SynGen#
Synchronous generator group.
SynGen replaces StaticGen upon the initialization of dynamic studies. SynGen
and inverter-based resources contain parameters gammap and gammaq
for splitting the initial power of a StaticGen into multiple dynamic ones.
gammap, for example, is the active power ratio of the dynamic generator
to the static one. If a StaticGen is supposed to be replaced by one SynGen,
the gammap and gammaq should both be 1.
It is critical to ensure that gammap and gammaq, respectively, of
all dynamic power sources sum up to 1.0. Otherwise, the initial power
injections imposed by dynamic sources will differ from the static ones. The
initialization will then fail with mismatches power injection equations
corresponding to bus a and v.
Common Parameters: u, name, Sn, Vn, fn, bus, M, D, subidx
Common Variables: omega, delta
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 |
\(I_{d} {x'_d} + \psi_{d} - v_{f}\) |
Iq |
\(I_{q}\) |
Algeb |
\(I_{q} {x'_d} + \psi_{q}\) |
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 |
\(E\) |
\(I_{c} \left(r_{a} + i {x'_d}\right) + V_{c}\) |
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 |
\(v_{f0}\) |
\(I_{d0} {x'_d} + I_{q0} r_{a} + V_{q0}\) |
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.
Notes#
Parameters:
xd2andxq2must be equal to pass initialization.
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 |
0.300 |
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 |
\(u {e'_{q0}}\) |
e1d |
\({e'_d}\) |
State |
\(u {e'_{d0}}\) |
e2d |
\({e''_d}\) |
State |
\(u {e''_{d0}}\) |
e2q |
\({e''_q}\) |
State |
\(u {e''_{q0}}\) |
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 |
\(\psi_{aq0} u\) |
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 |
\(I_{q} \left(- x_{l} + {x'_q}\right) - {e''_q} + {e'_d}\) |
\({T''_{q0}}\) |
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 |
\(\gamma_{d1}\) |
\(\frac{- x_{l} + {x''_d}}{x'_{d} - x_{l}}\) |
ConstService |
gq1 |
\(\gamma_{q1}\) |
\(\frac{- x_{l} + {x''_q}}{- x_{l} + {x'_q}}\) |
ConstService |
gd2 |
\(\gamma_{d2}\) |
\(\frac{x'_{d} - {x''_d}}{\left(x'_{d} - x_{l}\right)^{2}}\) |
ConstService |
gq2 |
\(\gamma_{q2}\) |
\(\frac{- {x''_q} + {x'_q}}{\left(- x_{l} + {x'_q}\right)^{2}}\) |
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 |
\(E^{2c}_{S_{AT}}\) |
\(3.2 - 2 z^{SE2}_{S_{AT}}\) |
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) |