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 |
\(vp\) |
Algeb |
positive sequence voltage magnitude |
v_str |
|
ap |
\(ap\) |
Algeb |
positive sequence voltage phase |
v_str |
|
vnd |
\(vnd\) |
Algeb |
negative sequence voltage on d-axis (cos) |
v_str |
|
vnq |
\(vnq\) |
Algeb |
negative sequence voltage on q-axis (sin) |
v_str |
|
vzd |
\(vzd\) |
Algeb |
zero sequence voltage on d-axis (cos) |
v_str |
|
vzq |
\(vzq\) |
Algeb |
zero sequence voltage on q-axis (sin) |
v_str |
|
a |
\(a\) |
ExtAlgeb |
phase angle of single-phase eq. bus |
||
aa |
\(aa\) |
ExtAlgeb |
phase angle of bus for phase a |
||
ab |
\(ab\) |
ExtAlgeb |
phase angle of bus for phase b |
||
ac |
\(ac\) |
ExtAlgeb |
phase angle of bus for phase c |
||
v |
\(v\) |
ExtAlgeb |
voltage of single-phase eq. bus |
||
va |
\(va\) |
ExtAlgeb |
voltage of bus for phase a |
||
vb |
\(vb\) |
ExtAlgeb |
voltage of bus for phase b |
||
vc |
\(vc\) |
ExtAlgeb |
voltage of bus for phase c |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
vp |
\(vp\) |
Algeb |
\(\frac{va}{3} + \frac{vb}{3} + \frac{vc}{3}\) |
ap |
\(ap\) |
Algeb |
\(aa + ab + ac\) |
vnd |
\(vnd\) |
Algeb |
\(0.0\) |
vnq |
\(vnq\) |
Algeb |
\(0.0\) |
vzd |
\(vzd\) |
Algeb |
\(0.0\) |
vzq |
\(vzq\) |
Algeb |
\(0.0\) |
a |
\(a\) |
ExtAlgeb |
|
aa |
\(aa\) |
ExtAlgeb |
|
ab |
\(ab\) |
ExtAlgeb |
|
ac |
\(ac\) |
ExtAlgeb |
|
v |
\(v\) |
ExtAlgeb |
|
va |
\(va\) |
ExtAlgeb |
|
vb |
\(vb\) |
ExtAlgeb |
|
vc |
\(vc\) |
ExtAlgeb |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
vp |
\(vp\) |
Algeb |
\(- vp + \frac{\sqrt{\left(vb \sin{\left(- aa + ab + d_{120} \right)} - vc \sin{\left(aa - ac + d_{120} \right)}\right)^{2} + \left(va + vb \cos{\left(- aa + ab + d_{120} \right)} + vc \cos{\left(aa - ac + d_{120} \right)}\right)^{2}}}{3}\) |
ap |
\(ap\) |
Algeb |
\(aa - ap + \operatorname{atan}_{2}{\left(vb \sin{\left(- aa + ab + d_{120} \right)} - vc \sin{\left(aa - ac + d_{120} \right)},va + vb \cos{\left(- aa + ab + d_{120} \right)} + vc \cos{\left(aa - ac + d_{120} \right)} \right)}\) |
vnd |
\(vnd\) |
Algeb |
\(va \cos{\left(aa \right)} + vb \cos{\left(ab - d_{120} \right)} + vc \cos{\left(ac + d_{120} \right)} - vnd\) |
vnq |
\(vnq\) |
Algeb |
\(va \sin{\left(aa \right)} + vb \sin{\left(ab - d_{120} \right)} + vc \sin{\left(ac + d_{120} \right)} - vnq\) |
vzd |
\(vzd\) |
Algeb |
\(va \cos{\left(aa \right)} + vb \cos{\left(ab \right)} + vc \cos{\left(ac \right)} - vzd\) |
vzq |
\(vzq\) |
Algeb |
\(va \sin{\left(aa \right)} + vb \sin{\left(ab \right)} + vc \sin{\left(ac \right)} - vzq\) |
a |
\(a\) |
ExtAlgeb |
\(u \left(v^{2} \left(g + ghk\right) - v vp \left(bhk \sin{\left(a - ap \right)} + ghk \cos{\left(a - ap \right)}\right)\right)\) |
aa |
\(aa\) |
ExtAlgeb |
\(\frac{u \left(- v va \left(- bhk \sin{\left(a - aa \right)} + ghk \cos{\left(a - aa \right)}\right) + va^{2} \left(g + ghk\right)\right)}{3}\) |
ab |
\(ab\) |
ExtAlgeb |
\(\frac{u \left(- v vb \left(bhk \sin{\left(- a + ab + d_{120} \right)} + ghk \cos{\left(- a + ab + d_{120} \right)}\right) + vb^{2} \left(g + ghk\right)\right)}{3}\) |
ac |
\(ac\) |
ExtAlgeb |
\(\frac{u \left(- v vc \left(- bhk \sin{\left(a - ac + d_{120} \right)} + ghk \cos{\left(a - ac + d_{120} \right)}\right) + vc^{2} \left(g + ghk\right)\right)}{3}\) |
v |
\(v\) |
ExtAlgeb |
\(u \left(- v^{2} \left(b + bhk\right) - v vp \left(- bhk \cos{\left(a - ap \right)} + ghk \sin{\left(a - ap \right)}\right)\right)\) |
va |
\(va\) |
ExtAlgeb |
\(\frac{u \left(v va \left(bhk \cos{\left(a - aa \right)} + ghk \sin{\left(a - aa \right)}\right) - va^{2} \left(b + bhk\right)\right)}{3}\) |
vb |
\(vb\) |
ExtAlgeb |
\(\frac{u \left(v vb \left(bhk \cos{\left(- a + ab + d_{120} \right)} - ghk \sin{\left(- a + ab + d_{120} \right)}\right) - vb^{2} \left(b + bhk\right)\right)}{3}\) |
vc |
\(vc\) |
ExtAlgeb |
\(\frac{u \left(v vc \left(bhk \cos{\left(a - ac + d_{120} \right)} + ghk \sin{\left(a - ac + d_{120} \right)}\right) - vc^{2} \left(b + bhk\right)\right)}{3}\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
yhk |
\(y_{hk}\) |
\(\frac{u}{r + i x}\) |
ConstService |
ghk |
\(g_{hk}\) |
\(\operatorname{re}{\left(yhk\right)}\) |
ConstService |
bhk |
\(b_{hk}\) |
\(\operatorname{im}{\left(yhk\right)}\) |
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) |