PSS Tuning

7/21/2019 PSS Tuning

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Tuning of PowerSystem Stabilizer



Why PSS?

Exciters which are essential for maintaining steady statestability, transient stability and fast control of terminal voltagecan contribute to oscillatory instability in power system

This type of instability can endanger system security and limit

power transfer

The Major factors that contribute to Oscillatory instability are : Generator or tie line loading

Transfer capability of the transmission line ower factor of the generator !"# gain



Why PSS?

Block diagram representation for small signal performance

of system with AVR and Exciter



Why PSS?

Case study:

$or a specific case, the parameters of a system with a thyristor

exciter and system conditions such that K 5 is negative are as

follows:

%&'&()*& %+'&() %,'-( %.'&(/ T, '&(*& %)'0-(&+

%1'-( T#'-(-+ Gex2s3 ' % ! 4'(- %5'-(-

%) is negative for high values of external system reactance andhigh generator outputs



Why PSS?amping and !ynchroni"ing tor#ue components at the rotor

$scillation %re#uency:

!ssumed rotor oscillation fre6uency is &- rad7s

The net 8ynchroni9ing tor6ue coefficient is %s'&(/&. pu tor6ue7rad

The damping tor6ue coefficient is %5 ' 0&+(+ pu tor6ue7pu speed

change

Thus, there is negative damping which results in Oscillatory

instability of system

r E T ω δ ∆−∆=∆ 27.128714.1



KA K s(∆ψfd) K s= K 1+ K s(∆ψfd) K D(∆ψfd)

- 0-(--+) &()//) &(+

&- 0-(--* &()/& -(1&.

&) 0-(--* &()/& -(-+.

)- -(--+* &()** 0.(-*-

&-- -(-/+ &(11*+ 0/(/11

+-- -(+/-. &(/&. 0&+(++

Effect of the !"# on %s and %5 at ; '&- rad7s for different

values of !"# gain % !

$rom the table it can be seen that as the !"# gain increases the

damping becomes negative which ma<es the system Oscillatory

instable



Introduction to PSS

The basic intent of adding a ower 8ystem 8tabili9er is to

enhance damping by controlling its excitation using auxiliary

stabili9ing signal, thus extending power transfer limits

This is done by providing a component of electrical tor6ue in

phase with the rotor speed deviations



Structure and Tuning of PSS

Block Diaghram of PSS



Wash out Circuit

rovided to eliminate steady state bias in the output of

88 which will modify the generator terminal voltage =s expected to respond only to transient variations in the

input signal and not to the dc offsets in the signal



Wash out circuit:!election of time constant & ' w (:

>ash out circuit acts essentially as a high pass filter and itmust pass all fre6uencies that are of interest

=f only local mode are of interest, the time constant ' w can bechosen in the range of & to +

=f inter area modes are also to be damped, then 'w must bechosen in the range of &- to +-

There is also noticeable improvement in the first swing stabilitywhen ' w is increased from &() to &-



Dynamic Compensator rovided to compensate for phase lag

Transfer function of 5ynamic compensator with two lead0lag

stages which is used in the industry is

)1)(1(

)1)(1()(

42

31

sT sT

sT sT K sT

s

++

++=

K s is the gain of PSS ,

i!e "onstants 1 to 4 a#e "hosen to $#o%ide a $hase &ead fo# the

in$'t signa& in the #ange of f#e'en"ies that a#e of inte#est (.1 to

3. *)

%or design purposes) the *!! transfer function is approximated to

'&s() the transfer function of the dynamic compensator



Dynamic Compensator he $&ots of the $hase ang&e of the one stage &ead &ag

"o!$ensato# -ith %a#iation in f#e'en" a#e sho-n /e&o- fo#diffe#ent %a&'es of the "ent#e f#e'en" f c defined /

212

1

T T f c

π

=

Depending on phase compensation required f c and n are selected



System With PSS

Block diagram representation for small signal performance

of system with AVR and *!!



Dynamic Compensator!election of time Constants:

!s in practice both the generator and the exciter exhibit

fre6uency dependent gain and phase characteristics, 88

transfer function Gpss2s3, should provide phase compensation

between the exciter input and the electrical tor6ue

To provide pure damping tor6ue at all fre6uencies, ideally the

phase characteristics of 88 must balance the phase

characteristics of the plant transfer function 2GE2s33 at allfre6uencies, which is not practical



Dynamic Compensator

'he following design criteria is used for phasecompensation of *!!

The compensated phase lag 2phase of 2s3 'GE2s3 882s33should pass through *- degrees at fre6uency around () 492for fre6uency input signal this can be reduced to +(- 4?3

The compensated phase lag at local mode fre6uency shouldbe below .) degrees, preferably near +- degrees

The gain of the compensator at high fre6uencies2 which isproportional to T&T+7T,T.3 should be minimi9ed



Dynamic Compensator

!election of gain:

#oot locus analysis is performed and the optimal 88 gainis chosen for the particular tuning condition as the gain thatresults in maximum damping of the least damped mode

$rom the studies carried out in @A, the optimal gain 2%opt3 isrelated to the value of the gain 2%=3 that results in instability

%or speed input sta+ili"ers K opt ,-./ K 0

%or fre#uency input sta+ili"ers K opt ,1./ K = %or power input sta+ili"ers K opt ,-.2 K 0



Torsional ilter

Torsional $ilter in the 88 is essentially a band reject or a low

pass filter to attenuate the first torsional mode fre6uency(

The transfer function of the filter can be expressed as

22

2

2

)(nn

n

s s

s FILT

ω ζω

ω

++

=



Torsional ilter

'he criteria for designing of the torsional filter are:

The maximum possible change in damping of any

torsional mode is less than some fraction of the inherent

torsional damping

The phase lag of the filter in the fre6uency range of & to

49 is minimi9ed



!imiter: >hen load rejection ta<es place, the !"# acts to reduce the terminal

voltage whereas 88 action calls for higher value of the terminal voltage

Bimiter limits the output of the 88 to prevent the 88 counter the action

of !"#

Cegative limit of 88 output is of importance during bac< swing of therotor 2 after the initial acceleration is over3

88 action in the negative direction must be curtailed more than in the

positive direction

Ontario hydro uses 0-(-) p(u as the lower limit and -(& to -(+ as the higher

limit



"#ample:

! synchronous generator is connected to an infinite bus throughan external reactance xe'-(. pu( The generator is initially

supplying power of & p(u with terminal voltage at &(- pu( The

infinite bus voltage is &(-( ! static exciter with a single time

constant !"# is considered 2%E'+--, TE'-(-)3( 5esign a speed

input 88 to damp local modes(The machine data: xd'&(1, x6'&()), xd

D '-(+ , Td-D'1(-,

4' ), 5'-, f '1- 49

!ol : The initial conditions and %& to %1 are calculated from the

operating point



The phase angle of GE2s3 as a function of ; is shown below

The phase angle decreases as fre6uency increases( !t therotor oscillation of about rad7sec, the phase lag is )o ( !t

the cut off fre6uency of () 49 2++ rad7sec3, the phase lag is

around &+-o

hase angle of GE2j;3 "s $re6uency



! compensator transfer function

2

1

1

)1()(

sT

sT K sT s

+

+=

>ith a centre fre6uency of () 49 is selected( The maximum

Bead 2which occurs at () 493 is selected as - deg so that the

Fompensated phase lag is *- deg at () 49( The ratio of n'T&7T+

has to satisfy tan-1 T1ωc – tan-1 T2ωc = 30o

where

nT T T f cc

221

112 === π ω

o

n

n 3)1

tantan 11

=−−−



The solution of above e6uation is n'( The time constants are

selected as

T&'-(-/ s, T+'-(-+1 s

The phase angle of the compensator is shown below

The phase lead provided by the 88 at the rotor oscillation

fre6uency is around &*o( This results in compensated phase lag

of about &1o at rad7s(

Phase angle of Compensator T(jω)



The phase angle of the compensated phase 2 '&s(3E*&s( (

is shown below

The washout crcut tme constant s T w s selecte! as

2"0 s as the P## s manl$ !esgne! for !ampng localmo!es of fre%uenc$ aroun! 1 &'

Fompensated phase angle "s fre6uency



!election of gain & K s (:

4ethod -:

The loci of two roots 2eigen values3, one corresponding to the

local 2rotor3 mode and the other corresponding to exciter mode as

gain K s is varied are shown in below figure

#oot Boci with variation in stabili9er gain



The root corresponding to the local mode moves to the left as

%s increases from 9ero and for higher 88 gain, the fre6uency

of oscillation continues to decrease until the complex root splitsinto two real parts(

The root corresponding to exciter mode moves to the right and

crosses imaginary axis at around %s'.

The optimum value of gain %s is the value at which the critical

mode is maximum damped( =n this case value of %s'&1

4ethod 1:

The value of gain' %s2at which system is unstable3 7 +)



The plot of the variation of angle of GE2j;3 for four different

operating conditions is shown in fig

$peration of *!! for different operating conditions:

"ariation of hase of GE2j;3 for different operating conditions



$rom the above fig( it can be seen that the phase lag of GE2j;3

is maximum for full load 2g'&(-3 and strong system 2xe'-(.3

conditions( 4ence 88 designed for the operating conditions

g'&(-, xe'-(. is expected to operate satisfactorily at other

operating conditions



$peration of PSS for !argedisturbance The data of the above example is ta<en for simulation of a

phase at the generator terminals( The limits on 88 output areH-(-) and limits on Efd are H1(- ( The fault is cleared in . cycles(

!ssuming the post fault system condition identical to prefault

system( The results of the simulation with and without 88 are

shown below

otor angle thout P## otor angle th P##



%eferences P#a/ha K'nd'#, 0Po-e# Sste! Sta/i&it and ont#o&,

(oo), ata 5"6#a-*i&&, 27

K Padia#, 0 Power Sstem Sta!ilit and "ontrol , (oo),

S P'/&i"ations, 29

:.;. <a#sen and D.A. S-ann, 0 #ppling Power Sstem

Sta!ili$ers% part I%II and III , ::: #ans. ;o&. PAS1,, $$.

317349, >'ne 1?81

P.K'nd'#, 5.K&ein, 6.>. oge#s and 5.S. @!o,

0A$$&i"ation of $o-e# sste! sta/i&ie#s fo# enhan"e!entof o%e#a&& sste! sta/i&it, ::: #ans. on Po-e#

Sste!s, ;o&. 4, o. 2, $$. 914929, 5a 1?8?



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PSS Tuning

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