TRANSFORMERS (II) EPO540 ELECTRICAL MACHINES prepared by Kanendra
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TRANSFORMERS (II)
EPO540
ELECTRICAL MACHINES
prepared by Kanendra
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1. Per-Unit (PU) System
Quantities are expressed in a per-unit (pu) system to simplify computation
Two major advantages in using a per-unit system:
1. Parameters and variables expressed in pu quantity have a narrow numerical
range – simplifies computations and make it possible to quickly check thecorrectness of the computed values
2. No need to refer to circuit quantities form one side to another, therefore
commons mistakes are removed
The pu quantity is defined as follows:
=
ℎ
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1. Per-Unit (PU) System
Usually base values of power and voltage are selected first and base values of
current and impedance are obtained as follows:
=
=
=
In transformer, base power is the same for primary and secondary. However
the base voltage, V base are different and usually assigned to the rated voltage
Also in transformer, voltages, current and impedances are expressed in a per-
unit system have the same per unit values in either side of the winding
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1. Per-Unit (PU) System
1, =1
1
=1
1
=/
/=
=
= ,
1, =1
1
=1
1
=
=
=
= ,
1, =
1
1 =
(2)
(2) =
= ,
Full-load copper loss in pu system
,=1 1
,| = 1
1
= 1
1
11
= 1
1/1
= 1
1
= 1,
Transformer resistance expressed in per-unit represents the full load copper
loss in per-unit form
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2. Three Phase Transformers
Three phase system is used to generate and transmit bulk / massive electrical
supply
Three phase transformers are required to step up or step down voltages in the
various stages of power transmission
Three phase transformers can be built:
1. Suitably connecting a bank of three single – phase transformers
2. Constructing a three phase transformer on a common magnetic structure
A set of three similar single phase transformers may be connected to form a
three phase transformer
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2. Three Phase Transformers
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Three single-phase transformers
connected wye-wyeThree phase transformer
on common core
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2. Three Phase Transformers
The primary and secondary windings may be connected in either wye (Y) or
delta (Δ) configurations. Possible connections:
1. Y – Δ : commonly used to STEP DOWN a high voltage to a lower voltage
2. Δ – Y : commonly used to STEP UP voltages
3. Δ – Δ : can be configured as “open delta” or “V connection” – onetransformer can be removed for repair / maintenance and the remaining two
continue to deliver power
4. Y – Y : rarely used due to problems with exciting current and induced
voltages
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2. Three Phase Transformers
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Y – Δ transformer connection
Δ – Δ transformer connection
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2. Three Phase Transformers
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Δ – Y transformer connection
Y – Y transformer connection
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3. Phase Shift
Some of the three phase transformer connection results in a phase shift
between the primary and secondary line-to-line voltages
Consider a three phase transformer with (Y – Δ) configuration and its phasor
diagram:
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Y – Δ transformer connection
Phasor diagram
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3. Phase Shift
The property of phase shift in Y – Δ or Δ – Y connections can be used
advantageously in some application: Multiple rectifiers
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12 pulse rectifier
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4. Single Phase Equivalent Circuit
If the three transformers are practically identical and the source and load are
balanced, then the voltages and currents on both primary and secondary sides
are balanced
A single-phase equivalent circuit can be conveniently obtained if all sources,
transfromer windings, and load impedance are considered to be Y-connected
Y – Δ transformation can be used for the Δ– connected load
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4. Single Phase Equivalent Circuit
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For wye Y)
IP = IL
VP = V
L/sqrt(3)
For delta Δ)
IP = IL/sqrt(3)
VP = VL