DynShaft#
Dynamic shaft model group for multi-mass torsional models.
Common Parameters: u, name, syn
Available models: SHAFT5
SHAFT5#
5-mass torsional shaft model (HP-IP-LP-Rotor-EX) for synchronous generators.
The model adds torsional dynamics to a synchronous generator by introducing 4 additional mass-spring-damper sections connected in series with the generator rotor.
The 5 masses represent:
HP: High-pressure turbine section
IP: Intermediate-pressure turbine section
LP: Low-pressure turbine section
Rotor: Generator rotor (existing SynGen omega/delta)
EX: Exciter mass
The mechanical torque (tm) from the governor drives the HP mass. The generator's omega equation is modified to remove tm and add shaft coupling torques from LP and EX masses.
At steady state, all mass speeds equal 1.0 p.u. and the spring torques balance the mechanical torque through the chain.
References#
Milano, F. (2010). Power System Modelling and Scripting, Section 15.1.10.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
syn |
Synchronous generator idx |
mandatory,unique |
|||
MHP |
\(M_{HP}\) |
HP mass start-up time (2*H_HP) |
0.092 |
MWs/MVA |
non_zero,non_negative,power |
MIP |
\(M_{IP}\) |
IP mass start-up time (2*H_IP) |
0.156 |
MWs/MVA |
non_zero,non_negative,power |
MLP |
\(M_{LP}\) |
LP mass start-up time (2*H_LP) |
0.858 |
MWs/MVA |
non_zero,non_negative,power |
MEX |
\(M_{EX}\) |
EX mass start-up time (2*H_EX) |
0.068 |
MWs/MVA |
non_zero,non_negative,power |
KHP |
\(K_{HP}\) |
HP-IP spring constant |
19.303 |
p.u. |
non_zero,non_negative,power |
KIP |
\(K_{IP}\) |
IP-LP spring constant |
34.929 |
p.u. |
non_zero,non_negative,power |
KLP |
\(K_{LP}\) |
LP-Rotor spring constant |
52.038 |
p.u. |
non_zero,non_negative,power |
KEX |
\(K_{EX}\) |
Rotor-EX spring constant |
1.550 |
p.u. |
non_zero,non_negative,power |
DHP |
\(D_{HP}\) |
HP mass self-damping |
0 |
p.u. |
power |
DIP |
\(D_{IP}\) |
IP mass self-damping |
0 |
p.u. |
power |
DLP |
\(D_{LP}\) |
LP mass self-damping |
0 |
p.u. |
power |
DEX |
\(D_{EX}\) |
EX mass self-damping |
0 |
p.u. |
power |
D12 |
\(D_{12}\) |
HP-IP mutual damping |
0 |
p.u. |
power |
D23 |
\(D_{23}\) |
IP-LP mutual damping |
0 |
p.u. |
power |
D34 |
\(D_{34}\) |
LP-Rotor mutual damping |
0 |
p.u. |
power |
D45 |
\(D_{45}\) |
Rotor-EX mutual damping |
0 |
p.u. |
power |
ue |
\(u_e\) |
effective online status |
0 |
||
Sn |
\(S_n\) |
Generator power rating |
0 |
||
fn |
\(f_n\) |
Rated frequency |
0 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
dHP |
\(dHP\) |
State |
HP turbine angle |
rad |
v_str |
wHP |
\(wHP\) |
State |
HP turbine speed |
p.u. |
v_str |
dIP |
\(dIP\) |
State |
IP turbine angle |
rad |
v_str |
wIP |
\(wIP\) |
State |
IP turbine speed |
p.u. |
v_str |
dLP |
\(dLP\) |
State |
LP turbine angle |
rad |
v_str |
wLP |
\(wLP\) |
State |
LP turbine speed |
p.u. |
v_str |
dEX |
\(dEX\) |
State |
Exciter mass angle |
rad |
v_str |
wEX |
\(wEX\) |
State |
Exciter mass speed |
p.u. |
v_str |
omega |
\(\omega\) |
ExtState |
Generator rotor speed |
||
delta |
\(\delta\) |
ExtState |
Generator rotor angle |
||
tm |
\(tm\) |
ExtAlgeb |
Mechanical torque from generator |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
dHP |
\(dHP\) |
State |
\(\delta_{0 gen} + \frac{tm_{0}}{KLP} + \frac{tm_{0}}{KIP} + \frac{tm_{0}}{KHP}\) |
wHP |
\(wHP\) |
State |
\(1\) |
dIP |
\(dIP\) |
State |
\(\delta_{0 gen} + \frac{tm_{0}}{KLP} + \frac{tm_{0}}{KIP}\) |
wIP |
\(wIP\) |
State |
\(1\) |
dLP |
\(dLP\) |
State |
\(\delta_{0 gen} + \frac{tm_{0}}{KLP}\) |
wLP |
\(wLP\) |
State |
\(1\) |
dEX |
\(dEX\) |
State |
\(\delta_{0 gen}\) |
wEX |
\(wEX\) |
State |
\(1\) |
omega |
\(\omega\) |
ExtState |
|
delta |
\(\delta\) |
ExtState |
|
tm |
\(tm\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
dHP |
\(dHP\) |
State |
\(Ob ue \left(wHP - 1\right)\) |
|
wHP |
\(wHP\) |
State |
\(ue \left(- D_{12} \left(wHP - wIP\right) - DHP \left(wHP - 1\right) + KHP \left(- dHP + dIP\right) + tm\right)\) |
\(M_{HP}\) |
dIP |
\(dIP\) |
State |
\(Ob ue \left(wIP - 1\right)\) |
|
wIP |
\(wIP\) |
State |
\(ue \left(- D_{12} \left(- wHP + wIP\right) - D_{23} \left(wIP - wLP\right) - DIP \left(wIP - 1\right) + KHP \left(dHP - dIP\right) + KIP \left(- dIP + dLP\right)\right)\) |
\(M_{IP}\) |
dLP |
\(dLP\) |
State |
\(Ob ue \left(wLP - 1\right)\) |
|
wLP |
\(wLP\) |
State |
\(ue \left(- D_{23} \left(- wIP + wLP\right) - D_{34} \left(- \omega + wLP\right) - DLP \left(wLP - 1\right) + KIP \left(dIP - dLP\right) + KLP \left(- dLP + \delta\right)\right)\) |
\(M_{LP}\) |
dEX |
\(dEX\) |
State |
\(Ob ue \left(wEX - 1\right)\) |
|
wEX |
\(wEX\) |
State |
\(ue \left(- D_{45} \left(- \omega + wEX\right) - DEX \left(wEX - 1\right) + KEX \left(- dEX + \delta\right)\right)\) |
\(M_{EX}\) |
omega |
\(\omega\) |
ExtState |
\(ue \left(- D_{34} \left(\omega - wLP\right) - D_{45} \left(\omega - wEX\right) + KEX \left(dEX - \delta\right) + KLP \left(dLP - \delta\right) - tm\right)\) |
|
delta |
\(\delta\) |
ExtState |
\(0\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
tm |
\(tm\) |
ExtAlgeb |
\(0\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
Ob |
\(\Omega_b\) |
\(2 \pi fn\) |
ConstService |
Config Fields in [SHAFT5]
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) |