3-Lesson Notes Lec 6(TRAFO)

7/31/2019 3-Lesson Notes Lec 6(TRAFO)

1/17

Transformers

Lecture 6


2/17

Transformers utilization

As engineers, you should have seen some transformers while you driving or

walking by some substations near power plants, industrial cities or closer to your

houses!


3/17

Practical Transformer

Winding resistance

Flux leakage

Finite permeability

Core losses

Figure 1-a

Contrary to an ideal transformer, a practical transformer has


4/17

Transformer Model

physical reasoning

mathematic model of coupled

circuits

Winding resistance in serieswith leakage inductance

Magnetizing inductance inparallel with core resistance

Figure 1-b


5/17

Referred equivalent circuits

Practical transformer is equivalent to lumped parameters

circuit and ideal transformer

Figure 2


6/17

The ideal transformer can be shifted to either side as in Figures 3 and 4and the

circuit parameters reduced to the appropriate values

Figure 3

Figure 4

E1=E2= aE2

V

2=aV2

I2=I2/a

Xl2=a2xl2

R2=a2R2


7/17

Approximate Equivalent Circuits

I1R1 and I1Xl1 are small

Therefore, |E1| = |V1|

Shunt branch can be moved tosupply terminal

I

small (5% of rated current)Shunt branch removed

Figure 5-a

Figure 5-b-c


8/17


9/17


10/17

EXAMPLE

An Engineer needs to know the parameters of a 46KVA Transformer which has a2300V/230V winding. His results are:

Open Circuit Test: 230V 11.2A 1150W

Short Circuit Test: 160V 28.0A 1150W

We must first determine which side Low or High the test was performed on.

For the Open Circuit test we compare the tested voltage to the rated voltage of thetransformer.

In this example we see that the Open Circuit Test voltage is the same as the Low siderated operating voltage, thus we know the test was performed on the low side and thehigh side was left open.

Next we need to determine which side the Short Circuit Test was performed on, sowe compare the Current this time.


11/17

Example (continued)

So now we know where the tests were performed.

Open Circuit Test: 230V 11.2A 1150W -H.V. Left open, and tested on Low side

Short Circuit Test: 160V 28.0A 1150W -L.V. Shorted, and tested on High side

So we know that the Open Circuit parameters are Referred to Primary.

So we will use the Referred to Primary parameters for the Open Circuit test.

What we know:


12/17

Example (continued)

Now remember how the Short Circuit Test proved out that the L.V. side was shorted?

This means our equivalent calculations are Referred to the H.V. side. So in effect what weare calculating are ourX2 and R2 values. If we want ourX1 and R1 values, we must divideby our transformation ratio.

To complete our Primary Referred Circuit we must find ourR1 and X1 values. And giventhe fact that the transformer is stepping up voltage from 230 to 2300, we can see that it is a1:10 ratio, orN1 = 1,N2 = 10.


13/17

To complete our Primary Referred Circuit we must find ourR1 and X1 values.And given the fact that the transformer is stepping up voltage from 230 to 2300,we can see that it is a 1:10 ratio, orN

1= 1,N

2= 10.

Now of course one might think this is the end, but that is far from the truth. At

this time we know enough about the circuit to go further if we desire. From herewe can obtain the terminal voltages for simulation, a very important factor indesigning a system!

Example (continued)


14/17


15/17

Voltage regulation

No load V2=V1/a

Loaded V2=V1/a V2

Voltage regulation =

Maximum voltage regulation

occur ifL= eq1

%100xVfl

VflVnl

Figure 8 a-b

Figure 8 a


16/17

Efficiency

cucout

out

PPPP

++

=

2

2

2222

222

cos

cos

eqc RIPIV

IV

++

=

Max efficiency occurs for:

Fixed and22

V

Fixed and2V 2I 1cos 2 =

Pc=Core Losses in Watts

Pcu= Copper Losses in Watts

2

2

2 eqc RIP=


17/17

Autotransformer

Another type of transformer is known as the autotransformer.

It consists of a single tapped primary where the center tap is commonto both primary and secondary (not isolated).

some of the turns on the coil are used for the primary and some are

used for the secondary.

an example of a variable autotransformer is known as a variac.

A variac is a single coil with a sweeping arm for the center common,this allows the ratio of primary turns:secondary turns to be alteredeasily.

3-Lesson Notes Lec 6(TRAFO)

Documents