Transformers

Lecture 52 September 2003

MMME2104Design & Selection of Mining Equipment

Electrical Component

Lecture Outline

• Transformers introduction• Ideal Transformers• Non-Ideal (actual) Transformers• Transformer losses and power rating• Three-phase transformers• Transformer construction

TransformersMake 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

Transformers: Operating Principle

Voltage induced in a coil (flux linking equation):

V = 4.44fNΦmax

whereV = induced voltage (V)F = flux frequency (Hz)N = number of turns in coilΦmax = peak value of flux (Wb)

Ideal TransformersZero leakage flux:• Fluxes produced by the primary and secondary currents

are confined within the coreThe windings have no resistance:• Induced voltages equal applied voltagesThe core has infinite permeability• Reluctance of the core is zero• Negligible current is required to establish magnetic fluxLoss-less magnetic core• No hysteresis or eddy currents

Ideal Transformers

Voltage / Current relationships:

ratioturnsaNN

ii

VV

2

1

1

2

2

1 ====

power in = power out MMF 1 = MMF 2

Ideal Transformers

Impedance Ratio:

- can “refer” impedance parameters on primary side to secondary side, or vice versa

2

1

2

2

1

2

2

1

1

2

1 aii

VV

iV

iV

ZZ =×=÷=

22

1 ZaZ =

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

Actual Transformers

Primary winding flux: Φ1 = ΦM + ΦL1

Secondary winding flux: Φ2 = ΦM - ΦL2

Turns ratio now relates to induced voltages, rather than applied voltage

a = N1/N2 = e1/e2

dtdN

dtdiLRi

dtdN

dtdNRiV MML Φ++=Φ+Φ+= 1

11111

11111

dtdN

dtdiLRi

dtdN

dtdNRiV MML Φ++−=Φ+Φ−−= 2

22222

22222

Core losses

Core magnetisation

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

Transformer RatingTransformer 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

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

Three Phase TransformersCan 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!

3-Phase Transformer WindingsStar-Star:• Can develop voltage imbalance and harmonic

issuesDelta-Delta:• Circulating path good for harmonicsStar-Delta or Delta-Star:• Star-Delta quite common since it utilises

insulation so well (effective turns ratio increase)

Transformer ConstructionPower transformers are designed such that their

characteristics approach the ideal:• To attain high permeability, cores are made of iron-

based materials• To minimise core losses, core is laminated from high-

resistivity, 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