2/8/2016

Lesson 9: Practical
Model
Transformerand
Calculations
ET 332b Ac Motors,
and Power
Generators
Lesson
9_et332b.pptx

Systems

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Lesson 9_et332b.pptx

Lesson
9_et332b.pptx

Learning
Objectives
After this presentation you will be able
to:
 Identify factors that contribute
-idealtooperation of
power
non
Draw the schematic model
 transformers -ideal
of a
and include all
non transformer
Reflect impedances through
 parameters -ideala
 Identify
non -up and step down transformer
transformer
Compute connections
 step transformer voltages and currents using the
circuit
full
model.

Transformer Circuit Model

Equivalent Circuit Model for Leakage and Coil Resistance
Leakage Leakage
Flux Flux

Leakage flux
creates leakage
Not all developed flux links inductance that
primary to secondary. has leakage
Leakage flux only links the reactance. This
turns of the coil that causes additional
generates it voltage drops
across the coils

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Lesson 9_et332b.pptx

Leakage Reactance and Voltage Drop

Define inductive voltage drop
Ep+Elp

Vs
Vp

Vp  Ep  Elp Es-Els
Vs  Es Els

Where:Vp = net voltage induced in primary

Ep = voltage induced due to mutual flux
Elp = voltage induced in primary due to leakage
Vs = net voltage induced in secondary
Es = voltage induced due to mutual flux
Els = voltage induced in the secondary due to
leakage
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Coil Resistance and Total Voltage

Drop
Resistance of windings modeled by lumped resistance
Secondary coil
Primary coil resistance
resistance
Ideal
transformer
purely turns
ratio

Primary side Secondary side

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Lesson 9_et332b.pptx

Lesson 9_et332b.pptx

Circuit Model of Non

-ideal Transformers
Use ideal transformer impedance formulas to get equivalent
Zin
Zin is called the reflected or referred impedance

Zin
2
Vs  N 
From ideal Zin  a 

2

a2   p 
 Ns 
 
 Is 
transformers  

Circuit Model of
 Vs   (Rs  jXls)
Non-ideal Zload

 Is 

Zin  a2 (Rs  jXls)a2 Zload

Zin  a2 Rs  ja2 Xls a2 Zload
Transformers
From Ohm's Law

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Where: a2∙Rs = secondary R referred to primary

a2 ∙ Xls = secondary Xls referred to primary
a2 ∙ Zload = load impedance referred to
primary

Referring the secondary impedances to the primary side

effectively removes the need for the ideal transformer.
The turns ratio captures all the effects

Lesson 9_et332b.pptx

Circuit Model of -Non

ideal Transformers
Transformer circuit with ideal turns ratio removed

Zin

Can solve this circuit to find anything-ideal

abouttransformer
non operation.
Voltage drop, power losses, primary and secondary currents and voltages.

Simplified Circuit Model

Another simplifying assumption: I0 << Iload. Combine primary and
secondary impedances

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Lesson 9_et332b.pptx

Zeq

Zin
2 2
Equivalent series impedance referredZeqto (R p  a R s )  j (X lp  a X ls )
primary side

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0
Lesson 9_et332b.pptx

Simplified Model
-Referred to Secondary
The impedanceZeq can be referred to the secondary side instead. Just
2
divide the impedance components . by a

Resistance of the primary

winding referred to secondary
Leakage reactance of the primary
Equivalent impedance
winding referred to secondary
referred to the Rp Xlp
   
ZeqS   2  R s  j  2  Xls 
secondary side
   
a  a 

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Lesson 9_et332b.pptx

Series Impedance of Transformers

Power transformers are bi-directional devices. They can
operate with a V source attached to either primary or
secondary winding.
Step
-down operation: load Referring Z's to high side
connected to low voltage coil
ZeqHS  a 2 ZeqLS
ZloadHS  a 2 ZloadLS

Step-up operation: load connected

to the high voltage winding
High side Low side

ZeqHS
ZeqLS  2
Referring Z's to a
low side ZloadHS
ZloadLS  2 High side Low side
a

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Lesson 9_et332b.pptx

Transformer Problems
Example 9-1: A 100 kVA, 7200 -480 V 60 Hz single phase
transformer has the following parameters all given in ohms:

RLS = 0.00800 RHS = 1.96 RfeHS = 53.2

XLS = 0.01510 XHS = 4.55 XMHS = 7800

This transformer is operated in the step-down mode and

delivers 75% of its rated power to a load that has a power
factor of 0.93 lagging. Find:

a) draw the equivalent circuit model of the transformer with

the equivalent series Z's referred to the high voltage side
b) find the total Zin of the transformer at the high side
c) input Z of the transformer with the load disconnected

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d) input voltage at 75% load required to maintain rated load

voltage
e) exciting current with the load disconnected.
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Example 9-1 Solution (1)

Draw circuit model and find
Zeq

Find Load
Current

Ans

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Lesson 9_et332b.pptx

Example -91 Solution(2)

b) Find theZin as seen on the HV side

Ans

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Example 9-1 Solution (3)

c) Zin with the load disconnected

Ans

d) Input voltage required at

load to maintains=480
V V

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Lesson 9_et332b.pptx

Example-19Solution
(4)
e) Exciting current with load disconnected

With load disconnected only current

o is I

Ans

Remember

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Example 9-1 Solution (5)

Find oI as percent of rate load I

Typical values:
-5%
3 of rated for large
Ans power transformers.

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Lesson 9_et332b.pptx

Transformer Voltage Drop and Impedance

Example-2:9 The equivalent resistance and reactance
kVA, of a
2400-480V transformer's
50 windings areWRand
= 2.80
X = 6.00
W.
(high side). A load 20o is connected to the low voltage
1 of
Determine: 0 side.

a) equivalent impedance of the transformer and load

b) primary current if rated voltage is applied to
combined
c) voltage across the
primary
load.

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Example 9-2 Solution (1)

Refer Z
L to primary side

Ans

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Lesson 9_et332b.pptx

Example -92 Solution(2)

Find the current and voltage on primary

Ans

Now refer to secondary side

Ans

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ET 332b Ac Motors, Generators and Power Systems

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