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Determining Transformer Phase Angle Displacement 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. 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. 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 ´. 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‘ B - B‘ C - C‘ = A1 – A2 = B1 – B2 = C1 – C2 A or A1 is the polarity end of the winding Secondary winding a - a‘ b - b‘ c - c‘ = a1 – a2 = b1 – b2 = c1 – c2 a or a1 is the polarity end of the winding 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 Winding Displacement Based on Connection Type Primary Delta Wye Delta Wye Secondary Wye Delta Delta Wye Displacement 30° 30° None None 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 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 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 Standard Delta Connection 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 ? H1 H2 H3 N X1 X2 X3 Closing The Delta On Single Phase Banks We Can Close These Deltas Any Way We Wish But Will They Connect to Other Transformers C B A primary primary secondary a b c n secondary primary secondary V A-B C B A V B-C V C-A primary primary primary V a-n - + V c-n - + + - V b-n secondary a b c Van – vbn + vba = 0 n secondary secondary V A-B C B A V B-C V C-A primary primary primary V a-n - + V c-n - + + - V b-n secondary Van – vbn + vba = 0 a Vba = -van+vbn b c n secondary secondary From Our Windings we see that van – vbn + vba = 0 Solving for Vba High Side Vector then vba = -van + vbn V A-B We Can Display The Equation Using Vectors & Find Vba V ab V C-A V B-C Low Side Vectors V a-n V a-n V ab V c-n We Can Move a Vector Anywhere We Want To As Long As We Don’t Change The Length Or Direction V ab V ba V b-n -Van V c-n -Van V ba V b-n We Can Display the Vector Addition Two ways With The same Result Conclusion LS L-L Voltage Leads HS L-L voltage By 30 ° B V A-B A H1 V B-C V C-A C H2 H3 V a-n - + N V c-n X1 + - + X2 X3 V b-n V A-B b V a-n a c Van – vbn + vba = 0 V ab V ab Vba = -van+vbn Conclusion V ab leads V AB by 30° V C-A V B-C V b-n V c-n V ba -Van B V A-C C H1 V B-A V C-B A H2 H3 V a-n - + - N V c-n X1 + - + X2 X3 V b-n b a V A-B Van – vcn + vca = 0 V a-n V ac Vca = -van+vcn Conclusion V ac lags V AC by 30° c V C-A V B-C V ac V b-n V c-n V ca -Van 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 H2 X2 30° LEADING SECONDARY b COUNTERCLOCKWISE B C ROTATION H2 X3 a X2 c H1 X3 30 H1 H3 H3 A X1 X1 Ref H1 H2 H3 S F S F A S N X3 X2 X1 S F B F S C F S F Reference Point B A C B A C primary primary H1 H2 H3 secondary secondary N X1 primary X2 secondary a X3 b c a b B c C H1 n A H2 a A c H3 c B N X1 X2 C c a B A X3 b b C a b Solve The Following Pairs of Transformers A B C CØ primary BØ AØ primary primary HV ________ LV By 30° secondary secondary secondary c b a n C A H1 B H2 H3 HV ________ LV By 30° N Can These Transformers Be Paralleled ? X1 b X2 c X3 a Solve The Following Pairs of Transformers A B C primary primary primary HV ________ LV By 30° secondary secondary secondary c b a n A B H1 C H2 H3 HV ________ LV By 30° N Can These Transformers Be Paralleled ? X1 b X2 c X3 a Solve The Following Pairs of Transformers C B A primary primary primary HV ________ LV By 30° secondary secondary secondary a b c n B H1 HV ________ LV By 30° N Can These Transformers Be Paralleled ? C X1 b A H2 X2 c H3 X3 a Solve The Following Pairs of Transformers C B A primary primary primary HV ________ LV By 30° secondary secondary secondary a b c n C H1 HV ________ LV By 30° N Can These Transformers Be Paralleled ? A X1 c B H2 X2 a H3 X3 b Solve The Following Pairs of Transformers C B A primary primary primary HV ________ LV By 30° secondary secondary secondary a b c n C H1 HV ________ LV By 30° N Can These Transformers Be Paralleled ? A X1 c B H2 X2 a H3 X3 b Practice 1 C B A B C A primary H1 H2 primary H3 AØ N c Fig. 1 BØ secondary secondary X1 primary X2 X3 b a CØ secondary Fig. 2 n a b c B A H1 N X1 b Fig. 3 C H2 H3 X2 X3 a c Practice 1 Solution C B A B C A primary H1 H2 primary H3 AØ BØ secondary secondary N X1 c Fig. 1 primary X2 X3 b a CØ secondary Fig. 2 n a b c V a-n B Solution V A-B A C V ab H1 V ab V C-A V B-C V c-n V ba H2 H3 V b-n -Van N X1 b Fig. 3 X2 X3 a c Practice 2 A B C A B C primary AØ secondary n a b c primary primary BØ secondary primary primary AØ CØ BØ secondary secondary secondary Fig. 2 primary CØ secondary Fig. 2 n a b c A B H1 N X1 a Fig. 3 C H2 H3 X2 X3 b c Practice 2 Solution A B C A B C primary primary AØ primary BØ secondary secondary primary CØ AØ secondary primary BØ secondary secondary Fig.6 n a b c primary CØ secondary Fig. 7 n a b c V a-n A V A-C B C V ac V ac V C-B H1 V b-n V c-n H2 H3 V ca V B-A -Van N X1 a Fig. 8 X2 X3 b c Does HV Lead or Lag LV? H1 N Fig. 8 X1 H2 X2 H3 X3 Does HV Lead or Lag LV? H1 N Fig. 8 V x1-n V H1-H3 V x1-x3 V x1-x2 V x1-x3 V H3-H2 V H2-H1 V x3-n -V x1 V x2-n V x3-x1 X1 H2 X2 H3 X3 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