Windings are the physical foundation for generating rotating magnetic fields. This chapter transitions from the physical structure of windings to a tractable mathematical description. Starting with a typical three-phase winding, it introduces fundamental geometric parameters such as slot number, pole number, pitch, and phase belt. The chapter derives the rectangular MMF wave of a single coil and the sinusoidal rotating MMF wave produced by balanced three-phase excitation, and employs the mathematical tool of “space vectors” to represent current, voltage, and flux linkage. The Clarke and Park transformations are introduced to link the three-phase stationary ABC frame with the two-phase rotating DQ frame. Under the constraint of equal-amplitude transformation, the power and torque conversion relationships between orthogonal two-phase and symmetrical three-phase systems are provided.

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Three-Phase AC Windings and Their Magnetic Fields

  • Yeqin Wang,
  • Zaimin Zhong,
  • Stephan Rinderknecht

摘要

Windings are the physical foundation for generating rotating magnetic fields. This chapter transitions from the physical structure of windings to a tractable mathematical description. Starting with a typical three-phase winding, it introduces fundamental geometric parameters such as slot number, pole number, pitch, and phase belt. The chapter derives the rectangular MMF wave of a single coil and the sinusoidal rotating MMF wave produced by balanced three-phase excitation, and employs the mathematical tool of “space vectors” to represent current, voltage, and flux linkage. The Clarke and Park transformations are introduced to link the three-phase stationary ABC frame with the two-phase rotating DQ frame. Under the constraint of equal-amplitude transformation, the power and torque conversion relationships between orthogonal two-phase and symmetrical three-phase systems are provided.