1. Determining Transformer Phase Angle Displacement

2. Transformers Do Not Change Or Create Phases A transformer can not act as a phase changing device and change single-phase into three-phase or three-phase into single phase. To make the transformer connections compatible with three-phase supplies we need to connect them together in a particular way to form a Three Phase Transformer Configuration. A three phase transformer or 3φ transformer can be constructed either by connecting together three single-phase transformers, thereby forming a so-called three phase transformer bank, or by using one pre-assembled and balanced three phase transformer which consists of three pairs of single phase windings mounted onto one single laminated core.

3. Advantages Of A Three Phase Transformer The advantages of building a single three phase transformer is that for the same kVA rating it will be smaller, cheaper and lighter than three individual single phase transformers connected together because the copper and iron core are used more effectively. As well as having fewer bushings. The methods of connecting the primary and secondary windings are the same, whether using just one Three Phase Transformer or three separate Single Phase Transformers.

4. How We Label The standard method for marking three phase transformer windings is to label the polarity end of three primary windings with capital letters A, B and C, and the non polarity end of the winding as A´ (called A prime) B ´and C ´. The secondary windings are labeled with small (lower case) letters a, b and c and a ´, b ´and c ´.

5. Another Method of Labeling Each winding has two ends and may be labeled 1 and 2. For example the A phase winding may be labeled A1 and A2 Primary Winding A - A‘ = A1 – A2 B - B‘ = B1 – B2 C - C‘ = C1 – C2 A or A1 is the polarity end of the winding Secondary winding a - a‘ = a1 – a2 b - b‘ = b1 – b2 c - c‘ = c1 – c2 a or a1 is the polarity end of the winding

6. Phase Angle Displacement Between Windings REMEMBER There is never any phase displacement or shift between two windings REMEMBER There MAY be a phase displacement or shift between the line voltages of two transformers depending on how the windings are connected

7. Winding Displacement Based on Connection Type PrimarySecondaryDisplacement DeltaWye30° WyeDelta30° Delta None Wye None

8. Phase Angle Displacement Between Transformer Banks To connect two transformers for parallel operation each transformer’s line voltages must be in phase with the other transformer Transformers operating in parallel may be in the same substation connected to the same bus or in substations at different locations If the voltages are not in phase with one another a fault condition will exist when the connection is attempted

9. Delta - Wye Connection Displacement REMEMBER If one winding is connected ∆ and the other winding connected Y there will always be a phase shift of 30 ⁰ between the line voltages Whether the shift is leading or lagging depends on how the ∆ is closed If one transformer is leading and the other is lagging then the associated phase voltages will have an angle of 60 ⁰ between them

10. Wye – Wye Transformers Wye – Wye transformers will have no phase angle shift between the voltages on the primary and secondary Trying to connect a Δ – Y transformer to a Y- Y transformer will result in a 30 ⁰ shift between the voltages on the secondary and they will not connect

11. Standard Delta Connection N H1H2H3 X1X2 X3 ? ? ? All Three Phase Transformers will Have The Delta Closed As Shown Below The Question Then Becomes To which Bushing Do We Connect Our System Phases

12. Closing The Delta On Single Phase Banks primary secondary primary secondary primary secondary A a B C b c n We Can Close These Deltas Any Way We Wish But Will They Connect to Other Transformers

13. primary secondary primary secondary primary secondary A a B C b c n + ++ - - - V A-B V B-C V C-A V a-n V b-n V c-n Van – vbn + vba = 0

14. primary secondary primary secondary primary secondary A a B C b c n + ++ - - - V A-B V B-C V C-A V a-n V b-n V c-n Van – vbn + vba = 0 Vba = -van+vbn

15. V a-n V b-n V c-n -Van V ba V ab High Side Vector Low Side Vectors V a-n V b-n V c-n -Van V ba V ab From Our Windings we see that van – vbn + vba = 0 Solving for Vba then vba = -van + vbn We Can Display The Equation Using Vectors & Find Vba We Can Display the Vector Addition Two ways With The same Result V A-B V B-C V C-A V ab We Can Move a Vector Anywhere We Want To As Long As We Don’t Change The Length Or Direction Conclusion LS L-L Voltage Leads HS L-L voltage By 30 °

16. N H1H2H3 X1X2 X3 AB C a bc V A-B V B-C V C-A V a-n V b-n V c-n ++ + --- Van – vbn + vba = 0 Vba = -van+vbn V a-n V b-n V c-n -Van V ba V ab V A-B V B-C V C-A V ab Conclusion V ab leads V AB by 30°

17. N H1H2H3 X1X2 X3 CB A c ba V A-C V B-A V C-B V a-n V b-n V c-n ++ + --- Van – vcn + vca = 0 Vca = -van+vcn V a-n V b-n V c-n -Van V ca V ac V A-B V B-C V C-A V ac Conclusion V ac lags V AC by 30°

18. Specification: Phasing Rotation Pick a fixed reference point Spin the circle such that the H terminals pass the reference point in the order 1-2-3 CCW - Counterclockwise Rotation if the circle rotates CCW CW - Clockwise Rotation if the circle rotates CW Displacement Pick a fixed reference point Spin the circle according to it’s rotation from above Leading If the X1 Terminal passes the reference point before the H1 - Secondary leads the Primary Lagging If the X1 Terminal passes the reference point after the H1 - Secondary lags the Primary Displacement Angle The angle between the H1 and X1 terminal Reference Point

19. primary secondary primary secondary primary secondary A a B C b c n N H1H2H3 X1X2 X3 AB C a bc N H1H2H3 X1X2 X3 CB A c ba A B C a b c C B A c b a

20. primary secondary primary secondary primary secondary C c B A b a n N H1H2H3 X1X2 X3 AC B c ba HV ________ LV By 30° Can These Transformers Be Paralleled ? Solve The Following Pairs of Transformers AØ BØ CØ

21. N H1H2H3 X1X2 X3 BA C c ba HV ________ LV By 30° Can These Transformers Be Paralleled ? Solve The Following Pairs of Transformers

22. primary secondary primary secondary primary secondary A a B C b c n N H1H2H3 X1X2 X3 CB A c ba HV ________ LV By 30° Can These Transformers Be Paralleled ? Solve The Following Pairs of Transformers

23. primary secondary primary secondary primary secondary A a B C b c n N H1H2H3 X1X2 X3 AC B a cb HV ________ LV By 30° Can These Transformers Be Paralleled ? Solve The Following Pairs of Transformers

24. primary secondary primary secondary primary secondary A a B C b c n N H1H2H3 X1X2 X3 AC B a cb HV ________ LV By 30° Can These Transformers Be Paralleled ? Solve The Following Pairs of Transformers

25. N H1H2H3 X1X2 X3 BCA b ca Fig. 1 N H1H2H3 X1X2 X3 ABC a bc Fig. 3 primary secondary primary secondary primary secondary C n B A a b c Fig. 2 AØBØCØ Practice 1

26. N H1H2H3 X1X2 X3 BCA b ca Fig. 1 N H1H2H3 X1X2 X3 ABC a bc Fig. 3 primary secondary primary secondary primary secondary C n B A a b c Fig. 2 AØBØCØ V A-B V B-C V C-A V ab Solution Practice 1 Solution V a-n V b-n V c-n -Van V ba V ab

27. N H1H2H3 X1X2 X3 BAC b ac Fig. 3 primary secondary primary secondary primary secondary C n B A a b c Fig. 2 AØBØCØ primary secondary primary secondary primary secondary C n B A a b c Fig. 2 AØBØCØ Practice 2

28. N H1H2H3 X1X2 X3 BAC b ac Fig. 8 primary secondary primary secondary primary secondary C n B A a b c Fig.6 AØBØCØ primary secondary primary secondary primary secondary C n B A a b c Fig. 7 AØBØCØ V a-n V b-n V c-n -Van V ca V ac V A-C V B-A V C-B V ac Practice 2 Solution

29. N H1H2H3 X1X2 X3 Fig. 8 Does HV Lead or Lag LV?

30. N H1H2H3 X1X2 X3 Fig. 8 Does HV Lead or Lag LV? V x1-n V x2-n -V x1 V x3-x1 V x1-x2 V x3-n V x1-x3 V H1-H3 V H2-H1 V H3-H2 V x1-x3

31. Lets Keep it Simple If a transformer bank is connect so that the polarity of the any winding is connected to AØ and the non-polarity of the same winding is connected to CØ then the HS L-L voltage leads the LS L-L voltage by 30° A-Cʹ then HS leads If a transformer bank is connect so that the polarity of the any winding is connected to AØ and the non-polarity of the same winding is connected to BØ then the HS L-L voltage lags the LS L-L voltage by 30° A-Bʹ then HS lags