Introduction
• A transformer is a device that changes ac electric power at
one voltage level to ac electric power at another voltage
level through the action of a magnetic field.
• There are two or more stationary electric circuits that are
coupled magnetically.
• It involves interchange of electric energy between two or
more electric systems
• Transformers provide much needed capability of changing
the voltage and current levels easily.
• They are used to step-up generator voltage to an appropriate
voltage level for power transfer.
• Stepping down the transmission voltage at various levels for
distribution and power utilization.
Transformer Classification
• In terms of number of windings
• Conventional transformer: two windings
• Autotransformer: one winding
• Others: more than two windings
• In terms of number of phases
• Single-phase transformer
• Three-phase transformer
• Depending on the voltage level at which the winding is operated
• Step-up transformer: primary winding is a low voltage (LV)
winding
• Step-down transformer : primary winding is a high voltage (HV)
winding
Primary and Secondary Windings
A two-winding transformer consists of two windings interlinked by
a mutual magnetic field.
• Primary winding – energized by connecting it to an input
source
• Secondary winding – winding to which an electrical load is
connected and from which output energy is drawn.
Primary winding Secondary winding
Ideal Transformers
An ideal transformer is a lossless device with an input winding
and an output winding. It has the following properties:
• No iron and copper losses
• No leakage fluxes
• A core of infinite magnetic permeability and of infinite
electrical resistivity
• Flux is confined to the core and winding resistances are
negligible
Ideal Transformers
An ideal transformer is a lossless device with an input winding
and an output winding.
fM
The relationships between the input voltage and the output voltage,
and between the input current and the output current, are given by the
following equations.
v p (t ) i s (t )
In instantaneous quantities = =a
v s (t ) i p (t )
Ideal Transformers
v p (t ) i s (t ) N p
= = =a
v s (t ) i p (t ) N s
Vp I
In rms quantities = s =a
Vs I p
Np: Number of turns on the primary winding
Ns: Number of turns on the secondary winding
vp(t): voltage applied to the primary side
vs(t): voltage at the secondary side
a: turns ratio
ip(t): current flowing into the primary side
is(t): current flowing into the secondary side
Derivation of the Relationship
d p (t )
df M (t ) …………….. (1)
v p (t ) = = Np
dt dt
d ( t ) df (t ) …………….. (2)
v s (t ) = s = N s M
dt dt
v p (t ) N p
= = a ………………......……….. (3)
v s (t ) N s
Dividing (1) by (2)
From Ampere’s law N p i p (t ) = N s i s (t )
i s (t ) N p …………………..……….. (4)
= =a
i p (t ) N s
v p (t ) i s (t ) N p ………………….. (5)
Equating (3) and (4) = = =a
v s (t ) i p (t ) N s
Power in an Ideal Transformer
Real power P supplied to the transformer by the primary circuit
Pin = V p I p cos p
p = s =
Real power coming out of the secondary circuit
Vp
Pout = V s I s cos s = ( )
aI p cos = V p I p cos = Pin
a
Thus, the output power of an ideal transformer is equal to its input power.
The same relationship applies to reactive Q and apparent power S:
I
Qin = V p I p sin = (aV s ) s cos = V s I s sin = Qout
a
S in = V p I p = V s I s = S out
Impedance Transformation through a Transformer
Ip Is
Impedance of the load:
Vp Vs ZL
ZL = Vs/Is
The impedance of the primary circuit:
Z’L = Vp/Ip
= (aVs)/(Is /a)
= a2 (Vs / Is )
= a2 ZL
Ip Is
Z’L
Vp Vs
Theory of Operation of Single-Phase Real Transformers
Leakage flux: flux that goes through one of the transformer windings
but not the other one
Mutual flux: flux that remains in the core and links both windings
Theory of Operation of Single-Phase Real Transformers
f P = f M + f LP
f S = f M + f LS
fp: total average primary flux
fM : flux linking both primary and secondary windings
fLP: primary leakage flux
fS: total average secondary flux
fLS: secondary leakage flux
Magnetization Current
E1
When an ac power source is connected to a transformer, a current flows
in its primary circuit, even when the secondary circuit is open circuited.
This current is the current required to produce flux in the ferromagnetic
core and is called excitation current. It consists of two components:
1. The magnetization current Im, which is the current required to
produce the flux in the transformer core
2. The core-loss current Ih+e, which is the current required to make up
for hysteresis and eddy current losses
