Branch Modeling
Lecture #16
EEE 574
Dr. Dan Tylavsky
© 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 + jX
BSH
BSH
© Copyright 1999 Daniel Tylavsky
Branch Modeling
R + jX
Node specification may
include a fixed reactor or
shunt capacitor.
BSH
BSH
– 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:
Impedance
I1 Side R + j X=Z=Y-1
+
1:a
I2
Tap
Side
+
V1
-
V2
-
– We want to find an equivalent circuit in the form:
I1
I2
Ya
+
Yb
V1
-
+
Yc
V2
-
© Copyright 1999 Daniel Tylavsky
Branch Modeling
– We want to find an equivalent circuit in the form:
I1
+
I2
Ya
Yb
+
Yc
V1
-
V2
-
I1
Y11 
V1 V
 Ya  Yb
I1
Y12 
V2
V2Ya

 Ya
V2
2 0
V1  0
– Calculate the short-circuit
V1Ya
I2

 Ya
admittance parameters for Y21 
V1 V 0
V1
this two-port circuit.
I1  Y11V1  Y12V2
I 2  Y21V1  Y22V2
2
I2
Y22 
V2
 Ya  Yc
V1  0
© Copyright 1999 Daniel Tylavsky
Branch Modeling
Impedance
I1 Bus R + j X=Z=Y-1
1:a
+
V2

V1 
a
V1
-
I2
Tap
BusY11
+
V2
-
I1

V1 V
Y
2 0
I1
Y12 
V2
V2 Y
Y
a


V2
a
V 0
– Calculate the short-circuit
I1
Y
admittance parameters forY21  I 2
 *  *
V1 V 0 a V1 a
the xfmr as a two port.
– For the ideal transformer:
I2
I1
Y
1
2
V1 V2

1
a
– By power balance:
Y22 
V1I1*  V2 I 2* 
V2

V1  0
a aV1 '
*

a2
I
V2 *
I1  I 2  1* or I 2 a *  I1
a
a
© Copyright 1999 Daniel Tylavsky
Branch Modeling
– Equating like coefficients.– Can be solved if one
constraint is redundant.
Y11  Ya  Yb  Y
– This is the case if a=a*.
Y
Y12  Ya  
a
• Turns ratio is real (no phase shift.)
Y
Y21  Ya  *
a
Y
Y22  Ya  Yc  2
a
– With 4 equations & 3
unknowns, the system is
over-determined.
Ya 
Y
a
Y
 Yb  Y
a
Y
 a 1 
 Yb  Y 
 Y

a
a


Y
Y
Y
Ya  Yc  2 
 Yc  2
a
a
a
Ya  Yb  Y 
 Yc 
Y
Y
1 a 


Y

2 
a
a2
 a 
© Copyright 1999 Daniel Tylavsky
Branch Modeling
I1
+
Impedance
 a 1 
Y
Bus V1  a 
-
Y
I2
a
+
Tap
1 a 
Y 2 
 a  V2 Bus
-
© Copyright 1999 Daniel Tylavsky
Branch Modeling
– Teams: For the following circuit show the equivalent
model is.
I1
I2
Y
1:a
+
+
V1
I1
+
V2
-
V1
-
aY

Y a2  a

I2
+
Y 1  a 
V2
-
– 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
Impedance
I1 Bus R + j X=Z=Y-1
1:a
+
V2

V1 
a
V1
-
I2
Tap
Bus
+
V2
-
 ↑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 Types
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.
The End