Abstract
Two basic variants of combined star-delta stator windings of induction machines are analysed. The aim of the use of the combined winding is to suppress a chosen group of higher spatial harmonics of the current layer and magnetic flux density in the air gap and the magnetic flux in the yoke. The suppression of the higher spatial harmonics results in decreasing the losses and improving the energy efficiency of the machine. The differential equations are stated for both the considered variants. On the basis of the numerical solution of these equations, the ability of individual variants to suppress higher harmonics has been shown. The validity of the equations has been verified by experimental measurements on a physical model of an induction machine with the combined star-delta stator winding.
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Abbreviations
- i :
-
Current of single conductor
- \({{\varvec{i}}}_{\nu }\) :
-
Space vector of \(\nu \hbox {th}\) space harmonic of current layer
- \(\gamma \) :
-
Angle determining position of conductor in complex reference plane
- \(\beta \) :
-
Angle determining position of phase winding in complex reference plane
- \(N_d \) :
-
Number of conductors in slot
- \({{\varvec{i}}}_{Nd\nu } \) :
-
Space vector of \(\nu \hbox {th}\) current wave of slot
- \({{\varvec{i}}}_{N\nu } \) :
-
Space vector of \(\nu \hbox {th}\) current wave of phase
- \(\kappa _\nu \) :
-
Winding factor for spatial harmonic of order \(\nu \)
- \(Q_f \) :
-
Number of slots of phase winding
- \({{\varvec{i}}}_{n\delta } \) :
-
Current wave of fundamental harmonic of delta-connected winding
- \(i_{A\delta }, i_{B\delta }, i_{C\delta } \) :
-
Phase currents of delta-connected winding
- \(\kappa _\delta \) :
-
Winding factor for delta-connected winding
- \(N_\delta \) :
-
Number of conductors of single phase of delta-connected winding
- \({{\varvec{u}}}_\delta \) :
-
Symmetrical component of phase voltages of delta-connected winding
- a :
-
Complex operator \(\hbox {e}^{j\frac{2\pi }{3}}\)
- \({{\varvec{i}}}_\delta \) :
-
Symmetrical component of stator current of delta-connected winding
- \(\alpha \) :
-
Angle between axes of delta- and star-connected windings
- \(\kappa _\lambda \) :
-
Winding factor for star-connected winding
- \(N_\lambda \) :
-
Number of conductors in phase of star-connected winding
- \(i_{A\lambda },\,i_{B\lambda },\,i_{C\lambda } \) :
-
Phase currents of star-connected winding
- \({{\varvec{u}}}_\lambda \) :
-
Symmetrical component of phase voltages of star-connected winding
- \(R_\lambda \) :
-
Stator resistance of star-connected winding
- \(R_\delta \) :
-
Stator resistance of delta-connected winding
- \(L_{\sigma \lambda } \) :
-
Leakage inductance of star-connected winding
- \(L_{\sigma \delta } \) :
-
Leakage inductance of delta-connected winding
- \(L_{h\lambda } \) :
-
Main inductance of star-connected winding
- \(L_{h\delta } \) :
-
Main inductance of delta-connected winding
- \(L_1 \) :
-
Inductance of single conductor
- \(R_\mathrm{R}\) :
-
Rotor resistance
- \(L_{\sigma \mathrm{R}} \) :
-
Rotor leakage inductance
- \(m_\mathrm{R} \) :
-
Number of rotor phases
- \(\kappa _\mathrm{R} \) :
-
Winding factor of rotor
- \(N_\mathrm{R} \) :
-
Number of conductors of single rotor phase
- \(T_\delta \) :
-
Torque generated by delta-connected winding
- \(T_\lambda \) :
-
Torque generated by star-connected winding
- J :
-
Moment of inertia
- \(\omega _\mathrm{m} \) :
-
Mechanical angular speed
- T :
-
Resulting torque
- \(T_\mathrm{l} \) :
-
Load torque
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Acknowledgements
This work was supported by the Czech Science Foundation under research Grant 16-07795S and by the institutional support RVO 61388998. The authors would like to thank the company ATAS elektromotory Náchod, a.s., for cooperation and manufacturing the experimental machine.
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Schreier, L., Bendl, J. & Chomat, M. Comparison of properties of two basic variants of combined star-delta stator winding of induction machines. Electr Eng 100, 2155–2164 (2018). https://doi.org/10.1007/s00202-018-0695-7
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DOI: https://doi.org/10.1007/s00202-018-0695-7