Equivalent circuits for the hunting of electrical machinery

Kron, Gabriel

doi:10.1109/ee.1942.6436294

Cited by 22 publications

(26 citation statements)

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“…Due to the interaction of 6kAE1 harmonics with the rotor slot permeance wave, there is a periodicity of slot harmonics. The harmonics described by equation (21) are not present for all combinations of p and R: This is because the only flux which can produce voltage in a three-phase stator winding is the one that has a number of pole-pairs which the winding itself may produce [27]. To be precise, for a healthy machine to produce a spectrum of principal slot harmonics, the polepair number R AE np; where n is the harmonic order number, should be equal to the polepair number of the space harmonics produced by a phase of the stator winding.…”

Section: Speed Estimation From Motor Current Rshmentioning

confidence: 97%

Neural State Filtering for Adaptive Induction Motor Speed Estimation

Bharadwaj¹,

Parlos²

2003

Mechanical Systems and Signal Processing

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Section: Speed Estimation From Motor Current Rshmentioning

confidence: 97%

Neural State Filtering for Adaptive Induction Motor Speed Estimation

Bharadwaj¹,

Parlos²

2003

Mechanical Systems and Signal Processing

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“…Assume that the system has no variation in the z direction and is excited by a sinusoidally distributed, rotating-current sheet on the stator surface. The field in the air gap must satisfy Laplace's equation, V 2 H = 0, and if the current distribution produces p pairs of poles, the solutions of this equation are of the form 3 -4 and // e = {/4r<"-'> -cos (w o t -pd) sin (co 0 / -pd) (1) where H r and H % are the radial and circumferential components of field strength. The constants A and B can be determined from the boundary conditions, which are that, at the inner surface, // ft is zero, and at the outer surface, // e is equal to the surface current.…”

Section: -Dimensional Cylindrical Configurationmentioning

confidence: 99%

“…1 The approach can also be applied to certain unconventional machines, e.g. linear induction motors, and in cases when detailed analysis is extremely difficult, it can often be used intuitively to predict directions of resultant forces or torques.…”

mentioning

confidence: 99%

Travelling magnetic waves in electrical machines described by rotating vectors

Brown

1969

Proc. Inst. Electr. Eng. UK

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In the special case of machines with rotor dimensions small compared with the wavelength, the travellingwave description of the magnetic field gives little insight into the forces and torques that might be expected. It is shown that a more local description of the field in terms of contrarotating vectors can lead to a simple explanation of the behaviour of these machines. v 1 IntroductionThe travelling-or rotating-wave approach to conventional machines is well established, and has led to the development of equivalent circuits which include the effects of space-harmonic fields or of unbalanced operation. 1 The approach can also be applied to certain unconventional machines, e.g. linear induction motors, and in cases when detailed analysis is extremely difficult, it can often be used intuitively to predict directions of resultant forces or torques. Occasionally, however, and particularly when 'rotor' dimensions are extremely small compared with the wavelength of the field, this intuitive application of the travelling-wave approach seems to break down. 2 It is in these 'small-rotor' cases that the rotating-vector approach developed in this paper is particularly effective. 2Basis of rotating-vector concept 2-dimensional cylindrical configurationConsider a smooth, uniform air gap, the inner cylinder being of high-permeability low-conductivity material. Assume that the system has no variation in the z direction and is excited by a sinusoidally distributed, rotating-current sheet on the stator surface. The field in the air gap must satisfy Laplace's equation, V 2 H = 0, and if the current distribution produces p pairs of poles, the solutions of this equation are of the form 3 -4 and // e = {/4r<"-'> -cos (w o t -pd) sin (co 0 / -pd) (1)where H r and H % are the radial and circumferential components of field strength. The constants A and B can be determined from the boundary conditions, which are that, at the inner surface, // ft is zero, and at the outer surface, // e is equal to the surface current.Referring to Fig. la, it will be seen that at any point r, 6 in the air gap, the resultant field-strength vector H can be resolved into its radial and tangential components, or into two contrarotating vectors, one of magnitude Ar^~] ) and the other of magnitude Br~{ p+l ). The angular velocity of these vectors is o> 0 (i.e. 2n x supply frequency) and not a> o lp, the wave velocity.Alternatively, since Hi 2 b 2 where a = Ar^~]) + Br and b = Ar p~] -Br-(

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“…However, as early as the 1950's, several authors published on spatial-harmonic content of machines with an arbitrary number of phases and higher time-harmonic orders. Both Kron [21] and White [22] considered such multi-phase machines, Kron also considered higher time-harmonic orders. However, neither Kron nor White presented clear equations to determine which harmonic orders are present in the electric machine.…”

Section: A Literaturementioning

confidence: 99%

Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

2016

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The use of power electronics has led to a growing importance of higher time-harmonic content in electrical machines. To gain insight in phenomena related to these higher harmonics, such as noise and losses, a good understanding of the magnetic field's harmonic content is mandatory. Moreover, the development of fast and accurate, harmonic-based, analytical models requires a qualitative knowledge of the machine's time-and spatial-harmonic content. Although the harmonic content of electric machines is an extensively studied topic, previous publications tended to focus on one type of synchronous machines and often didn't consider higher time-harmonic orders. This work complements the existing theory by providing a more general approach, thereby covering machines and operating points that weren't covered until now. It considers both three-phase and multi-phase machines with an odd number of phases. The winding distribution can either have an integer or a fractional number of slots per pole and per phase and higher time-harmonic content is regarded as well. Note that saturation is neglected. Despite its general validity, the work succeeds at providing one simple equation to determine the machine's time-and spatial-harmonic content. Moreover, the work also extensively discusses the physical causes of the harmonic content. The combination of this general validity, the simple result and the insight in the physics makes that this work is a strong tool to both study harmonic-related phenomena in electric machines and to develop harmonic-based analytical models.

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Equivalent circuits for the hunting of electrical machinery

Cited by 22 publications

References 0 publications

Neural State Filtering for Adaptive Induction Motor Speed Estimation

Neural State Filtering for Adaptive Induction Motor Speed Estimation

Travelling magnetic waves in electrical machines described by rotating vectors

Time- and Spatial-Harmonic Content in Synchronous Electrical Machines

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