Interface#
Group for interface models.
Available models: Fortescue
Fortescue#
Fortescue's symmetric component interface.
This model interfaces a positive-sequence, single-phase-equivalent bus with three buses representing three phases. It is effectively a transformer with one terminal on the primary side and three on the secondary. Only the positive sequence component on the secondary winding is used for simulation.
The positive-sequence voltage magnitude and angle of the secondary winding
are named vp
and ap
.
The negative and zero sequence variables given in the d- and q-axis due the
angle being undefined when the voltage is zero. The negative sequence
voltages are vnd
and vnq
for the d- anx q-axis, respectively.
Likewise, the zero-sequence voltages are vzd
and vzq
.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus |
bus idx for the single-phase equivalent |
mandatory |
|||
busa |
bus idx for phase a |
mandatory |
|||
busb |
bus idx for phase b |
mandatory |
|||
busc |
bus idx for phase c |
mandatory |
|||
Sn |
\(S_n\) |
Power rating |
100 |
MW |
non_zero |
r |
\(r\) |
resistance |
0.001 |
p.u. |
z |
x |
\(x\) |
short-circuit reactance |
0.025 |
p.u. |
non_zero,z |
g |
iron loss |
0 |
p.u. |
y |
|
b |
magnetizing susceptance |
0.005 |
p.u. |
y |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
---|---|---|---|---|---|
vp |
\(V_{p}\) |
Algeb |
positive sequence voltage magnitude |
v_str |
|
ap |
\(\theta_{p}\) |
Algeb |
positive sequence voltage phase |
v_str |
|
vnd |
\(V_{nd}\) |
Algeb |
negative sequence voltage on d-axis (cos) |
v_str |
|
vnq |
\(V_{nq}\) |
Algeb |
negative sequence voltage on q-axis (sin) |
v_str |
|
vzd |
\(V_{zd}\) |
Algeb |
zero sequence voltage on d-axis (cos) |
v_str |
|
vzq |
\(V_{zq}\) |
Algeb |
zero sequence voltage on q-axis (sin) |
v_str |
|
a |
\(\theta_{1}\) |
ExtAlgeb |
phase angle of single-phase eq. bus |
||
aa |
\(\theta_{a}\) |
ExtAlgeb |
phase angle of bus for phase a |
||
ab |
\(\theta_{b}\) |
ExtAlgeb |
phase angle of bus for phase b |
||
ac |
\(\theta_{c}\) |
ExtAlgeb |
phase angle of bus for phase c |
||
v |
\(V_{1}\) |
ExtAlgeb |
voltage of single-phase eq. bus |
||
va |
\(V_{a}\) |
ExtAlgeb |
voltage of bus for phase a |
||
vb |
\(V_{b}\) |
ExtAlgeb |
voltage of bus for phase b |
||
vc |
\(V_{c}\) |
ExtAlgeb |
voltage of bus for phase c |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
---|---|---|---|
vp |
\(V_{p}\) |
Algeb |
\(\frac{V_{a}}{3} + \frac{V_{b}}{3} + \frac{V_{c}}{3}\) |
ap |
\(\theta_{p}\) |
Algeb |
\(\theta_{a} + \theta_{b} + \theta_{c}\) |
vnd |
\(V_{nd}\) |
Algeb |
\(0.0\) |
vnq |
\(V_{nq}\) |
Algeb |
\(0.0\) |
vzd |
\(V_{zd}\) |
Algeb |
\(0.0\) |
vzq |
\(V_{zq}\) |
Algeb |
\(0.0\) |
a |
\(\theta_{1}\) |
ExtAlgeb |
|
aa |
\(\theta_{a}\) |
ExtAlgeb |
|
ab |
\(\theta_{b}\) |
ExtAlgeb |
|
ac |
\(\theta_{c}\) |
ExtAlgeb |
|
v |
\(V_{1}\) |
ExtAlgeb |
|
va |
\(V_{a}\) |
ExtAlgeb |
|
vb |
\(V_{b}\) |
ExtAlgeb |
|
vc |
\(V_{c}\) |
ExtAlgeb |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
---|---|---|---|
vp |
\(V_{p}\) |
Algeb |
\(- V_{p} + \frac{\sqrt{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2} + \left(V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2}}}{3}\) |
ap |
\(\theta_{p}\) |
Algeb |
\(\theta_{a} - \theta_{p} + \operatorname{atan}_{2}{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)},V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)} \right)}\) |
vnd |
\(V_{nd}\) |
Algeb |
\(V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(120^{o} - \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{c} \right)} - V_{nd}\) |
vnq |
\(V_{nq}\) |
Algeb |
\(V_{a} \sin{\left(\theta_{a} \right)} - V_{b} \sin{\left(120^{o} - \theta_{b} \right)} + V_{c} \sin{\left(120^{o} + \theta_{c} \right)} - V_{nq}\) |
vzd |
\(V_{zd}\) |
Algeb |
\(V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(\theta_{b} \right)} + V_{c} \cos{\left(\theta_{c} \right)} - V_{zd}\) |
vzq |
\(V_{zq}\) |
Algeb |
\(V_{a} \sin{\left(\theta_{a} \right)} + V_{b} \sin{\left(\theta_{b} \right)} + V_{c} \sin{\left(\theta_{c} \right)} - V_{zq}\) |
a |
\(\theta_{1}\) |
ExtAlgeb |
\(u \left(V_{1}^{2} \left(g + g_{hk}\right) - V_{1} V_{p} \left(b_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)}\right)\right)\) |
aa |
\(\theta_{a}\) |
ExtAlgeb |
\(\frac{u \left(- V_{1} V_{a} \left(- b_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)}\right) + V_{a}^{2} \left(g + g_{hk}\right)\right)}{3}\) |
ab |
\(\theta_{b}\) |
ExtAlgeb |
\(\frac{u \left(- V_{1} V_{b} \left(b_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)} + g_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) + V_{b}^{2} \left(g + g_{hk}\right)\right)}{3}\) |
ac |
\(\theta_{c}\) |
ExtAlgeb |
\(\frac{u \left(- V_{1} V_{c} \left(- b_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) + V_{c}^{2} \left(g + g_{hk}\right)\right)}{3}\) |
v |
\(V_{1}\) |
ExtAlgeb |
\(u \left(- V_{1}^{2} \left(b + b_{hk}\right) - V_{1} V_{p} \left(- b_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)}\right)\right)\) |
va |
\(V_{a}\) |
ExtAlgeb |
\(\frac{u \left(V_{1} V_{a} \left(b_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)}\right) - V_{a}^{2} \left(b + b_{hk}\right)\right)}{3}\) |
vb |
\(V_{b}\) |
ExtAlgeb |
\(\frac{u \left(V_{1} V_{b} \left(b_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)} - g_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) - V_{b}^{2} \left(b + b_{hk}\right)\right)}{3}\) |
vc |
\(V_{c}\) |
ExtAlgeb |
\(\frac{u \left(V_{1} V_{c} \left(b_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) - V_{c}^{2} \left(b + b_{hk}\right)\right)}{3}\) |
Services#
Name |
Symbol |
Equation |
Type |
---|---|---|---|
yhk |
\(y_{hk}\) |
\(\frac{u}{r + i x}\) |
ConstService |
ghk |
\(g_{hk}\) |
\(\operatorname{re}{\left(y_{hk}\right)}\) |
ConstService |
bhk |
\(b_{hk}\) |
\(\operatorname{im}{\left(y_{hk}\right)}\) |
ConstService |
d120 |
\(120^o\) |
\(\frac{2 \pi}{3}\) |
ConstService |
Config Fields in [Fortescue]
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) |