ACLine#
Common Parameters: u, name, bus1, bus2, r, x
Common Variables: v1, v2, a1, a2
Available models: Line
Line#
AC transmission line model.
The model is also used for two-winding transformer. Transformers can set the
tap ratio in tap and/or phase shift angle phi.
To reduce the number of variables, line injections are summed at bus equations and are not stored. Current injections are not computed.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus1 |
idx of from bus |
||||
bus2 |
idx of to bus |
||||
Sn |
\(S_n\) |
Power rating |
100 |
MW |
non_zero |
fn |
\(f\) |
rated frequency |
60 |
Hz |
|
Vn1 |
\(V_{n1}\) |
AC voltage rating |
110 |
kV |
non_zero |
Vn2 |
\(V_{n2}\) |
rated voltage of bus2 |
110 |
kV |
non_zero |
r |
\(r\) |
line resistance |
0.000 |
p.u. |
z |
x |
\(x\) |
line reactance |
0.000 |
p.u. |
non_zero,z |
b |
shared shunt susceptance |
0 |
p.u. |
y |
|
g |
shared shunt conductance |
0 |
p.u. |
y |
|
b1 |
\(b_1\) |
from-side susceptance |
0 |
p.u. |
y |
g1 |
\(g_1\) |
from-side conductance |
0 |
p.u. |
y |
b2 |
\(b_2\) |
to-side susceptance |
0 |
p.u. |
y |
g2 |
\(g_2\) |
to-side conductance |
0 |
p.u. |
y |
trans |
transformer branch flag |
0 |
bool |
||
tap |
\(t_{ap}\) |
transformer branch tap ratio |
1 |
float |
non_negative |
phi |
\(\phi\) |
transformer branch phase shift in rad |
0 |
radian |
|
rate_a |
\(R_{ATEA}\) |
long-term flow limit (placeholder) |
0 |
MVA |
|
rate_b |
\(R_{ATEB}\) |
short-term flow limit (placeholder) |
0 |
MVA |
|
rate_c |
\(R_{ATEC}\) |
emergency flow limit (placeholder) |
0 |
MVA |
|
owner |
owner code |
||||
xcoord |
x coordinates |
||||
ycoord |
y coordinates |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
a1 |
\(a_{1}\) |
ExtAlgeb |
phase angle of the from bus |
||
a2 |
\(a_{2}\) |
ExtAlgeb |
phase angle of the to bus |
||
v1 |
\(v_{1}\) |
ExtAlgeb |
voltage magnitude of the from bus |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
voltage magnitude of the to bus |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
a1 |
\(a_{1}\) |
ExtAlgeb |
|
a2 |
\(a_{2}\) |
ExtAlgeb |
|
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
a1 |
\(a_{1}\) |
ExtAlgeb |
\(u \left(- itap v_{1} v_{2} \left(- bhk \sin{\left(- a_{1} + a_{2} + \phi \right)} + ghk \cos{\left(- a_{1} + a_{2} + \phi \right)}\right) + itap_{2} v_{1}^{2} \left(gh + ghk\right)\right)\) |
a2 |
\(a_{2}\) |
ExtAlgeb |
\(u \left(- itap v_{1} v_{2} \left(bhk \sin{\left(- a_{1} + a_{2} + \phi \right)} + ghk \cos{\left(- a_{1} + a_{2} + \phi \right)}\right) + v_{2}^{2} \left(gh + ghk\right)\right)\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(u \left(- itap v_{1} v_{2} \left(- bhk \cos{\left(- a_{1} + a_{2} + \phi \right)} - ghk \sin{\left(- a_{1} + a_{2} + \phi \right)}\right) - itap_{2} v_{1}^{2} \left(bh + bhk\right)\right)\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(u \left(itap v_{1} v_{2} \left(bhk \cos{\left(- a_{1} + a_{2} + \phi \right)} - ghk \sin{\left(- a_{1} + a_{2} + \phi \right)}\right) - v_{2}^{2} \left(bh + bhk\right)\right)\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
gh |
\(g_h\) |
\(0.5 g + g_{1}\) |
ConstService |
bh |
\(b_h\) |
\(0.5 b + b_{1}\) |
ConstService |
gk |
\(g_k\) |
\(0.5 g + g_{2}\) |
ConstService |
bk |
\(b_k\) |
\(0.5 b + b_{2}\) |
ConstService |
yh |
\(y_h\) |
\(u \left(i bh + gh\right)\) |
ConstService |
yk |
\(y_k\) |
\(u \left(i bk + gk\right)\) |
ConstService |
yhk |
\(y_{hk}\) |
\(\frac{u}{r + i \left(x + 1.0 \cdot 10^{-8}\right) + 1.0 \cdot 10^{-8}}\) |
ConstService |
ghk |
\(g_{hk}\) |
\(\operatorname{re}{\left(yhk\right)}\) |
ConstService |
bhk |
\(b_{hk}\) |
\(\operatorname{im}{\left(yhk\right)}\) |
ConstService |
itap |
\(1/t_{ap}\) |
\(\frac{1}{tap}\) |
ConstService |
itap2 |
\(1/t_{ap}^2\) |
\(\frac{1}{tap^{2}}\) |
ConstService |
Config Fields in [Line]
Option |
Symbol |
Value |
Info |
Accepted values |
|---|---|---|---|---|
allow_adjust |
1 |
allow adjusting upper or lower limits |
(0, 1) |
|
adjust_lower |
0 |
adjust lower limit |
(0, 1) |
|
adjust_upper |
1 |
adjust upper limit |
(0, 1) |