EE341 Energy Conversion Ali Keyhani Transformer Lecture - PowerPoint PPT Presentation

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EE341 Energy Conversion Ali Keyhani Transformer Lecture

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Lecture #2. 3-Phase Transformer. 2. 3-phase Transformers ... Problem 2. Three single-phase transformers each rated at 4.4 kVA, 220 volts ... – PowerPoint PPT presentation

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Title: EE341 Energy Conversion Ali Keyhani Transformer Lecture


1
EE341 Energy Conversion Ali KeyhaniTransformer
Lecture 2
3-Phase Transformer
2
3-phase Transformers
  • 1.Three single-phase transformers connected in a
    three-phase bank.
  • 2. Three sets of windings wrapped on a common
    core.

3
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

4
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5
a)
  • VLP240x 415.2V
  • VLS120x 207.6V

6
b)
7
c)
2. Y-?
3. ? -Y
4. ? - ?
1. Y-Y
Y-Y
8
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9
The voltage ratio of each phase
The line voltage ratio
From the above
10
  • Y-?. The secondary voltage is shifted 30?
    relative to the primary voltage.

11
  • 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.

12
?-Y
From above we have
13
  • For ?-Y connection, the secondary Voltage Lags
    the primary Voltage by 30

?-?
?-?
for
14
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.

15
Solution
pf1.0
pf1.0
16
?-Y
17
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.

18
Solution
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22
P.U. equivalent circuit
23
Open Delta
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26
For open delta
27
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
28
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.
29
Per-Unit Circuit
One-phase circuits
Where
30
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31
Three-phase circuits
32
The Zb is defined for one-phase circuits
33
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34
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
35
Method1
Using ?-Y
36
Method 2
Using Y-equivalent
37
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j
j
j
j
39
j
40
Example
41
j
RsjXs
jXM
42
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jXM
44
jXM
jXs
45
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.

46
jXs
47
RsjXsZs
48
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49
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)

50
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.

51
j0.10
j0.10
52
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54
  • 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.
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