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.
6. 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
7. Ideal Transformers
Voltage / Current relationships:
V1 i2 N1
= =
= a = turns ratio
V2 i1 N 2
power in = power out
MMF 1 = MMF 2
8. 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
9.
10. 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
11. 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
13. 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
14. 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
15. 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
16. 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!
17.
18.
19.
20.
21. 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)
22.
23. 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
