformation der elektrischen Spannungen und Ströme erhält man ein Gleichungssystem mit konstanten Koeffizienten Die Zahl der räumlichen Harmonischen ist so groß, daß die Berechnung der Wechselkomponenten des elektromagnetischen Moments und damit des parasitären synchronen Moments möglich ist. Die Anwendung des mathematischen Modells wird anhand eines Beispiels für dynamischen und statischen Betrieb vorgestellt.

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List of symbols and abbreviations N number of bars of the rotor cage - L ₈ total self inductance of stator phase winding - M ₈ mutual inductance of stator windings - R _rg,L _rg resistance and leakage inductance of a rotor end ring segment-respectively - R _b,L _b resistance and leakage inductance of a rotor cage bar-respectively - k=0,1, ... N—1 number of the rotor currents symmetric component and theM _sr matrix column corresponding to it - l equivalent axial length of stator core - equivalent width of air-gap - p pole pair numer - z number of turns per phase - v order of harmonic - k _sv stator winding coefficient for thev-th harmonic - k _rv rotor winding coefficient for thev-th harmonic - k _skv skewness coefficient for thev-th harmonic - U _s stator voltage vector in symmetrical components - U _r rotor voltage vector in symmetrical components - i _s stator current vector in symmetrical components - O zero matrix - R _s stator resistance matrix - R _r rotor resistance matrix - LL _s stator inductance matrix - L _rr rotor inductance matrix - M _sr matrix of stator-rotor mutual inductances - T _e electromagnetic torque - T _m motor load torque - rotor position angle - ₀ initial rotor position angle - rotor angular velocity - (*) conjugation index of a complex number - Re {y} real part of a complex number - Im {y} imaginary part of a complex number - T transposition index - [X] ^x highest integer not greater thanX and of the same sign asX - U r.m.s. value of the phase voltage - _u pulsation of supply voltage     

异步电动机T型等值电路参数估算的新方法探讨

提出一种基于铭牌数据的三相异步电动机T型等值电路参数的新估算方法 ,有较强的实用价值。并为进一步研究更加准确的的异步电动机参数辨识方法打下良好基础     

TEFC induction motors thermal models: a parameter sensitivity analysis

With the increasing pressures on electric motor manufacturers to develop smaller and more efficient electric motors, there is a trend to carry out more thermal analysis in parallel with the traditional electromagnetic design. It has been found that attention to thermal design can be rewarded by major improvements in the overall performance. Thus, there is a requirement for accurate and reliable thermal analysis models that can be easily incorporated into motor design software. In this paper, emphasis is given to thermal sensitivity analysis of totally enclosed fan-cooled induction motors. In particular, thermal parameters are modified and their effects on the temperature rise shown. The results are useful for identifying the most important thermal parameters and enable robust designs to be developed that are insensitive to manufacturing tolerances.     

笼型感应电机流体流动对温度场分布的影响

以一台Y802-2型笼型感应电机为例,对中小型感应电机三维流体流动与传热进行了研究。根据样机的通风结构及传热特点,建立外部近似无限大流场空间与电机三维有限元结构模型,并在电机内外流场空间中建立了转子表面旋转流体薄层和风扇旋转流体区域。给定流场空间中运动区域与静止区域边界条件及基本假设,采用有限体积法对流体运动方程和能量方程进行耦合求解,可以得到流场中流体介质的运动状态以及电机内外各个表面的散热系数,并以此为依据对电机三维全域温度场进行数值计算。将流体场耦合计算得到的温度场分布和传统温度场计算结果分别与实验测量值进行了比较,证明了中小型感应电机三维流体场与温度场存在着强烈的耦合关系,基于流体流动的温度场计算结果较传统方法得到的温度分布更具准确性与合理性。     

高速短初级直线感应电动机等效电路模型及时变参数辨识

由于受到动态纵向边端效应和铁心饱和的影响,直线感应电机传统等效电路模型电磁参数时变.针对此,本文提出了多因素耦合影响下高速短初级直线感应电机等效电路模型及其时变参数辨识方法.首先,分析不同工况下电机推力变化规律;其次,分析电机电磁参数与运行工况之间的规律,提出激磁电感和次级电阻修正系数,构建直线感应电机改进等效电路模型,并通过响应面分析法计算两个修正系数;最后,开展样机静态堵驻实验和动态实验.计算和实测结果表明:推力计算值与实测值误差不超过4.1％,端口基波正序阻抗的实部、虚部计算值与实测值误差不超过4.7％,验证了时变参数辨识的准确性.     

Sensorless vector control of induction motors at very low speed using a nonlinear inverter model and parameter identification

The performance of vector-controlled induction motor drives without a speed sensor is generally poor at very low speed. The reasons are offset and drift components in the acquired feedback signals, voltage distortions caused by the nonlinear behavior of the switching converter, and the increased sensitivity against model parameter mismatch. New modeling and identification techniques are proposed to overcome these problems. A pure integrator is employed for stator flux estimation which permits high-estimation bandwidth. Compensation of the drift components is done by offset identification. The nonlinear voltage distortions are corrected by a self-adjusting inverter model. A further improvement is a novel method for online adaptation of the stator resistance. Experiments demonstrate smooth steady-state operation and high dynamic performance at extremely low speed.     

Analysis of currents and an electromagnetic torque in steady states of induction squirrel-cage motors with asymmetric stator windings

Contents The paper presents a mathematical model of an asynchronous squirrel-cage motor with arbitrarily asymmetrical stator windings. The structure of the mathematical model equations is analysed in detail using the assumption about the symmetry of the rotor cage. A particular arrangement of the mutual inductance matrix of stator windings and rotor cage meshes is shown. As a result of applying of a special analysis method, the frequency spectrum of currents and electromagnetic torque in steady state of a squirrel-cage motor with asymmetrical stator windings is determined. Relationships are given which allow to calculate the currents and the electromagnetic torque quantitatively.—An analysis of a short-circuit of an elementary coil in one of the phases of an otherwise fully symmetrical motor is given as an application example.

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Analyse der Ströme und des Moments einer stationär betriebenen Käfigläfer-Asynchronmaschine mit unsymmetrischen Ständerspulen

Übersicht In dem Aufsatz wird das mathematische Modell einer Käfigläufer-Asynchronmaschine mit beliebig unsymmetrischen Ständerspulen vorgestellt. Die Struktur der Gleichungen des mathematischen Modells wird unter Ausnutzung der Symmetrie des Rotorkäfigs eingehend untersucht. Der besondere Aufbau der Matrix der Gegeninduktivitäten zwischen den Ständerspulen und den Maschen des Rotorkäfigs wird dargestellt. Als Ergebnis der Anwendung einer speziellen Methode der Analyse wurden die spektralen Zusammensetzungen der Ströme und des Moments einer stationär betriebenen Maschine mit den unsymmetrischen Ständerspulen bestimmt. Die Zusammenhänge, die eine quantitative Berechnung der Ströme und des Moments ermöglichen, wurden angegeben.—Eine Analyse der Maschine, die eine kurzgeschlossene Spule in einem Ständerstrang besitzt und die sonst symmetrisch ist, wurde als Anwendungsbeispiel dargestellt.

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List of symbols A transformation matrix - C matrix of constraints - I unit matrix - i _r vector of the meshes currents in the rotor cage - i _s vector of currents of the elementary stator coils - i _sc vector of currents of the stator after used the matrix of constraints - L _s ,L _r matrices of leakage inductances of the elementary stator coils and of the rotor cage meshes - L _s ^m ,L _r ^m matrices of self and mutual inductances of elementary stator coils and of rotor cage meshes following from main flux - L _ss ,L _se matrices of slot and of end-connections leakage inductances of the elementary stator coils - M _sr () matrix of mutual inductances of elementary stator coils and rotor cage meshes - R _r matrix of resistances of rotor cage meshes - R _s matrix of elementary stator coils resistances - S, T transformation matrices - U _s vector of voltages of the elementary stator coils - b _r ,b _s effective width of rotor and of stator slot mouth - c _rv coefficient of rotor slot pitch - c _sv coefficient of stator slot pitch accounting for the trapezoidal form of a m.m.f. - g _v coefficient of rotor slot skew - J moment of inertia - k _rv span factor of cage mesh - k _svi span factor of elementary stator coil - k _cs ,k _cr Carter coefficients of stator and rotor - l equivalent length of the motor iron - M number of elementary stator coils - N number of rotor slots - r mean radius of the air-gap - R _b resistance of a cage bar - R _e resistance of end-ring segment of the cage - T _e electromagnetic torque - T _m mechanical load torque - x _s rotor slot skewness angle - y _i pitch of a coil - z _i ,z _j numbers of turns in a coil - _i position angle of the center of a coil - , value and equivalent value of the air-gap - magnetic conductance - ₀ initial rotor position angle - angular velocity - ₀ pulsation of the voltage - () ^T transposition of vector or matrix - (*) conjugate value     

Detection of rotor faults in squirrel-cage induction machines atstandstill for batch tests by means of the Vienna monitoring method

This paper addresses the possibility of integration of an induction machine rotor fault monitoring technique into batch tests. Conventional monitoring techniques are designed for operating conditions near nominal speed and load. Generally, load torque is not available at batch test as the test sample should not or cannot be clutched. However, at standstill, shaft torque and rotor currents are big enough to enable rotor monitoring. Therefore, short-circuit tests are applicable for diagnostic purposes. This application is demonstrated by means of the Vienna Monitoring Method, which is a model-based torque evaluation technique     

Rotor bar fault diagnosis in three phase induction motors by monitoring fluctuations of motor current zero crossing instants

This study describes broken bar detection in induction motors without using additional sensor. It is based on observation of the fluctuations of stator current zero crossing times (ZCT). Instead of sampling motor current with a high resolution A/D converter, zero crossing instants are recorded as waveforms cross zero. Fluctuations in the intervals between successive zero crossings of the three phase current waveforms are analysed using Fast Fourier Transforms (FFT). Diagnostic information is found in the spectrum of the ZCT signal through the presence of specific fault related frequencies. A rotor bar fault is manifested as an increase in the amplitude of the 2sf and other spectral components. This paper analyses the effect of an electrically unbalanced rotor on the ZCT spectrum of stator current, and discusses the various frequency components associated with rotor bar faults seen in the ZCT spectrum. It is important to eliminate the dependence of the index on the parameters of the induction motor. Particularly, the effect of motor inertia, supply harmonics, and variable load are discussed to increase the reliability of the rotor fault index, and simulation results are presented. It is found that the 2sf frequency component is independent of inertia, load, and harmonics, and thus it is suitable as an index for broken rotor bar.     

Effects of rotor bar and end-ring faults over the signals of a position estimation strategy for induction motors

The effect of rotor faults, such as broken bars and end-rings, over the signals of a position estimation strategy for induction motor drives is analyzed using a multiple coupled circuit model. The objective of this analysis is to establish the possibility of using the estimation strategy signals for fault diagnosis in variable-speed electric drives. This strategy is based on the effect produced by inductance variation on the zero-sequence voltage, when exciting the motor with a predefined inverter switching pattern. Experimental results illustrate the feasibility of the proposal.     

EMTDC异步电动机模型及起动过程仿真

详细介绍了EMTDC中三相异步电动机模型,尤其是机械部分模型,给出了机械部分与电气部分的接口以及暂态求解过程.基于EMTDC对正常情况、定子匝间短路及转子断条故障时的起动转速-转矩关系进行了仿真研究,得出了仿真曲线,分析结果证明利用EMTDC可为内部故障诊断提供一个仿真环境.     

A simplified equivalent thermal circuit for the substitution of a stator in an induction motor

Based on a review of investigations of the thermal behavior of induction motors, it has been established that the stator winding of an induction motor is subject to very high values of temperature in most applications and work regimes. The analysis of techniques to determine the temperatures of different units of an induction motor helped us to propose the use of equivalent thermal circuits, in particular, a simplified substitution circuit for the determination of winding and a magnetic conductor of a stator. The thermal equilibrium equations were found. A technique to calculate the thermal resistances of a stator by means of a laboratory setup was developed. The setup considers the features of cooling specific types of motors; thus, it is unnecessary to observe an induction motor as an aerodynamic system. The technique was tested using a setup containing a 14-kW short-circuited induction motor. The temperatures in different units of a motor were measured using chromel–copel thermocouples, and its load simulated the load of a traction electric drive of transport vehicles. The results of the experimental investigation are presented to show the influence of the rotor speed and the cooling air flow on the thermal resistances.