SynGen#
Synchronous generator group.
Common Parameters: u, name, Sn, Vn, fn, bus, M, D, subidx
Common Variables: omega, delta, tm, te, vf, XadIfd, vd, vq, Id, Iq, a, v
Available models: GENCLS, GENROU, PLBVFU1
GENCLS#
Classical generator 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 |
|||
gen |
static generator index |
mandatory |
|||
coi |
center of inertia index |
||||
coi2 |
center of inertia index |
||||
Sn |
\(S_n\) |
Power rating |
100 |
MVA |
|
Vn |
\(V_n\) |
AC voltage rating |
110 |
||
fn |
\(f\) |
rated frequency |
60 |
||
D |
\(D\) |
Damping coefficient |
0 |
power |
|
M |
\(M\) |
machine start up time (2H) |
6 |
non_zero,non_negative,power |
|
ra |
\(r_a\) |
armature resistance |
0 |
z |
|
xl |
\(x_l\) |
leakage reactance |
0 |
z |
|
xd1 |
\(x'_d\) |
d-axis transient reactance |
0.302 |
z |
|
kp |
\(k_p\) |
active power feedback gain |
0 |
||
kw |
\(k_w\) |
speed feedback gain |
0 |
||
S10 |
\(S_{1.0}\) |
first saturation factor |
0 |
||
S12 |
\(S_{1.2}\) |
second saturation factor |
1 |
||
gammap |
\(\gamma_P\) |
P ratio of linked static gen |
1 |
||
gammaq |
\(\gamma_Q\) |
Q ratio of linked static gen |
1 |
||
subidx |
Generator idx in plant; only used by PSS/E data |
0 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
delta |
\(\delta\) |
State |
rotor angle |
rad |
v_str |
omega |
\(\omega\) |
State |
rotor speed |
pu (Hz) |
v_str |
Id |
\(I_{d}\) |
Algeb |
d-axis current |
v_str |
|
Iq |
\(I_{q}\) |
Algeb |
q-axis current |
v_str |
|
vd |
\(V_{d}\) |
Algeb |
d-axis voltage |
v_str |
|
vq |
\(V_{q}\) |
Algeb |
q-axis voltage |
v_str |
|
tm |
\(\tau_{m}\) |
Algeb |
mechanical torque |
v_str |
|
te |
\(\tau_{e}\) |
Algeb |
electric torque |
v_str |
|
vf |
\(v_{f}\) |
Algeb |
excitation voltage |
pu |
v_str |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
d-axis armature excitation current |
p.u (kV) |
v_str |
Pe |
\(P_{e}\) |
Algeb |
active power injection |
v_str |
|
Qe |
\(Q_{e}\) |
Algeb |
reactive power injection |
v_str |
|
psid |
\(\psi_{d}\) |
Algeb |
d-axis flux |
v_str |
|
psiq |
\(\psi_{q}\) |
Algeb |
q-axis flux |
v_str |
|
a |
\(\theta\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(V\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
delta |
\(\delta\) |
State |
\(\delta_{0}\) |
omega |
\(\omega\) |
State |
\(u\) |
Id |
\(I_{d}\) |
Algeb |
\(I_{d0} u\) |
Iq |
\(I_{q}\) |
Algeb |
\(I_{q0} u\) |
vd |
\(V_{d}\) |
Algeb |
\(V_{d0} u\) |
vq |
\(V_{q}\) |
Algeb |
\(V_{q0} u\) |
tm |
\(\tau_{m}\) |
Algeb |
\(\tau_{m0}\) |
te |
\(\tau_{e}\) |
Algeb |
\(\tau_{m0} u\) |
vf |
\(v_{f}\) |
Algeb |
\(u v_{f0}\) |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
\(u v_{f0}\) |
Pe |
\(P_{e}\) |
Algeb |
\(u \left(I_{d0} V_{d0} + I_{q0} V_{q0}\right)\) |
Qe |
\(Q_{e}\) |
Algeb |
\(u \left(I_{d0} V_{q0} - I_{q0} V_{d0}\right)\) |
psid |
\(\psi_{d}\) |
Algeb |
\(\psi_{d0} u\) |
psiq |
\(\psi_{q}\) |
Algeb |
\(\psi_{q0} u\) |
a |
\(\theta\) |
ExtAlgeb |
|
v |
\(V\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
delta |
\(\delta\) |
State |
\(2 \pi f u \left(\omega - 1\right)\) |
|
omega |
\(\omega\) |
State |
\(u \left(- D \left(\omega - 1\right) - \tau_{e} + \tau_{m}\right)\) |
\(M\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Id |
\(I_{d}\) |
Algeb |
\(I_{d} xq + \psi_{d} - v_{f}\) |
Iq |
\(I_{q}\) |
Algeb |
\(I_{q} xq + \psi_{q}\) |
vd |
\(V_{d}\) |
Algeb |
\(V u \sin{\left(\delta - \theta \right)} - V_{d}\) |
vq |
\(V_{q}\) |
Algeb |
\(V u \cos{\left(\delta - \theta \right)} - V_{q}\) |
tm |
\(\tau_{m}\) |
Algeb |
\(- \tau_{m} + \tau_{m0}\) |
te |
\(\tau_{e}\) |
Algeb |
\(- \tau_{e} + u \left(- I_{d} \psi_{q} + I_{q} \psi_{d}\right)\) |
vf |
\(v_{f}\) |
Algeb |
\(u v_{f0} - v_{f}\) |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
\(- X_{ad}I_{fd} + u v_{f0}\) |
Pe |
\(P_{e}\) |
Algeb |
\(- P_{e} + u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
Qe |
\(Q_{e}\) |
Algeb |
\(- Q_{e} + u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
psid |
\(\psi_{d}\) |
Algeb |
\(- \psi_{d} + u \left(I_{q} r_{a} + V_{q}\right)\) |
psiq |
\(\psi_{q}\) |
Algeb |
\(\psi_{q} + u \left(I_{d} r_{a} + V_{d}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
\(- u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
v |
\(V\) |
ExtAlgeb |
\(- u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
p0 |
\(P_0\) |
\(P_{0s} \gamma_{P}\) |
ConstService |
q0 |
\(Q_0\) |
\(Q_{0s} \gamma_{Q}\) |
ConstService |
_V |
\(V_c\) |
\(V e^{i \theta}\) |
ConstService |
_S |
\(S\) |
\(P_{0} - i Q_{0}\) |
ConstService |
_I |
\(I_c\) |
\(\frac{S}{\operatorname{conj}{\left(V_{c} \right)}}\) |
ConstService |
_E |
\(E\) |
\(I_{c} \left(r_{a} + i xq\right) + V_{c}\) |
ConstService |
_deltac |
\(\delta_c\) |
\(\log{\left(\frac{E}{\left|{E}\right|} \right)}\) |
ConstService |
delta0 |
\(\delta_0\) |
\(u \operatorname{im}{\left(\delta_{c}\right)}\) |
ConstService |
vdq |
\(V_{dq}\) |
\(V_{c} u e^{- \delta_{c} + 0.5 i \pi}\) |
ConstService |
Idq |
\(I_{dq}\) |
\(I_{c} u e^{- \delta_{c} + 0.5 i \pi}\) |
ConstService |
Id0 |
\(I_{d0}\) |
\(\operatorname{re}{\left(I_{dq}\right)}\) |
ConstService |
Iq0 |
\(I_{q0}\) |
\(\operatorname{im}{\left(I_{dq}\right)}\) |
ConstService |
vd0 |
\(V_{d0}\) |
\(\operatorname{re}{\left(V_{dq}\right)}\) |
ConstService |
vq0 |
\(V_{q0}\) |
\(\operatorname{im}{\left(V_{dq}\right)}\) |
ConstService |
tm0 |
\(\tau_{m0}\) |
\(u \left(I_{d0} \left(I_{d0} r_{a} + V_{d0}\right) + I_{q0} \left(I_{q0} r_{a} + V_{q0}\right)\right)\) |
ConstService |
psid0 |
\(\psi_{d0}\) |
\(I_{q0} r_{a} u + V_{q0}\) |
ConstService |
psiq0 |
\(\psi_{q0}\) |
\(- I_{d0} r_{a} u - V_{d0}\) |
ConstService |
vf0 |
\(v_{f0}\) |
\(I_{d0} xq + I_{q0} r_{a} + V_{q0}\) |
ConstService |
Config Fields in [GENCLS]
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) |
|
vf_lower |
1 |
lower limit for vf warning |
||
vf_upper |
5 |
upper limit for vf warning |
GENROU#
Round rotor generator with quadratic saturation.
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 |
|||
gen |
static generator index |
mandatory |
|||
coi |
center of inertia index |
||||
coi2 |
center of inertia index |
||||
Sn |
\(S_n\) |
Power rating |
100 |
MVA |
|
Vn |
\(V_n\) |
AC voltage rating |
110 |
||
fn |
\(f\) |
rated frequency |
60 |
||
D |
\(D\) |
Damping coefficient |
0 |
power |
|
M |
\(M\) |
machine start up time (2H) |
6 |
non_zero,non_negative,power |
|
ra |
\(r_a\) |
armature resistance |
0 |
z |
|
xl |
\(x_l\) |
leakage reactance |
0 |
z |
|
xd1 |
\(x'_d\) |
d-axis transient reactance |
0.302 |
z |
|
kp |
\(k_p\) |
active power feedback gain |
0 |
||
kw |
\(k_w\) |
speed feedback gain |
0 |
||
S10 |
\(S_{1.0}\) |
first saturation factor |
0 |
||
S12 |
\(S_{1.2}\) |
second saturation factor |
1 |
||
gammap |
\(\gamma_P\) |
P ratio of linked static gen |
1 |
||
gammaq |
\(\gamma_Q\) |
Q ratio of linked static gen |
1 |
||
xd |
\(x_d\) |
d-axis synchronous reactance |
1.900 |
z |
|
xq |
\(x_q\) |
q-axis synchronous reactance |
1.700 |
z |
|
xd2 |
\(x''_d\) |
d-axis sub-transient reactance |
0.204 |
z |
|
xq1 |
\(x'_q\) |
q-axis transient reactance |
0.500 |
z |
|
xq2 |
\(x''_q\) |
q-axis sub-transient reactance |
0.300 |
z |
|
Td10 |
\(T'_{d0}\) |
d-axis transient time constant |
8 |
||
Td20 |
\(T''_{d0}\) |
d-axis sub-transient time constant |
0.040 |
||
Tq10 |
\(T'_{q0}\) |
q-axis transient time constant |
0.800 |
||
Tq20 |
\(T''_{q0}\) |
q-axis sub-transient time constant |
0.020 |
||
subidx |
Generator idx in plant; only used by PSS/E data |
0 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
delta |
\(\delta\) |
State |
rotor angle |
rad |
v_str |
omega |
\(\omega\) |
State |
rotor speed |
pu (Hz) |
v_str |
e1q |
\(e'_{q}\) |
State |
q-axis transient voltage |
v_str |
|
e1d |
\(e'_{d}\) |
State |
d-axis transient voltage |
v_str |
|
e2d |
\(e''_{d}\) |
State |
d-axis sub-transient voltage |
v_str |
|
e2q |
\(e''_{q}\) |
State |
q-axis sub-transient voltage |
v_str |
|
Id |
\(I_{d}\) |
Algeb |
d-axis current |
v_str |
|
Iq |
\(I_{q}\) |
Algeb |
q-axis current |
v_str |
|
vd |
\(V_{d}\) |
Algeb |
d-axis voltage |
v_str |
|
vq |
\(V_{q}\) |
Algeb |
q-axis voltage |
v_str |
|
tm |
\(\tau_{m}\) |
Algeb |
mechanical torque |
v_str |
|
te |
\(\tau_{e}\) |
Algeb |
electric torque |
v_str |
|
vf |
\(v_{f}\) |
Algeb |
excitation voltage |
pu |
v_str |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
d-axis armature excitation current |
p.u (kV) |
v_str |
Pe |
\(P_{e}\) |
Algeb |
active power injection |
v_str |
|
Qe |
\(Q_{e}\) |
Algeb |
reactive power injection |
v_str |
|
psid |
\(\psi_{d}\) |
Algeb |
d-axis flux |
v_str |
|
psiq |
\(\psi_{q}\) |
Algeb |
q-axis flux |
v_str |
|
psi2q |
\(\psi_{aq}\) |
Algeb |
q-axis air gap flux |
v_str |
|
psi2d |
\(\psi_{ad}\) |
Algeb |
d-axis air gap flux |
v_str |
|
psi2 |
\(\psi_{a}\) |
Algeb |
air gap flux magnitude |
v_str |
|
Se |
\(S_e(|\psi_{a}|)\) |
Algeb |
saturation output |
v_str |
|
XaqI1q |
\(X_{aq}I_{1q}\) |
Algeb |
q-axis reaction |
p.u (kV) |
v_str |
a |
\(\theta\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(V\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
delta |
\(\delta\) |
State |
\(\delta_{0}\) |
omega |
\(\omega\) |
State |
\(u\) |
e1q |
\(e'_{q}\) |
State |
\(e'_{q0} u\) |
e1d |
\(e'_{d}\) |
State |
\(e'_{d0}\) |
e2d |
\(e''_{d}\) |
State |
\(e''_{d0} u\) |
e2q |
\(e''_{q}\) |
State |
\(e''_{q0}\) |
Id |
\(I_{d}\) |
Algeb |
\(I_{d0} u\) |
Iq |
\(I_{q}\) |
Algeb |
\(I_{q0} u\) |
vd |
\(V_{d}\) |
Algeb |
\(V_{d0} u\) |
vq |
\(V_{q}\) |
Algeb |
\(V_{q0} u\) |
tm |
\(\tau_{m}\) |
Algeb |
\(\tau_{m0}\) |
te |
\(\tau_{e}\) |
Algeb |
\(\tau_{m0} u\) |
vf |
\(v_{f}\) |
Algeb |
\(u v_{f0}\) |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
\(u v_{f0}\) |
Pe |
\(P_{e}\) |
Algeb |
\(u \left(I_{d0} V_{d0} + I_{q0} V_{q0}\right)\) |
Qe |
\(Q_{e}\) |
Algeb |
\(u \left(I_{d0} V_{q0} - I_{q0} V_{d0}\right)\) |
psid |
\(\psi_{d}\) |
Algeb |
\(\psi_{d0} u\) |
psiq |
\(\psi_{q}\) |
Algeb |
\(\psi_{q0} u\) |
psi2q |
\(\psi_{aq}\) |
Algeb |
\(\psi_{aq0}\) |
psi2d |
\(\psi_{ad}\) |
Algeb |
\(\psi_{ad0} u\) |
psi2 |
\(\psi_{a}\) |
Algeb |
\(u \left|{\psi''_{0,dq}}\right|\) |
Se |
\(S_e(|\psi_{a}|)\) |
Algeb |
\(S_{e0} u\) |
XaqI1q |
\(X_{aq}I_{1q}\) |
Algeb |
\(0\) |
a |
\(\theta\) |
ExtAlgeb |
|
v |
\(V\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
delta |
\(\delta\) |
State |
\(2 \pi f u \left(\omega - 1\right)\) |
|
omega |
\(\omega\) |
State |
\(u \left(- D \left(\omega - 1\right) - \tau_{e} + \tau_{m}\right)\) |
\(M\) |
e1q |
\(e'_{q}\) |
State |
\(- X_{ad}I_{fd} + v_{f}\) |
\(T'_{d0}\) |
e1d |
\(e'_{d}\) |
State |
\(- X_{aq}I_{1q}\) |
\(T'_{q0}\) |
e2d |
\(e''_{d}\) |
State |
\(- I_{d} \left(x'_{d} - x_{l}\right) - e''_{d} + e'_{q}\) |
\(T''_{d0}\) |
e2q |
\(e''_{q}\) |
State |
\(I_{q} \left(x'_{q} - x_{l}\right) - e''_{q} + e'_{d}\) |
\(T''_{q0}\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
Id |
\(I_{d}\) |
Algeb |
\(I_{d} x''_{d} + \psi_{d} - \psi_{ad}\) |
Iq |
\(I_{q}\) |
Algeb |
\(I_{q} x''_{q} + \psi_{q} + \psi_{aq}\) |
vd |
\(V_{d}\) |
Algeb |
\(V u \sin{\left(\delta - \theta \right)} - V_{d}\) |
vq |
\(V_{q}\) |
Algeb |
\(V u \cos{\left(\delta - \theta \right)} - V_{q}\) |
tm |
\(\tau_{m}\) |
Algeb |
\(- \tau_{m} + \tau_{m0}\) |
te |
\(\tau_{e}\) |
Algeb |
\(- \tau_{e} + u \left(- I_{d} \psi_{q} + I_{q} \psi_{d}\right)\) |
vf |
\(v_{f}\) |
Algeb |
\(u v_{f0} - v_{f}\) |
XadIfd |
\(X_{ad}I_{fd}\) |
Algeb |
\(- X_{ad}I_{fd} + u \left(S_e(|\psi_{a}|) \psi_{ad} + e'_{q} + \left(- x'_{d} + x_{d}\right) \left(I_{d} \gamma_{d1} - \gamma_{d2} e''_{d} + \gamma_{d2} e'_{q}\right)\right)\) |
Pe |
\(P_{e}\) |
Algeb |
\(- P_{e} + u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
Qe |
\(Q_{e}\) |
Algeb |
\(- Q_{e} + u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
psid |
\(\psi_{d}\) |
Algeb |
\(- \psi_{d} + u \left(I_{q} r_{a} + V_{q}\right)\) |
psiq |
\(\psi_{q}\) |
Algeb |
\(\psi_{q} + u \left(I_{d} r_{a} + V_{d}\right)\) |
psi2q |
\(\psi_{aq}\) |
Algeb |
\(\gamma_{q1} e'_{d} - \psi_{aq} + e''_{q} \left(1 - \gamma_{q1}\right)\) |
psi2d |
\(\psi_{ad}\) |
Algeb |
\(\gamma_{d1} e'_{q} + \gamma_{d2} e''_{d} \left(x'_{d} - x_{l}\right) - \psi_{ad}\) |
psi2 |
\(\psi_{a}\) |
Algeb |
\(- \psi_{a}^{2} + \psi_{ad}^{2} + \psi_{aq}^{2}\) |
Se |
\(S_e(|\psi_{a}|)\) |
Algeb |
\(B^q_{S_{AT}} z_{0}^{SL} \left(- A^q_{S_{AT}} + \psi_{a}\right)^{2} - S_e(|\psi_{a}|) \psi_{a}\) |
XaqI1q |
\(X_{aq}I_{1q}\) |
Algeb |
\(S_e(|\psi_{a}|) \gamma_{qd} \psi_{aq} - X_{aq}I_{1q} + e'_{d} + \left(- x'_{q} + x_{q}\right) \left(- I_{q} \gamma_{q1} - \gamma_{q2} e''_{q} + \gamma_{q2} e'_{d}\right)\) |
a |
\(\theta\) |
ExtAlgeb |
\(- u \left(I_{d} V_{d} + I_{q} V_{q}\right)\) |
v |
\(V\) |
ExtAlgeb |
\(- u \left(I_{d} V_{q} - I_{q} V_{d}\right)\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
p0 |
\(P_0\) |
\(P_{0s} \gamma_{P}\) |
ConstService |
q0 |
\(Q_0\) |
\(Q_{0s} \gamma_{Q}\) |
ConstService |
gd1 |
\(\gamma_{d1}\) |
\(\frac{x''_{d} - x_{l}}{x'_{d} - x_{l}}\) |
ConstService |
gq1 |
\(\gamma_{q1}\) |
\(\frac{x''_{q} - x_{l}}{x'_{q} - x_{l}}\) |
ConstService |
gd2 |
\(\gamma_{d2}\) |
\(\frac{- x''_{d} + x'_{d}}{\left(x'_{d} - x_{l}\right)^{2}}\) |
ConstService |
gq2 |
\(\gamma_{q2}\) |
\(\frac{- x''_{q} + x'_{q}}{\left(x'_{q} - x_{l}\right)^{2}}\) |
ConstService |
gqd |
\(\gamma_{qd}\) |
\(\frac{- x_{l} + x_{q}}{x_{d} - x_{l}}\) |
ConstService |
_S12 |
\(S_{1.2}\) |
\(S_{1.2} - _fS12 + 1\) |
ConstService |
SAT_E1 |
\(E^{1c}_{S_{AT}}\) |
\(1.0\) |
ConstService |
SAT_E2 |
\(E^{2c}_{S_{AT}}\) |
\(1.2\) |
ConstService |
SAT_SE1 |
\(SE^{1c}_{S_{AT}}\) |
\(S_{1.0}\) |
ConstService |
SAT_SE2 |
\(SE^{2c}_{S_{AT}}\) |
\(S_{1.2} - 2 z^{SE2}_{S_{AT}} + 2\) |
ConstService |
SAT_a |
\(a_{S_{AT}}\) |
\(\sqrt{\frac{E^{1c}_{S_{AT}} SE^{1c}_{S_{AT}}}{E^{2c}_{S_{AT}} SE^{2c}_{S_{AT}}}} \left(\operatorname{Indicator}{\left(SE^{2c}_{S_{AT}} > 0 \right)} + \operatorname{Indicator}{\left(SE^{2c}_{S_{AT}} < 0 \right)}\right)\) |
ConstService |
SAT_A |
\(A^q_{S_{AT}}\) |
\(E^{2c}_{S_{AT}} - \frac{E^{1c}_{S_{AT}} - E^{2c}_{S_{AT}}}{a_{S_{AT}} - 1}\) |
ConstService |
SAT_B |
\(B^q_{S_{AT}}\) |
\(\frac{E^{2c}_{S_{AT}} SE^{2c}_{S_{AT}} \left(a_{S_{AT}} - 1\right)^{2} \left(\operatorname{Indicator}{\left(a_{S_{AT}} > 0 \right)} + \operatorname{Indicator}{\left(a_{S_{AT}} < 0 \right)}\right)}{\left(E^{1c}_{S_{AT}} - E^{2c}_{S_{AT}}\right)^{2}}\) |
ConstService |
_V |
\(V_c\) |
\(V e^{i \theta}\) |
ConstService |
_S |
\(S\) |
\(P_{0} - i Q_{0}\) |
ConstService |
_Zs |
\(Z_s\) |
\(r_{a} + i x''_{d}\) |
ConstService |
_It |
\(I_t\) |
\(\frac{S}{\operatorname{conj}{\left(V_{c} \right)}}\) |
ConstService |
_Is |
\(I_s\) |
\(I_{t} + \frac{V_{c}}{Z_{s}}\) |
ConstService |
psi20 |
\(\psi''_0\) |
\(I_{s} Z_{s}\) |
ConstService |
psi20_arg |
\(\theta_{\psi''0}\) |
\(\arg{\left(\psi''_{0} \right)}\) |
ConstService |
psi20_abs |
\(|\psi''_0|\) |
\(\left|{\psi''_{0}}\right|\) |
ConstService |
_It_arg |
\(\theta_{It0}\) |
\(\arg{\left(I_{t} \right)}\) |
ConstService |
_psi20_It_arg |
\(\theta_{\psi a It}\) |
\(- \theta_{It0} + \theta_{\psi''0}\) |
ConstService |
Se0 |
\(S_{e0}\) |
\(\frac{B^q_{S_{AT}} \left(- A^q_{S_{AT}} + |\psi''_{0|}\right)^{2} \operatorname{Indicator}{\left(|\psi''_{0|} \geq A^q_{S_{AT}} \right)}}{|\psi''_{0|}}\) |
ConstService |
_a |
\(a'\) |
\(|\psi''_{0|} \left(S_{e0} \gamma_{qd} + 1\right)\) |
ConstService |
_b |
\(b'\) |
\(\left(x''_{q} - x_{q}\right) \left|{I_{t}}\right|\) |
ConstService |
delta0 |
\(\delta_0\) |
\(\theta_{\psi''0} + \operatorname{atan}{\left(\frac{b' \cos{\left(\theta_{\psi a It} \right)}}{- a' + b' \sin{\left(\theta_{\psi a It} \right)}} \right)}\) |
ConstService |
_Tdq |
\(T_{dq}\) |
\(- i \sin{\left(\delta_{0} \right)} + \cos{\left(\delta_{0} \right)}\) |
ConstService |
psi20_dq |
\(\psi''_{0,dq}\) |
\(T_{dq} \psi''_{0}\) |
ConstService |
It_dq |
\(I_{t,dq}\) |
\(\operatorname{conj}{\left(I_{t} T_{dq} \right)}\) |
ConstService |
psi2d0 |
\(\psi_{ad0}\) |
\(\operatorname{re}{\left(\psi''_{0,dq}\right)}\) |
ConstService |
psi2q0 |
\(\psi_{aq0}\) |
\(- \operatorname{im}{\left(\psi''_{0,dq}\right)}\) |
ConstService |
Id0 |
\(I_{d0}\) |
\(\operatorname{im}{\left(I_{t,dq}\right)}\) |
ConstService |
Iq0 |
\(I_{q0}\) |
\(\operatorname{re}{\left(I_{t,dq}\right)}\) |
ConstService |
vd0 |
\(V_{d0}\) |
\(- I_{d0} r_{a} + I_{q0} x''_{q} + \psi_{aq0}\) |
ConstService |
vq0 |
\(V_{q0}\) |
\(- I_{d0} x''_{d} - I_{q0} r_{a} + \psi_{ad0}\) |
ConstService |
tm0 |
\(\tau_{m0}\) |
\(u \left(I_{d0} \left(I_{d0} r_{a} + V_{d0}\right) + I_{q0} \left(I_{q0} r_{a} + V_{q0}\right)\right)\) |
ConstService |
vf0 |
\(v_{f0}\) |
\(I_{d0} \left(- x''_{d} + x_{d}\right) + \psi_{ad0} \left(S_{e0} + 1\right)\) |
ConstService |
psid0 |
\(\psi_{d0}\) |
\(I_{q0} r_{a} u + V_{q0}\) |
ConstService |
psiq0 |
\(\psi_{q0}\) |
\(- I_{d0} r_{a} u - V_{d0}\) |
ConstService |
e1q0 |
\(e'_{q0}\) |
\(I_{d0} \left(x'_{d} - x_{d}\right) - S_{e0} \psi_{ad0} + v_{f0}\) |
ConstService |
e1d0 |
\(e'_{d0}\) |
\(I_{q0} \left(- x'_{q} + x_{q}\right) - S_{e0} \gamma_{qd} \psi_{aq0}\) |
ConstService |
e2d0 |
\(e''_{d0}\) |
\(I_{d0} \left(- x_{d} + x_{l}\right) - S_{e0} \psi_{ad0} + v_{f0}\) |
ConstService |
e2q0 |
\(e''_{q0}\) |
\(- I_{q0} \left(x_{l} - x_{q}\right) - S_{e0} \gamma_{qd} \psi_{aq0}\) |
ConstService |
Discretes#
Name |
Symbol |
Type |
Info |
|---|---|---|---|
SL |
\(SL\) |
LessThan |
Blocks#
Name |
Symbol |
Type |
Info |
|---|---|---|---|
SAT |
\(S_{AT}\) |
ExcQuadSat |
Config Fields in [GENROU]
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) |
|
vf_lower |
1 |
lower limit for vf warning |
||
vf_upper |
5 |
upper limit for vf warning |
PLBVFU1#
PLBVFU1 model: playback of voltage and frequency as a generator.
The internal voltage and frequency are named Vflt and omega.
Rotor angle is named delta.
The current implementation relies on a TimeSeries device
to provide the voltage and frequency signals.
See ieee14_plbvfu1.xlsx and plbvf.xlsx in
andes/cases/ieee14 for an example.
Voltage and frequeny data needs to be specified in per unit. Nominal values are not yet supported.
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 |
|||
gen |
static generator index |
mandatory |
|||
Sn |
\(S_n\) |
Power rating |
100 |
MVA |
|
Vn |
\(V_n\) |
AC voltage rating |
110 |
||
ra |
\(r_a\) |
armature resistance |
0 |
z |
|
xs |
\(x_s\) |
generator transient reactance |
0.200 |
non_zero,z |
|
fn |
\(f_n\) |
rated frequency |
60 |
||
Vflag |
playback voltage signal |
1 |
bool |
||
fflag |
playback frequency signal |
1 |
bool |
||
filename |
playback file name |
string |
mandatory |
||
Vscale |
\(V_{scale}\) |
playback voltage scale |
1 |
pu |
non_negative |
fscale |
\(f_{scale}\) |
playback frequency scale |
1 |
pu |
non_negative |
Tv |
\(T_v\) |
filtering time constant for voltage |
0.200 |
s |
non_negative |
Tf |
\(T_f\) |
filtering time constant for frequency |
0.200 |
s |
non_negative |
subidx |
Generator idx in plant; only used by PSS/E data |
0 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
Vflt |
\(V_{flt}\) |
State |
filtered voltage |
pu |
v_str |
omega |
\(\omega\) |
State |
filtered frequency |
pu |
v_str |
delta |
\(\delta\) |
State |
rotor angle |
rad |
v_str |
a |
\(\theta\) |
ExtAlgeb |
Bus voltage phase angle |
||
v |
\(V\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
Vflt |
\(V_{flt}\) |
State |
\(1/V_{scale} Vts - V_{offs}\) |
omega |
\(\omega\) |
State |
\(1/f_{scale} fts - f_{offs}\) |
delta |
\(\delta\) |
State |
\(\delta_{0}\) |
a |
\(\theta\) |
ExtAlgeb |
|
v |
\(V\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
Vflt |
\(V_{flt}\) |
State |
\(1/V_{scale} Vts - V_{flt} - V_{offs}\) |
\(T_v\) |
omega |
\(\omega\) |
State |
\(1/f_{scale} fts - \omega - f_{offs}\) |
\(T_f\) |
delta |
\(\delta\) |
State |
\(2 \pi f_{n} u \left(\omega - 1\right)\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
a |
\(\theta\) |
ExtAlgeb |
\(- \frac{V V_{flt} x_{s} \sin{\left(\delta - \theta \right)}}{r_{a}^{2} + x_{s}^{2}} + \frac{V r_{a} \left(V - V_{flt} \cos{\left(\delta - \theta \right)}\right)}{r_{a}^{2} + x_{s}^{2}}\) |
v |
\(V\) |
ExtAlgeb |
\(\frac{V V_{flt} r_{a} \sin{\left(\delta - \theta \right)}}{r_{a}^{2} + x_{s}^{2}} + \frac{V x_{s} \left(V - V_{flt} \cos{\left(\delta - \theta \right)}\right)}{r_{a}^{2} + x_{s}^{2}}\) |
Services#
Name |
Symbol |
Equation |
Type |
|---|---|---|---|
zs |
\(zs\) |
\(r_{a} + i x_{s}\) |
ConstService |
zs2n |
\(zs2n\) |
\(r_{a}^{2} - x_{s}^{2}\) |
ConstService |
Ec |
\(E_c\) |
\(V e^{i \theta} + \left(r_{a} + i x_{s}\right) \operatorname{conj}{\left(\frac{\left(p + i q\right) e^{- i \theta}}{V} \right)}\) |
ConstService |
E0 |
\(E_0\) |
\(\left|{E_{c}}\right|\) |
ConstService |
delta0 |
\(\delta_0\) |
\(\arg{\left(E_{c} \right)}\) |
ConstService |
Vts |
\(Vts\) |
\(0\) |
ConstService |
fts |
\(fts\) |
\(0\) |
ConstService |
ifscale |
\(1/f_{scale}\) |
\(\frac{1}{f_{scale}}\) |
ConstService |
iVscale |
\(1/V_{scale}\) |
\(\frac{1}{V_{scale}}\) |
ConstService |
foffs |
\(f_{offs}\) |
\(1/f_{scale} fts - 1\) |
ConstService |
Voffs |
\(V_{offs}\) |
\(1/V_{scale} Vts - E_{0}\) |
ConstService |
Config Fields in [PLBVFU1]
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) |