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

\(x'_{F1}\)

State

State in 2nd order LPF

v_str

F1_y

\(y_{F1}\)

State

Output of 2nd order LPF

v_str

F2_x1

\(x'_{F2}\)

State

State #1 in 2nd order lead-lag

v_str

F2_x2

\(x''_{F2}\)

State

State #2 in 2nd order lead-lag

v_str

LL1_x

\(x'_{LL1}\)

State

State in lead-lag

v_str

LL2_x

\(x'_{LL2}\)

State

State in lead-lag

v_str

WO_x

\(x'_{WO}\)

State

State in washout filter

v_str

omega

\(\omega\)

ExtState

Generator speed

p.u.

vsout

\(v_{sout}\)

Algeb

PSS output voltage to exciter

sig

\(S_{ig}\)

Algeb

Input signal

v_str

F2_y

\(y_{F2}\)

Algeb

Output of 2nd order lead-lag

v_str

LL1_y

\(y_{LL1}\)

Algeb

Output of lead-lag

v_str

LL2_y

\(y_{LL2}\)

Algeb

Output of lead-lag

v_str

Vks_y

\(y_{Vks}\)

Algeb

Gain output

v_str

WO_y

\(y_{WO}\)

Algeb

Output of washout filter

v_str

Vss

\(V_{ss}\)

Algeb

Voltage output before output limiter

tm

\(\tau_{m}\)

ExtAlgeb

Generator mechanical input

te

\(\tau_{e}\)

ExtAlgeb

Generator electrical output

v

\(V\)

ExtAlgeb

Bus (or busr, if given) terminal voltage

f

\(f\)

ExtAlgeb

Bus frequency

vi

\(v_{i}\)

ExtAlgeb

Exciter input voltage

Initialization Equations#

Name

Symbol

Type

Initial Value

F1_x

\(x'_{F1}\)

State

\(0\)

F1_y

\(y_{F1}\)

State

\(S_{ig}\)

F2_x1

\(x'_{F2}\)

State

\(0\)

F2_x2

\(x''_{F2}\)

State

\(y_{F1}\)

LL1_x

\(x'_{LL1}\)

State

\(y_{F2}\)

LL2_x

\(x'_{LL2}\)

State

\(y_{LL1}\)

WO_x

\(x'_{WO}\)

State

\(y_{Vks}\)

omega

\(\omega\)

ExtState

vsout

\(v_{sout}\)

Algeb

sig

\(S_{ig}\)

Algeb

\(u_{e} \left(V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW}}{(Sb/Sn)}\right)\)

F2_y

\(y_{F2}\)

Algeb

\(y_{F1}\)

LL1_y

\(y_{LL1}\)

Algeb

\(y_{F2}\)

LL2_y

\(y_{LL2}\)

Algeb

\(y_{LL1}\)

Vks_y

\(y_{Vks}\)

Algeb

\(K_{S} y_{LL2}\)

WO_y

\(y_{WO}\)

Algeb

\(x'_{WO} z_1^{LT_{WO}}\)

Vss

\(V_{ss}\)

Algeb

tm

\(\tau_{m}\)

ExtAlgeb

te

\(\tau_{e}\)

ExtAlgeb

v

\(V\)

ExtAlgeb

f

\(f\)

ExtAlgeb

vi

\(v_{i}\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

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

T (LHS)

F1_x

\(x'_{F1}\)

State

\(- A_{1} x'_{F1} + S_{ig} - y_{F1}\)

\(A_2\)

F1_y

\(y_{F1}\)

State

\(x'_{F1}\)

F2_x1

\(x'_{F2}\)

State

\(- A_{3} x'_{F2} - x''_{F2} + y_{F1}\)

\(A_4\)

F2_x2

\(x''_{F2}\)

State

\(x'_{F2}\)

LL1_x

\(x'_{LL1}\)

State

\(- x'_{LL1} + y_{F2}\)

\(T_2\)

LL2_x

\(x'_{LL2}\)

State

\(- x'_{LL2} + y_{LL1}\)

\(T_4\)

WO_x

\(x'_{WO}\)

State

\(- x'_{WO} + y_{Vks}\)

\(T_6\)

omega

\(\omega\)

ExtState

\(0\)

Algebraic Equations#

Name

Symbol

Type

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

vsout

\(v_{sout}\)

Algeb

\(V_{ss} u_{e} z_i^{OLIM} - v_{sout}\)

sig

\(S_{ig}\)

Algeb

\(- S_{ig} + u_{e} \left(V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_2^{SW} \left(f - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW} v^{dV/dt} + \frac{\tau_{e} s_3^{SW}}{(Sb/Sn)}\right)\)

F2_y

\(y_{F2}\)

Algeb

\(A_{4} A_{5} x'_{F2} + A_{4} x''_{F2} - A_{4} y_{F2} + A_{6} \left(- A_{3} x'_{F2} - x''_{F2} + y_{F1}\right) + \left(z_1^{LT_{F2}}\right)^{4} \left(- x''_{F2} + y_{F2}\right)\)

LL1_y

\(y_{LL1}\)

Algeb

\(T_{1} \left(- x'_{LL1} + y_{F2}\right) + T_{2} x'_{LL1} - T_{2} y_{LL1} + \left(z_1^{LT_{LL1}}\right)^{2} \left(- x'_{LL1} + y_{LL1}\right)\)

LL2_y

\(y_{LL2}\)

Algeb

\(T_{3} \left(- x'_{LL2} + y_{LL1}\right) + T_{4} x'_{LL2} - T_{4} y_{LL2} + \left(z_1^{LT_{LL2}}\right)^{2} \left(- x'_{LL2} + y_{LL2}\right)\)

Vks_y

\(y_{Vks}\)

Algeb

\(K_{S} y_{LL2} - y_{Vks}\)

WO_y

\(y_{WO}\)

Algeb

\(T_{5} z_0^{LT_{WO}} \left(- x'_{WO} + y_{Vks}\right) + T_{6} x'_{WO} z_1^{LT_{WO}} - T_{6} y_{WO}\)

Vss

\(V_{ss}\)

Algeb

\(L_{SMAX} z_u^{VLIM} + L_{SMIN} z_l^{VLIM} - V_{ss} + y_{WO} z_i^{VLIM}\)

tm

\(\tau_{m}\)

ExtAlgeb

\(0\)

te

\(\tau_{e}\)

ExtAlgeb

\(0\)

v

\(V\)

ExtAlgeb

\(0\)

f

\(f\)

ExtAlgeb

\(0\)

vi

\(v_{i}\)

ExtAlgeb

\(u_{e} v_{sout}\)

Services#

Name

Symbol

Equation

Type

ue

\(u_{e}\)

\(u u_{ee}\)

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

\(y_{L1}\)

State

State in lag transfer function

v_str

L2_y

\(y_{L2}\)

State

State in lag transfer function

v_str

WO_x

\(x'_{WO}\)

State

State in washout filter

v_str

LL1_x

\(x'_{LL1}\)

State

State in lead-lag

v_str

LL2_x

\(x'_{LL2}\)

State

State in lead-lag

v_str

LL3_x

\(x'_{LL3}\)

State

State in lead-lag

v_str

omega

\(\omega\)

ExtState

Generator speed

p.u.

vsout

\(v_{sout}\)

Algeb

PSS output voltage to exciter

sig

\(S_{ig}\)

Algeb

Input signal

v_str

sig2

\(S_{ig2}\)

Algeb

Input signal 2

v_str

IN

\(I_{N}\)

Algeb

Sum of inputs

v_str

WO_y

\(y_{WO}\)

Algeb

Output of washout filter

v_str

LL1_y

\(y_{LL1}\)

Algeb

Output of lead-lag

v_str

LL2_y

\(y_{LL2}\)

Algeb

Output of lead-lag

v_str

LL3_y

\(y_{LL3}\)

Algeb

Output of lead-lag

v_str

VSS_x

\(x_{VSS}\)

Algeb

Value before limiter

v_str

VSS_y

\(y_{VSS}\)

Algeb

Output after limiter and post gain

v_str

tm

\(\tau_{m}\)

ExtAlgeb

Generator mechanical input

te

\(\tau_{e}\)

ExtAlgeb

Generator electrical output

v

\(V\)

ExtAlgeb

Bus (or busr, if given) terminal voltage

f

\(f\)

ExtAlgeb

Bus frequency

vi

\(v_{i}\)

ExtAlgeb

Exciter input voltage

v2

\(V\)

ExtAlgeb

Bus (or busr2, if given) terminal voltage

f2

\(f_{2}\)

ExtAlgeb

Bus frequency 2

Initialization Equations#

Name

Symbol

Type

Initial Value

L1_y

\(y_{L1}\)

State

\(K_{1} S_{ig}\)

L2_y

\(y_{L2}\)

State

\(K_{2} S_{ig2}\)

WO_x

\(x'_{WO}\)

State

\(I_{N}\)

LL1_x

\(x'_{LL1}\)

State

\(y_{WO}\)

LL2_x

\(x'_{LL2}\)

State

\(y_{LL1}\)

LL3_x

\(x'_{LL3}\)

State

\(y_{LL2}\)

omega

\(\omega\)

ExtState

vsout

\(v_{sout}\)

Algeb

sig

\(S_{ig}\)

Algeb

\(V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW}}{(Sb/Sn)}\)

sig2

\(S_{ig2}\)

Algeb

\(V s_5^{SW2} + s_1^{SW2} \left(\omega - 1\right) + s_4^{SW2} \left(\tau_{m} - \tau_{m0}\right) + \frac{\tau_{m0} s_3^{SW2}}{(Sb/Sn)}\)

IN

\(I_{N}\)

Algeb

\(u_{e} \left(y_{L1} + y_{L2}\right)\)

WO_y

\(y_{WO}\)

Algeb

\(x'_{WO} z_1^{LT_{WO}}\)

LL1_y

\(y_{LL1}\)

Algeb

\(y_{WO}\)

LL2_y

\(y_{LL2}\)

Algeb

\(y_{LL1}\)

LL3_y

\(y_{LL3}\)

Algeb

\(y_{LL2}\)

VSS_x

\(x_{VSS}\)

Algeb

\(y_{LL3}\)

VSS_y

\(y_{VSS}\)

Algeb

\(L_{SMAX} z_u^{lim_{VSS}} + L_{SMIN} z_l^{lim_{VSS}} + x_{VSS} z_i^{lim_{VSS}}\)

tm

\(\tau_{m}\)

ExtAlgeb

te

\(\tau_{e}\)

ExtAlgeb

v

\(V\)

ExtAlgeb

f

\(f\)

ExtAlgeb

vi

\(v_{i}\)

ExtAlgeb

v2

\(V\)

ExtAlgeb

f2

\(f_{2}\)

ExtAlgeb

Differential Equations#

Name

Symbol

Type

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

T (LHS)

L1_y

\(y_{L1}\)

State

\(K_{1} S_{ig} - y_{L1}\)

\(T_1\)

L2_y

\(y_{L2}\)

State

\(K_{2} S_{ig2} - y_{L2}\)

\(T_2\)

WO_x

\(x'_{WO}\)

State

\(I_{N} - x'_{WO}\)

\(T_4\)

LL1_x

\(x'_{LL1}\)

State

\(- x'_{LL1} + y_{WO}\)

\(T_6\)

LL2_x

\(x'_{LL2}\)

State

\(- x'_{LL2} + y_{LL1}\)

\(T_8\)

LL3_x

\(x'_{LL3}\)

State

\(- x'_{LL3} + y_{LL2}\)

\(T_{10}\)

omega

\(\omega\)

ExtState

\(0\)

Algebraic Equations#

Name

Symbol

Type

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

vsout

\(v_{sout}\)

Algeb

\(u_{e} y_{VSS} z_i^{OLIM} - v_{sout}\)

sig

\(S_{ig}\)

Algeb

\(- S_{ig} + V s_5^{SW} + s_1^{SW} \left(\omega - 1\right) + s_2^{SW} \left(f - 1\right) + s_4^{SW} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW} v^{dv} + \frac{\tau_{e} s_3^{SW}}{(Sb/Sn)}\)

sig2

\(S_{ig2}\)

Algeb

\(- S_{ig2} + V s_5^{SW2} + s_1^{SW2} \left(\omega - 1\right) + s_2^{SW2} \left(f_{2} - 1\right) + s_4^{SW2} \left(\tau_{m} - \tau_{m0}\right) + s_6^{SW2} v^{dv2} + \frac{\tau_{e} s_3^{SW2}}{(Sb/Sn)}\)

IN

\(I_{N}\)

Algeb

\(- I_{N} + u_{e} \left(y_{L1} + y_{L2}\right)\)

WO_y

\(y_{WO}\)

Algeb

\(T_{3} z_0^{LT_{WO}} \left(I_{N} - x'_{WO}\right) + T_{4} x'_{WO} z_1^{LT_{WO}} - T_{4} y_{WO}\)

LL1_y

\(y_{LL1}\)

Algeb

\(T_{5} \left(- x'_{LL1} + y_{WO}\right) + T_{6} x'_{LL1} - T_{6} y_{LL1} + \left(z_1^{LT_{LL1}}\right)^{2} \left(- x'_{LL1} + y_{LL1}\right)\)

LL2_y

\(y_{LL2}\)

Algeb

\(T_{7} \left(- x'_{LL2} + y_{LL1}\right) + T_{8} x'_{LL2} - T_{8} y_{LL2} + \left(z_1^{LT_{LL2}}\right)^{2} \left(- x'_{LL2} + y_{LL2}\right)\)

LL3_y

\(y_{LL3}\)

Algeb

\(T_{9} \left(- x'_{LL3} + y_{LL2}\right) + T_{10} x'_{LL3} - T_{10} y_{LL3} + \left(z_1^{LT_{LL3}}\right)^{2} \left(- x'_{LL3} + y_{LL3}\right)\)

VSS_x

\(x_{VSS}\)

Algeb

\(- x_{VSS} + y_{LL3}\)

VSS_y

\(y_{VSS}\)

Algeb

\(L_{SMAX} z_u^{lim_{VSS}} + L_{SMIN} z_l^{lim_{VSS}} + x_{VSS} z_i^{lim_{VSS}} - y_{VSS}\)

tm

\(\tau_{m}\)

ExtAlgeb

\(0\)

te

\(\tau_{e}\)

ExtAlgeb

\(0\)

v

\(V\)

ExtAlgeb

\(0\)

f

\(f\)

ExtAlgeb

\(0\)

vi

\(v_{i}\)

ExtAlgeb

\(u_{e} v_{sout}\)

v2

\(V\)

ExtAlgeb

\(0\)

f2

\(f_{2}\)

ExtAlgeb

\(0\)

Services#

Name

Symbol

Equation

Type

ue

\(u_{e}\)

\(u u_{ee}\)

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',)