final three phase transformer
TRANSCRIPT
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THREE PHASE TRANSFORMERS
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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 • There is an advantage of bank of three single phase 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
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•The construction of a single three phase transformer is preferred today, it is lighter, smaller, cheaper and slightly more efficient.Disadvatages•Difficult to handle, ship and set in place for operation•Difficult and costly to repair
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Three Phase TransformersA three-phase transformer is made of three sets of primary and secondary windings, each set wound around one leg of an iron core assembly. Essentially it looks like three single-phase transformers sharing a joined core as in Figure.
Three phase transformer core has three sets of windings.Those sets of primary and secondary windings will be connected in either Δ or Y configurations to form a complete unit. The various combinations of ways that these windings can be connected together in will be the focus of this section.
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Three Phase Transformers
• How the core of compact three phase is built
• φa+φb+φc=0 and central leg can be removed
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Three Phase Transformers
• The two constructions
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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 (Δ)
• 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-Δ
(c) Delta-wye Δ-Y
(d) Delta-Delta Δ-Δ
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Primary - Secondary
Y - Y
Y - Δ
Δ - Y
Δ - Δ
The reasons for choosing a Y or Δ configuration for transformer winding connections are the same as for any other three-phase application: Y connections provide the opportunity for multiple voltages, while Δ connections enjoy a higher level of reliability (if one winding fails open, the other two can still maintain full line voltages to the load).
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Three Phase Transformers
WYE-WYE connection-economical for small rating, high voltage transformers as the no. of turns per phase and amount of insulation required is less.
• In Y-Y connection, primary voltage on each phase is VφP=VLP/√3
• 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 VLS=√3 VφS
• Overall the voltage ratio of transformer is:
aV
V
V
V
S
P
LS
LP
3
3
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AdvantagesNo. of turns per phase and the amount of insulation is min. because Vp=VL/ √3 (57.7%)no phase displacement b/w primary and secondarywith star point on both sides, neutral can be providedDisadvantages:Distortion of voltages caused by Third and fifth harmonics due to exciting currentsInterference due to harmonics
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Three Phase TransformersΔ- Δ Connection
• In Δ-Δ connection VLP= VφP and VLS= VφS
• Voltage ratio : VLP/VLS= VφP / VφS =a Δ-Δ
• This configuration has no phase shift and there is no concern about unbalanced loads.
• Used in systems which carry large currents on low voltages and where continuity of service is to be maintained even when one of the phase develop fault.
• Less conductor reqd. as I φ P=ILP/√3
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Advantages•No phase displacement
•No distortion of flux as harmonic currents does not flow in line wires
•Less conductor area as I φ P=ILP/√3
Disadvantages
•More insulation reqd. than Y-Y
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Three Phase Transformers• WYE-DELTA CONNECTION• Such connections are used where voltage is to be
stepped down, e.g.at the end of transmission line.• The neutral of primary winding is earthed.• Y; VLP=√3 VφP, while : for Δ; VLS= VφS • Voltage ratio of each phase : VφP/ VφS=a• VLP/ VLS= √3 VφP/ VφS= √3 a Y-Δ• This configuration causes secondary voltage to be
shifted 30◦ relative to primary voltage
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Three Phase Transformers
• WYE-DELTA CONNECTION
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• Neutral of primary winding is earthed• Saving in insulation on primary side as insulation
is stressed to 57.7% of line voltage• Y-Δ doesn’t have shortcomings of Y-Y regarding
generation of third harmonic voltage since the Δ provide a circulating path for 3rd Harmonic
• Y-Δ is more stable w.r.t. unbalanced loads, since Δ partially redistributes any imbalance that occurs
• This configuration causes secondary voltage to be shifted 30◦ relative to primary voltage
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Three Phase TransformersΔ-Y Connection
• In Δ-Y primary line voltage is equal to primary phase voltage VLP=VφP, in secondary VLS=√3VφS
• Line to line voltage ratio ;
• VLP/ VLS = VφP/ [√3 VφS ]=a/√3 Δ-Y
• This connection has the same advantages & phase shifts as Y- Δ
• And Secondary voltage lags primary voltage by 30◦ with abc phase sequence
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•Such connections are used where it is necessary to step-up the voltage, e.g. at the beginning of h.v. transmission line.
•Popular in distribution system because it can serve both the three phase power equipment and the single phase lightning circuits.
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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 :
S1φ,base= Sbase/3 • base phase current, and impedance are:• Iφ,base= S1φ,base/ Vφ,base= Sbase /(3Vφ,base)• Zbase=(Vφ,base)²/ S1φ,base • Zbase=3(Vφ,base)²/ Sbase • Relation between line base voltage, and phase base voltage
depends on connection of windings, if connected in Δ ; VL,base=Vφ,base and
• if connected in Wye: VL,base= √3Vφ,base • Base line current in 3 phase transformer: • IL,base= Sbase/ (√3 VL,base)
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THREE PHASE TRANSFORMERSPER UNIT
• A 50 kVA 13800/208 V Δ-Y distribution transformer has a resistance of 1 percent & a reactance of 7 percent per unit
(a) what is transformer’s phase impedance referred to H.V. side?
(b) Calculate this transformer’s voltage regulation at full load and 0.8 PF lagging using the calculated high-side impedance
(c) Calculate this transformer’s voltage regulation under the same conditions, using the per-unit system
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THREE PHASE TRANSFORMERSPER UNIT
• SOLUTION• (a) Base of High voltage=13800 V, Sbase=50 kVA • Zbase=3(Vφ,base)²/Sbase=3(13800)²/50000=11426Ω• The per unit impedance of transformer is:• Zeq=0.01+j 0.07 pu • Zeq=Zeq,pu Zbase =(0.01+j0.07 pu)(11426)= 114.2 + j 800 Ω • (b) to determine V.R. of 3 phase Transformer bank, V.R. of any
single transformer can be determined • V.R. =(VφP-a VφS)/ (aVφS) x 100%• Rated phase voltage on primary 13800 V, rated phase current
on primary: Iφ=S/(3 Vφ) =50000/(3x13800)=1.208 A
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THREE PHASE TRANSFORMERSPER UNIT
• Example …• Rated secondary phase voltage: 208 V/√3=120V• Referred to H.V. V’φS=a VφS13800 V• At rated voltage & current of secondary:
VφP=a VφS+Req Iφ + j Xeq Iφ =
13800/_0◦ +(114.2)(1.208/_-36.87)+(j800)(1.208)/_-36.87)= 13800+138/_-36.87+966.4/_53.13= 13800+110.4-j82.8+579.8+j773.1= 14490+j690.3= 14506/_2.73◦ V
V.R. = (VφP-a VφS )/ (a VφS ) 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◦ puVP=1/_0◦ +(0.01) (1/_-36.87◦)+(j0.07)(1/_-
36.87◦)=1+0.008-j0.006+0.042+ j0.056
=1.05+j0.05=1.051/_2.73◦
• V.R.= (1.051-1.0)/1.0 x100% = 5.1%