Abstract
This paper presents an important method for the algebraic synthesis of the winding layout of AC machines. It applies in general to integral-slot and fractional-slot windings, including non-overlapping windings, so it can be claimed to unify the synthesis task. Moreover, it results in the highest possible winding factor at the working harmonic. A harmonic content analysis is presented, including the calculation of the winding factor by the closed-form expression of Klíma for several examples, which also applies in general to the entirety of this class of windings. Exact agreement with the calculation based on the DFT corroborates the results.
Zusammenfassung
In diesem Beitrag wird eine Methode für die algebraische Wicklungsauslegung von Drehfeldmaschinen vorgestellt. Die Systematik ist gültig für symmetrische Ganzloch- und Bruchlochwicklungen mit verteilten sowie geometrisch konzentrierten Spulen und vereinheitlicht die Syntheseaufgabe. Darüber hinaus führt es zum höchstmöglichen Wicklungsfaktor der Arbeitswelle. Eine Analysemethodik des Oberwellengehalts wird vorgestellt, die die Berechnung der Wicklungsfaktoren durch den geschlossenen Ausdruck von Klíma einschließt, der allgemein für die Gesamtheit dieser Klasse von Wicklungen gilt. Die Untersuchung schließt mit der Anwendung des Ansatzes auf mehrere Beispiele. Eine exakte Übereinstimmung mit der Berechnung auf Basis der DFT untermauert die Ergebnisse.
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Abbreviations
- \(Q\) :
-
Number of stator slots
- \(p\) :
-
Number of pole pairs
- \(\mathrm{{b}}\) :
-
Subscript: basic winding
- \(k_{\mathrm{{w}}}\) :
-
Winding factor
- \(k_{\mathrm{{d}}}\) :
-
Distribution (breadth) factor
- \(k_{\mathrm{{p}}}\) :
-
Pitch (chording) factor
- \(m\) :
-
Number of phases
- \(n_{\mathrm{{l}}}\) :
-
Number of layers
- \(T_{\mathrm{{ph}}}\) :
-
Series turns per phase
- \(I_{\mathrm{{c}}}\) :
-
Coil current
- \(T_{\mathrm{{c}}}\) :
-
Coil turns
- \(q\) :
-
Slots per pole and phase, \(q =\frac{Q}{m2p}\)
-
: -
Reduced numerator/denominator of \(q\)
- \(q_{1}\) :
-
Slot number assigned to positive phase belts
- \(q_{2}\) :
-
Slot number assigned to negative phase belts
- \(t\) :
-
Winding symmetry factor
- \(y_{\mathrm{{p}}}\) :
-
Theoretical coil pitch
- \(y_{\mathrm{{d}}}\) :
-
Implemented coil pitch
- \(Y_{\mathrm{{k}}}\) :
-
Fictitious commutator pitch
- \(\nu \) :
-
Harmonic order
- \(\text{gcd}\) :
-
Greatest common divisor
- \(\text{SC}\) :
-
Enhanced symmetrical component
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Germishuizen, J., Steckel, R. & Kremser, A. Algebraic synthesis and analysis of windings for AC machines. Elektrotech. Inftech. 138, 78–84 (2021). https://doi.org/10.1007/s00502-021-00873-6
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DOI: https://doi.org/10.1007/s00502-021-00873-6