DCLink#
Basic DC links
Common Parameters: u, name
Available models: Ground, R, L, C, RCp, RCs, RLs, RLCs, RLCp
Ground#
Ground model that sets the voltage of the connected DC node.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node |
Node index |
mandatory |
|||
voltage |
\(V_0\) |
Ground voltage (typically 0) |
0 |
p.u. |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
Ficticious current injection from ground |
v_str |
|
v |
\(v\) |
ExtAlgeb |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(0\) |
v |
\(v\) |
ExtAlgeb |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(u \left(- V_{0} + v\right)\) |
v |
\(v\) |
ExtAlgeb |
\(- I_{dc}\) |
Config Fields in [Ground]
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) |
R#
Resistive dc line
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(\frac{u \left(- v_{1} + v_{2}\right)}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(- I_{dc} + \frac{u \left(- v_{1} + v_{2}\right)}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [R]
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) |
L#
Inductive dc line
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
L |
DC line inductance |
0.001 |
p.u. |
non_zero,r |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
Inductance current |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(0\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(- u \left(v_{1} - v_{2}\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{L}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{L}\) |
Config Fields in [L]
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) |
C#
Capacitive dc branch
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
C |
DC capacitance |
0.001 |
p.u. |
non_zero,g |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
Capacitor current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(0\) |
Idc |
\(I_{dc}\) |
Algeb |
\(0\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(- I_{dc} u\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [C]
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) |
RCp#
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
\(R\) |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
C |
\(C\) |
DC capacitance |
0.001 |
p.u. |
non_zero,g |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
Capacitor current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(v_{1} - v_{2}\) |
Idc |
\(I_{dc}\) |
Algeb |
\(\frac{- v_{1} + v_{2}}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(- u \left(I_{dc} - \frac{v_{C}}{R}\right)\) |
\(C\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [RCp]
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) |
RCs#
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
\(R\) |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
C |
\(C\) |
DC capacitance |
0.001 |
p.u. |
non_zero,g |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
Capacitor current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(v_{1} - v_{2}\) |
Idc |
\(I_{dc}\) |
Algeb |
\(\frac{- v_{1} + v_{2}}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
vC |
\(v_{C}\) |
State |
\(- I_{dc} u\) |
\(C\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(I_{dc} \left(1 - u\right) + u \left(- I_{dc} R - v_{1} + v_{2} + v_{C}\right)\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [RCs]
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) |
RLs#
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
\(R\) |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
L |
\(L\) |
DC line inductance |
0.001 |
p.u. |
non_zero,r |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
Inductance current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(\frac{v_{1} - v_{2}}{R}\) |
Idc |
\(I_{dc}\) |
Algeb |
\(- \frac{u \left(v_{1} - v_{2}\right)}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(u \left(- I_{L} R + v_{1} - v_{2}\right)\) |
\(L\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(- I_{L} u - I_{dc}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [RLs]
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) |
RLCs#
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
\(R\) |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
L |
\(L\) |
DC line inductance |
0.001 |
p.u. |
non_zero,r |
C |
\(C\) |
DC capacitance |
0.001 |
p.u. |
non_zero,g |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
Inductance current |
p.u. |
v_str |
vC |
\(v_{C}\) |
State |
Capacitor current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(0\) |
vC |
\(v_{C}\) |
State |
\(v_{1} - v_{2}\) |
Idc |
\(I_{dc}\) |
Algeb |
\(0\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(u \left(- I_{L} R + v_{1} - v_{2} - v_{C}\right)\) |
\(L\) |
vC |
\(v_{C}\) |
State |
\(I_{L} u\) |
\(C\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(- I_{L} - I_{dc}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [RLCs]
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) |
RLCp#
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
node1 |
Node 1 index |
mandatory |
|||
node2 |
Node 2 index |
mandatory |
|||
Vdcn1 |
\(V_{dcn1}\) |
DC voltage rating on node 1 |
100 |
kV |
non_zero |
Vdcn2 |
\(V_{dcn2}\) |
DC voltage rating on node 2 |
100 |
kV |
non_zero |
Idcn |
\(I_{dcn}\) |
DC current rating |
1 |
kA |
non_zero |
R |
\(R\) |
DC line resistance |
0.010 |
p.u. |
non_zero,r |
L |
\(L\) |
DC line inductance |
0.001 |
p.u. |
non_zero,r |
C |
\(C\) |
DC capacitance |
0.001 |
p.u. |
non_zero,g |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
Inductance current |
p.u. |
v_str |
vC |
\(v_{C}\) |
State |
Capacitor current |
p.u. |
v_str |
Idc |
\(I_{dc}\) |
Algeb |
Current from node 2 to 1 |
p.u. |
v_str |
v1 |
\(v_{1}\) |
ExtAlgeb |
DC voltage on node 1 |
||
v2 |
\(v_{2}\) |
ExtAlgeb |
DC voltage on node 2 |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(0\) |
vC |
\(v_{C}\) |
State |
\(v_{1} - v_{2}\) |
Idc |
\(I_{dc}\) |
Algeb |
\(\frac{- v_{1} + v_{2}}{R}\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
|
v2 |
\(v_{2}\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
IL |
\(I_{L}\) |
State |
\(u v_{C}\) |
\(L\) |
vC |
\(v_{C}\) |
State |
\(- u \left(- I_{L} + I_{dc} - \frac{v_{C}}{R}\right)\) |
\(C\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Idc |
\(I_{dc}\) |
Algeb |
\(I_{dc} \left(1 - u\right) + u \left(- v_{1} + v_{2} + v_{C}\right)\) |
v1 |
\(v_{1}\) |
ExtAlgeb |
\(- I_{dc}\) |
v2 |
\(v_{2}\) |
ExtAlgeb |
\(I_{dc}\) |
Config Fields in [RLCp]
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) |