modeling of power transformers a static device. transformers the transformer enables us to utilize...
TRANSCRIPT
Modeling of Power
Transformers
A Static Device
Transformers
The transformer enables us to utilize different voltage
levels across the system for the most economical
value.
Stepping up the generator voltage to high voltage, is
done through power transformers to minimize losses
and increase the transmission capacity of the lines.
This transmission voltage level is then stepped down in
many stages for distribution and utilization purposes.
General Theory
A transformer contains two or more windings linked by a mutual field.
The primary winding is connected to an alternating voltage source.
The input current results in an alternating flux whose magnitude depends on the voltage and number of turns of the primary winding.
The alternating flux links the secondary winding and induces a voltage in it with a value that depends on the number of turns of the secondary winding.
Transformers
Basic components of single phase transformer
Laminated iron core
Primary winding
NP
Secondary winding
NS LoadSupply
Transformers
5.2 Single phase transformer arrangement
PrimaryWinding
SecondaryWinding
Multi-layerLaminatedIron Core
X1X
2H1 H2
WindingTerminals
Transformers
Polarity for transformer
0 5 10 15 20100
0
100
Vp t( )
Vs t( )
t
milli s
0 5 10 15 20100
0
100
Vp t( )
Vs t( )
t
milli s
H1
H2
X2
X1
VpVs
H1
H2 X2
X1
Vp Vs
(a) (b)
Transformers
Small transformer construction
a) Lamination b) Iron core with winding
Iron core
Terminals
Secondarywinding
Insulation
Transformers
Dry-type three-phase transformer
Transformers
Oil Insulated and cooled transformer
Winding
Iron corebehind the steel
bar
Radiator
Steeltank
Insulation
Bushing
Power Transformers
Transformation ratio
Primary (supply) Secondary (Load)
Transformers at no load
The no load current I is needed to supply the no load
losses and to magnetize the transformer core.
Im
Ic E1
I
c
E1
I
I
Ic Im
Loaded Transformer
Z2’ is the load impedancereferred to the primary
Transformer losses
The transformer losses are divided into electrical losses
(copper losses) and Magnetic losses (Iron losses).
Copper losses in both the primary and secondary windings.
Magnetic losses, these losses are divided into eddy current
losses and hysteresis losses.
2221
21 RIRI
mhysteriseseddymag IVPPP 1
Equivalent circuit
V1: Primary voltage (supply)I1 : Primary current.V2: Secondary voltage (load)I2: : Secondary current
Exact Circuit
Approximate Circuit
The no load current ranges from 1% to 3% of the full load current.Therefore, the circuit can be simplified to circuit (b).
(a) (b)
Phasor Diagram
)('2
'21 eqeq jXRIVV
Performance Measures
The percent regulation
The transformer efficiency
Voltage Regulation
sincos '2
'2
'21 eqeq XIRIVVVR
Example
A 100-kVA, 400/2000 V, single-phase transformer has the following parameters
R1 = 0.01 R2 = 0.25 ohms
X1 = 0.03 ohms X2 = 0.75 ohms
The transformer supplies a load of 90 kVA at 2000 V and 0.8 PF lagging.
Calculate the primary voltage and current using the simplest equivalent circuit.
Find also the V.R. and efficiency for the transformer