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

\(Id\)

Algeb

d-axis current

v_str

Iq

\(Iq\)

Algeb

q-axis current

v_str

vd

\(vd\)

Algeb

d-axis voltage

v_str

vq

\(vq\)

Algeb

q-axis voltage

v_str

tm

\(tm\)

Algeb

mechanical torque

v_str

te

\(te\)

Algeb

electric torque

v_str

vf

\(vf\)

Algeb

excitation voltage

pu

v_str

XadIfd

\(XadIfd\)

Algeb

d-axis armature excitation current

p.u (kV)

v_str

Pe

\(Pe\)

Algeb

active power injection

v_str

Qe

\(Qe\)

Algeb

reactive power injection

v_str

psid

\(psid\)

Algeb

d-axis flux

v_str

psiq

\(psiq\)

Algeb

q-axis flux

v_str

a

\(a\)

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

\(Id\)

Algeb

\(Id_{0} u\)

Iq

\(Iq\)

Algeb

\(Iq_{0} u\)

vd

\(vd\)

Algeb

\(u vd_{0}\)

vq

\(vq\)

Algeb

\(u vq_{0}\)

tm

\(tm\)

Algeb

\(tm_{0}\)

te

\(te\)

Algeb

\(tm_{0} u\)

vf

\(vf\)

Algeb

\(u vf_{0}\)

XadIfd

\(XadIfd\)

Algeb

\(u vf_{0}\)

Pe

\(Pe\)

Algeb

\(u \left(Id_{0} vd_{0} + Iq_{0} vq_{0}\right)\)

Qe

\(Qe\)

Algeb

\(u \left(Id_{0} vq_{0} - Iq_{0} vd_{0}\right)\)

psid

\(psid\)

Algeb

\(psid_{0} u\)

psiq

\(psiq\)

Algeb

\(psiq_{0} u\)

a

\(a\)

ExtAlgeb

v

\(v\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

RHS of Equation "T x' = f(x, y)"

T (LHS)

delta

\(\delta\)

State

\(2 \pi fn u \left(\omega - 1\right)\)

omega

\(\omega\)

State

\(u \left(- D \left(\omega - 1\right) - te + tm\right)\)

\(M\)

Algebraic Equations#

Name

Symbol

Type

RHS of Equation "0 = g(x, y)"

Id

\(Id\)

Algeb

\(Id xq + psid - vf\)

Iq

\(Iq\)

Algeb

\(Iq xq + psiq\)

vd

\(vd\)

Algeb

\(- u v \sin{\left(a - \delta \right)} - vd\)

vq

\(vq\)

Algeb

\(u v \cos{\left(a - \delta \right)} - vq\)

tm

\(tm\)

Algeb

\(- tm + tm_{0}\)

te

\(te\)

Algeb

\(- te + u \left(- Id psiq + Iq psid\right)\)

vf

\(vf\)

Algeb

\(u vf_{0} - vf\)

XadIfd

\(XadIfd\)

Algeb

\(- XadIfd + u vf_{0}\)

Pe

\(Pe\)

Algeb

\(- Pe + u \left(Id vd + Iq vq\right)\)

Qe

\(Qe\)

Algeb

\(- Qe + u \left(Id vq - Iq vd\right)\)

psid

\(psid\)

Algeb

\(- psid + u \left(Iq ra + vq\right)\)

psiq

\(psiq\)

Algeb

\(psiq + u \left(Id ra + vd\right)\)

a

\(a\)

ExtAlgeb

\(- u \left(Id vd + Iq vq\right)\)

v

\(v\)

ExtAlgeb

\(- u \left(Id vq - Iq vd\right)\)

Services#

Name

Symbol

Equation

Type

p0

\(P_0\)

\(gammap p0s\)

ConstService

q0

\(Q_0\)

\(gammaq q0s\)

ConstService

_V

\(V_c\)

\(v e^{i a}\)

ConstService

_S

\(S\)

\(p_{0} - i q_{0}\)

ConstService

_I

\(I_c\)

\(\frac{_S}{\operatorname{conj}{\left(_V \right)}}\)

ConstService

_E

\(E\)

\(_I \left(ra + i xq\right) + _V\)

ConstService

_deltac

\(\delta_c\)

\(\log{\left(\frac{_E}{\left|{_E}\right|} \right)}\)

ConstService

delta0

\(\delta_0\)

\(u \operatorname{im}{\left(_deltac\right)}\)

ConstService

vdq

\(V_{dq}\)

\(_V u e^{- _deltac + 0.5 i \pi}\)

ConstService

Idq

\(I_{dq}\)

\(_I u e^{- _deltac + 0.5 i \pi}\)

ConstService

Id0

\(I_{d0}\)

\(\operatorname{re}{\left(Idq\right)}\)

ConstService

Iq0

\(I_{q0}\)

\(\operatorname{im}{\left(Idq\right)}\)

ConstService

vd0

\(V_{d0}\)

\(\operatorname{re}{\left(vdq\right)}\)

ConstService

vq0

\(V_{q0}\)

\(\operatorname{im}{\left(vdq\right)}\)

ConstService

tm0

\(\tau_{m0}\)

\(u \left(Id_{0} \left(Id_{0} ra + vd_{0}\right) + Iq_{0} \left(Iq_{0} ra + vq_{0}\right)\right)\)

ConstService

psid0

\(\psi_{d0}\)

\(Iq_{0} ra u + vq_{0}\)

ConstService

psiq0

\(\psi_{q0}\)

\(- Id_{0} ra u - vd_{0}\)

ConstService

vf0

\(v_{f0}\)

\(Id_{0} xq + Iq_{0} ra + vq_{0}\)

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:

  • xd2 and xq2 must 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

\(e1q\)

State

q-axis transient voltage

v_str

e1d

\(e1d\)

State

d-axis transient voltage

v_str

e2d

\(e2d\)

State

d-axis sub-transient voltage

v_str

e2q

\(e2q\)

State

q-axis sub-transient voltage

v_str

Id

\(Id\)

Algeb

d-axis current

v_str

Iq

\(Iq\)

Algeb

q-axis current

v_str

vd

\(vd\)

Algeb

d-axis voltage

v_str

vq

\(vq\)

Algeb

q-axis voltage

v_str

tm

\(tm\)

Algeb

mechanical torque

v_str

te

\(te\)

Algeb

electric torque

v_str

vf

\(vf\)

Algeb

excitation voltage

pu

v_str

XadIfd

\(XadIfd\)

Algeb

d-axis armature excitation current

p.u (kV)

v_str

Pe

\(Pe\)

Algeb

active power injection

v_str

Qe

\(Qe\)

Algeb

reactive power injection

v_str

psid

\(psid\)

Algeb

d-axis flux

v_str

psiq

\(psiq\)

Algeb

q-axis flux

v_str

psi2q

\(psi2q\)

Algeb

q-axis air gap flux

v_str

psi2d

\(psi2d\)

Algeb

d-axis air gap flux

v_str

psi2

\(\psi_{2}\)

Algeb

air gap flux magnitude

v_str

Se

\(Se\)

Algeb

saturation output

v_str

XaqI1q

\(XaqI1q\)

Algeb

q-axis reaction

p.u (kV)

v_str

a

\(a\)

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

\(e1q\)

State

\(e1q0 u\)

e1d

\(e1d\)

State

\(e1d0 u\)

e2d

\(e2d\)

State

\(e2d0 u\)

e2q

\(e2q\)

State

\(e2q0 u\)

Id

\(Id\)

Algeb

\(Id_{0} u\)

Iq

\(Iq\)

Algeb

\(Iq_{0} u\)

vd

\(vd\)

Algeb

\(u vd_{0}\)

vq

\(vq\)

Algeb

\(u vq_{0}\)

tm

\(tm\)

Algeb

\(tm_{0}\)

te

\(te\)

Algeb

\(tm_{0} u\)

vf

\(vf\)

Algeb

\(u vf_{0}\)

XadIfd

\(XadIfd\)

Algeb

\(u vf_{0}\)

Pe

\(Pe\)

Algeb

\(u \left(Id_{0} vd_{0} + Iq_{0} vq_{0}\right)\)

Qe

\(Qe\)

Algeb

\(u \left(Id_{0} vq_{0} - Iq_{0} vd_{0}\right)\)

psid

\(psid\)

Algeb

\(psid_{0} u\)

psiq

\(psiq\)

Algeb

\(psiq_{0} u\)

psi2q

\(psi2q\)

Algeb

\(psi2q0 u\)

psi2d

\(psi2d\)

Algeb

\(psi2d0 u\)

psi2

\(\psi_{2}\)

Algeb

\(u \left|{\psi_{20 dq}}\right|\)

Se

\(Se\)

Algeb

\(Se_{0} u\)

XaqI1q

\(XaqI1q\)

Algeb

\(0\)

a

\(a\)

ExtAlgeb

v

\(v\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

RHS of Equation "T x' = f(x, y)"

T (LHS)

delta

\(\delta\)

State

\(2 \pi fn u \left(\omega - 1\right)\)

omega

\(\omega\)

State

\(u \left(- D \left(\omega - 1\right) - te + tm\right)\)

\(M\)

e1q

\(e1q\)

State

\(- XadIfd + vf\)

\({T'_{d0}}\)

e1d

\(e1d\)

State

\(- XaqI1q\)

\({T'_{q0}}\)

e2d

\(e2d\)

State

\(- Id \left(xd_{1} - xl\right) + e1q - e2d\)

\({T''_{d0}}\)

e2q

\(e2q\)

State

\(Iq \left(- xl + xq_{1}\right) + e1d - e2q\)

\({T''_{q0}}\)

Algebraic Equations#

Name

Symbol

Type

RHS of Equation "0 = g(x, y)"

Id

\(Id\)

Algeb

\(Id xd_{2} - psi2d + psid\)

Iq

\(Iq\)

Algeb

\(Iq xq_{2} + psi2q + psiq\)

vd

\(vd\)

Algeb

\(- u v \sin{\left(a - \delta \right)} - vd\)

vq

\(vq\)

Algeb

\(u v \cos{\left(a - \delta \right)} - vq\)

tm

\(tm\)

Algeb

\(- tm + tm_{0}\)

te

\(te\)

Algeb

\(- te + u \left(- Id psiq + Iq psid\right)\)

vf

\(vf\)

Algeb

\(u vf_{0} - vf\)

XadIfd

\(XadIfd\)

Algeb

\(- XadIfd + u \left(Se psi2d + e1q + \left(xd - xd_{1}\right) \left(Id gd_{1} + e1q gd_{2} - e2d gd_{2}\right)\right)\)

Pe

\(Pe\)

Algeb

\(- Pe + u \left(Id vd + Iq vq\right)\)

Qe

\(Qe\)

Algeb

\(- Qe + u \left(Id vq - Iq vd\right)\)

psid

\(psid\)

Algeb

\(- psid + u \left(Iq ra + vq\right)\)

psiq

\(psiq\)

Algeb

\(psiq + u \left(Id ra + vd\right)\)

psi2q

\(psi2q\)

Algeb

\(e1d gq_{1} + e2q \left(1 - gq_{1}\right) - psi2q\)

psi2d

\(psi2d\)

Algeb

\(e1q gd_{1} + e2d gd_{2} \left(xd_{1} - xl\right) - psi2d\)

psi2

\(\psi_{2}\)

Algeb

\(- \psi_{2}^{2} + psi2d^{2} + psi2q^{2}\)

Se

\(Se\)

Algeb

\(SAT_{B} SL_{z0} \left(- SAT_{A} + \psi_{2}\right)^{2} - Se \psi_{2}\)

XaqI1q

\(XaqI1q\)

Algeb

\(Se gqd psi2q - XaqI1q + e1d + \left(xq - xq_{1}\right) \left(- Iq gq_{1} + e1d gq_{2} - e2q gq_{2}\right)\)

a

\(a\)

ExtAlgeb

\(- u \left(Id vd + Iq vq\right)\)

v

\(v\)

ExtAlgeb

\(- u \left(Id vq - Iq vd\right)\)

Services#

Name

Symbol

Equation

Type

p0

\(P_0\)

\(gammap p0s\)

ConstService

q0

\(Q_0\)

\(gammaq q0s\)

ConstService

gd1

\(\gamma_{d1}\)

\(\frac{xd_{2} - xl}{xd_{1} - xl}\)

ConstService

gq1

\(\gamma_{q1}\)

\(\frac{- xl + xq_{2}}{- xl + xq_{1}}\)

ConstService

gd2

\(\gamma_{d2}\)

\(\frac{xd_{1} - xd_{2}}{\left(xd_{1} - xl\right)^{2}}\)

ConstService

gq2

\(\gamma_{q2}\)

\(\frac{xq_{1} - xq_{2}}{\left(- xl + xq_{1}\right)^{2}}\)

ConstService

gqd

\(\gamma_{qd}\)

\(\frac{- xl + xq}{xd - xl}\)

ConstService

_S12

\(S_{1.2}\)

\(S_{12} - _fS12 + 1\)

ConstService

SAT_E1

\(E^{1c}_{S_{AT}}\)

\(1.0\)

ConstService

SAT_E2

\(E^{2c}_{S_{AT}}\)

\(3.2 - 2 SAT_{zSE2}\)

ConstService

SAT_SE1

\(SE^{1c}_{S_{AT}}\)

\(S_{10}\)

ConstService

SAT_SE2

\(SE^{2c}_{S_{AT}}\)

\(S_{12} - 2 SAT_{zSE2} + 2\)

ConstService

SAT_a

\(a_{S_{AT}}\)

\(\sqrt{\frac{SAT_{E1} SAT_{SE1}}{SAT_{E2} SAT_{SE2}}} \left(\operatorname{Indicator}{\left(SAT_{SE2} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{SE2} < 0 \right)}\right)\)

ConstService

SAT_A

\(A^q_{S_{AT}}\)

\(SAT_{E2} - \frac{SAT_{E1} - SAT_{E2}}{SAT_{a} - 1}\)

ConstService

SAT_B

\(B^q_{S_{AT}}\)

\(\frac{SAT_{E2} SAT_{SE2} \left(SAT_{a} - 1\right)^{2} \left(\operatorname{Indicator}{\left(SAT_{a} > 0 \right)} + \operatorname{Indicator}{\left(SAT_{a} < 0 \right)}\right)}{\left(SAT_{E1} - SAT_{E2}\right)^{2}}\)

ConstService

_V

\(V_c\)

\(v e^{i a}\)

ConstService

_S

\(S\)

\(p_{0} - i q_{0}\)

ConstService

_Zs

\(Z_s\)

\(ra + i xd_{2}\)

ConstService

_It

\(I_t\)

\(\frac{_S}{\operatorname{conj}{\left(_V \right)}}\)

ConstService

_Is

\(I_s\)

\(_It + \frac{_V}{_Zs}\)

ConstService

psi20

\({\psi''_0}\)

\(_Is _Zs\)

ConstService

psi20_arg

\(\theta_{\psi''0}\)

\(\arg{\left(\psi_{20} \right)}\)

ConstService

psi20_abs

\(|{\psi''_0}|\)

\(\left|{\psi_{20}}\right|\)

ConstService

_It_arg

\(\theta_{It0}\)

\(\arg{\left(_It \right)}\)

ConstService

_psi20_It_arg

\(\theta_{\psi a It}\)

\(- _It_{arg} + \psi_{20 arg}\)

ConstService

Se0

\(S_{e0}\)

\(\frac{SAT_{B} \left(- SAT_{A} + \psi_{20 abs}\right)^{2} \operatorname{Indicator}{\left(\psi_{20 abs} \geq SAT_{A} \right)}}{\psi_{20 abs}}\)

ConstService

_a

\({a'}\)

\(\psi_{20 abs} \left(Se_{0} gqd + 1\right)\)

ConstService

_b

\({b'}\)

\(\left(- xq + xq_{2}\right) \left|{_It}\right|\)

ConstService

delta0

\(\delta_0\)

\(\psi_{20 arg} + \operatorname{atan}{\left(\frac{_b \cos{\left(_psi20_{It arg} \right)}}{- _a + _b \sin{\left(_psi20_{It arg} \right)}} \right)}\)

ConstService

_Tdq

\(T_{dq}\)

\(- i \sin{\left(\delta_{0} \right)} + \cos{\left(\delta_{0} \right)}\)

ConstService

psi20_dq

\({\psi''_{0,dq}}\)

\(_Tdq \psi_{20}\)

ConstService

It_dq

\(I_{t,dq}\)

\(\operatorname{conj}{\left(_It _Tdq \right)}\)

ConstService

psi2d0

\(\psi_{ad0}\)

\(\operatorname{re}{\left(\psi_{20 dq}\right)}\)

ConstService

psi2q0

\(\psi_{aq0}\)

\(- \operatorname{im}{\left(\psi_{20 dq}\right)}\)

ConstService

Id0

\(I_{d0}\)

\(\operatorname{im}{\left(It_{dq}\right)}\)

ConstService

Iq0

\(I_{q0}\)

\(\operatorname{re}{\left(It_{dq}\right)}\)

ConstService

vd0

\(V_{d0}\)

\(- Id_{0} ra + Iq_{0} xq_{2} + psi2q0\)

ConstService

vq0

\(V_{q0}\)

\(- Id_{0} xd_{2} - Iq_{0} ra + psi2d0\)

ConstService

tm0

\(\tau_{m0}\)

\(u \left(Id_{0} \left(Id_{0} ra + vd_{0}\right) + Iq_{0} \left(Iq_{0} ra + vq_{0}\right)\right)\)

ConstService

vf0

\(v_{f0}\)

\(Id_{0} \left(xd - xd_{2}\right) + psi2d0 \left(Se_{0} + 1\right)\)

ConstService

psid0

\(\psi_{d0}\)

\(Iq_{0} ra u + vq_{0}\)

ConstService

psiq0

\(\psi_{q0}\)

\(- Id_{0} ra u - vd_{0}\)

ConstService

e1q0

\({e'_{q0}}\)

\(Id_{0} \left(- xd + xd_{1}\right) - Se_{0} psi2d0 + vf_{0}\)

ConstService

e1d0

\({e'_{d0}}\)

\(Iq_{0} \left(xq - xq_{1}\right) - Se_{0} gqd psi2q0\)

ConstService

e2d0

\({e''_{d0}}\)

\(Id_{0} \left(- xd + xl\right) - Se_{0} psi2d0 + vf_{0}\)

ConstService

e2q0

\({e''_{q0}}\)

\(- Iq_{0} \left(xl - xq\right) - Se_{0} gqd psi2q0\)

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

\(Vflt\)

State

filtered voltage

pu

v_str

omega

\(\omega\)

State

filtered frequency

pu

v_str

delta

\(\delta\)

State

rotor angle

rad

v_str

a

\(a\)

ExtAlgeb

Bus voltage phase angle

v

\(v\)

ExtAlgeb

Bus voltage magnitude

Initialization Equations#

Name

Symbol

Type

Initial Value

Vflt

\(Vflt\)

State

\(- Voffs + Vts iVscale\)

omega

\(\omega\)

State

\(- foffs + fts ifscale\)

delta

\(\delta\)

State

\(\delta_{0}\)

a

\(a\)

ExtAlgeb

v

\(v\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

RHS of Equation "T x' = f(x, y)"

T (LHS)

Vflt

\(Vflt\)

State

\(- Vflt - Voffs + Vts iVscale\)

\(T_v\)

omega

\(\omega\)

State

\(- foffs + fts ifscale - \omega\)

\(T_f\)

delta

\(\delta\)

State

\(2 \pi fn u \left(\omega - 1\right)\)

Algebraic Equations#

Name

Symbol

Type

RHS of Equation "0 = g(x, y)"

a

\(a\)

ExtAlgeb

\(\frac{Vflt v xs \sin{\left(a - \delta \right)}}{ra^{2} + xs^{2}} + \frac{ra v \left(- Vflt \cos{\left(a - \delta \right)} + v\right)}{ra^{2} + xs^{2}}\)

v

\(v\)

ExtAlgeb

\(- \frac{Vflt ra v \sin{\left(a - \delta \right)}}{ra^{2} + xs^{2}} + \frac{v xs \left(- Vflt \cos{\left(a - \delta \right)} + v\right)}{ra^{2} + xs^{2}}\)

Services#

Name

Symbol

Equation

Type

zs

\(zs\)

\(ra + i xs\)

ConstService

zs2n

\(zs2n\)

\(ra^{2} - xs^{2}\)

ConstService

Ec

\(E_c\)

\(v e^{i a} + \left(ra + i xs\right) \operatorname{conj}{\left(\frac{\left(p + i q\right) e^{- i a}}{v} \right)}\)

ConstService

E0

\(E_0\)

\(\left|{Ec}\right|\)

ConstService

delta0

\(\delta_0\)

\(\arg{\left(Ec \right)}\)

ConstService

Vts

\(Vts\)

\(0\)

ConstService

fts

\(fts\)

\(0\)

ConstService

ifscale

\(1/f_{scale}\)

\(\frac{1}{fscale}\)

ConstService

iVscale

\(1/V_{scale}\)

\(\frac{1}{Vscale}\)

ConstService

foffs

\(f_{offs}\)

\(fts ifscale - 1\)

ConstService

Voffs

\(V_{offs}\)

\(- E_{0} + Vts iVscale\)

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)