Motor#
Induction Motor group
Common Parameters: u, name
Available models: Motor3, Motor5
Motor3#
Third-order induction motor model.
See "Power System Modelling and Scripting" by F. Milano.
To simulate motor startup, set the motor status u to 0
and use a Toggle to control the model.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus |
interface bus id |
mandatory |
|||
Sn |
\(S_n\) |
Power rating |
100 |
||
Vn |
\(V_n\) |
AC voltage rating |
110 |
||
fn |
\(f\) |
rated frequency |
60 |
||
rs |
\(r_s\) |
rotor resistance |
0.010 |
non_zero,z |
|
xs |
\(x_s\) |
rotor reactance |
0.150 |
non_zero,z |
|
rr1 |
\(r_{R1}\) |
1st cage rotor resistance |
0.050 |
non_zero,z |
|
xr1 |
\(x_{R1}\) |
1st cage rotor reactance |
0.150 |
non_zero,z |
|
rr2 |
\(r_{R2}\) |
2st cage rotor resistance |
0.001 |
non_zero,z |
|
xr2 |
\(x_{R2}\) |
2st cage rotor reactance |
0.040 |
non_zero,z |
|
xm |
\(x_m\) |
magnetization reactance |
5 |
non_zero,z |
|
Hm |
\(H_m\) |
Inertia constant |
3 |
kWs/KVA |
power |
c1 |
\(c_1\) |
1st coeff. of Tm(w) |
0.100 |
||
c2 |
\(c_2\) |
2nd coeff. of Tm(w) |
0.020 |
||
c3 |
\(c_3\) |
3rd coeff. of Tm(w) |
0.020 |
||
zb |
\(z_b\) |
Allow working as brake |
1 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
slip |
\(slip\) |
State |
v_str |
||
e1d |
\(e1d\) |
State |
real part of 1st cage voltage |
v_str |
|
e1q |
\(e1q\) |
State |
imaginary part of 1st cage voltage |
v_str |
|
vd |
\(vd\) |
Algeb |
d-axis voltage |
||
vq |
\(vq\) |
Algeb |
q-axis voltage |
||
p |
\(p\) |
Algeb |
v_str |
||
q |
\(q\) |
Algeb |
v_str |
||
Id |
\(Id\) |
Algeb |
v_str |
||
Iq |
\(Iq\) |
Algeb |
|||
te |
\(te\) |
Algeb |
v_str |
||
tm |
\(tm\) |
Algeb |
v_str |
||
a |
\(a\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(v\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
slip |
\(slip\) |
State |
\(1.0 u\) |
e1d |
\(e1d\) |
State |
\(0.05 u\) |
e1q |
\(e1q\) |
State |
\(0.9 u\) |
vd |
\(vd\) |
Algeb |
|
vq |
\(vq\) |
Algeb |
|
p |
\(p\) |
Algeb |
\(u \left(Id vd + Iq vq\right)\) |
q |
\(q\) |
Algeb |
\(u \left(Id vq - Iq vd\right)\) |
Id |
\(Id\) |
Algeb |
\(1\) |
Iq |
\(Iq\) |
Algeb |
|
te |
\(te\) |
Algeb |
\(u \left(Id e1d + Iq e1q\right)\) |
tm |
\(tm\) |
Algeb |
\(u \left(aa + bb slip + c_{2} slip^{2}\right)\) |
a |
\(a\) |
ExtAlgeb |
|
v |
\(v\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
slip |
\(slip\) |
State |
\(u \left(- te + tm\right)\) |
\(M\) |
e1d |
\(e1d\) |
State |
\(u \left(e1q slip wb - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)\) |
|
e1q |
\(e1q\) |
State |
\(u \left(- e1d slip wb - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
vd |
\(vd\) |
Algeb |
\(- u v \sin{\left(a \right)} - vd\) |
vq |
\(vq\) |
Algeb |
\(u v \cos{\left(a \right)} - vq\) |
p |
\(p\) |
Algeb |
\(- p + u \left(Id vd + Iq vq\right)\) |
q |
\(q\) |
Algeb |
\(- q + u \left(Id vq - Iq vd\right)\) |
Id |
\(Id\) |
Algeb |
\(u \left(- Id rs + Iq x_{1} - e1d + vd\right)\) |
Iq |
\(Iq\) |
Algeb |
\(u \left(- Id x_{1} - Iq rs - e1q + vq\right)\) |
te |
\(te\) |
Algeb |
\(- te + u \left(Id e1d + Iq e1q\right)\) |
tm |
\(tm\) |
Algeb |
\(- tm + u \left(aa + bb slip + c_{2} slip^{2}\right)\) |
a |
\(a\) |
ExtAlgeb |
\(p\) |
v |
\(v\) |
ExtAlgeb |
\(q\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
wb |
\(\omega_b\) |
\(2 \pi fn\) |
ConstService |
x0 |
\(x_0\) |
\(xm + xs\) |
ConstService |
x1 |
\(x'\) |
\(\frac{xm xr_{1}}{xm + xr_{1}} + xs\) |
ConstService |
T10 |
\(T'_0\) |
\(\frac{xm + xr_{1}}{rr_{1} wb}\) |
ConstService |
M |
\(M\) |
\(2 Hm\) |
ConstService |
aa |
\(\alpha\) |
\(c_{1} + c_{2} + c_{3}\) |
ConstService |
bb |
\(\beta\) |
\(- c_{2} - 2 c_{3}\) |
ConstService |
Config Fields in [Motor3]
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) |
Motor5#
Fifth-order induction motor model.
See "Power System Modelling and Scripting" by F. Milano.
To simulate motor startup, set the motor status u to 0
and use a Toggle to control the model.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus |
interface bus id |
mandatory |
|||
Sn |
\(S_n\) |
Power rating |
100 |
||
Vn |
\(V_n\) |
AC voltage rating |
110 |
||
fn |
\(f\) |
rated frequency |
60 |
||
rs |
\(r_s\) |
rotor resistance |
0.010 |
non_zero,z |
|
xs |
\(x_s\) |
rotor reactance |
0.150 |
non_zero,z |
|
rr1 |
\(r_{R1}\) |
1st cage rotor resistance |
0.050 |
non_zero,z |
|
xr1 |
\(x_{R1}\) |
1st cage rotor reactance |
0.150 |
non_zero,z |
|
rr2 |
\(r_{R2}\) |
2st cage rotor resistance |
0.001 |
non_zero,z |
|
xr2 |
\(x_{R2}\) |
2st cage rotor reactance |
0.040 |
non_zero,z |
|
xm |
\(x_m\) |
magnetization reactance |
5 |
non_zero,z |
|
Hm |
\(H_m\) |
Inertia constant |
3 |
kWs/KVA |
power |
c1 |
\(c_1\) |
1st coeff. of Tm(w) |
0.100 |
||
c2 |
\(c_2\) |
2nd coeff. of Tm(w) |
0.020 |
||
c3 |
\(c_3\) |
3rd coeff. of Tm(w) |
0.020 |
||
zb |
\(z_b\) |
Allow working as brake |
1 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
slip |
\(slip\) |
State |
v_str |
||
e1d |
\(e1d\) |
State |
real part of 1st cage voltage |
v_str |
|
e1q |
\(e1q\) |
State |
imaginary part of 1st cage voltage |
v_str |
|
e2d |
\(e2d\) |
State |
real part of 2nd cage voltage |
v_str |
|
e2q |
\(e2q\) |
State |
imag part of 2nd cage voltage |
v_str |
|
vd |
\(vd\) |
Algeb |
d-axis voltage |
||
vq |
\(vq\) |
Algeb |
q-axis voltage |
||
p |
\(p\) |
Algeb |
v_str |
||
q |
\(q\) |
Algeb |
v_str |
||
Id |
\(Id\) |
Algeb |
v_str |
||
Iq |
\(Iq\) |
Algeb |
v_str |
||
te |
\(te\) |
Algeb |
v_str |
||
tm |
\(tm\) |
Algeb |
v_str |
||
a |
\(a\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(v\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
slip |
\(slip\) |
State |
\(1.0 u\) |
e1d |
\(e1d\) |
State |
\(0.05 u\) |
e1q |
\(e1q\) |
State |
\(0.9 u\) |
e2d |
\(e2d\) |
State |
\(0.05 u\) |
e2q |
\(e2q\) |
State |
\(0.9 u\) |
vd |
\(vd\) |
Algeb |
|
vq |
\(vq\) |
Algeb |
|
p |
\(p\) |
Algeb |
\(u \left(Id vd + Iq vq\right)\) |
q |
\(q\) |
Algeb |
\(u \left(Id vq - Iq vd\right)\) |
Id |
\(Id\) |
Algeb |
\(0.9 u\) |
Iq |
\(Iq\) |
Algeb |
\(0.1 u\) |
te |
\(te\) |
Algeb |
\(u \left(Id e2d + Iq e2q\right)\) |
tm |
\(tm\) |
Algeb |
\(u \left(aa + bb slip + c_{2} slip^{2}\right)\) |
a |
\(a\) |
ExtAlgeb |
|
v |
\(v\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
slip |
\(slip\) |
State |
\(u \left(- te + tm\right)\) |
\(M\) |
e1d |
\(e1d\) |
State |
\(u \left(e1q slip wb - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)\) |
|
e1q |
\(e1q\) |
State |
\(u \left(- e1d slip wb - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)\) |
|
e2d |
\(e2d\) |
State |
\(u \left(e1q slip wb - slip wb \left(e1q - e2q\right) + \frac{- Iq \left(x_{1} - x_{2}\right) + e1d - e2d}{T_{20}} - \frac{Iq \left(x_{0} - x_{1}\right) + e1d}{T_{10}}\right)\) |
|
e2q |
\(e2q\) |
State |
\(u \left(- e1d slip wb + slip wb \left(e1d - e2d\right) + \frac{Id \left(x_{1} - x_{2}\right) + e1q - e2q}{T_{20}} - \frac{- Id \left(x_{0} - x_{1}\right) + e1q}{T_{10}}\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
vd |
\(vd\) |
Algeb |
\(- u v \sin{\left(a \right)} - vd\) |
vq |
\(vq\) |
Algeb |
\(u v \cos{\left(a \right)} - vq\) |
p |
\(p\) |
Algeb |
\(- p + u \left(Id vd + Iq vq\right)\) |
q |
\(q\) |
Algeb |
\(- q + u \left(Id vq - Iq vd\right)\) |
Id |
\(Id\) |
Algeb |
\(u \left(- Id rs + Iq x_{2} - e2d + vd\right)\) |
Iq |
\(Iq\) |
Algeb |
\(u \left(- Id x_{2} - Iq rs - e2q + vq\right)\) |
te |
\(te\) |
Algeb |
\(- te + u \left(Id e2d + Iq e2q\right)\) |
tm |
\(tm\) |
Algeb |
\(- tm + u \left(aa + bb slip + c_{2} slip^{2}\right)\) |
a |
\(a\) |
ExtAlgeb |
\(p\) |
v |
\(v\) |
ExtAlgeb |
\(q\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
wb |
\(\omega_b\) |
\(2 \pi fn\) |
ConstService |
x0 |
\(x_0\) |
\(xm + xs\) |
ConstService |
x1 |
\(x'\) |
\(\frac{xm xr_{1}}{xm + xr_{1}} + xs\) |
ConstService |
T10 |
\(T'_0\) |
\(\frac{xm + xr_{1}}{rr_{1} wb}\) |
ConstService |
M |
\(M\) |
\(2 Hm\) |
ConstService |
aa |
\(\alpha\) |
\(c_{1} + c_{2} + c_{3}\) |
ConstService |
bb |
\(\beta\) |
\(- c_{2} - 2 c_{3}\) |
ConstService |
x2 |
\(x''\) |
\(\frac{xm xr_{1} xr_{2}}{xm xr_{1} + xm xr_{2} + xr_{1} xr_{2}} + xs\) |
ConstService |
T20 |
\(T''_0\) |
\(\frac{\frac{xm xr_{1}}{xm + xr_{1}} + xr_{2}}{rr_{2} wb}\) |
ConstService |
Config Fields in [Motor5]
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) |