1. Three Phase Transformers
By Rahul Nehra (Lecturer,EE Deptt.)

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
φa+φb+φc=0 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 (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

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 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:
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 Δ
(a) 3rd harmonic components of voltage in Δ 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
VLP=√3 VφP, while : VLS= VφS
Voltage ratio of each phase : VφP/ VφS=a
VLP/ VLS= √3 VφP/ VφS= √3 a  Y-Δ
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
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 Transformers Y-Δ 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 Δ-Y Connection
DELTA-WYE 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/√  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

14. Three Phase Transformers Δ- Δ Connection
DELTA-DELTA 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 or harmonics

15. Three Phase Transformers Δ- Δ Connection

16. THREE PHASE TRANSFORMERS PER 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)

17. 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 transformer’s 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

18. 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(ωt+θ) V
The maximum flux reached during first half-cycle of applied voltage depends on θ
If θ=90◦ or : v(t)=VM cos(ωt)
& no residual flux in core  max. flux would be : φmax=Vmax/(ωNP)
However if θ=0 the max. flux would be φmax=2Vmax/(ωNP) and is twice the steady-state flux

19. 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 θ is not 90◦ this excess current exist, therefore power system & transformer must be able to withstand these currents

20. The End