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Nipu Kumar Das 1 Department of EEE, CUET
Electrical Machine-I
Three Phase Transformer
EEE-
Nipu Kumar Das 2 Department of EEE, CUET
THREE PHASE TRANSFORMER
Why Three Phase Transformer?
Almost all electrical power generation and most of
power transmission throughout the world today is three
phase ac circuits.
Advantages of 3φ AC Power Systems Over Single Phase AC Power
Systems:
1) It is possible to get more power per pound of metal from a
3 φ machine.
2) Power delivered to 3φ load is constant at all times, instead of
pulsing as it does in single phase system.
3) 3 φ Systems also make the use of 3 φ induction easier by
allowing them to start without special auxiliary starting windings
Nipu Kumar Das 3 Department of EEE, CUET
THREE PHASE TRANSFORMER
Construction:
3 φ transformer circuits can be construct in one of two
ways:
1. Three single-phase
transformers connected in
a three-phase bank
2. Three sets of windings
wrapped on a common
core
Nipu Kumar Das 4 Department of EEE, CUET
THREE PHASE TRANSFORMER
Windings of a single phase transformer:
have only two coils namely primary and secondary.
Primary is energized with single phase supply and load
is connected across the secondary.
Windings of a in a 3-phase transformer :
there will be 3 numbers of primary coils and 3 numbers
of secondary coils.
These 3 primary coils and the three secondary coils are t
o be properly connected so that the voltage level of a bal
anced 3-phase supply may be changed to another 3-phas
e balanced system of different voltage level.
Nipu Kumar Das 7 Department of EEE, CUET
CONNECTIONS FOR A 3-PHASE TRANSFORMER BANK
The transformers that work on the 3-phase supply have star, mesh
or zig-zag connected windings on either primary secondary or
both.
These connections are broadly classified into 4 popular vector gro
ups.
1. Group I: zero phase displacement between the primary and the
secondary.
2. Group II: 180◦ phase displacement.
3. Group III: 30◦ lag phase displacement of the secondary with res
pect to the primary.
4. Group IV: 30◦ lead phase displacement of the secondary with re
spect to the primary.
Nipu Kumar Das 8 Department of EEE, CUET
THREE PHASE TRANSFORMER CONNECTION
Four possible connections for a 3-phase transformer
bank are:
1. Y-Y
2. Y-∆
3. ∆-Y
Nipu Kumar Das 9 Department of EEE, CUET
G ROUP 1: 0
0 PHASE SHIFT .
Nipu Kumar Das 10 Department of EEE, CUET
GROUP 2: 180
PHASE SHIFT
.
Nipu Kumar Das 13 Department of EEE, CUET
3-PHASE TRANSFORMER Y-Y CONNECTION
.
In Y-Y connection, the primary
voltage on each phase of the
transformer is given by
The secondary phase voltage is
The primary phase voltage is
related to secondary phase voltage
by the turns ration of the
transformer is defined as:
P
V
LP
V
S
V
LS
V
ainY Y S
V
P
V
LS
V
LP
V
Nipu Kumar Das 14 Department of EEE, CUET
Star connected primary with secondary coils left alone
.
Nipu Kumar Das 15 Department of EEE, CUET
Both primary & secondary are star connected
.
Nipu Kumar Das 16 Department of EEE, CUET
3-PHASE TRANSFORMER Y-Y CONNECTION
is it a valid star connection?
If not why?
Nipu Kumar Das 19 Department of EEE, CUET
3-PHASE TRANSFORMER Y- (^) ∆ CONNECTION
Y-∆ connection : The primary voltage on each phase of the transformer is
The secondary phase voltage is
The voltage ratio of each phase is:
The overall voltage ratio is
P
VLP V
φ
S
V
LS
V
= = 3 ainY −∆ S
V
P
V
LS
V
LP
V
a ( 3 ) S
V
P
V
Nipu Kumar Das 20 Department of EEE, CUET
3-PHASE TRANSFORMER Y- (^) ∆ CONNECTION
The Y-∆ connection has no problem with third harmonic components
due to circulating currents in ∆. It is also more stable to unbalanced
loads since the ∆ partially redistributes any imbalance that occurs.
One problem associated with this connection is that the secondary
voltage is shifted by 30^0 with respect to the primary voltage. This can
cause problems when paralleling 3-phase transformers since transfor
mers secondary voltages must be in-phase to be paralleled. Therefore
, we must pay attention to these shifts.
In the U.S., it is common to make the secondary voltage to lag the pri
mary voltage. The connection shown in the previous slide will do it.
Nipu Kumar Das 21 Department of EEE, CUET
3-PHASE TRANSFORMER Y-∆ CONNECTION .
Nipu Kumar Das 22 Department of EEE, CUET
3-PHASE TRANSFORMER ∆-Y CONNECTION
P
V
LP
V
S
V
LS
V
a in Y
S
V
P
V
LS
V
LP
V
∆-Y connection :
The primary voltage on each phase of the transformer is
The secondary phase voltage is
The voltage ratio of each phase is:
The overall voltage ratio is
The same advantages and the same phase shift as the Y-∆ connection.
a ( 3 ) S
V
P
V
Nipu Kumar Das 25 Department of EEE, CUET
3-PHASE TRANSFORMER: PER-UNIT SYSTEM
The per-unit system applies to the 3-phase transformers as well as to single phase transformers. If the total base VA value of the transformer bank is Sbase , then the base VA value of one of the transformers will be
Therefore, the base phase current and impedance of the transformer are:
base
S
base
S =
base
V
base
S
base
V
base
S
base
I
2 2
base
S
base
V
base
S
base
V
base
Z
= =^ φ
Nipu Kumar Das 26 Department of EEE, CUET
3-PHASE TRANSFORMER: PER-UNIT SYSTEM
The line quantities on 3-phase transformer banks can also be represented in per-unit system.
If the windings are in ∆ connected:
If the windings are in Y:
And the base line current in a 3-phase transformer bank is given by:
The application of the per-unit system to 3-phase transformer problems is similar to its application in single-phase situations. The voltage regulation of the transformer bank is the same.
, , base
V
L base
V
φ
, base
V
Lbase
V
φ
Lbase
V
base
S
L base
I =
Nipu Kumar Das 27 Department of EEE, CUET
3-PHASE TRANSFORMER: PER-UNIT SYSTEM
Example 2-9: A 50 kVA, 13800/208 V, ∆-Y transformer
has a resistance of 1% and a reactance of 7% per unit.
i. What is the transformer’s phase impedance referred to
the high voltage side?
ii. What is the transformer’s voltage regulation at full load
and 0.8 PF lagging, using the calculated high-side
impedance?
iii. What is the transformer’s voltage regulation under the
same conditions, using the per-unit system?
Nipu Kumar Das 28 Department of EEE, CUET
3-PHASE TRANSFORMER: PER-UNIT SYSTEM
Solution:
(i)
The per-unit impedance of the transformer is:
Therefore, the high-side impedance in ohms is:
2
S base
base
V
base
Z
=^ φ
11 , 426 50000
2
S base
base
V
base
Z^ φ
j pu base
Z
Zeq Z (^) pu = = 0. 01 + 0. 07
= × = + × Ω
j
j base Zeq Zpu Z
Nipu Kumar Das 31 Department of EEE, CUET
3-PHASE TRANSFORMER: PER-UNIT SYSTEM
Thus, the voltage regulation in per-unit system will be:
The voltage regulation in per-unit system is the same as computed in volts
VR =^1.^051 −^1 × =
Nipu Kumar Das 32 Department of EEE, CUET
Transformer ratings
Transformers have the following major ratings:
i. Apparent power;
ii. Voltage;
iii. Current;
iv. Frequency.
Nipu Kumar Das 33 Department of EEE, CUET
Transformer ratings: Voltage and Frequency
. The voltage rating of a transformer serve two functions a) To protect the winding insulation from breakdown due excessive voltage applied to it. b) related to the magnetization curve and magnetization current of the transformer flux
Magnetization current
If a steady-state voltage is:
V ( t )= VM sin ω t
applied to the transformer’s primary winding, the transformer’s flux will be
An increase in voltage will lead to a proportional increase in flux. However, after some point (in a saturation region), such increase in flux would require an unacceptable increase in magnetization current!
t Np
M
V
N p
t Vtdt ω ω
φ ( )=^1 ∫ () =− cos
Nipu Kumar Das 34 Department of EEE, CUET
Transformer ratings: Voltage and Frequency
Therefore, the maximum applied voltage (and thus the rated voltage) is set by the maximum acceptable magnetization current in the core. We notice that the maximum flux is also related to the frequency:
Therefore, to maintain the same maximum flux, a change in frequency (say, 50 Hz instead of 60 Hz) must be accompanied by the corresponding correction in the maximum allowed voltage. This reduction in applied voltage with frequency is called derating. As a result, a 50 Hz transformer may be operated a t a 20% higher voltage on 60 Hz if this would not cause insulation damage.
N p
V
ω
φ (^) max = max
Nipu Kumar Das 37 Department of EEE, CUET
the maximum flux during the first half-cycle will be
Which is twice higher than a normal steady-state flux!
N p
V
t Np
V
V t dt Np
t (^) M M M ω
ω π ω ω
φ ω
π ω / 2 0
( )^1 sin( ) cos
/ 0
Doubling the maximum flux in the core can bring the core in a saturation and, therefore, may result in a huge magnetization current! Normally, the voltage phase angle cannot be controlled. As a result, a large inrush current is possible during the first several cycles after the transformer is turned ON. The transformer and the power system must be able to handle these currents.
Nipu Kumar Das 38 Department of EEE, CUET
Transformer ratings: Information Plate
Rated voltage, currents, and (or) power is typically shown on the transformer’s information plate.
Additional information, such as per-unit series impedance, type of cooling, etc. can also be specified on the plate.
Nipu Kumar Das 39 Department of EEE, CUET
Instrument transformers
Two special-purpose transformers are uses to take measurements: potential and cur rent transformers.
A potential transformer has a high-voltage primary, low-voltage secondary, and ve ry low power rating. It is used to provide an accurate voltage samples to instrument s monitoring the power system.
A current transformer samples the current in a line and reduces it to a safe and mea surable level. Such transformer consists of a secondary winding wrapped around a ferromagnetic ring with a single primary line (that may carry a large current )runni ng through its center. The ring holds a small sample of the flux from the primary li ne. That flux induces a secondary voltage. Windings in current transformers are loosely coupled: the mutual flux is much smaller than the leakage flux. The voltage and current ratios do not apply although the secondary current is directly proportional to the primary. Current transformers must be short-circuited at all times since very high voltages can appear across their terminals.
Nipu Kumar Das 40 Department of EEE, CUET
THREE PHASE TRANSFORMER
