Stabilizer Transfer Functions

 

As indicated previously, each of these stabilizer models have a unique transfer function.  The schematic diagram of each is given below.

Single Input Power System Stabilizer (PSS1A)

 

 

Where,

 

A1, A2  =

Filter constants

KS  =

PSS gain [pu]

T1  =

First Lead time constant [s]

T2  =

First Lag time constant [s]

T4  =

Second Lag time constant [s]

T3  =

Second Lead time constant [s]

T5  =

Washout time constant [s]

T6  =

Transducer time constant [s]

VRMAX, VRMIN  =

Maximum and minimum regulator outputs [pu]

VS1  =

Input

VST  =

Output [pu]

VSTMAX, VSTMIN  =

PSS output maximum and minimum limits [pu]

 

 Dual Input Power System Stabilizer (PSS2B)

 

 

 

Where,

 

KS1  =

PSS gain [pu]

KS2  =

Second signal gain [pu]

KS3  =

Second signal second gain [pu]

M, N  =

Integer Filter Constants

T1  =

First lead time constant [s]

T2  =

First lag time constant [s]

T3  =

Second lead time constant [s]

T4  =

Second lag time constant [s]

T5  =

Third lag time constant [s]

T6  =

First signal transducer time constant [s]

T7  =

Second signal transducer time constant [s]

T8  =

Filter lead time constant [s]

T9  =

Filter lag time constant [s]

T10  =

Third lead time constant [s]

T11  =

PSS lag compensating time constant [s]

TW1  =

First signal first washout time [s]

TW2  =

First signal second washout time [s]

TW3  =

Second signal first washout time [s]

TW4  =

Second signal second washout time [s]

VSI1, VSI2  =

Inputs [pu]

VSI1MAX , VSI1MIN  =

First signal maximum and minimum inputs [pu]

VSI2MAX , VSI2MIN  =

Second signal maximum and minimum inputs [pu]

VST  =

Output [pu]

VSTMAX, VSTMIN  =

PSS output Maximum and minimum limits [pu]

 

Dual Input Power System Stabilizer (PSS3B)

 

 

 

Where,

 

A1, A2, A3, A4,
A
5, A6, A7 A8  =

Filter coefficients [s]

KS1  =

First input signal gain [pu]

KS2  =

Second input signal gain [pu]

T1  =

First transducer time constant [s]

T2  =

Second transducer time constant [s]

TW1  =

First signal washout time constant [s]

TW2  =

Second signal washout time constant [s]

TW3  =

Washout time constant [s]

VSI1, VSI2  =

Inputs [pu]

Output [pu]

VSTMAX, VSTMIN  =

PSS output maximum and minimum limits [pu]

 

Dual Input Power System Stabilizer (PSS4B)

PSS4B (1992):

 

 

 

Where,

 

2H  =

Synchronous machine inertia constant [s]

KS1  =

First signal gain [pu]

KS2  =

Second signal gain [pu]

M  =

Synchronous machine inertia constant

T0  =

System start-up time constant [s]

T1  =

First transducer time constant [s]

T2  =

First signal washout time constant [s]

T3  =

Second transducer time constant [s]

T4  =

Second signal washout time constant [s]

VS2, VS3  =

Inputs

VST  =

Output [pu]

VSTMAX, VSTMIN  =

PSS output maximum and minimum limits [pu]

 

PSS4B (2005):

 

 

 

Where,

 

BWI  =

3dB bandwidth of the notch filter [Hz]

H  =

Inertia constant [s]

KH  =

Gain in common branch [pu]

KH1  =

Gain in positive branch [pu]

KH2  =

Gain in negative branch [pu]

KH11  =

Proportional gain in first block [pu]

KH17  =

Proportional gain in first block [pu]

KI  =

Gain in common branch [pu]

KI1  =

Gain in positive branch [pu]

KI2  =

Gain in negative branch [pu]

KI11  =

Proportional gain in first block [pu]

KI17  =

Proportional gain in first block [pu]

KL  =

Gain in common branch [pu]

KL1  =

Gain in positive branch [pu]

KL2  =

Gain in negative branch [pu]

KL11  =

Proportional gain in first block [pu]

KL17  =

Proportional gain in first block [pu]

TH1  =

Derivative time constant in first block [s]

TH2  =

Lag time constant in first block [s]

TH3  =

Lead time constant in second block [s]

TH4  =

Lag time constant in second block [s]

TH5  =

Lead time constant in third block [s]

TH6  =

Lag time constant in third block [s]

TH7  =

Derivative time constant in first block [s]

TH8  =

Lag time constant in first block [s]

TH9  =

Lead time constant in second block [s]

TH10  =

Lag time constant in second block [s]

TH11  =

Lead time constant in third block [s]

TH12  =

Lag time constant in third block [s]

TI1  =

Derivative time constant in first block [s]

TI2  =

Lag time constant in first block [s]

TI3  =

Lead time constant in second block [s]

TI4  =

Lag time constant in second block [s]

TI5  =

Lead time constant in third block [s]

TI6  =

Lag time constant in third block [s]

TI7  =

Derivative time constant in first block [s]

TI8  =

Lag time constant in first block [s]

TI9  =

Lead time constant in second block [s]

TI10  =

Lag time constant in second block [s]

TI11  =

Lead time constant in third block [s]

TI12  =

Lag time constant in third block [s]

TL1  =

Derivative time constant in first block [s]

TL2  =

Lag time constant in first block [s]

TL3  =

Lead time constant in second block [s]

TL4  =

Lag time constant in second block [s]

TL5  =

Lead time constant in third block [s]

TL6  =

Lag time constant in third block [s]

TL7  =

Derivative time constant in first block [s]

TL8  =

Lag time constant in first block [s]

TL9  =

Lead time constant in second block [s]

TL10  =

Lag time constant in second block [s]

TL11  =

Lead time constant in third block [s]

TL12  =

Lag time constant in third block [s]

vHMAX, vHMIN  =

Maximum and minimum limits [pu]

vIMAX, vIMIN  =

Maximum and minimum limits [pu]

vLMAX, vLMIN  =

Maximum and minimum limits [pu]

vST   =

Output [pu]

vSTMAX, vSTMIN  =

PSS output maximum and minimum limits [pu]

WNI  =

Tuned frequency of the notch filter [Hz]

 

Transient Excitation Booster with Dual Action Terminal Voltage Limiter (DEC1A)

 

 

 

Where,

 

ESC  =

Speed change reference [pu]

KAN  =

Integrator gain [pu]

KETL  =

Terminal voltage limiter gain [pu]

TAN  =

Integrator time constant [s]

TD  =

Reset delay time [s]

TL1  =

Voltage limiter lead time [s]

TL2  =

Voltage limiter lag time [s]

TW5  =

DEC washout time constant [s]

VA  =

Regulator internal voltage [pu]

VAL  =

Regulator voltage reference [pu]

VAN  =

Internal signal

VANMAX  =

Integrator maximum limit [pu]

VOMAX, VOMIN  =

Terminal voltages maximum and minimum deviation over reference [pu]

VO, VP  =

Limiter signals [pu]

VS  =

Output [pu]

VSMAX, VSMIN  =

PSS plus DEC maximum and minimum limits [pu]

VST  =

Power system stabilizer output [pu]

VT  =

Synchronous machine terminal voltage input [pu]

VTC =

Terminal voltage level reference [pu]

vTM, vTN  =

Bang-Bang controller maximum and minimum limits [pu]

VTLMT  =

Terminal voltage reference [pu]

W  =

Speed input [pu]

 

Open Loop Transient Excitation Booster (DEC2A)

 

 

 

Where,

 

TD1  =

Controller time constant [s]

TD2  =

DEC washout time constant [s]

VD  =

Discontinuous controller internal voltage

VDMAX, VDMIN  =

DEC maximum and minimum limits [pu]

VK  =

Trigger signal amplitude [pu]

VS  =

Output [pu]

VST  =

Power system stabilizer output [pu]

VT  =

Synchronous machine terminal voltage input [pu]

VTLIMIT  =

Terminal voltage maximum limit [pu]

 

Temporary Interrupter of Stabilizing Signal (DEC3A)

 

 

 

Where,

 

TDR  =

Reset time delay [s]

VS  =

Output [pu]

VST  =

Power system stabilizer output [pu]

VT  =

Synchronous machine terminal voltage input [pu]

VTMIN  =

Controller input reference [pu]

 

 

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