Final PptRAMANA

7/23/2019 Final PptRAMANA

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FUZZIFIED MULTIOBJECTIVE PSO FORCEED WITH VOLTAGE STABILITY

CONSTRAINT

Under the esteemed guidance ofDr.N.Subrahmanyam

byB.RAMANA APPARAO

(061717)


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Objectives of the Project Work

To solve bas! "!onom! #oa$ Ds%a&!h Problem '&h uel !os&mnma&on as ob*e!&ve +un!&on usn, PSO.

To solve "msson Ds%a&!h Problem '&h "mssonmnma&on as ob*e!&ve +un!&on usn, PSO.

To solve Rea!&ve Po'er Ds%a&!h Problem '&h A!&ve Po'erloss mnma&on as ob*e!&ve +un!&on usn, PSO. To solve Po'er Ds%a&!h Problem '&h S&abl&y -n$e as

ob*e!&ve +un!&on usn, PSO.

To solve mul&ob*e!&ve %roblem usn, +u+e$ PSO


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OVERVIEW OF THE PROJECT

-n&ro$u!&on Par&!le S'arm O%&ma&on "!onom! Ds%a&!h /sn, PSO "msson Ds%a&!h /sn, PSO Rea!&ve Po'er Ds%a&!h /sn, PSO ol&a,e S&abl&y -m%rovemen& /sn, PSO u+e$ PSO +or Mul&ob*e!&ve Problem on!lusons Re+eren!es


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INTRODUCTION

Po'er sys&em shoul$ be o%era&e$ su!h a +ashon &ha& smul&aneously realan$ rea!&ve %o'er s o%&me$. Real %o'er o%&ma&on %roblem s &he &ra$&onal e!onom! $s%a&!h 'h!h

mnmes &he real %o'er ,enera&on !os&

Rea!&ve %o'er shoul$ be o%&me$ &o %rov$e be&&er vol&a,e %ro+le as 'ellas &o re$u!e &o&al sys&em &ransmsson loss. Thus &he ob*e!&ve o+ rea!&ve%o'er o%&ma&on %roblem !an be seen as mnma&on o+ real Po'er lossover &he &ransmsson lnes.

vol&a,e s&abl&y n$e has be!ome an m%or&an& &as2 +or many vol&a,es&abl&y s&u$es. These n$!es %rov$e relable n+orma&on abou& %rom&y

o+ vol&a,e ns&abl&y n a %o'er sys&em. /sually3 &her values !han,esbe&'een 0 (no loa$) an$ 1 (vol&a,e !olla%se).


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INTRODUCTION

On &he o&her han$ &hermal %o'er %lan&s ('h!h !on&rbu&e ma*or %ar& o+ele!&r! %o'er ,enera&on) !rea&e envronmen&al %ollu&on by em&&n,&o! ,ases su!h as !arbon $o$e (O4)3 sul%hur $o$e (SO4)3n&ro,en o$es (NO)

The +our ob*e!&ves o+ mnma&on o+ +uel !os& 3 mnma&on o+ emsson3

mnma&on o+ losses an$ mnma&on o+ sys&em s&abl&y n$e are!on+l!&n, an$ non !ommensurable

Assumn, &he $e!son ma2er (DM) has m%re!se or +uy ,oals o+sa&s+yn, ea!h o+ &he ob*e!&ves3 &he mul&ob*e!&ve %roblem !an be+ormula&e$ as a +uy sa&s+a!&on mama&on %roblem 'h!h s bas!ally amnma %roblem.

The &ra$e o++ solu&on s ob&ane$ usn, +uy mnma a%%roa!h a+&er &hen$v$ual ob*e!&ves are mnme$ usn, Par&!le S'arm O%&ma&on(PSO) 'h!h s a %o%ula&on base$ s&o!has&! o%&ma&on &e!hn5ue


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PARTICLE SWARM OPTIMIZATION

PSO smula&es &he behavour o+ br$ +lo!2n,

Su%%ose a ,rou% o+ br$s are ran$omly sear!hn, +oo$ n an area

There s only one %e!e o+ +oo$ n &he area ben, sear!he$

All &he br$s $o no& 2no' 'here &he +oo$ s

Bu& &hey 2no' ho' +ar &he +oo$ s n ea!h &era&on

So 'ha&s &he bes& s&ra&e,y &o +n$ &he +oo$ The e++e!&ve one s &o +ollo' &he br$ 'h!h s neares& &o &he

+oo$.


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ECONOMIC DISPATCH USING PSO

(1) PROBLEM FORMULATION

Objective Function:

The ob*e!&ve o+ "D %roblem s &o mnme &he &o&al ,enera&on !os&o+ a %o'er sys&em over some a%%ro%ra&e %ero$3 'hle sa&s+yn, varous!ons&ran&s.

The e!onom! $s%a&!h %roblem s a !ons&rane$ o%&ma&on%roblem an$ & !an be ma&hema&!ally e%resse$ as +ollo's8

Mnme

T9To&al !os& o+ ,enera&on (Rs:hr) n 9 Number o+ ,enera&ors P 9 Real %o'er ,enera&on o+ &h ,enera&or

9 uel !os& +un!&on o+ &h ,enera&or

( )n

T i i

i=1

F = F P


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The ,enera&on !os& +un!&on s usually e%resse$ as a 5ua$ra&! +un!&on o+

real %o'er ,enera&on

'here3 a , ban$!are +uel !os& !oe++!en&s

Equality Constraint:

'here3 PD 8 &o&al sys&em $eman$ (MW)

PL 8 &ransmsson loss o+ &he sys&em (MW)

n n2

T i i i i i i i

i=1 i=1

F = F (P )= a +b P +c P

n

i D L

i=1

P =P +P


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Inequality Constraint

Pmn 8 mnmum %o'er ou&%u& lm& o+ &h ,enera&or (M;)

Pma. 8 mamum %o'er ou&%u& lm& o+ &h ,enera&or (M;)

Net!or" Losses

'here3 Bijare !ons&an&s !alle$ B!oe++!en&s or loss !oe++!en&s

Evaluation Function8

n n

L i ij j i i0 00i=1 i=1 i

P = P B P + P B + B

imin i imax

P P P

1

1

1

n

i D loss

i

D

f

P P P

kP

=

= +


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(2)AL#ORIT$M

1. Rea$ &he sys&em $a&a (1) 4. Se& &era&on !oun&91.


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. Mo$+y &he member velo!&y Vo+ ea!h n$v$ual a!!or$n, &o

vi!"#$% &$ vi! c"$rand"$%'besti ( i) ! c*$rand*$%gbesti ( i))

i!"# i! vi!"

C. -+ vi!"Vma3 &hen vi!"9 Vmaan$ + vi!"(Vma3 &hen vi!"9 (Vma).

10. Mo$+y &he member %os&on o+ ea!h n$v$ual P a!!or$n, &o

Par(2E1)9Par(2)E(2E1)

11. -n!remen& &era&on !oun& by 1.-+ &he number o+ &era&ons rea!hes &hemamum3&hen ,o &o S&e% 1


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() CA%E %TU&IE% AN& RE%ULT%

()+ -. bus s/stem8

The PSO %arame&ers use$ n &hs !ase s&u$y are8

No o+ %ar&!les 9 60

learnn, +a!&ors !194.0?3 !494.0?

'e,h& +a!&or '91.4 !ons&r!&on +a!&or F90.7C4? G

Mamumnumber o+ &era&ons9100

Mnmum o+ all &he 4? n$e%en$en& runs8

0.27236910.583711381.671279806.498033

!abi"i!# $n%&xL' (*)+mii'n (,/)F&" '! (/)


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To&al Sys&em ,enera&on 94C


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0 10 20 30 40 50 60 70 80 90 100

0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

Iterations

Losses Vs Iterations

0 10 20 30 40 50 60 70 80 90 100310

320

330

340

350

360

370

380

390

Iterations

EmisioninKg/hr

Emission Vs Iterations

Total syste* losses Total E*ission release

!EEE " #us $yste%


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()+ 01 bus s/stem:

6.18832736.141642148.67573752.445076

!abi"i!# $n%&xL' (*)+mii'n (,/)F&" '! (/)

*ini*u* o' all +, in-e.en-ent runs

&otal $yste% 'eneration 122*+,1+,2-W


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0 10 20 30 40 50 60 70 80 90 100752

753

754

755

756

757

758

759

760

Iterations

costin$/hr

Cost Vs Iterations for IEEE 57 bus system

0 10 20 30 40 50 60 70 80 90 100146.5

147

147.5

148

148.5

149

Iterations

Emisioninkg/hr

Emission vs Iterations for IEEE 57 bus sysetm

0 10 20 30 40 50 60 70 80 90 100

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Iterations

LossesinP.U


Total 'uel Cost versus iterations

Total E*ission release

Total syste* losses

!EEE . #us$yste%


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EMISSION DISPATCH USING PSO

Thermal %o'er %lan&s ('h!h !on&rbu&e ma*or %ar& o+ ele!&r! %o'er

,enera&on) !rea&e envronmen&al %ollu&on by em&&n, &o! ,ases su!has !arbon $o$e (O4)3 sul%hur $o$e (SO4)3 n&ro,en o$es (NO)

The emsson +un!&on !an be e%resse$ as &he sum o+ all &y%es o+emssons su!h as NOH3 SO43 %ar&!ula&e ma&erals an$ &hermal ra$a&on

'&h su&able %r!n, +or ea!h %ollu&an& em&&e$.

-n &hs %ro*e!& only NOHemsson s &a2en n&o a!!oun&3 sn!e & s more

harm+ul &han o&her %ollu&an&s.


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/+0 PROBLEM FORMULATION

Objective Function

The ob*e!&ve o+ emsson $s%a&!h s &o mnme &he &o&alenvronmen&al $e,ra$a&on or &he &o&al %ollu&an& emsson $ue &o &he burnn, o++uels +or %ro$u!&on o+ %o'er &o mee& &he loa$ $eman$ .

The emsson $s%a&!h %roblem !an be $e+ne$ as &he +ollo'n, o%&ma&on%roblem

8 &o&al emsson release (F,:hr)

2i, 3i, 4 8 emsson !oe++!en&s o+ &he ith,enera&n, un&

2

1

n

i i i i i

i

Minimize E P P =

= + +


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Sub*e!& &o $eman$ !ons&ran&s

Evaluation Function

'here3 s a s!aln, !ons&an& ( 9 ?0 n &hs s&u$y).

n

i D L

i=1

P =P +P

imin i imaxP P P

1

1

1

n

i D loss

i

D

f

P P P

k P=

=

+


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(2) CA%E %TU&IE% AN& RE%ULT%

()+ -. bus s/stem8 The PSO %arame&ers use$ n &hs !ase s&u$y are8

No o+ %ar&!les9 60

learnn, +a!&ors !194.0?3 !494.0?

'e,h& +a!&or '91.4

!ons&r!&on +a!&or F90.7C4? G

Mamum number o+ &era&ons9100

Mnmum o+ all &he 4? n$e%en$en& runs8

0.2670704.404039229.144834932.094511

!abi"i!# $n%&xL' (*)+mii'n (,/)F&" '! (/)


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Sys&em ,enera&on 947.0=0


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0 10 20 30 40 50 60 70 80 90 100860

870

880

890

900

910

920

930

940

Iterations

Costin$/hr

Cost Vs Iterations

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Iterations

Loss

Loss Vs Iterations

Total 'uel cost Total syste* losses

!EEE " #us$yste%


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()+ 01 bus s/stem:

6.6708523.525670144.904969767.669895

!abi"i!# $n%&xL' (*)+mii'n (,/)F&" '! (/)

*ini*u* o' all +, in-e.en-entruns

&otal $yste% 'eneration 1,,"*"2+."-W


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0 10 20 30 40 50 60 70 80 90 100144.5

145

145.5

146

146.5

147

147.5

Iterations

em

issionKg/h

r

Emission release IEEE 57 bus system

Total E*ission release versus Iterations 'or IEEE ,1 Bus syste*


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REACTIVE POWER OPTIMISATION USING PSO

The %ur%ose o+ Rea!&ve Po'er Ds%a&!h s manly &o m%rove &he vol&a,e%ro+le n &he sys&em an$ &o mnme &he real %o'er &ransmsson loss 'hlesa&s+yn, &he un& an$ sys&em !ons&ran&s.

Ths ,oal s a!heve$ by %ro%er a$*us&men& o+ rea!&ve %o'er !on&rolvarables l2e Ienera&or bus vol&a,e ma,n&u$es (,)3 &rans+ormer &a%se&&n,s (&)3 rea!&ve %o'er ,enera&on o+ &he !a%a!&or ban2 (J!).


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REACTIVE POWER OPTIMISATION

USING PSO(1)PROBLEM FORMULATION

Objective Function

The ob*e!&ve o+ RPD s &o $en&+y &he rea!&ve %o'er !on&rolvarables3 'h!h mnmes &he real %o'er loss (Ploss) o+ &he sys&em

)c'2(min 2

1 1

2

1

ijViVjVjVigijPFtNbus

i

Nbus

j

Nline

k

lossk +== = ==


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Equality Constraints Real %o'er balan!e8

Rea!&ve Po'er Balan!e8

Evaluation 'unction

=

+ =Nbus

j

ijijijijjii bgVVP1

0)inc'(

=

=Nbus

j

ijijijijjii bgVVQ1

0)c'in(

100Fi!(ii)=

100+"'


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Inequality Constraints:

Kol&a,e lm&s 8

K Ienera&or rea!&ve %o'er lm&s :

K a%a!&or rea!&ve %o'er ,enera&on lm&s 8

K Trans+ormer &a% se&&n, lm&s 8

KTransmsson lne +lo' lm&s 8

Biii NiVVV 5

maxmin

ggigigi NiQQQ 5maxmin

ccicici NiQQQ 5maxmin

Tkkk Nittt 5maxmin

lll NlSS 5

max


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REACTIVE POWER OPTIMISATION USING PSO ALGO!T"M

1. &a% !/& #!&m %a!a

2. F'm b ma!ix .F'm B1 b ma!ix. D&c'm'& B1 b# /'"&,#%&c'm'i!i'n

3. an%'m"# ini!ia"i& '"a!i'n an% :&"'ci!i& '; a!ic"&

4. &! Pb&!=0 an% i!&a!i'n c'n!=1

5. &! a!ic"& c'n!=16. D&c'%& !/& a!ic"&. D&c'%&% a!ic"& i:& !/& :a"& '; :'"!a& mani!%&< !a

:a"& an% /n!.

7. F'm !/& b an% B2 b ma!ix. D&c'm'& B2 b# /'"&,# %&c'm'i!i'n

8. n FD "'a% ;"'. F'm c'n:&&% :'"!a& c'm!& !'!a" #!&m !anmii'n

L'< !abi"i!# in%&x< &mii'n c'!< ;&" c'!.

9. a"c"a!& !/& &:a"a!i'n :a"& '; &ac/ in%i:i%a" in !/& '"a!i'n 'ma& &ac/

in%i:i%a"> &:a"a!i'n :a"& i!/ i!Pbest . $; !/& &:a"a!i'n :a"& '; &ac/

in%i:i%a" i b&!!& !/an !/& &:i'Pbes!< !/& c&n! :a"& i &! !' b& Pb&!


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10. -n!remen& n$v$ual !oun& by 1. -+ !oun& %o%ula&on se ,o &o s&e% (6).11. The bes& evalua&on value amon, &he Pbests s $eno&e$ as gbest

14. Mo$+y &he member velo!&y Vo+ ea!h n$v$ual.

1


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() CA%E %TU&IE% AN& RE%ULT%

()+ -. bus s/stem8 > #o'er vol&a,e ma,n&u$e lm&s a& all buses s 0.C? %.u

> u%%er lm&s s 1.1 +or all &he P buses

> u%%er lm&s s 1.0? +or all &he PJ buses

> lo'er an$ u%%er lm&s o+ &he &rans+ormer &a%%n, are

0.C an$ 1.1 %.u.

> mamum ,enera&on9100

0.2724434.328367233.701959945.214704

!abi"i!# $n%&xL' (*)+mii'n (,/)F&" '! (/)

Mini*u* o' all t2e +, in-e.en-entresults


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0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Iterations

Lossesin

P.U


Total losses versus Iterations 'or IEEE () bus syste*


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0 10 20 30 40 50 60 70 80 90 100850

860

870

880

890

900

910

920

930

940

Iterations

Costin$/hr

Cost Vs Iterations

0 10 20 30 40 50 60 70 80 90 100230

240

250

260

270

280

290

300

Iterations

Emisioninkg/hr

Emision Vs Iterations

Total Cost Total E*ission Release

!EEE " bussyste%


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1.0242

1.035562101

/n! c&!anc&F'm-T' b&.?'

Positions of ta' changing transformers

5hunt suce'tance va6ues

0.9000028-274

0.900004-123

0.900006-102

0.900006-91

Ta :a"&F'm-T' b&.?'


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() + 01 bus s/stem

2.19104422.679544149.425212754.82509

!abi"i!#

$n%&x

L' (*)+mii'n

(,/)

F&" '!

(/)

-ini%u% of all 2 in/e0en/entruns

0 10 20 30 40 50 60 70 80 90 1000.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

Iteartions

L

osses

in

P.U

Losses Vs Iterations for IEEE 57 bus system

trans%ission loss versus !terations


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0.90000032-34

0.9875007-297

0.90000024-266

1.00000024-25?

1.05000024-25=

1.05000020-21%roblem mnmes +uel !os& by !on&rolln,

!on&rollable ,enera&or ou&%u&s 'hle 2ee%n, &he P bus vol&a,esun!han,e$

Then &he sys&em losses3 s&abl&y n$e an$ emsson !om%u&e$ a& &hs%o'er $s%a&!h are very h,h !om%are$ '&h &he resul&s ob&ane$ 'henres%e!&ve ones are &a2en as ob*e!&ve

Smlarly +or &he remann, &hree %roblems .e emsson3 s&abl&y n$e3&ransmsson losses o%&mma&on

The +our ob*e!&ves o+ mnma&on o+ +uel !os& 3 mnma&on o+ emsson3mnma&on o+ losses an$ mnma&on o+ sys&em s&abl&y n$e are!on+l!&n, an$ non !ommensurable

Ths &ra$e>o++ solu&on s ob&ane$ usn, a +uy $e!son sa&s+a!&onmama&on me&ho$.

FUZZIFIED PSO FOR MULTIOBJECTIVE


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PROBLEM(1)PROBLEM FORMULATION

Assumn, &he $e!son ma2er (DM) has m%re!se or +uy ,oals o+sa&s+yn, ea!h o+ &he ob*e!&ves3 &he mul&ob*e!&ve %roblem !an be+ormula&e$ as a +uy sa&s+a!&on mama&on %roblem 'h!h s bas!allya mn>ma %roblem

mnme I(H) 9 !om%romse$ solu&on o+ I1(H1)3 I4 (H4)3 I


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PROBLEM

#e& 1(H) be &he +uel !os& n :hr +or &h !on&rol ve!&or.

4(H) be &he losses n P./ +or &h !on&rol ve!&or


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PROBLEM The m%re!se or +uy ,oal o+ &he DM +or ea!h o+ &he ob*e!&ve

+un!&ons s 5uan&+e$ by $e+nn, &her !orres%on$n, membersh%+un!&ons 7i ('here 91 &o = )

-n !ase o+ a mnma&on %roblem3

90 or &en$s &o ero3 + + +ma an$

9 1 or &en$s &o 13 + + +mn.

'here +maan$ +mnare &he una!!e%&able an$ $esrable level +orres%e!&vely

The membersh% +un!&on !an be $e+ne$ as

i imax

maxi i

i imin i imaxmax min

i i

i imin

0 F F

F -FG = F F F

F -F

1 F H F

Me*bers2i. 'unction 'or it2 objective


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PROBLEM Membershi' function for 8ue6 cost8

;here 1ma9ma 1(H1)3 1(H4)3 1(H


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PROBLEM Membershi' function for stabi6it/ +nde

Membershi' function for mission re6ease

3 3max

max

3 33 3min 3 3maxmax min

3 3

3 3min

0 F F

F -F (E)G = F F F

F -F

1 F HF

Where F%a %a F(314)5 F(324)5 F(34)5 F(3,4)6

F%in %in F(314)5 F(324)5 F(34)5 F(3,4)6

4 4max

max

4 44 4min 4 4maxmax min

4 4

4 4min

0 F F

F -F (E)G = F F FF -F

1 F HF

Where F,%a %a F,(314)5 F,(324)5 F,(34)5 F,(3,4)6

F,%in %in F,(314)5 F,(324)5 F,(34)5 F,(3,4)6



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FUZZIFIED PSO FOR MULTIOBJECTIVEPROBLEM

The mamum $e,ree o+ overall sa&s+a!&on !an be a!heve$ bymamn, a s!alar 3 'h!h s &he n&erse!&on o+ &he +our +uymembersh% +un!&ons.

There+ore ob*e!&ve +un!&on s mama&on o+ 9 ma (13 43


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PROBLEM2)AL#ORIT$M

1. Rea$ &he sys&em $a&a

4. Rea$ &he values o+ +e$ !os&3 loss3 n$e3 emsson +or ea!h sub%roblems


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PROBLEM14. u+y +uel !os&3 loss3 emsson an$ n$e usn, above e5ua&ons1


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PROBLEMResults o' various sub .roble*s 'or IEEE () Bus syste*

Optimization Problem Fuel Cost

(!"r#

$osses

( %& #

'tabilit

)n*e+

,mission

( -!"r#

F&" c'! minimia!i'nb 'b"&m &"!

806.498033 10.583711 0.272369 381.671279

L'& minimia!i'n b

'b"&m &"!

945.214704 4.328367 0.272443 233.701959

!abi"i!# $n%&xminimia!i'n b 'b"&m

897.142571 33.557655 0.162446 375.611008

+mii'n minimia!i'nb 'b"&m

932.094511 4.404039 0.267070 229.144834

Fin$l t%$&e off solution 926.200519 4.634725 0.266459 242.142237



56/61


PROBLEM

The +nal &ra$e o++ solu&on +or -"""


57/61


PROBLEM

0.987528-274

0.9754-123

1.16-102

0.96-91Ta :a"&F'm-T' b&.?'

Positions o' ta. c2an3in3 trans'or*ers 'or IEEE () bus syste*

1.0242

1.009617101

/n! c&!anc&F'm-T' b&.?'

%2unt suce.tance values 'or IEEE () bussyste*

$yste% 'eneration 277*",.2&otal loa/ 27*, -W



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PROBLEM9esu6ts of various sub 'rob6ems for + 01 Bus s/stem

Optimization Problem Fuel Cost(!"r#

$osses( %& #

'tabilit)n*e+

,mission( -!"r#

F&" c'! minimia!i'nb 'b"&m &"!

806.498033 10.583711 0.272369 381.671279

L'& minimia!i'n b'b"&m &"!

945.214704 4.328367 0.272443 233.701959

!abi"i!# $n%&xminimia!i'n b 'b"&m

897.142571 33.557655 0.162446 375.611008

+mii'n minimia!i'nb 'b"&m

932.094511 4.404039 0.267070 229.144834

Fin$l t%$&e off solution 753.439822 32.462026 2.323327 148.82172

CONCLUSIONS


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CONCLUSIONS An al,or&hm have been $evelo%e$ &o ,e& &he +nal &ra$e>o++ solu&on +or &he

+our $++eren& sub %roblems .e. +uel !os&3 emsson 3losses an$ s&abl&y n$emnma&on usn, u+e$ mul&ob*e!&ve PSO

The solu&on al,or&hm has been &es&e$ +or &'o &es& sys&ems '&h -"""


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REFERENCES

L1 Allen U. ;oo$3 Bru!e . ;ollenber,3 VPo'er Ienera&on3 O%era&on3 An$ on&rolW3 Uohn ;leyX Sona3 -n!.3 Ne' or23 400=

L4 Pa%ya Du&&a 3 A.F.Snha> --T Fhara,%ur Pro+essor3 V"nvronmen&al "!onom! Ds%a&!h!ons&rane$ by vol&a,e s&abl&y usn, PSOW "le!&r!al "n,neern,3 --T Fhara,%ur>-""" 4006

LYa'ary, 8e66o&, + VA Survey o+Par&!le S'arm O%&ma&on A%%l!a&ons n "le!&r! Po'er Sys&emsW -""" Trans. On"volu&onary om%u&a&on 4006

L= Z'e>#ee Ian,3 VPar&!le S'arm O%&ma&on &o Solvn, &he "!onom! Ds%a&!h ons$ern,&he Ienera&or ons&ran&sW3 -""" Tans. on Po'er Sys&.3 ol 13 No. 11C?3 Au,.400C74 >C7

L6U.Y.Tala53."l>Ya'ary3an$M."."l>Ya'ary3 VA Summary o+ "nvronmen&al:"!onom! Ds%a&!hal,or&hms3W -""" Trans. Po'er Sys&.3 vol. C3 %%. 1?0[1?163 Au,. 1CC=.


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