ENERGY CONVERSION ONE (Course 25741)

1
ENERGY CONVERSION ONE (Course 25741)

• Chapter Two
• TRANSFORMERS
• continued

2
Three Phase Transformers

• Almost all major generation Distribution
  Systems in the world are three phase ac systems
• Three phase transformers play an important role
  in these systems
• Transformer for 3 phase cct.s is either
• (a) constructed from 3 single phase
  transformers, or
• (b) another approach is to employ a common
  core for
• the three sets of windings of the three
  phases
• The construction of a single three phase
  transformer is the preferred today, it is
  lighter, smaller, cheaper and slightly more
  efficient
• There is an advantage that each unit in the bank
  could be replaced individually in the event of a
  fault, however this does not outweigh the other
  advantages of combined 3 ph. unit

3
Three Phase Transformers

• How the core of compact three phase is built
• fafbfc0 and central leg can be removed

4
Three Phase Transformers

• The two constructions

5
Three Phase Transformers

• 3 phase transformer connections
• The windings of primary and secondary (in any
  construction) can be connected in either a wye
  (Y) or delta (?)
• This provides a total of 4 possible connections
  for 3
• phase transformer (if Neutral is not
  grounded)
• (a) Wye-wye Y-Y
• (b) Wye-delta Y-?
• (c) Delta-wye ?-Y
• (d) Delta-Delta ?-?

6
Three Phase Transformers

• To analyze a 3-phase transformer, each single
  transformer in the bank should be analyzed
• Any single phase in bank behaves exactly like 1
  phase transformer just studied
• impedance, V.R., efficiency, similar
  calculations for 3 ph. are done on per phase
  basis, using the same technique already used in
  single phase Transformer
• The applications, advantages and disadvantages of
  each type of three phase connections will be
  discussed next

7
Three Phase Transformers

• WYE-WYE connection
• In Y-Y connection, primary voltage on each phase
  is VfPVLP/v3
• Primary phase voltage is related to secondary
  phase voltage by turns ratio of transformer
• Phase voltage of secondary is related to Line
  voltage of secondary by VLSv3 VfS
• Overall the voltage ratio of transformer is
• 
  Y-Y

8
Three Phase Transformers

• Two serious concerns on Y-Y connection
• 1- if loads on transformer cct. are
  unbalanced,
• voltages on phases of transformer severely
  
• unbalanced, also source is loaded in an
• unbalanced form
• 2- Third harmonic voltages can be large
  (there
• is no path for passage of third harmonic
  
• current)
• Both concerns on unbalance load condition large
  3rd Harmonic voltages can be rectified as
  follows

9
Three Phase Transformers

• Solidly grounding the neutrals of windings
• specially primary winding, this connection
  provide a path for 3rd harmonic current flow,
  produced and do not let build up of large 3rd
  voltages . Also provides a return path for any
  current imbalances in load
• Adding a third winding (tertiary) connected in ?
• (a) 3rd harmonic components of voltage in ?
  will add up, causing a circulating current flow
  within winding
• (b) tertiary winding should be large enough to
  handle circulating currents (normally 1/3 of
  power rating of two main windings)
• One of these corrective techniques should be
  employed with Y-Y, however normally very few
  transformer with this type of connection is
  employed (others can do the same job)

10
Three Phase Transformers

• WYE-DELTA CONNECTION
• VLPv3 VfP, while VLS VfS
• Voltage ratio of each phase VfP/ VfSa
• VLP/ VLS v3 VfP/ VfS v3 a ? Y-?
• Y-? doesnt have shortcomings of Y-Y regarding
  generation of third harmonic voltage since the ?
  provide a circulating path for 3rd Harmonic
• Y-? is more stable w.r.t. unbalanced loads, since
  ? partially redistributes any imbalance that
  occurs
• This configuration causes secondary voltage to be
  shifted 30? relative to primary voltage
• If secondary of this transformer should be
  paralleled with secondary of another transformer
  without phase shift, there would be a problem

11
Three Phase Transformers

• WYE-DELTA CONNECTION

12
Three Phase TransformersY-? Connection

• The phase angles of secondaries must be equal if
  they are to be paralleled, it means that
  direction of phase shifts also should be the same
• In figure shown here, secondary lags primary if
  abc phase sequence applied,
• However secondary leads primary when acb phase
  sequence applied

13
Three Phase Transformers?-Y Connection

• DELTA-WYE CONNECTION
• In ?-Y primary line voltage is equal to primary
  phase voltage VLPVfP, in secondary VLSv3VfS
• Line to line voltage ratio
• VLP/ VLS VfP/ v3 VfS a/v3 ? ?-Y
• This connection has the same advantages phase
  shifts as Y- ?
• And Secondary voltage lags primary voltage by 30?
  with abc phase sequence

14
Three Phase Transformers?- ? Connection

• DELTA-DELTA CONNECTION
• In ?-? connection VLP VfP and VLS VfS
• Voltage ratio VLP/VLS VfP / VfS a ? ?-?
• This configuration has no phase shift and there
  is no concern about unbalanced loads or harmonics

15
Three Phase Transformers?- ? Connection
16
THREE PHASE TRANSFORMERSPER UNIT

• In 3 phase, similarly a base is selected
• If Sbase is for a three phase system, the per
  phase basis is S1f,base Sbase/3
• base phase current, and impedance are
• If,base S1f,base/ Vf,base Sbase /(3Vf,base)
• Zbase(Vf,base)²/ S1f,base
• Zbase3(Vf,base)²/ Sbase
• Relation between line base voltage, and phase
  base voltage depends on connection of windings,
  if connected in ? VL,baseVf,base
  and
• if connected in Wye VL,base v3Vf,base
• Base line current in 3 phase transformer
• IL,base Sbase/ (v3 VL,base)

17
THREE PHASE TRANSFORMERSPER UNIT

• A 50 kVA 13800/208 V ?-Y distribution
  transformer has a resistance of 1 percent a
  reactance of 7 percent per unit
• (a) what is transformers phase impedance
  referred to H.V. side?
• (b) Calculate this transformers voltage
  regulation at full load and 0.8 PF lagging using
  the calculated high-side impedance
• (c) Calculate this transformers voltage
  regulation under the same conditions, using the
  per-unit system

18
THREE PHASE TRANSFORMERSPER UNIT

• SOLUTION
• (a) Base of High voltage13800 V, Sbase50 kVA
• Zbase3(Vf,base)²/Sbase3(13800)²/5000011426O
• The per unit impedance of transformer is
• Zeq0.01j 0.07 pu
• ZeqZeq,pu Zbase (0.01j0.07 pu)(11426)
• 114.2 j 800 O
• (b) to determine V.R. of 3 phase Transformer
  bank, V.R. of any single transformer can be
  determined
• V.R. (VfP-a VfS)/ (aVfS) x 100
• Rated phase voltage on primary 13800 V, rated
  phase current on primary IfS/(3 Vf)
  50000/(3x13800)1.208 A

19
THREE PHASE TRANSFORMERSPER UNIT

• Example
• Rated secondary phase voltage 208 V/v3120V
• Referred to H.V. ? VfSa VfS13800 V
• At rated voltage current of secondary
• VfPa VfSReq If j Xeq If
• 13800/_0? (114.2)(1.208/_-36.87)(j800)(1.208)
  /_-36.87) 13800138/_-36.87966.4/_53.13
  13800110.4-j82.8579.8j773.1 14490j690.3
  14506/_2.73? V
• V.R. (VfP-a VfS )/ (a VfS ) x 100
• 
  (14506-13800)/13800 x 100 5.1

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THREE PHASE TRANSFORMERSPER UNIT

• Example
• (c) V.R. using per unit system
• output voltage 1/_0? current 1/_-36.87? pu
• VP1/_0? (0.01) (1/_-36.87?)(j0.07)(1/_-36.87?)
  10.008-j0.0060.042 j0.056
• 1.05j0.051.051/_2.73?
• V.R. (1.051-1.0)/1.0 x100 5.1

21
Apparent Power Rating of a Transformer

• Apparent power rating Voltage rating set
  current flow of windings
• Current flow important as it controls I²R losses
• in turn control heating of coils
• Heating is critical, since overheating the
  coils reduce insulation life
• Actual VA rating of a transformer may be more
  than a single value
• In real Transformer (a) may be a VA rating
  for transformer by itself, (b) another (higher)
  rating for transformer with forced cooling
• If a transformers voltage reduced for any reason
  (i.e. operating with lower frequency than normal)
  then transformer VA rating must reduced by an
  equal amount, otherwise current exceed
  permissible level cause overheating

22
Inrush Current

• This is caused by applied voltage level at
  energization of transformer, or due to residual
  flux in the transformer core
• Suppose that voltage is v(t)VM sin(?t?) V
• The maximum flux reached during first half-cycle
  of applied voltage depends on ?
• If ?90? or v(t)VM cos(?t)
• no residual flux in core ? max. flux would
  be fmaxVmax/(?NP)
• However if ?0 the max. flux would be
  fmax2Vmax/(?NP) and is twice the steady-state
  flux

23
Inrush Current

• With this high maximum flux if the magnetization
  curve examined it shows passage of enormous
  magnetizing current, (looks like short circuit in
  part of cycle)
• In these cases that ? is not 90? this excess
  current exist, therefore power system
  transformer must be able to withstand these
  currents

24
Transformer Nameplate

• Example