Generalised theory of induction motors with asymmetrical primary windings, and its application to the analysis and performance prediction of shaded-pole motors

Butler, O.I.; Wallace, A.K.

doi:10.1049/piee.1968.0122

Cited by 16 publications

(2 citation statements)

References 15 publications

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“…It may readily be shown, using a previous paper of the authors, 8 that the tapped-quadrature windings of Fig. 4 are equivalent to the nonquadrature windings of Fig.…”

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confidence: 92%

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Equivalent circuit for nonquadrature, tapped-quadrature and shaded-pole single-phase induction motor

Wallace

Butler

1968

Proc. Inst. Electr. Eng. UK

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SynopsisIt is shown that the nonquadrature, tapped-quadrature and shaded-pole forms of single-phase induction motor can be equivalent to a conventional quadrature motor having a common line impedance. It follows that a single equivalent circuit can be used to determine the performance of each form of motor, provided that appropriate values are employed for the circuit elements in each case. In consequence, the same arrangement of a given type of analogue computer can be used to predict the performance of all three special forms of single-phase motor, as well as the conventional quadrature motor. Further, in contrast to some existing equivalent circuits, the presented circuit has the advantage of direct representation of the actual supply currents taken by each form of motor without any transformation of the supply voltage. -xu -dU -z\ N M{ , List of symbolsThe suffixes 1 and n are used to denote quantities associated with the fundamental and /Jth-harmonic space m.m.f.s, respectively./?" = electrical angular displacement of the phasewinding magnetic axes E M |, E A | = e.m.f.s induced in main and auxiliary windings, respectively, by air-gap fluxes E Y \ -e.m.f.s in tapped portions of main winding = e.m.f. in quadrature-axis winding of tappedquadrature windings E qX = e.m.f. in direct-and quadrature-axis windings of equivalent quadrature motor / = current drawn from supply > IA = main-and auxiliary-winding currents Iqn = currents of effective direct-and quadratureaxis windings of equivalent-quadrature motor N Ai = effective number of fundamental turns of main and auxiliary windings , N A = actual number of turns of main and auxiliary windings Nyn -number of turns in tapped portions of main winding number of turns in quadrature winding of tapped-quadrature motor N dn , N qn = number of effective turns of direct-and quadrature-axis windings of equivalent quadrature motor R,\ = resistance of secondary windings referred to effective fundamental of main winding S = fractional speed V = supply voltage XM\ = primary-to-secondary mutual reactance referred to effective fundamental of main winding X rX = secondary leakage reactance referred to effective fundamental of main winding Paper 5699 P, first received 1st July and in revised form 4th September N Zn = X' MA = portion of main-winding leakage reactance due to leakage flux which also links auxiliary winding X' AM = portion of auxiliary-winding leakage reactance due to leakage flux which also links main winding X MA = mutual reactance between main winding and auxiliary winding = \f(X' MA X' AM ) Z M , Z A = complete leakage impedance of main and auxiliary windings, including any externally connected elements Z' M , Z' A = (Z M -JX'MA) and (Z A -jX' AM )Z c = common-line impedance of equivalent quadrature motor Z d , Z q -leakage impedance of direct-axis and quadrature-axis windings of equivalent quadrature motor Z x , Z Y , Z z = leakage impedance of respective limbs of tapped-quadrature motor 1

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“…It may readily be shown, using a previous paper of the authors, 8 that the tapped-quadrature windings of Fig. 4 are equivalent to the nonquadrature windings of Fig.…”

mentioning

confidence: 92%

“…The general circuit will be derived, first, by demonstrating that all such motors can be represented by a quadrature motor having a common-line impedance and, secondly, using a recent method of analysis which is particularly suited for the present purpose. 8 …”

Section: Introductionmentioning

confidence: 99%