tf conn
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trafo connTRANSCRIPT
12.1 APPENDIX XII. TRANSFORMER CONNECTION SYMMETRICAL COMPONENT NETWORKS
12.1 Transformer Configuration Impedance Network Diagrams
ZT
LVHV
Positive-Sequence
a : 1
HV
ZT
a : 1
LV
Negative-Sequence
ZT
LV
Zero-Sequence
3ZG
HV
a : 1
3ZGHigh Low
Figure XII. 1 Wye-Grounded.–Wye-Grounded Transformer Sequence Impedance Networks
ZT
HV
Positive-Sequence
a : 1
HV
ZT
a : 1
LV
Negative-Sequence
ZT
a : 1
Zero-Sequence
3ZG
HV
Figure XII. 2: Wye Grounded–Wye Transformer Sequence Impedance Networks
ZT
LV
Zero-Sequence
HV
a : 1ZT
LVHV
Positive-Sequence
a : 1
HV
ZT
a : 1
LV
Negative-Sequence
Figure XII. 3: Wye–Wye Transformer Sequence Impedance Networks
ZT
30o : 1a
LVHV
Positive-Sequence
HV
ZT
-30o : 1a
LV
Negative-Sequence
LV
High
ZT
a : 1
Zero-Sequence
3ZG
HV
Figure XII. 4: Wye-Grounded–Delta Transformer Sequence Impedance Networks
ZT
30o : 1a
LVHV
Positive-Sequence
ZT
-30o : 1a
LVHV
Negative-Sequence
ZT
LV
Zero-Sequence
3ZG Low
HV
a : 1
Figure XII. 5: Delta–Wye-Grounded Transformer Sequence Impedance Networks
ZT
30o : 1a
LVHV
Positive-Sequence
ZT
-30o : 1a
LVHV
Negative-Sequence
ZT
LV
Zero-Sequence
HV
a : 1
Figure XII. 6: Delta–Wye Transformer Sequence Impedance Networks
ZT
LVHV
Positive-Sequence Negative-Sequence
a : 1
HV
ZT
a : 1
LV
ZT
LV
Zero-Sequence
HV
a : 1
Figure XII. 7: Delta-Delta Transformer Sequence Impedance Networks
LVHV LV
HV
Positive-Sequence
aH : aM
ZHTZMT
MV LV
ZLT
aH : aL
HV
Negative-Sequence
aH : aM
ZHTZMT
MV LV
ZLT
aH : aL
aH : aM
Zero-Sequence
HV
3ZMG3ZHG
ZHTZMT
MV LV
aH : aL
ZLT
Figure XII. 8: Wye-Grounded–Wye-Grounded–Delta Tertiary Transformer Sequence Impedance Networks
12.2 Two-Source Faulted Networks Symmetrical Component Impedance Network Diagrams
12.2.1 Single-Line-to-Ground Faults
ESB
RF
ISBVSB
ESC
VSC
ERB
IRB VRB
ERC
VRCIRCISC
ESA
ISAVSA
ERA
IRA VRA
IF
ZS
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
m *
(1-m
) *
ZR
Figure XII. 9: Single-Line-to-Ground Fault Three-Line Diagram
Rs
Rs
Es
Z1s m*ZL1 (1-m)*ZL1 Z1r
Er
Z2s m*ZL1 (1-m)*ZL1 Z2r
Z0s m*ZL0 (1-m)*ZL0 Z0r
3RF
V2FV2S I2SI2S
I1F= I2F= I0F
V0SI0S V0F
+
-
+
-V1S V1F
Figure XII. 10: Single-Line-to-Ground Fault Symmetrical Component Diagram
12.2.2 Line-to-Line Faults
RF
ESB
ISBVSB
ESC
VSC
ERB
IRB VRB
ERC
VRCIRCISC
ESA
ISAVSA
ERA
IRA VRA
ZS
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
m *
(1-m
) *
ZR
Figure XII. 11: Line-to-Line Fault Three-Line Diagram
+
-
Rs
Rs
Rs
Es
Z1s m*ZL1 (1-m)*ZL1 Z1r
Er
Z2s m*ZL1 (1-m)*ZL1 Z2r
Z0s m*ZL0 (1-m)*ZL0 Z0r
RF
V2FV2S I2SI2S
IA1 = -IA2
V0SI0S
+
-V1S V1F
V0F
Figure XII. 12: Line-to-Line Fault Symmetrical Component Diagram
12.2.3 Line-to-Line-to-Ground Faults
RF
RG 3I0
RF
ESB
ISBVSB
ESC
VSC
ERB
IRB VRB
ERC
VRCIRCISC
ESA
ISAVSA
ERA
IRA VRA
ZS
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
m *
(1-m
) *
ZR
Figure XII. 13: Line-to-Line-to-Ground Fault Three-Line Diagram
Rs
Rs
Rs
Es
Z1s m*ZL1 (1-m)*ZL1 Z1r
Er
Z2s m*ZL1 (1-m)*ZL1 Z2r
Z0s m*ZL0 (1-m)*ZL0 Z0r
RF
V2FV2SI2S
I2S
V0SI0S
RF
RF+3 RG
+
-
+
-V1S
V1F
V0F
Figure XII. 14: Line-to-Line-to-Ground Fault Symmetrical Component Diagram
12.2.4 Three-Line-to-Ground Faults
RG3I0
RF
RF
RF
ESB
ISBVSB
ESC
VSC
ERB
IRB VRB
ERC
VRCIRCISC
ESA
ISAVSA
ERA
IRA VRA
ZS
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
m *
(1-m
) *
ZR
Figure XII. 15: Three-Line-to-Ground Fault Three-Line Diagram
Rs
Rs
Rs
Es
Z1s m*ZL1 (1-m)*ZL1 Z1r
Er
Z2s m*ZL1 (1-m)*ZL1 Z2r
Z0s m*ZL0 (1-m)*ZL0 Z0r
RF
V2FV2SI2S
I2S
V0SI0S
RF
RF+3 RG
+
-
+
-V1S V1F
V0F
Figure XII. 16: Three-Line-to-Ground Fault Symmetrical Component Diagram
12.2.5 Single-Line Open
ESB
ISBVSB
ESC
VSC
ERB
IRB VRB
ERC
VRCIRCISC
ESA
ISAVSA
ERA
IRA VRA
ZS
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
| Zs
Zm
Zm
|| Z
m Z
s Z
m|
| Zm
Zm
Zs|
m *
(1-m
) *
ZR
Figure XII. 17: Single-Line Open Three-Line Diagram
Rr
Rr
RrRs
Rs
Rs
Es
Z1s m*ZL1 (1-m)*ZL1 Z1r
Er
Z2s m*ZL1 (1-m)*ZL1 Z2r
Z0s m*ZL0 (1-m)*ZL0 Z0r
V2S I2RI2S
V0SI0S
+
-
+
-V1S
I0R
I1RI1S
Figure XII. 18: Single-Line Open Symmetrical Component Diagram