16. 3 Phase Circuits

• Three Phase Circuits


  • More power out of a given generator
  • Coils all around the stator
• Balanced Load


  Total power in all three phases is constant over the a.c. cycle so motor torques are constant
• Single phase at 50 Hz

  Power oscillates at 100 Hz
• Three phase motors


  Can make very simple motors (rotating field)
• Alternator


  • Electromagnet rotating inside 6 coils
  • AA' connected in series – one phase winding – RED
  • BB' connected in series – one phase winding – YELLOW
  • CC' connected in series – one phase winding – BLUE
• Rotor flux linking A and A'

  Peaks at qA = 0o
• VP at RMS value


  VA phase emf
• Single Phase a.c. Generator (alternator)


  1. Magnetic field via D.C. Currents

  2. Rotating Field:

  3. Large voltages, heavy insulation, inertia

  4. Low current losses (I2R) at slip rings and brushes

  5. Small alternators use permanent magnets (brushless)
• Maximum emf when field cuts coils at 90o
• Distribution Factor


  0.644 for single phase, maximum of 0.966 for 3 phase system
• 3 phase: Three identical single phases
• 3 phase, 6 wire

  3 sine waves 120o out of phase
• Phasor representation of 3 phase voltages
• 3 phase, 4 wire system

  • Load in STAR Configuration
  • Balanced load (all same), no current in neutral - wire not necessary
• Single phase


  Each load 2 lines – total current 600A
• 3 phase 6 wire

  Each line requires 200A (Area = 1/3 single phase)
• 3 phase 4 wire

  Saving 3.5:6 wrt 3 phase, 6 wire system (neutral takes less current)
• National Grid Savings (cables)
• Line and Phase Quantities in STAR, Y


  • Phase Voltage Vph developed between appropriate line and neutral
  • Line Voltage VL difference (phasor) in potential between any pair of lines
  • Line Current = Phase Current i.e. IL = Iph

  
• Relationship between line and phase voltages
• 400 kV transmission line

  • 400 kV rms between lines (i.e. line voltage)
  • Between line and earth
  • Peak between line and earth
• Standard "medium" voltage distribution in UK

  • 415V between lines
  • Phase voltage = between line and neutral
  • Domestic consumer voltages
• Supply: 415V, 50Hz, 3 phase balanced load


  1. Calculate:

  2. Phase voltage

  3. Line current drawn from supply

  4. Power dissipated
• Delta or Mesh Connection


  • VL = Vph
  • Current along each line is a phasor difference of a pair of phase currents
• Power Dissipation in Star and Delta Loads

  • Per Phase: Pph = Vph Iph cos(F) Watts
  • Total Power: PT = 3 Pph = 3 x Vph Iph cos(F) Watts
  • Star Connected Load
  • Delta Connected Load
• Delta


  • Power factor = 0.8
  • Pdelta = 3 Pstar
• Advantages of 3 phase Systems

  • Whole of stator of a 3 phase system is used (single phase uses 2/3 of stator)
  • Better distribution factor
  • 3 phase, 4 wire provides cable savings
  • 3 phase, 4 wire provides a.c. for industrial and domestic users
  • For a given machine size, 3 phase power output is greater and more constant
  • 3 phase produces a rotating magnetic field – single phase produces a pulsating field
  • 3 phase motors are inherently self starting - single phase are not
  • Torque produced by 3 phase motors is smooth – single phase motor torque is pulsating