Lecture-7
Three Phase Transformers
Mesfin T.
Addis Ababa University
College of Technology and Built Environment
School of Electrical and Computer Engineering
Introduction Electrical Machines
ECEG-3151
April 1, 2025
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Overview
Overview
1 Overview
2 Objective
3 Introduction
4 Transformer Banks
5 Transformer Connections
Delta-Delta Connection
Delta-Wye Connection
Wye-Delta Connection
Wye-Wye Connection
Open-Delta Connection
6 Three-phase Transformers
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Objective
Lecture Objectives
The objectives of this lecture are:
To discuss three-phase transformer connections and three-phase
transformers.
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Introduction
Introduction
In the operation of power systems, transformers are required to change
the voltage levels throughout the network.
three-phase circuits use three-phase transformers
can be achieved by using a bank of three single-phase transformers
may be a 3-phase unit having three primary windings and three
secondary windings on a 3-legged core
using a bank of three single phase transformers, the windings may
be connected in a variety of ways
the primary side may be connected in a wye or delta configuration
independent of the secondary connection
the secondary side may be connected in a wye or delta configuration
independent of the primary connection
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Transformer Banks
Transformer Banks
3-phase transformer banks can be analyzed using simplifying
assumptions
excitation currents are negligible
winding impedances are negligible
total apparent input power equals the total apparent output power
Single-phase transformers connected into a 3-phase bank
retain all basic single-phase properties
individual voltage and current transformations are based on the
single- phase turns ratio
phase shift between primary and secondary is zero
3-phase transformer banks can introduce a phase shift between the
three-phase primary and the three-phase secondary
function of the primary and secondary winding connections
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Transformer Connections Delta-Delta Connection
Transformer Connections
Delta-Delta (∆ − ∆) Connection
Three single-phase transformers connected delta-delta.
the H1 terminal of each
transformer is
connected to the H2
terminal of the next
transformer
the X1 terminal of each
transformer is
connected to the X2
terminal of the next
transformer Figure 1: ∆ − ∆ connection.
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Transformer Connections Delta-Delta Connection
the primary-side line voltage is transformed to the
secondary-side line voltage
the primary and secondary voltages and currents are in-phase
Figure 2: Schematic diagram of ∆ − ∆ connection of a transformer.
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Transformer Connections Delta-Delta Connection
Example (1)
Three single-phase transformers are connected in delta-delta (∆ − ∆)
configuration to step down a line voltage of 138kV to 4160V to supply
power to a manufacturing plant. If the plant draws 21M W at 0.86
power factor lagging, calculate
a) the apparent power drawn by the plant
b) currents in the HV lines and the LV lines
c) current in the primary and secondary windings of each transformer
d) the load carried by each transformer
Solution:
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Transformer Connections Delta-Delta Connection
Example (1)
Three single-phase transformers are connected in delta-delta (∆ − ∆)
configuration to step down a line voltage of 138kV to 4160V to supply
power to a manufacturing plant. If the plant draws 21M W at 0.86
power factor lagging, calculate
a) the apparent power drawn by the plant
b) currents in the HV lines and the LV lines
c) current in the primary and secondary windings of each transformer
d) the load carried by each transformer
Solution:
a) The apparent power drawn by the plant is
P
S=
cos ϕ
21
= = 24.4M V A
0.86
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Transformer Connections Delta-Delta Connection
Example (1)
b) Current in each HV line is
S 24.4 × 106 V A
I1 = √ =√ = 102 A
3E 3 × 138, 000 V
Current in each LV line is
S 24.4 × 106 V A
I2 = √ = √ = 3386 A
3E 3 × 4160 V
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Transformer Connections Delta-Delta Connection
Example (1)
b) Current in each HV line is
S 24.4 × 106 V A
I1 = √ =√ = 102 A
3E 3 × 138, 000 V
Current in each LV line is
S 24.4 × 106 V A
I2 = √ = √ = 3386 A
3E 3 × 4160 V
c) The current in each primary winding is
102
IP = √ = 58.9 A
3
The current in each secondary winding is
3386
IS = √ = 1955 A
3
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Transformer Connections Delta-Delta Connection
Example (1)
d) Because the plant load is balanced, each transformer carries
one-third of the total load, or
24.4
M V A = 8.13 M V A
3
The individual transformer load can also be obtained by
multiplying the primary voltage times the primary current:
S= EP IP
= 138, 000 V × 58.9 A
= 8.13 M V A
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Transformer Connections Delta-Wye Connection
Delta-Wye (∆ − Y ) Connection
Three single-phase transformers connected delta-wye.
the H1 terminal of each
transformer is
connected to the H2
terminal of the next
transformer.
the X2 terminals of all
transformers are
connected together to
form a neutral terminal.
Figure 3: ∆ − Y connection.
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Transformer Connections Delta-Wye Connection
the primary-side line voltage is transformed to the
secondary-side phase voltage
the delta-wye connection produces a 30o phase shift between
the primary and secondary voltages and currents
Figure 4: Schematic diagram of ∆ − Y connection of a transformer.
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Transformer Connections Delta-Wye Connection
Example (2)
Three single-phase step-up transformers rated at 40M V A,
13.2kV /80kV are connected in a delta-wye (∆ − Y ) configuration to a
13.2kV transmission line. If the 80kV load is 90M V A, calculate
a) the secondary line voltage
b) the currents in each winding of the transformer
c) the line currents in the LV and HV transmission lines
Solution:
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Transformer Connections Delta-Wye Connection
Example (2)
Three single-phase step-up transformers rated at 40M V A,
13.2kV /80kV are connected in a delta-wye (∆ − Y ) configuration to a
13.2kV transmission line. If the 80kV load is 90M V A, calculate
a) the secondary line voltage
b) the currents in each winding of the transformer
c) the line currents in the LV and HV transmission lines
Solution:
The easiest way to solve this problem is to consider the windings of
only one transformer, say, transformer-P (consider figure-5, on the next
slide).
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Transformer Connections Delta-Wye Connection
Example (2)
Figure 5: Figure for example-2.
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Transformer Connections Delta-Wye Connection
Example (2)
Figure 5: Figure for example-2.
a) The voltage across the primary winding is obviously 13.2kV . The
voltage across the secondary is, therefore, 80kV . The voltage
between the outgoing lines 1,2 and 3 is:
√
ES = 80kV × 3 = 138.5kV
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Transformer Connections Delta-Wye Connection
Example (2)
b) The load carried by each transformer is
90
S = M V A = 30 M V A
3
The current in the primary winding is
30 M V A
IP = = 2273A
13.2 KV
The current in the seconday winding is
30 M V A
IS = = 375A
80 KV
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Transformer Connections Delta-Wye Connection
Example (2)
b) The load carried by each transformer is
90
S = M V A = 30 M V A
3
The current in the primary winding is
30 M V A
IP = = 2273A
13.2 KV
The current in the seconday winding is
30 M V A
IS = = 375A
80 KV
c) The current in each incoming line A, B, C is
√
I = 2273 × 3 A = 3937A
The current in each outgoing line 1, 2, 3 is
I = 375A
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Transformer Connections Wye-Delta Connection
Wye-Delta (Y − ∆) Connection
The currents in a wye-delta connection are identical to those in the delta-
wye connection
the primary and secondary connections are simply interchanged
the H2 terminals of all transformers are connected together to
form a neutral terminal
the X1 terminal of each transformer is connected to the X2
terminal of the next transformer
Again, the connection results in a 30o phase shift between the primary
and secondary voltages and currents
the primary-side phase voltage is transformed to the secondary
side line voltage
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Transformer Connections Wye-Wye Connection
Wye-Wye (Y − Y ) Connection
Three single-phase transformers connected wye-wye
the H2 terminals of all transformers are connected together to
form a neutral terminal
the X2 terminals of all transformers are connected together to
form a neutral terminal
the primary-side phase voltage is transformed to the
secondary-side phase voltage
the neutral terminal of the primary side of the transformer
must be connected back to the source with a low impedance
path to avoid secondary voltage magnitude distortion with
unbalanced loads
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Transformer Connections Wye-Wye Connection
the connection produces no phase shifts
Figure 6: Schematic diagram of Y − Y connection of a transformer.
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Transformer Connections Open-Delta Connection
Open-Delta Connection
It is possible to transform the voltage of a 3-phase system using only 2
transformers.
open-delta arrangement
is identical to a
delta-delta connection,
less one transformer
limited use due to a
86.6% reduction in the
installed power
capability
Figure 7: Open − Delta connection.
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Transformer Connections Open-Delta Connection
two 50kV A transformers could carry 100kV A, but limited to
86.6kV A in an open-delta connection
used in emergency conditions
used in metering of power system voltages
Figure 8: Schematic diagram of Open − Delta connection of a transformer.
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Transformer Connections Open-Delta Connection
Example (3)
Two single-phase 150kV A, 7200V /600V transformers are connected in
open-delta. Calculate the maximum 3-phase load they can carry
Solution:
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Transformer Connections Open-Delta Connection
Example (3)
Two single-phase 150kV A, 7200V /600V transformers are connected in
open-delta. Calculate the maximum 3-phase load they can carry
Solution:
Although each transformer has a rating of 150kV A, the two together
cannot carry a load of 300kV A. The following calculations show why:
The nominal secondary current of each transformer is
150 kV A
IS = = 250A
600 V
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Transformer Connections Open-Delta Connection
Example (3)
The current I, in lines 1, 2, 3 cannot, therefore, exceed 250A (figure-8 ).
Consequently, the maximum load that the transformers can carry is
√
S= 3EI
√
= 3 × 600V × 250A = 259, 800V A
∼
= 260kV A
Thus, the ratio
maximum load = 260kV A
installed transformer rating = 300kV A
0.867 or 86.7%
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Three-phase Transformers
Three-phase Transformers
A transformer bank composed of three single-phase units may be re-
placed by one 3-phase transformer.
the magnetic core has three flux-carrying legs
two yokes, bottom and top, couple the flux of the three legs
the sum of the three fluxes equals zero
each leg contains the primary and secondary windings of one of
the phases
the windings are connected delta or wye, internal to the
transformer tank
only six terminals are brought out of the tank
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Three-phase Transformers
Questions?
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