Electrical Machines II Lecture Notes

Course Overview

• Focus on:
  • Three-phase induction motors
  • Single-phase induction motors
  • Synchronous motors
• Essential prerequisites:
  • Basic knowledge of windings in electrical machines
  • Prior coursework in transformers and DC machines

Basic Principles of Rotating Machines

• Common underlying principles for all standard electrical motors (DC, single-phase, three-phase induction & synchronous motors)
• Study centers around steady-state performance analysis of machines
• Importance of drawing equivalent circuits for performance prediction

Transformer Equivalent Circuit

• Start with the transformer equivalent circuit from circuit analysis perspective.
• Key Components:
  • Primary side:
    • Resistance (r1), Leakage reactance (xl1)
    • Magnetizing inductance (jXm)
  • Secondary side:
    • Resistance (r2), Leakage reactance (xl2)
• Transformer ratios:
  • a = N1/N2 (primary to secondary turns ratio)
  • Primary connected to the source (V1)
• Assume no core loss for initial analysis

Inductance Concept

• Definition of inductance:
  • Inductance (L): Flux linkage per unit current
• Inductance of a coil:
  • L = (N * PHI) / I
  • Flux (PHI) includes both mutual and leakage components
• Leakage inductance (Ll1, Ll2) is crucial for self-inductance calculations

Mutual Inductance

• Mutual inductance is defined for two coils sharing a magnetic circuit.
  • M21: Flux linkage with coil 2 due to current in coil 1
  • M12: Flux linkage with coil 1 due to current in coil 2
• Important conclusion:
  • M12 = M21 for coils sharing the same magnetic circuit

Magnetic Circuit Analysis

• Magnetomotive force (mmf) for flux calculation:
  • PHIm1 = mmf / reluctance
  • PHIm2 = mmf / reluctance
• Use of reluctance formula:
  • Reluctance (R) = (l_mean) / (µ0 * A)

Summary of Key Equations

• Self Inductance of Coils:
  • L1 = N1 * PHIm1 / I1 + Ll1
  • L2 = N2 * PHIm2 / I2 + Ll2
• Mutual Inductance Equations:
  • M21 = N2 * PHIm1 / I1
  • M12 = N1 * PHIm2 / I2
• Final conclusion on Mutual Inductance:
  • M = M12 = M21

Future Topics

• Next units will focus on deriving the transformer equivalent circuit considering self and mutual inductances, without core losses.