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 Toggler
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 |
\(\sigma\) |
State |
v_str |
||
e1d |
\(e'_{d}\) |
State |
real part of 1st cage voltage |
v_str |
|
e1q |
\(e'_{q}\) |
State |
imaginary part of 1st cage voltage |
v_str |
|
vd |
\(V_{d}\) |
Algeb |
d-axis voltage |
||
vq |
\(V_{q}\) |
Algeb |
q-axis voltage |
||
p |
\(P\) |
Algeb |
v_str |
||
q |
\(Q\) |
Algeb |
v_str |
||
Id |
\(I_{d}\) |
Algeb |
v_str |
||
Iq |
\(I_{q}\) |
Algeb |
|||
te |
\(\tau_{e}\) |
Algeb |
v_str |
||
tm |
\(\tau_{m}\) |
Algeb |
v_str |
||
a |
\(\theta\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(V\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
---|---|---|---|
slip |
\(\sigma\) |
State |
\(1.0 u\) |
e1d |
\(e'_{d}\) |
State |
\(0.05 u\) |
e1q |
\(e'_{q}\) |
State |
\(0.9 u\) |
vd |
\(V_{d}\) |
Algeb |
|
vq |
\(V_{q}\) |
Algeb |
|
p |
\(P\) |
Algeb |
\(u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
q |
\(Q\) |
Algeb |
\(u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Id |
\(I_{d}\) |
Algeb |
\(1\) |
Iq |
\(I_{q}\) |
Algeb |
|
te |
\(\tau_{e}\) |
Algeb |
\(u \left(I_{d} e'_{d} + I_{q} e'_{q}\right)\) |
tm |
\(\tau_{m}\) |
Algeb |
\(u \left(\alpha + \beta \sigma + \sigma^{2} c_{2}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
|
v |
\(V\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
---|---|---|---|---|
slip |
\(\sigma\) |
State |
\(u \left(- \tau_{e} + \tau_{m}\right)\) |
\(M\) |
e1d |
\(e'_{d}\) |
State |
\(u \left(\omega_{b} \sigma e'_{q} - \frac{I_{q} \left(- x' + x_{0}\right) + e'_{d}}{T'_{0}}\right)\) |
|
e1q |
\(e'_{q}\) |
State |
\(u \left(- \omega_{b} \sigma e'_{d} - \frac{- I_{d} \left(- x' + x_{0}\right) + e'_{q}}{T'_{0}}\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
---|---|---|---|
vd |
\(V_{d}\) |
Algeb |
\(- V u \sin{\left(\theta \right)} - V_{d}\) |
vq |
\(V_{q}\) |
Algeb |
\(V u \cos{\left(\theta \right)} - V_{q}\) |
p |
\(P\) |
Algeb |
\(- P + u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
q |
\(Q\) |
Algeb |
\(- Q + u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Id |
\(I_{d}\) |
Algeb |
\(u \left(- I_{d} r_{s} + I_{q} x' + V_{d} - e'_{d}\right)\) |
Iq |
\(I_{q}\) |
Algeb |
\(u \left(- I_{d} x' - I_{q} r_{s} + V_{q} - e'_{q}\right)\) |
te |
\(\tau_{e}\) |
Algeb |
\(- \tau_{e} + u \left(I_{d} e'_{d} + I_{q} e'_{q}\right)\) |
tm |
\(\tau_{m}\) |
Algeb |
\(- \tau_{m} + u \left(\alpha + \beta \sigma + \sigma^{2} c_{2}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
\(P\) |
v |
\(V\) |
ExtAlgeb |
\(Q\) |
Services#
Name |
Symbol |
Equation |
Type |
---|---|---|---|
wb |
\(\omega_b\) |
\(2 \pi f\) |
ConstService |
x0 |
\(x_0\) |
\(x_{m} + x_{s}\) |
ConstService |
x1 |
\(x'\) |
\(\frac{x_{m} x_{R1}}{x_{m} + x_{R1}} + x_{s}\) |
ConstService |
T10 |
\(T'_0\) |
\(\frac{x_{m} + x_{R1}}{\omega_{b} r_{R1}}\) |
ConstService |
M |
\(M\) |
\(2 H_{m}\) |
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 Toggler
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 |
\(\sigma\) |
State |
v_str |
||
e1d |
\(e'_{d}\) |
State |
real part of 1st cage voltage |
v_str |
|
e1q |
\(e'_{q}\) |
State |
imaginary part of 1st cage voltage |
v_str |
|
e2d |
\(e''_{d}\) |
State |
real part of 2nd cage voltage |
v_str |
|
e2q |
\(e''_{q}\) |
State |
imag part of 2nd cage voltage |
v_str |
|
vd |
\(V_{d}\) |
Algeb |
d-axis voltage |
||
vq |
\(V_{q}\) |
Algeb |
q-axis voltage |
||
p |
\(P\) |
Algeb |
v_str |
||
q |
\(Q\) |
Algeb |
v_str |
||
Id |
\(I_{d}\) |
Algeb |
v_str |
||
Iq |
\(I_{q}\) |
Algeb |
v_str |
||
te |
\(\tau_{e}\) |
Algeb |
v_str |
||
tm |
\(\tau_{m}\) |
Algeb |
v_str |
||
a |
\(\theta\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(V\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
---|---|---|---|
slip |
\(\sigma\) |
State |
\(1.0 u\) |
e1d |
\(e'_{d}\) |
State |
\(0.05 u\) |
e1q |
\(e'_{q}\) |
State |
\(0.9 u\) |
e2d |
\(e''_{d}\) |
State |
\(0.05 u\) |
e2q |
\(e''_{q}\) |
State |
\(0.9 u\) |
vd |
\(V_{d}\) |
Algeb |
|
vq |
\(V_{q}\) |
Algeb |
|
p |
\(P\) |
Algeb |
\(u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
q |
\(Q\) |
Algeb |
\(u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Id |
\(I_{d}\) |
Algeb |
\(0.9 u\) |
Iq |
\(I_{q}\) |
Algeb |
\(0.1 u\) |
te |
\(\tau_{e}\) |
Algeb |
\(u \left(I_{d} e''_{d} + I_{q} e''_{q}\right)\) |
tm |
\(\tau_{m}\) |
Algeb |
\(u \left(\alpha + \beta \sigma + \sigma^{2} c_{2}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
|
v |
\(V\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
---|---|---|---|---|
slip |
\(\sigma\) |
State |
\(u \left(- \tau_{e} + \tau_{m}\right)\) |
\(M\) |
e1d |
\(e'_{d}\) |
State |
\(u \left(\omega_{b} \sigma e'_{q} - \frac{I_{q} \left(- x' + x_{0}\right) + e'_{d}}{T'_{0}}\right)\) |
|
e1q |
\(e'_{q}\) |
State |
\(u \left(- \omega_{b} \sigma e'_{d} - \frac{- I_{d} \left(- x' + x_{0}\right) + e'_{q}}{T'_{0}}\right)\) |
|
e2d |
\(e''_{d}\) |
State |
\(u \left(\omega_{b} \sigma e'_{q} - \omega_{b} \sigma \left(- e''_{q} + e'_{q}\right) - \frac{I_{q} \left(- x' + x_{0}\right) + e'_{d}}{T'_{0}} + \frac{- I_{q} \left(x' - x''\right) - e''_{d} + e'_{d}}{T''_{0}}\right)\) |
|
e2q |
\(e''_{q}\) |
State |
\(u \left(- \omega_{b} \sigma e'_{d} + \omega_{b} \sigma \left(- e''_{d} + e'_{d}\right) - \frac{- I_{d} \left(- x' + x_{0}\right) + e'_{q}}{T'_{0}} + \frac{I_{d} \left(x' - x''\right) - e''_{q} + e'_{q}}{T''_{0}}\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
---|---|---|---|
vd |
\(V_{d}\) |
Algeb |
\(- V u \sin{\left(\theta \right)} - V_{d}\) |
vq |
\(V_{q}\) |
Algeb |
\(V u \cos{\left(\theta \right)} - V_{q}\) |
p |
\(P\) |
Algeb |
\(- P + u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
q |
\(Q\) |
Algeb |
\(- Q + u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Id |
\(I_{d}\) |
Algeb |
\(u \left(- I_{d} r_{s} + I_{q} x'' + V_{d} - e''_{d}\right)\) |
Iq |
\(I_{q}\) |
Algeb |
\(u \left(- I_{d} x'' - I_{q} r_{s} + V_{q} - e''_{q}\right)\) |
te |
\(\tau_{e}\) |
Algeb |
\(- \tau_{e} + u \left(I_{d} e''_{d} + I_{q} e''_{q}\right)\) |
tm |
\(\tau_{m}\) |
Algeb |
\(- \tau_{m} + u \left(\alpha + \beta \sigma + \sigma^{2} c_{2}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
\(P\) |
v |
\(V\) |
ExtAlgeb |
\(Q\) |
Services#
Name |
Symbol |
Equation |
Type |
---|---|---|---|
wb |
\(\omega_b\) |
\(2 \pi f\) |
ConstService |
x0 |
\(x_0\) |
\(x_{m} + x_{s}\) |
ConstService |
x1 |
\(x'\) |
\(\frac{x_{m} x_{R1}}{x_{m} + x_{R1}} + x_{s}\) |
ConstService |
T10 |
\(T'_0\) |
\(\frac{x_{m} + x_{R1}}{\omega_{b} r_{R1}}\) |
ConstService |
M |
\(M\) |
\(2 H_{m}\) |
ConstService |
aa |
\(\alpha\) |
\(c_{1} + c_{2} + c_{3}\) |
ConstService |
bb |
\(\beta\) |
\(- c_{2} - 2 c_{3}\) |
ConstService |
x2 |
\(x''\) |
\(\frac{x_{m} x_{R1} x_{R2}}{x_{m} x_{R1} + x_{m} x_{R2} + x_{R1} x_{R2}} + x_{s}\) |
ConstService |
T20 |
\(T''_0\) |
\(\frac{\frac{x_{m} x_{R1}}{x_{m} + x_{R1}} + x_{R2}}{\omega_{b} r_{R2}}\) |
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) |