final three phase transformer

THREE PHASE TRANSFORMERS

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

•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

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.


• How the core of compact three phase is built

• φa+φb+φc=0 and central leg can be removed


• The two constructions


• 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

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).


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

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

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

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

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


• WYE-DELTA CONNECTION

• 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

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

•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.

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)


• 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


• 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


• 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%


• 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%

final three phase transformer

Engineering