electrical machines

7/17/2019 Electrical Machines

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TRANSFORMERS (II)

EPO540

ELECTRICAL MACHINES

prepared by Kanendra



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





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





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




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






Three single-phase transformers

connected wye-wyeThree phase transformer

on common core




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






Y – Δ transformer connection

Δ – Δ transformer connection





Δ – Y transformer connection

Y – Y transformer connection



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:


Y – Δ transformer connection

Phasor diagram



3. Phase Shift

The property of phase shift in Y – Δ or Δ – Y connections can be used

advantageously in some application: Multiple rectifiers


12 pulse rectifier



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






For wye Y)

IP = IL

VP = V

L/sqrt(3)

For delta Δ)

IP = IL/sqrt(3)

VP = VL





Equivalent transformer circuit

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