lecture #16 eee 574 dr. dan tylavsky branch modeling
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Lecture #16
EEE 574
Dr. Dan Tylavsky
Branch Modeling
© Copyright 1999 Daniel Tylavsky
Branch Modeling– There are two types of branches we wish to model:
• Transmission Lines
• Transformers
– Let’s first look at transmission line modeling. • (Assuming nominal or equivalent pi model:)
R + j X
BSHBSH
© Copyright 1999 Daniel Tylavsky
Branch ModelingR + j X
BSHBSH
Node specification may include a fixed reactor or shunt capacitor.
– BSH may be specified in:• per unit (PU).
• MVAR = QSH=V2BSH, BSH>0 (where V is the nominal system voltage.)
– Branch/node may also include a switched reactor or capacitor.• Data format may not allow enough info to tell if shunt branch is lost when T-line is lost.
© Copyright 1999 Daniel Tylavsky
Branch Modeling Power flow data formats: (Many!)
• IEEE Common Format for Exchange of Solved Load Flow Data.– We’ll use and discuss this format.
• PECO (Philadelphia Electric Co.) Format.• WSCC (Western Systems Coordination Council) Format.• Etc.
© Copyright 1999 Daniel Tylavsky
Branch Modeling– IEEE Format
• T-Line (Branch) Data– Terminal Identifier - 4 digit right justified bus numbers
» Node From Cols. 1-4» Node To Cols. 6-9
– Circuit Number Cols. 17» Integer 1-9 used to identify parallel lines
– Branch Type Col. 19» 0 → Transmission Line
– Branch Impedance Cols. 20-39» R, X in 2F10.6
– Line Charging Cols. 41-49
» 2*BSH
© Copyright 1999 Daniel Tylavsky
Branch Modeling
© Copyright 1999 Daniel Tylavsky
Branch Modeling– Transformer Modeling:
– We want to find an equivalent circuit in the form:
Ya
YcYb
I2
+
V2
-
+
V1
-
I1
R + j X=Z=Y-1 1:a+
V2
-
+
V1
-
I1 I2
TapSide
ImpedanceSide
© Copyright 1999 Daniel Tylavsky
Branch Modeling
– Calculate the short-circuit admittance parameters for this two-port circuit.
2221212
2121111
VYVYI
VYVYI
ca
V
aa
V
aa
V
ba
V
YYV
IY
YV
YV
V
IY
YV
YV
V
IY
YYV
IY
02
222
1
1
01
221
2
2
02
112
01
111
1
2
1
2
– We want to find an equivalent circuit in the form:
Ya
YcYb
I2
+
V2
-
+
V1
-
I1
© Copyright 1999 Daniel Tylavsky
Branch Modeling
– Calculate the short-circuit admittance parameters for the xfmr as a two port.– For the ideal transformer:
R + j X=Z=Y-1 1:a+
V2
-
+
V1
-
I1 I2
TapBus
ImpedanceBus
a
VV 21
1
– By power balance: 1*
2*1
2*1
2*22
*11 IaIor
a
III
a
VIVIV
21
*1
02
222
*1
*1
01
221
2
2
02
112
01
111
'1
2
1
2
a
Y
aVa
I
V
IY
a
Y
Va
I
V
IY
a
Y
V
YaV
V
IY
YV
IY
V
V
V
V
a
VV 2
1
© Copyright 1999 Daniel Tylavsky
Branch Modeling– Equating like coefficients.
222
*21
12
11
a
YYYY
a
YYY
a
YYY
YYYY
ca
a
a
ba
– With 4 equations & 3 unknowns, the system is over-determined.
– Can be solved if one constraint is redundant.
22
22
1
1
a
aY
a
Y
a
YY
a
YY
a
Y
a
YYY
a
aY
a
YYY
YYa
YYYY
a
YY
c
cca
b
bba
a
– This is the case if a=a*.• Turns ratio is real (no phase shift.)
© Copyright 1999 Daniel Tylavsky
Branch ModelingI2
+
V2-
+
V1-
I1
a
aY
1
aY
2
1
a
aY
TapBus
ImpedanceBus
© Copyright 1999 Daniel Tylavsky
Branch Modeling
Y1:a+
V2
-
+
V1
-
I1 I2
– Teams: For the following circuit show the equivalent model is.
I2
+
V2-
+
V1-
I1
aaY 2
aY
aY 1
– This model cannot be used simply with IEEE format.– No division by ‘a’ is somewhat of an advantage.
© Copyright 1999 Daniel Tylavsky
Branch Modeling– IEEE Format
• Transformer (Branch) Data– Terminal Identifier - 4 digit right justified bus numbers
» Tap Bus Cols. 1-4» Impedance Bus Cols. 6-9
– Circuit Number Cols. 17» Integer 1-9 used to identify parallel transformers
© Copyright 1999 Daniel Tylavsky
Branch Modeling– IEEE Format
• Transformer (Branch) Data cont’d– Branch Type Col. 19
» 0 → transmission line» 1 → fixed voltage ratio and/or fixed phase angle.» 2 → fixed phase angle and variable voltage ratio with voltage control (ULTC).» 3 → fixed phase angle and variable voltage ratio w/ MVAR control. (rare)» 4 → fixed voltage ratio and variable phase angle w/ MW control.
© Copyright 1999 Daniel Tylavsky
Branch Modeling– IEEE Format
• Transformer (Branch) Data cont’d– Branch Impedance Cols. 20-39
» R, X in per-unit– Line Charging Cols. 41-49
» 2*BSH
– Control Bus Cols. 69-72» Specifies where the quantity being controlled is measured.
– Side Col. 74» 0 - controlled bus is at the transformers terminals» 1 - the remote controlled bus is near the tap side » 2 - the remote controlled bus is near the impedance side.
© Copyright 1999 Daniel Tylavsky
Branch Modeling
R + j X=Z=Y-1 1:a+
V2
-
+
V1
-
I1 I2
TapBus
ImpedanceBus
a
VV 2
1
↑Increase ‘a’ to ↑ increase voltage of bus located on ‘tap side’ of xfmr.
↓Decrease ‘a’ to ↑ increase voltage of bus on impedance side of the xfmr.
© Copyright 1999 Daniel Tylavsky
Branch Modeling
© Copyright 1999 Daniel Tylavsky
Branch Modeling
Transformer Types0 → transmission line1 → fixed voltage ratio and/or fixed phase angle.2 → fixed phase angle and variable voltage ratio with voltage control (ULTC).3 → fixed phase angle and variable voltage ratio w/ MVAR control. (rare)4 → fixed voltage ratio and variable phase angle w/ MW control.
The End