PSS#

Power system stabilizer group.

Common Parameters: u, name

Common Variables: vsout

Available models: IEEEST, ST2CUT

IEEEST#

IEEEST stabilizer model. Automatically adds frequency measurement devices if not provided.

Input signals (MODE):

  1. Rotor speed deviation (p.u.),

  2. Bus frequency deviation (p.u.) (*),

  3. Generator P electrical in Gen MVABase (p.u.),

  4. Generator accelerating power (p.u.),

  5. Bus voltage (p.u.),

  6. Derivative of p.u. bus voltage.

(*) Due to the frequency measurement implementation difference, mode 2 is likely to yield different results across software.

Note

Blocks are named F1, F2, LL1, LL2 and WO in sequence. Two limiters are named VLIM and OLIM in sequence.

Parameters#

Name

Symbol

Description

Default

Unit

Properties

idx

unique device idx

u

\(u\)

connection status

1

bool

name

device name

avr

Exciter idx

mandatory

MODE

Input signal

mandatory

busr

Optional remote bus idx

busf

BusFreq idx for mode 2

A1

\(A_1\)

filter time const. (pole)

1

A2

\(A_2\)

filter time const. (pole)

1

A3

\(A_3\)

filter time const. (pole)

1

A4

\(A_4\)

filter time const. (pole)

1

A5

\(A_5\)

filter time const. (zero)

1

A6

\(A_6\)

filter time const. (zero)

1

T1

\(T_1\)

first leadlag time const. (zero)

1

T2

\(T_2\)

first leadlag time const. (pole)

1

T3

\(T_3\)

second leadlag time const. (pole)

1

T4

\(T_4\)

second leadlag time const. (pole)

1

T5

\(T_5\)

washout time const. (zero)

1

T6

\(T_6\)

washout time const. (pole)

1

KS

\(K_S\)

Gain before washout

1

LSMAX

\(L_{SMAX}\)

Max. output limit

0.300

LSMIN

\(L_{SMIN}\)

Min. output limit

-0.300

VCU

\(V_{CU}\)

Upper enabling bus voltage

999

p.u.

VCL

\(V_{CL}\)

Upper enabling bus voltage

-999

p.u.

syn

Retrieved generator idx

0

bus

Retrieved bus idx

Sn

\(S_n\)

Generator power base

0

Variables#

Name

Symbol

Type

Description

Unit

Properties

F1_x

\(F_{1 x}\)

State

State in 2nd order LPF

v_str

F1_y

\(F_{1 y}\)

State

Output of 2nd order LPF

v_str

F2_x1

\(F_{2 x1}\)

State

State #1 in 2nd order lead-lag

v_str

F2_x2

\(F_{2 x2}\)

State

State #2 in 2nd order lead-lag

v_str

LL1_x

\(LL_{1 x}\)

State

State in lead-lag

v_str

LL2_x

\(LL_{2 x}\)

State

State in lead-lag

v_str

WO_x

\(WO_{x}\)

State

State in washout filter

v_str

omega

\(\omega\)

ExtState

Generator speed

p.u.

vsout

\(vsout\)

Algeb

PSS output voltage to exciter

sig

\(sig\)

Algeb

Input signal

v_str

F2_y

\(F_{2 y}\)

Algeb

Output of 2nd order lead-lag

v_str

LL1_y

\(LL_{1 y}\)

Algeb

Output of lead-lag

v_str

LL2_y

\(LL_{2 y}\)

Algeb

Output of lead-lag

v_str

Vks_y

\(Vks_{y}\)

Algeb

Gain output

v_str

WO_y

\(WO_{y}\)

Algeb

Output of washout filter

v_str

Vss

\(Vss\)

Algeb

Voltage output before output limiter

tm

\(tm\)

ExtAlgeb

Generator mechanical input

te

\(te\)

ExtAlgeb

Generator electrical output

v

\(v\)

ExtAlgeb

Bus (or busr, if given) terminal voltage

f

\(f\)

ExtAlgeb

Bus frequency

vi

\(vi\)

ExtAlgeb

Exciter input voltage

Initialization Equations#

Name

Symbol

Type

Initial Value

F1_x

\(F_{1 x}\)

State

\(0\)

F1_y

\(F_{1 y}\)

State

\(sig\)

F2_x1

\(F_{2 x1}\)

State

\(0\)

F2_x2

\(F_{2 x2}\)

State

\(F_{1 y}\)

LL1_x

\(LL_{1 x}\)

State

\(F_{2 y}\)

LL2_x

\(LL_{2 x}\)

State

\(LL_{1 y}\)

WO_x

\(WO_{x}\)

State

\(Vks_{y}\)

omega

\(\omega\)

ExtState

vsout

\(vsout\)

Algeb

sig

\(sig\)

Algeb

\(ue \left(SW_{s1} \left(\omega - 1\right) + \frac{SW_{s3} tm_{0}}{SnSb} + SW_{s4} \left(tm - tm_{0}\right) + SW_{s5} v\right)\)

F2_y

\(F_{2 y}\)

Algeb

\(F_{1 y}\)

LL1_y

\(LL_{1 y}\)

Algeb

\(F_{2 y}\)

LL2_y

\(LL_{2 y}\)

Algeb

\(LL_{1 y}\)

Vks_y

\(Vks_{y}\)

Algeb

\(KS LL_{2 y}\)

WO_y

\(WO_{y}\)

Algeb

\(WO_{LT z1} WO_{x}\)

Vss

\(Vss\)

Algeb

tm

\(tm\)

ExtAlgeb

te

\(te\)

ExtAlgeb

v

\(v\)

ExtAlgeb

f

\(f\)

ExtAlgeb

vi

\(vi\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

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

T (LHS)

F1_x

\(F_{1 x}\)

State

\(- A_{1} F_{1 x} - F_{1 y} + sig\)

\(A_2\)

F1_y

\(F_{1 y}\)

State

\(F_{1 x}\)

F2_x1

\(F_{2 x1}\)

State

\(- A_{3} F_{2 x1} + F_{1 y} - F_{2 x2}\)

\(A_4\)

F2_x2

\(F_{2 x2}\)

State

\(F_{2 x1}\)

LL1_x

\(LL_{1 x}\)

State

\(F_{2 y} - LL_{1 x}\)

\(T_2\)

LL2_x

\(LL_{2 x}\)

State

\(LL_{1 y} - LL_{2 x}\)

\(T_4\)

WO_x

\(WO_{x}\)

State

\(Vks_{y} - WO_{x}\)

\(T_6\)

omega

\(\omega\)

ExtState

\(0\)

Algebraic Equations#

Name

Symbol

Type

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

vsout

\(vsout\)

Algeb

\(OLIM_{zi} Vss ue - vsout\)

sig

\(sig\)

Algeb

\(- sig + ue \left(SW_{s1} \left(\omega - 1\right) + SW_{s2} \left(f - 1\right) + \frac{SW_{s3} te}{SnSb} + SW_{s4} \left(tm - tm_{0}\right) + SW_{s5} v + SW_{s6} dv_{v}\right)\)

F2_y

\(F_{2 y}\)

Algeb

\(A_{4} A_{5} F_{2 x1} + A_{4} F_{2 x2} - A_{4} F_{2 y} + A_{6} \left(- A_{3} F_{2 x1} + F_{1 y} - F_{2 x2}\right) + F_{2 LT1 z1} F_{2 LT2 z1} F_{2 LT3 z1} F_{2 LT4 z1} \left(- F_{2 x2} + F_{2 y}\right)\)

LL1_y

\(LL_{1 y}\)

Algeb

\(LL_{1 LT1 z1} LL_{1 LT2 z1} \left(- LL_{1 x} + LL_{1 y}\right) + LL_{1 x} T_{2} - LL_{1 y} T_{2} + T_{1} \left(F_{2 y} - LL_{1 x}\right)\)

LL2_y

\(LL_{2 y}\)

Algeb

\(LL_{2 LT1 z1} LL_{2 LT2 z1} \left(- LL_{2 x} + LL_{2 y}\right) + LL_{2 x} T_{4} - LL_{2 y} T_{4} + T_{3} \left(LL_{1 y} - LL_{2 x}\right)\)

Vks_y

\(Vks_{y}\)

Algeb

\(KS LL_{2 y} - Vks_{y}\)

WO_y

\(WO_{y}\)

Algeb

\(T_{5} WO_{LT z0} \left(Vks_{y} - WO_{x}\right) + T_{6} WO_{LT z1} WO_{x} - T_{6} WO_{y}\)

Vss

\(Vss\)

Algeb

\(LSMAX VLIM_{zu} + LSMIN VLIM_{zl} + VLIM_{zi} WO_{y} - Vss\)

tm

\(tm\)

ExtAlgeb

\(0\)

te

\(te\)

ExtAlgeb

\(0\)

v

\(v\)

ExtAlgeb

\(0\)

f

\(f\)

ExtAlgeb

\(0\)

vi

\(vi\)

ExtAlgeb

\(ue vsout\)

Services#

Name

Symbol

Equation

Type

ue

\(u_{e}\)

\(u uee\)

ConstService

Discretes#

Name

Symbol

Type

Info

dv

\(dV/dt\)

Derivative

Finite difference of bus voltage

SW

\(SW\)

Switcher

F2_LT1

\(LT_{F2}\)

LessThan

F2_LT2

\(LT_{F2}\)

LessThan

F2_LT3

\(LT_{F2}\)

LessThan

F2_LT4

\(LT_{F2}\)

LessThan

LL1_LT1

\(LT_{LL1}\)

LessThan

LL1_LT2

\(LT_{LL1}\)

LessThan

LL2_LT1

\(LT_{LL2}\)

LessThan

LL2_LT2

\(LT_{LL2}\)

LessThan

WO_LT

\(LT_{WO}\)

LessThan

VLIM

\(VLIM\)

Limiter

Vss limiter

OLIM

\(OLIM\)

Limiter

output limiter

Blocks#

Name

Symbol

Type

Info

F1

\(F1\)

Lag2ndOrd

F2

\(F2\)

LeadLag2ndOrd

LL1

\(LL1\)

LeadLag

LL2

\(LL2\)

LeadLag

Vks

\(Vks\)

Gain

WO

\(WO\)

WashoutOrLag

Config Fields in [IEEEST]

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)

freq_model

BusFreq

default freq. measurement model

('BusFreq',)

ST2CUT#

ST2CUT stabilizer model. Automatically adds frequency measurement devices if not provided.

Input signals (MODE and MODE2):

0 - Disable input signal 1 (s1) - Rotor speed deviation (p.u.), 2 (s2) - Bus frequency deviation (*) (p.u.), 3 (s3) - Generator P electrical in Gen MVABase (p.u.), 4 (s4) - Generator accelerating power (p.u.), 5 (s5) - Bus voltage (p.u.), 6 (s6) - Derivative of p.u. bus voltage.

(*) Due to the frequency measurement implementation difference, mode 2 is likely to yield different results across software.

Blocks are named LL1, LL2, LL3, LL4 in sequence. Two limiters are named VSS_lim and OLIM in sequence.

Parameters#

Name

Symbol

Description

Default

Unit

Properties

idx

unique device idx

u

\(u\)

connection status

1

bool

name

device name

avr

Exciter idx

mandatory

MODE

Input signal 1

mandatory

busr

Remote bus 1

busf

BusFreq idx for signal 1 mode 2

MODE2

Input signal 2

busr2

Remote bus 2

busf2

BusFreq idx for signal 2 mode 2

K1

\(K_1\)

Transducer 1 gain

1

K2

\(K_2\)

Transducer 2 gain

1

T1

\(T_1\)

Transducer 1 time const.

1

T2

\(T_2\)

Transducer 2 time const.

1

T3

\(T_3\)

Washout int. time const.

1

T4

\(T_4\)

Washout delay time const.

0.200

T5

\(T_5\)

Leadlag 1 time const. (1)

1

T6

\(T_6\)

Leadlag 1 time const. (2)

0.500

T7

\(T_7\)

Leadlag 2 time const. (1)

1

T8

\(T_8\)

Leadlag 2 time const. (2)

1

T9

\(T_9\)

Leadlag 3 time const. (1)

1

T10

\(T_{10}\)

Leadlag 3 time const. (2)

0.200

LSMAX

\(L_{SMAX}\)

Max. output limit

0.300

LSMIN

\(L_{SMIN}\)

Min. output limit

-0.300

VCU

\(V_{CU}\)

Upper enabling bus voltage

999

p.u.

VCL

\(V_{CL}\)

Upper enabling bus voltage

-999

p.u.

syn

Retrieved generator idx

0

bus

Retrieved bus idx

Sn

\(S_n\)

Generator power base

0

Variables#

Name

Symbol

Type

Description

Unit

Properties

L1_y

\(L_{1 y}\)

State

State in lag transfer function

v_str

L2_y

\(L_{2 y}\)

State

State in lag transfer function

v_str

WO_x

\(WO_{x}\)

State

State in washout filter

v_str

LL1_x

\(LL_{1 x}\)

State

State in lead-lag

v_str

LL2_x

\(LL_{2 x}\)

State

State in lead-lag

v_str

LL3_x

\(LL_{3 x}\)

State

State in lead-lag

v_str

omega

\(\omega\)

ExtState

Generator speed

p.u.

vsout

\(vsout\)

Algeb

PSS output voltage to exciter

sig

\(sig\)

Algeb

Input signal

v_str

sig2

\(sig_{2}\)

Algeb

Input signal 2

v_str

IN

\(IN\)

Algeb

Sum of inputs

v_str

WO_y

\(WO_{y}\)

Algeb

Output of washout filter

v_str

LL1_y

\(LL_{1 y}\)

Algeb

Output of lead-lag

v_str

LL2_y

\(LL_{2 y}\)

Algeb

Output of lead-lag

v_str

LL3_y

\(LL_{3 y}\)

Algeb

Output of lead-lag

v_str

VSS_x

\(VSS_{x}\)

Algeb

Value before limiter

v_str

VSS_y

\(VSS_{y}\)

Algeb

Output after limiter and post gain

v_str

tm

\(tm\)

ExtAlgeb

Generator mechanical input

te

\(te\)

ExtAlgeb

Generator electrical output

v

\(v\)

ExtAlgeb

Bus (or busr, if given) terminal voltage

f

\(f\)

ExtAlgeb

Bus frequency

vi

\(vi\)

ExtAlgeb

Exciter input voltage

v2

\(v_{2}\)

ExtAlgeb

Bus (or busr2, if given) terminal voltage

f2

\(f_{2}\)

ExtAlgeb

Bus frequency 2

Initialization Equations#

Name

Symbol

Type

Initial Value

L1_y

\(L_{1 y}\)

State

\(K_{1} sig\)

L2_y

\(L_{2 y}\)

State

\(K_{2} sig_{2}\)

WO_x

\(WO_{x}\)

State

\(IN\)

LL1_x

\(LL_{1 x}\)

State

\(WO_{y}\)

LL2_x

\(LL_{2 x}\)

State

\(LL_{1 y}\)

LL3_x

\(LL_{3 x}\)

State

\(LL_{2 y}\)

omega

\(\omega\)

ExtState

vsout

\(vsout\)

Algeb

sig

\(sig\)

Algeb

\(SW_{s1} \left(\omega - 1\right) + \frac{SW_{s3} tm_{0}}{SnSb} + SW_{s4} \left(tm - tm_{0}\right) + SW_{s5} v\)

sig2

\(sig_{2}\)

Algeb

\(SW_{2 s1} \left(\omega - 1\right) + \frac{SW_{2 s3} tm_{0}}{SnSb} + SW_{2 s4} \left(tm - tm_{0}\right) + SW_{2 s5} v_{2}\)

IN

\(IN\)

Algeb

\(ue \left(L_{1 y} + L_{2 y}\right)\)

WO_y

\(WO_{y}\)

Algeb

\(WO_{LT z1} WO_{x}\)

LL1_y

\(LL_{1 y}\)

Algeb

\(WO_{y}\)

LL2_y

\(LL_{2 y}\)

Algeb

\(LL_{1 y}\)

LL3_y

\(LL_{3 y}\)

Algeb

\(LL_{2 y}\)

VSS_x

\(VSS_{x}\)

Algeb

\(LL_{3 y}\)

VSS_y

\(VSS_{y}\)

Algeb

\(LSMAX VSS_{lim zu} + LSMIN VSS_{lim zl} + VSS_{lim zi} VSS_{x}\)

tm

\(tm\)

ExtAlgeb

te

\(te\)

ExtAlgeb

v

\(v\)

ExtAlgeb

f

\(f\)

ExtAlgeb

vi

\(vi\)

ExtAlgeb

v2

\(v_{2}\)

ExtAlgeb

f2

\(f_{2}\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

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

T (LHS)

L1_y

\(L_{1 y}\)

State

\(K_{1} sig - L_{1 y}\)

\(T_1\)

L2_y

\(L_{2 y}\)

State

\(K_{2} sig_{2} - L_{2 y}\)

\(T_2\)

WO_x

\(WO_{x}\)

State

\(IN - WO_{x}\)

\(T_4\)

LL1_x

\(LL_{1 x}\)

State

\(- LL_{1 x} + WO_{y}\)

\(T_6\)

LL2_x

\(LL_{2 x}\)

State

\(LL_{1 y} - LL_{2 x}\)

\(T_8\)

LL3_x

\(LL_{3 x}\)

State

\(LL_{2 y} - LL_{3 x}\)

\(T_{10}\)

omega

\(\omega\)

ExtState

\(0\)

Algebraic Equations#

Name

Symbol

Type

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

vsout

\(vsout\)

Algeb

\(OLIM_{zi} VSS_{y} ue - vsout\)

sig

\(sig\)

Algeb

\(SW_{s1} \left(\omega - 1\right) + SW_{s2} \left(f - 1\right) + \frac{SW_{s3} te}{SnSb} + SW_{s4} \left(tm - tm_{0}\right) + SW_{s5} v + SW_{s6} dv_{v} - sig\)

sig2

\(sig_{2}\)

Algeb

\(SW_{2 s1} \left(\omega - 1\right) + SW_{2 s2} \left(f_{2} - 1\right) + \frac{SW_{2 s3} te}{SnSb} + SW_{2 s4} \left(tm - tm_{0}\right) + SW_{2 s5} v_{2} + SW_{2 s6} dv_{2 v} - sig_{2}\)

IN

\(IN\)

Algeb

\(- IN + ue \left(L_{1 y} + L_{2 y}\right)\)

WO_y

\(WO_{y}\)

Algeb

\(T_{3} WO_{LT z0} \left(IN - WO_{x}\right) + T_{4} WO_{LT z1} WO_{x} - T_{4} WO_{y}\)

LL1_y

\(LL_{1 y}\)

Algeb

\(LL_{1 LT1 z1} LL_{1 LT2 z1} \left(- LL_{1 x} + LL_{1 y}\right) + LL_{1 x} T_{6} - LL_{1 y} T_{6} + T_{5} \left(- LL_{1 x} + WO_{y}\right)\)

LL2_y

\(LL_{2 y}\)

Algeb

\(LL_{2 LT1 z1} LL_{2 LT2 z1} \left(- LL_{2 x} + LL_{2 y}\right) + LL_{2 x} T_{8} - LL_{2 y} T_{8} + T_{7} \left(LL_{1 y} - LL_{2 x}\right)\)

LL3_y

\(LL_{3 y}\)

Algeb

\(LL_{3 LT1 z1} LL_{3 LT2 z1} \left(- LL_{3 x} + LL_{3 y}\right) + LL_{3 x} T_{10} - LL_{3 y} T_{10} + T_{9} \left(LL_{2 y} - LL_{3 x}\right)\)

VSS_x

\(VSS_{x}\)

Algeb

\(LL_{3 y} - VSS_{x}\)

VSS_y

\(VSS_{y}\)

Algeb

\(LSMAX VSS_{lim zu} + LSMIN VSS_{lim zl} + VSS_{lim zi} VSS_{x} - VSS_{y}\)

tm

\(tm\)

ExtAlgeb

\(0\)

te

\(te\)

ExtAlgeb

\(0\)

v

\(v\)

ExtAlgeb

\(0\)

f

\(f\)

ExtAlgeb

\(0\)

vi

\(vi\)

ExtAlgeb

\(ue vsout\)

v2

\(v_{2}\)

ExtAlgeb

\(0\)

f2

\(f_{2}\)

ExtAlgeb

\(0\)

Services#

Name

Symbol

Equation

Type

ue

\(u_{e}\)

\(u uee\)

ConstService

VOU

\(VOU\)

\(VCUr + v_{0}\)

ConstService

VOL

\(VOL\)

\(VCLr + v_{0}\)

ConstService

Discretes#

Name

Symbol

Type

Info

dv

\(dv\)

Derivative

dv2

\(dv2\)

Derivative

SW

\(SW\)

Switcher

SW2

\(SW2\)

Switcher

WO_LT

\(LT_{WO}\)

LessThan

LL1_LT1

\(LT_{LL1}\)

LessThan

LL1_LT2

\(LT_{LL1}\)

LessThan

LL2_LT1

\(LT_{LL2}\)

LessThan

LL2_LT2

\(LT_{LL2}\)

LessThan

LL3_LT1

\(LT_{LL3}\)

LessThan

LL3_LT2

\(LT_{LL3}\)

LessThan

VSS_lim

\(lim_{VSS}\)

HardLimiter

OLIM

\(OLIM\)

Limiter

output limiter

Blocks#

Name

Symbol

Type

Info

L1

\(L1\)

Lag

Transducer 1

L2

\(L2\)

Lag

Transducer 2

WO

\(WO\)

WashoutOrLag

LL1

\(LL1\)

LeadLag

LL2

\(LL2\)

LeadLag

LL3

\(LL3\)

LeadLag

VSS

\(VSS\)

GainLimiter

Config Fields in [ST2CUT]

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)

freq_model

BusFreq

default freq. measurement model

('BusFreq',)