EE341 Energy Conversion Ali Keyhani Transformer Lecture

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EE341 Energy Conversion Ali KeyhaniTransformer
Lecture 2
3-Phase Transformer
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3-phase Transformers

• 1.Three single-phase transformers connected in a
  three-phase bank.
• 2. Three sets of windings wrapped on a common
  core.

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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

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b)
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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
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• Y-?. The secondary voltage is shifted 30?
  relative to the primary voltage.

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• 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.

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

?-?
?-?
for
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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.

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Solution
pf1.0
pf1.0
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?-Y
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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.

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Solution
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P.U. equivalent circuit
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Open Delta
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For open delta
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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
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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.
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Per-Unit Circuit
One-phase circuits
Where
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Three-phase circuits
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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
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Method1
Using ?-Y
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Method 2
Using Y-equivalent
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j
j
j
j
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j
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Example
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j
RsjXs
jXM
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jXM
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jXM
jXs
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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.

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jXs
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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)

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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.

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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.