ELECTRICAL MACHINES
DET 204/3
JIMIRAFIZI BIN JAMIL
Transformer
Exact equivalent circuit of a transformer
Rp
Ip
Is/a
Xp
Rs
Xs
Ie
Vp
Ep
Es
Vs
Ep = primary induced voltage
Es = secondary induced voltage
Vp = primary terminal voltage
Vs = secondary terminal voltage
Ip = primary current
Is = secondary current
Ie = excitation current
IM = magnetizing current
XM = magnetizing reactance
IC = core current
RC = core resistance
Rp = resistance of primary winding
Rs = resistance of the secondary winding Xp = primary leakage reactance
Xs = secondary leakage reactance
Primary side
Secondary side
I p  Ie  Is / a
ES  I s ( Rs  jX s )  Vs
Ie  IC  I M
Vs  I s Z L
V p  I p ( R p  jX p )  E p
E p  I C RC
E p  I M ( jX M )
E p  I e ( RC // jX M )
Vp
Ep
Is N p
a



Vs Es I p N s
Exact equivalent circuit of a transformer
referred to primary side
Rp
Ip
a2Xs
Xp
Is/a
a2Rs
Ie
Vp
Ep
aVs
Exact equivalent circuit of a transformer
referred to secondary side
Rp/a2
aIp
Xp/a2
Rs
Is
Xs
aIe
Vp/a
aIc
Rc/a2
aIm
Ep/a = Es
XM/a2
Vs
Parameter determination of the transformer
• Open circuit test
– Provides magnetizing reactance and core loss
resistance
– Obtain components are connected in parallel
LV
A
Rated Voltage
V
W
HV
Experiment Setup:
In the open circuit test, transformer rated
voltage is applied to the low voltage side of the
transformer with the high voltage side let open.
Measurements of power, current, and voltage
are made on the low voltage side.
Since the high voltage side is open, the input
current IOC is equal to the excitation current
through the shunt excitation branch. Because
this current is very small, about 5% of rated
value, the voltage drop across the low voltage
winding and the winding copper losses are
neglected.
I oc
Yoc 
Voc
PF  cos  
  cos 1
Yoc 
Poc
Voc I oc
Poc
Voc I oc
I oc
1
1
    GC  jBM 
j
Voc
RC
XM
Exication Admittance
Short circuit test
– Provides combined leakage reactance and
winding resistance
– Obtain components are connected in series
A
V
W
Experiment Setup:
In the short circuit test, the low voltage side is
short circuited and the high voltage side is
connected to a variable, low voltage source.
Measurements of power, current, and voltage
are made on the high voltage side. The
applied voltage is adjusted until rated short
circuit currents flows in the windings. This
voltage is generally much smaller than the
rated voltage.
Z sc 
Vsc
I sc
PF  cos  
  cos 1
Psc
Vsc I sc
Psc
Vsc I sc
Z sc  Req  jX eq
Voltage Regulation (VR)
The voltage regulation of
defined as the change in
the secondary voltage
changes from full load to
primary held fixed.
VR 
VS ,nl  VS , fl
VS , fl
At no load, VS
Vp
VR  a
Req
X 100%
 VP
a
 VS , fl
VS , fl
a transformer is
the magnitude of
as the current
no load with the
Xeq
+
+
Vp/a
Vs
-
X 100%
Is
-
Phasor Diagram
Vp/a
jIsXeq
Vp/a > Vs
Voltage Regulation > 0
Vs
IsReq
Is
Lagging power factor
Vp/a
Vs is lower than Vp
jIsXeq
Is
Vs
IsReq
Unity power factor
Voltage Regulation = 0
Vp/a
Voltage Regulation < 0 @ -VR
jIsXeq
Is
IsReq
Vs
Leading power factor
Efficiency
The efficiency of a transformer is defined as
the ratio of the power output (Pout) to the power
input (Pin).
Pout

X 100%
Pin

Pout
Pout   P losses
Pcore = Peddy current + Physteresis
X 100%
Vs I s cos 

X 100%
Vs I s cos   Pcu  Pcore
Three Phase Transformer
Three phase transformer can be constructed
in two way:
1)To take three single-phase transformers
and connect them in a three phase bank.
2)To make a three phase transformer
consisting of three sets of windings
wrapped on a common core.
Advantages: Lighter, smaller, cheaper
and slightly more efficient
Three single transformer
banked composed of
independent transformers
Three phase transformer
wound on a single three
legged core
Three Phase Transformer Connections
Four possible connections for three phase
transformer:
1. Wye-Wye (Y-Y)
2. Wye-Delta (Y-Δ)
3. Delta-Wye (Δ-Y)
4. Delta-Delta (Δ-Δ)
Wye-Wye Connection
The overall voltage ratio is
Line Voltage
3VP
VLP

a
VLS
3VS
where a is the voltage ratio of each phase
Wye-Delta Connection
The overall voltage ratio is
VLP
 3a
VLS
where a is the voltage ratio of each phase
Delta-Delta Connection
The overall voltage ratio is
VLP VP

a
VLS VS
Delta-Wye Connection
The overall voltage ratio is
VLP
3

VLS
a
Assignment 3:
A three phase, 230V, 27kVA,0.8 power factor (lagging)
load is supplied by three 10kVA, 1330/230V, 50Hz
transformers connected in Star-Delta by means of a
common three phase feeder whose impedance is 0.003
+ j0.015Ω per phase. The transformers are supplied
from a three phase source through a three phase
feeder whose impedance is 0.8 + j5.0Ω per phase. The
equivalent impedance of one transformer referred to
the low voltage side is 0.12 + j0.25Ω. Determine the
required supply voltage if the load voltage is 230V.