The hard way requires a three line drawing of the transformers and a little vector addition. We’ll review the 6 most common transformer connections and determine the vector relationship between windings.
The first example is a Wye-Wye transformer with Wye-connected CTs as shown in the following example.
PHA H1
H2 H3
PHB PHC
X1 X2 X3
X0
1A
H1
GE/MULTILIN-745
400:5CT1 CT2
1200:5
G1
1B
H2 G2
1C
H3 G3
2A
H4 G4
2B
H5 G5
2C
H6 G6 H0
IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º IH1=IA@0º
IH2@-120º
IH3@120º
IX1=Ia@0º
IX2@-120º
IX3@120º
Figure 46: Wye-Wye Transformer
You should always start with the Wye-connected winding when determining phase relationships and the primary winding current phasors are plotted in the first vector diagram. Follow the current flowing through the H1 terminal into the IA winding. The currents are the same and all three-phase primary currents are plotted in the first phasor diagram of Figure 47.
As you follow the current through the transformer’s AØ primary winding, an opposite current flows out the aØ secondary winding and flows through the X1 bushing. The current flowing into the H1 bushing has the same phase relationship as the current flowing through the X1 Bushing. The secondary current is plotted in the second phasor diagram 180º from the actual current flowing into the relay to make the relationship between windings easier to understand.
Only the H1 and X1 currents are used when determining the vector relationships and are plotted in the third phasor diagram. Using this information, we can determine the transformer vector relationship is Y0y0; “Y” for the primary winding connection, “y”
for the secondary connection, and “0” to show that both windings are at the 0 o’clock position. We usually drop the first 0 and the correct notation would be "Yy0".
It is important to note that if the phasor diagrams were displayed on the actual relay software, 1 o'clock would be 30º and not -30º as shown because this relay uses the phase relationship in Figure 45. All examples in this book use the Figure 44 characteristic to better illustrate the difference between connections.
IA=IH1
Figure 47: Wye-Wye Transformer Phasor Diagram
Our next example uses a Delta-Delta transformer. There is no Wye-connected winding in this transformer configuration and we will start with the primary winding as defined by the CTs connected to F1a, F2a, F3a, F1b, F2b, and F3b.
PHA H1
H2 H3 PHB
PHC
X1 X2 X3
1A F1a
GENERAL ELECTRIC T-60
400:5CT1 CT2
1200:5
F1b 1B F2a F2b
1C F3a F3b
2A M1a M1b
2B M2a M2b
2C M3a M3b IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º
IH1=IA-IC@-30º
IH2@-150º
IH3@90º
IX1=Ia-Ic@-30º
IX2@-150º
IX3@90º
Figure 48: Delta-Delta Transformer Connections
The current flowing through H1 is the transformer “IA and -IC” currents because H1 is connected to the polarity of the AØ winding and the non-polarity of the CØ winding.
The first phasor diagram demonstrates the IA and -IC addition and the final result
“IH1” is found at the 1 o’clock position or -30º.
The current flowing through X1 is “Ia and -Ic” because X1 is connected to the polarity of the aØ winding and the non-polarity of the cØ winding. The secondary current is plotted in the second phasor diagram 180º from the actual current flowing into the relay to make the relationship between windings easier to understand. The second phasor diagram demonstrates the Ia and -Ic addition and the final result “IX1” is found at the 1 o’clock position or -30º.
Only the H1 and X1 currents are used when determining the vector relationships and are plotted in the third phasor diagram. Using this information, we can determine the transformer vector relationship is D1d1; “D” for the primary winding connection, “d”
for the secondary connection, and “1” to show that both windings are at the 1 o’clock position. It is important to note that if the phasor diagrams were displayed on the actual relay software, 1 o'clock would be 30º and not -30º as shown because this relay uses the phase relationship in Figure 45. All examples in this book use the Figure 44 characteristic to better illustrate the difference between connections.
The primary winding should always be at the 0 or 12 o’clock position and we can rotate both phasors as shown in the fourth phasor diagram to display a “D0d0” transformer.
The first “0” is usually dropped from the designation and the Delta-Delta connection is displayed as “Dd0.”
You could also change the reference instead of the phasors as shown in the fifth phasor diagram.
Figure 49: Delta-Delta Transformer Phasors
The next transformer is a Wye-Delta transformer with a Wye side primary because the Wye side, H-Bushing CTs are connected to 47, 49, 51, 46, 48, and 50.
PHA H1
BECKWITH ELECTRIC M-3310
46
IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º IH1=0º
Figure 50: Wye-Delta Transformer Connections
Starting with the Wye currents, draw a phasor diagram of the current flowing through the primary bushings (IH1, IH2, & IH3) which are equal to the phase (IA, IB, & IC) currents as shown in the first phasor diagram. The current flowing through X1 is “Ia and -Ic” because X1 is connected to the polarity winding of the aØ winding and the non-polarity of the cØ winding.
The secondary current is plotted in the second phasor diagram 180º from the actual current flowing into the relay to make the relationship between windings easier to understand. The second phasor diagram demonstrates the Ia and -Ic addition and the final result “IX1” which is found at the 1 o’clock position or -30º. The third phasor diagram displays the relationship between the primary and secondary windings which can be translated to “Y0d1” or “Yd1”
using correct notation.
0°12
-IcIX1=Ia-Ic
Ic Ib
The next example is a Wye-Delta transformer with a different delta configuration. The Wye or high voltage winding is the primary winding because the Wye side CTs are connected to the SEL-587 relay terminals Z01, Z03, Z05, Z02, Z04, and Z06.
PHA H1
SCHWEITZER ENGINEERING LABORATORIES SEL-587
102 IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º
IH1=0º
Figure 52: Wye-Delta Alternate Transformer Connections
Starting with the Wye currents, draw a phasor diagram of the current flowing through the primary bushings (IH1, IH2, & IH3) which are equal to the phase (IA, IB, & IC) currents as shown in the first phasor diagram.
The second phasor diagram displays the Delta-winding phasors with the phase currents in phase with the Wye-connected winding and the line current equal to “Ia-Ib” because the X1 bushing is connected to the aØ winding and the bØ non-polarity winding.
The third phasor shows the phase relationship between windings and can be described as Y0d11 or “Yd11”.
IX1=Ia-Ib-Ib IX1=d11
0°12
Figure 53: Wye-Delta Alternate Transformer Phasor Diagrams
The example in Figure 50 can easily become a Delta-Wye transformer by switching the protective relay connections as shown in the next example.
PHA H1
H2 H3 PHB
PHC
X1 X2 X3
1A 55
BECKWITH ELECTRIC M-3310
54
1B 57 56
1C 59 58
2A 47 46
2B 49 48
2C 51 50 H0
400:5CT1 CT2
1200:5
IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º IH1=0º
IH2@-120º
IH3@120º
IX1=Ia-Ic@-30º
IX3@90º IX2@-150º
Figure 54: Delta-Wye Transformer Connections
You should always start with the Wye-winding and the phase and line currents are drawn in the second phasor diagram because the Wye-winding is the secondary winding.
The first diagram follows the steps from Figure 50 for the Delta-winding because it is now the primary winding. The third diagram displays the phasor relationship between windings and the transformer is described as D1y0 based on this diagram.
The primary winding must always be at 12 o’clock and we can rotate the phasors or the clock to obtain the correct description D0y11 or “Dy11” as shown in the fourth and fifth phasor diagrams.
Figure 55: Delta-Wye Transformer Connections
The example in Figure 52 can easily become a Delta-Wye transformer by switching the protective relay connections as shown in the next example where the Delta-winding is connected to SEL-387 terminals Z01, Z03, Z05, Z02, Z04, and Z06
PHA H1
H2 H3 PHB
PHC
X1 X2 X3
IAW1
Z07
SCHWEITZER ENGINEERING LABORATORIES SEL-387
Z08
IBW1 ICW1
H0
400:5CT1 CT2
1200:5
Z09 Z10
Z11 Z12
IAW2
Z01 Z02
IBW2 ICW2
Z03 Z04
Z05 Z06 IA@0ºIB@-120ºIC@120º Ic@120ºIb@-120ºIa@0º
IH1=0º
IH2@-120º
IH3@120º
IX1=Ia-Ib@30º
IX3@150º IX2@-90º
Figure 56: Delta-Wye Alternate Transformer Connections
Starting with the Wye currents, draw a phasor diagram of the current flowing through the primary bushings (IH1, IH2, & IH3) which are equal to the phase (IA, IB, & IC) currents as shown in the second phasor diagram.
The first phasor diagram displays the Delta-winding phasors with the phase currents in phase with the Wye-connected winding and the line current equal to “Ia-Ib” because the X1 bushing is connected to the aØ winding and the bØ non-polarity winding.
The third diagram displays the phasor relationship between windings and the transformer is described as D11y0 based on this diagram.
The primary winding must always be at 12 o’clock and we can rotate the phasors or the clock to obtain the correct description D0y1 or “Dy1” as shown in the fourth and fifth phasor diagrams.
D11y0
Figure 57: Delta-Wye Alternate Transformer Phasor Diagrams