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  • 1. MMME2104 Design & Selection of Mining Equipment Electrical Component Transformers Lecture 5 2 September 2003
  • 2. Lecture Outline • • • • • • Transformers introduction Ideal Transformers Non-Ideal (actual) Transformers Transformer losses and power rating Three-phase transformers Transformer construction
  • 3. Transformers Make possible: • Power generation at the most economical level • Transmission and distribution at the most economical level • Power utilisation at the most economical level • Measurement of high voltages and high currents • Impedance matching • Electrical isolation between circuits
  • 4. Transformers: Operating Principle Voltage induced in a coil (flux linking equation): V = 4.44fNΦmax where V = induced voltage (V) F = flux frequency (Hz) N = number of turns in coil Φmax = peak value of flux (Wb)
  • 5. Ideal Transformers Zero leakage flux: • Fluxes produced by the primary and secondary currents are confined within the core The windings have no resistance: • Induced voltages equal applied voltages The core has infinite permeability • Reluctance of the core is zero • Negligible current is required to establish magnetic flux Loss-less magnetic core • No hysteresis or eddy currents
  • 6. Ideal Transformers Voltage / Current relationships: V1 i2 N1 = = = a = turns ratio V2 i1 N 2 power in = power out MMF 1 = MMF 2
  • 7. Ideal Transformers Impedance Ratio: Z1 V1 V2 V1 i2 2 = ÷ = × =a Z 2 i1 i2 V2 i1 Z1 = a 2 Z 2 - can “refer” impedance parameters on primary side to secondary side, or vice versa
  • 8. Actual Transformers • Have resistance in the windings • Not all of the flux produced by one winding links with the other (flux leakage) • Magnetic core has finite permeability • Core losses – Hysteresis – Eddy currents
  • 9. Actual Transformers Primary winding flux: Secondary winding flux: Φ1 = ΦM + ΦL1 Φ2 = ΦM - ΦL2 dΦ M di1 dΦ M dΦ L1 + N1 = i1 R1 + L1 + N1 V1 = i1 R1 + N1 dt dt dt dt dΦ M di2 dΦ M dΦ L 2 + N2 = −i2 R2 + L2 + N2 V2 = −i2 R2 − N 2 dt dt dt dt Turns ratio now relates to induced voltages, rather than applied voltage a = N1/N2 = e1/e2
  • 10. Core losses Core magnetisation
  • 11. Transformer Losses Transformer losses consist of: • Copper losses in the windings – Depend on load current • Hysteresis and eddy-current losses in the core – Constant for constant flux (constant voltage) conditions • Stray losses due to currents induced by leakage fluxes in the transformer structure – Negligible for a well-designed transformer
  • 12. Transformer Rating Transformer ratings are provided to keep the operating temperature within acceptable limits. A transformer’s rating is based upon the following: • Nominal current – To limit copper losses • Nominal voltage and frequency – To limit core losses – Transformer size based upon flux density limit in core material • Apparent power rating – Based on product of nominal current and nominal voltage – A transformer can become fully loaded at sufficient levels of reactive power, even if no real power is being delivered. • Cooling
  • 13. Transformer Cooling • Cooling of a transformer increases the rate of heat dissipation and hence improves the transformer rating: • Low-voltage indoor transformers (<200kVA) can be passively air-cooled via natural convection • Relative to air, oil is a better thermal conductor and electrical insulator, so it is invariably used for cooling of high-voltage, high-power transformers. • As power rating increases, radiators, heat exchangers and forced oil/air circulation may be added to improve power dissipation
  • 14. Three Phase Transformers Can be formed as: • 3 single phase transformers connected together – Star/Delta winding arrangements – Easy to replace failed units • Common core device – Lighter and cheaper than 3 individual units – 6 rather than 12 external connections – Whole transformer must be replaced if single winding fails • For both cases analysis procedure identical!
  • 15. 3-Phase Transformer Windings Star-Star: • Can develop voltage imbalance and harmonic issues Delta-Delta: • Circulating path good for harmonics Star-Delta or Delta-Star: • Star-Delta quite common since it utilises insulation so well (effective turns ratio increase)
  • 16. Transformer Construction Power transformers are designed such that their characteristics approach the ideal: • To attain high permeability, cores are made of ironbased materials • To minimise core losses, core is laminated from highresistivity, high-grade silicon steels • Leakage reactances are minimised by co-winding of the coils • Geometries are optimised to minimise turn lengths, maximise core window areas and achieve highest power densities