power transformer , per unit system

1. Power Transformer ,Per unit
system
Topic

4. A transformer is a device that transfers electrical energy
from one circuit to another through inductively coupled
electrical conductors.
Transformer is used to convert high alternate voltage
current or power level to low alternate voltage, current or
power level and vice versa.

5. A transformer consists of a rectangular core of soft
iron in the form of sheets insulated from one another.
Two separate coils of insulated wires, a primary coil
and a secondary coil are wound on the core. These
coils are well insulated from one another. The coil on
the input side is called primary coil and on the output
side is called secondary coil.

6. Main parts of a transformer

7. Laminated core
Windings
Insulating Materials
Transformer oil
Conservator
Breather
Cooling tubes
Buchholz Relay
Explosion vent

8. Transformer basically works on the principle of mutual
induction of two coils. A changing current in the first
circuit (the primary) creates changing magnetic field.
This changing magnetic field induces a changing voltage in
the second circuit (the secondary). This effect is called
mutual induction.
If a load is connected to the secondary circuit, electric
charge will flow in the secondary winding of the
transformer and transfer energy from the primary circuit to
the load connected in the secondary circuit.

10. Let the primary voltage is Vp
and induced voltage is Vs
According to Faradays law, for primary coil
Vp=NpΔΦ/Δt ---------(1)
Similarly for secondary coil
Vs=NsΔΦ/Δt ---------(2)
Dividing (1) by (2)
Vp /Vs=Np/Ns
Ns = Number of turns of primary coil
Np =Number of turns of secondary coil

11. Above equation shows that the magnitude of EMF
depends upon the number of the turns in the coil

13. There are generally two types of transformer
 Step up transformer
 Step down transformer
Some important types are given as:
 Auto-transformer
 Resonant transformer
 Instrument transformers
 Current transformer
 Voltage transformer

14. A step up transformer is a
device that converts low
alternate voltage to high
alternate voltage.
In another word, a
transformer in which
Ns>Np that is called step
up transformer.

15. A step up transformer
is a device that
converts high alternate
voltage to low
alternate voltage.
In another word, a
transformer in which
Np>Ns that is called
step up transformer.

16. An autotransformer
with a sliding brush
contact
An autotransformer has
only a single winding
with two end terminals,
plus a third at an
intermediate tap point.

17. Instrument Transformers are used in
AC system for measurement of
electrical quantities i.e. voltage,
current, power, energy, power factor,
frequency. Instrument transformers
are also used with protective relays
for protection of power system.

18. With the help of P.T, a 120V
voltmeter can be used to measure
very high voltages like 11KV.
The primary winding P.T is
connected across the line of
voltage to be measured. Hence the
full line voltage is impressed
across its terminal.
The primary current of a P.T
depends upon the secondary circuit
conditions

19. A CT may be considered as a
series transformer.
The primary current in a C.T
is independent of the
secondary circuit conditions
With the help of CT, a 5A
ammeter can be used measure
a high current like 200A

21.  Faraday’s law states that:
Vs = Ns.dΦ/dt
 where VS is the instantaneous voltage
 NS is the number of turns in the secondary coil.

22. Since the same magnetic flux passes through both the primary
and secondary coils in an ideal transformer, the instantaneous
voltage across the primary coil
Vp = Np.dΦ/dt
Taking the ratio of the two equations
for Vs and Vp gives the basic
equation for stepping up or stepping
down the voltage
Vs
Vp
=
𝑵𝒔
𝐍𝐩

23. The losses that occur in transformers have to be accounted for
in any accurate model of transformer behavior.
1. Copper (I2R) losses. Copper losses are the resistive
heating losses in the primary and secondary windings of the
transformer. They are proportional to the square of the current
in the windings.
2. Eddy current losses. Eddy current losses are resistive
heating losses in the core of the transformer. They are
proportional to the square of the voltage applied to the
transformer.

24. 3. Hysteresis losses. Hysteresis losses are associated with
the rearrangement of the magnetic domains in the core
during each half-cycle. They are a complex, nonlinear
function of the voltage applied to the transformer.
4. Leakage flux. The fluxes which escape the core and
pass through only one of the transformer windings are
leakage fluxes. These escaped fluxes produce a self-
inductance in the primary and secondary coils, and the
effects of this inductance must be accounted for.

27. actual quantity
quantity in per unit
base value of quantity

Per unit system, a system of dimensionless
parameters, is used for computational convenience
and for readily comparing the performance of a set
of transformers or a set of electrical machines.

28. Per Unit Conversion Procedure, 1f
Pick a 1f VA base for the entire system, SB
Pick a voltage base for each different voltage level, VB.
Voltage bases are related by transformer turns ratios.
Voltages are line to neutral.
Calculate the impedance base, ZB= (VB)2/SB
Calculate the current base, IB = VB/ZB
Convert actual values to per unit

29. For an electric element, we have : Power, Voltage,
Current and Impedance
Usually, the nominal apparent power (S) and nominal
voltages (V)are taken as the base values for power and
voltage The base values for the current and impedance
can be calculated
base
base
base
base
base
base
base
base
basebase
S
V
I
V
Z
V
S
I
VS
2
,



30. Per unit base calculations

31. A load takes 20 A at a power factor 0.9 lead when
connected to a 600 Voltage. If the base voltage and
apparent power are 600 and 6000 VA, determine the
variables and impedance in per unit system
60
10
600,6000



base
base
base
base
base
base
basebase
I
V
Z
V
S
I
VS
30
20
600
Z
Example:
Solution: