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EE341 Energy Conversion Ali Keyhani Transformer

Lecture 2

3-Phase Transformer

3-phase Transformers

- 1.Three single-phase transformers connected in a

three-phase bank. - 2. Three sets of windings wrapped on a common

core.

Problem

- Three-single phase transformers are connected

grounded Y-Y to two three phase loads connected

in ? and Y - a)Draw single-line diagram.
- b)The single-phase equivalent circuit with

transformer referred to HV side. - c)P.U equivalent circuit

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a)

- VLP240x 415.2V
- VLS120x 207.6V

b)

c)

2. Y-?

3. ? -Y

4. ? - ?

1. Y-Y

Y-Y

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The voltage ratio of each phase

The line voltage ratio

From the above

- Y-?. The secondary voltage is shifted 30?

relative to the primary voltage.

- Because of the phase shift. transformers can not

be connected in parallel unless they have proper

phase sequence. (ie. They are in phase with each

other). - Y Y parallel Y- ? ? NO
- Y- ? parallel Y- ? ? Yes. However, you must

identify the correct phase sequence.

?-Y

From above we have

- For ?-Y connection, the secondary Voltage Lags

the primary Voltage by 30

?-?

?-?

for

Problem 2

- Three identical single-phase transformers, each

rated 12.7kv/196.3kv, 333.33 MVA, 14short

circuit leakage reactance, are connected at (a)

Y-Y, (b) ? -Y. IF transformer banks (ie. Y-Y or

?-Y) are fully loaded at utility power factor and

loads are connected to HV windings, compute the

required voltage to be supplied to LV windings.

Solution

pf1.0

pf1.0

?-Y

Problem 1

- Three single-phase transformers each rated at 4.4

kVA, 220 volts(primary) to 440 volts (secondary),

60cps, gave the following test results on open

and short circuits tests. When the rated voltage

was applied to the primary side, .77 amp and 73

watts were measured at the primary winding with

the secondary winding open-circuited. When 3.41

of the rated secondary voltage was applied to the

secondary winding with the primary winding

short-circuited 10 amp and 60 watts were

measured at the primary winding. Transformers

are connected as a tree phase Y-Y. Determine - a) Estimate the parameters(ie., Rm,Xm,Rs and Xs)

draw the one phase equivalent circuit. and p.u

Eq. circuit - b) Determine the required primary voltage when

the 3?, Y-Y transformer is supplying full load at

a power factor of .6 lagging and rated voltage.(

Ignore Xm and Rm ). You must use per unit

analysis.

Solution

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P.U. equivalent circuit

Open Delta

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For open delta

The output of the open-delta bank is only 57.7

percent of the original banks rating.

What happens to the rest of the open-delta banks

rating? To find out, examine the Q of the open

delta bank.

Trans 1

Trans 2

Thus one transformer is producing reactive power

which the other one is consuming. It is this

power exchange of energy back and forth between

the two transformers that limits the power output

to 57.5 percent of the original banks rating

instead of the otherwise expected 66.7 percent.

Per-Unit Circuit

One-phase circuits

Where

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Three-phase circuits

The Zb is defined for one-phase circuits

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Example

Three single-phase 2SkVA, 34500/277 Volts

transformers are connected in ?-Y. Test

measure----/---- on high voltage side with the

low voltage side short circuited gives the

following data.

Determine the P.U. Equivalent circuits

Method1

Using ?-Y

Method 2

Using Y-equivalent

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j

j

j

j

j

Example

j

RsjXs

jXM

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jXM

jXM

jXs

Example 2

- An electric lamp is rated 120 volts, and 500

watts. If the voltage applied across the lamp is

twice the rated value, compute the per-unit

current that flows through the lamp. Use the

per-unit method.

jXs

RsjXsZs

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Voltage Regulations

a)VPRI/VSEC

- Vfl Desired load voltage at full load. It may be

equal to rated voltage, above or below the rated

voltage. - Vnl is the no-load rated voltage(ie. When the

pri. voltage has the desired value in order the

sec. voltage be at its desired value at full load)

Example

- A single-phase transformer rated 200kVA, 200/400V

and 10 short circuit reactance. Compute - a) The VR when the transformer is fully loaded at

unity power factor and rated voltage of 400V. - b)same except the load voltage is ten percent

above its rated value.

j0.10

j0.10

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- Problem 1 Three identical single-phase

transformers, rated each 12.7kV/196.3kV,

333.33MVA, 14 short circuit leakage reactance

are connected at (a) Y-Y, (b) ?-Y. If transformer

banks (ie. Y-Y or - ? -Y) are fully loaded at

unity power factor and loads are connected to HV

windings, compute the required voltage to be

supplied to LV windings. - Problem 2. Three single-phase transformers each

rated at 4.4 kVA, 220 volts (primary) to 440

volts (secondary), 60 cps, gave the following

test results on open and short circuit tests.

When the rated voltage was applied to the primary

side, .77 amp and 73 watts were measured at the

primary winding with the secondary winding

open-circuited. When 3.41 of the rated

secondary voltage was applied to the secondary

side, 10 amps and 60 watts were measured at the

secondary winding with the primary winding

short-circuited. Transformers are connected as a

three phase Y-Y. Determine - (20 points) a) Estimate the parameters(ie., Rm,

Xm, Rs and Xs) draw the one phase equivalent

circuit and p.u Eq.CKT - (20 points) b) Determine the required primary

voltage when the 3?, Y-Y transformer is supplying

full load at a power factor of .6 lagging and

rated voltage. (Ignore Xm and Rm). You must use

per unit analysis.