economic hvdc

8/17/2019 Economic Hvdc

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370 High-oltage DictCurnt Tranmiio

"

. "�E 4 ua@

:>

:o�roa 2

-00 0"r=a aa

U 0

0 200 00

-

600Lg f (m

00 1000

Fgu 7-9. Reactiv Power Requ rements of Long Overhead ac and dc Lnesat Full Load as a Fucton of the Length of Lne

A c lne tef e nt eqe reactve e The cnvertr at bthen f the ne a reactve pwer frm the ac stem cnnected Ths sneenent f the lne length, n cntat th ac here eactve pecnsumptn vaes almt learl th dtance, as h n Fe 7 9

The vtage at an pen en f a lng lne cnerabl hgher thanrate Th phenenn s calle the Ferran efect an a lmtng factfr ac nes The vtage at an pen en f a lng lne peent a pecalem when the ne ut n sece b fst cnnectng t t the man acsstem It s t easble t clse h en at eactl the ame ntant

Clea hs cult s ave n c lne.

7 ME ECNMI

CNSIDERATIN

The eslt f amle 73 ncate that a savng (reuctn n nelse euts n an ncrease n the requre vltage (nsulatn level) Ths sclear npectn Fgure 78 hng the vaatn f c nulatn levelth the lses, assumng PL an the ac nulatn level a the refeenceA cmrme chce can be �ae aed the ecnm trae-ff


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76 Som Economic Conidion 371

he annua variabe cos o operain a dc ine can be assumed o behe sum o wo pars. The irs is cos o power os in ransmission and hesecond is he anua amorized capia cos o ine and erina saions

converers) . The cos o dc osses can be epressed in erms o he ossraio) as

Cos o dc oes= 6where we deine as he annua cos o osses in he ac case. he ine andemina cos vary direcly wih he reuired insulaion evel which in uis voagedependen. es o he oss raio we hus wrie in he liho E.

Volae dependendc capia coss

amorized annuayThe consan is epressed as

= qA

08

I

Here we ake he voagedependen ac capia cos as he basis or comparison:

A= Volagedependen ac euipmen capiacos amorized annually

The acor q is inroduced o accoun or he cos o emina saions in

reaion o line coss. s a resu o he oreoin assumpions he oaannua costs o operaing he dc ine are

c = 0 8 +Bde 8

The vaaion o he coss C dc wih oss raio is shown in Figure 710 hecorrespondig ac costs are

Cac =A+B 9The olowin example ives he basis or economic choice o he oss

raio.

Example -4

Show ha or minimm oal annual cos o he dc line

Cos o lo= 0 cos o volaedependen euipmenSolution

For minimum cos

d 0


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72 igh-Voag Dict-Crnt Tnmiio

u

cE

Fgre 70 Varation of de Costs wth Loss Rato

s requres n ew of Eq (7. 8),

o

B-0 .8 = 02 y)3/2

c mples ha a e opmu

y

10

Cos of losses = 05cos of volae-depede eqpe) 711o e a feeln fo e umercal mplcaon of e above we have

e follown example


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1.6 Some onomic Consideions

Example 7·5

e annual cos of losses for a dc line is $ 4X 106• ssuming a edesign is optimal, find e corresponding capital cos of voltagedependent

equipment amortized annually Calculate the ratio o losses in the dc case toha of the equivalen ac opion Assume ta annual cost of the later is$5X 06Soution

From e previous example we have by Eq (711),Annual capial cos o volage-dependen equipmen= 2By

But

B y=4X 106us e required cos= 2X 4X 06 = 8X 106 dollars per yearWe are also gve

hus e required raio is

=5X 106y 5 X 06 = 4X 106

y=0.8Breakeen Beeen a and d

From Example 7-4, a he opimum we have by Eq (10):B y ' �

H

o

.

s

/

:

) us e minimum cos of he dc line in operaion is according o Eq (7.8,

G min =B y * + 0. 5 :

3B y *Bu we ave from Eq (7.10, 3 . 2 y * = 1 B

hus Eq (.12) is rewrien as= 3 /G m in 3 B 1 B

=1.72{ B

I/

7.12

.1


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3 HiVoage DictCurnt miio

The capal co of he a ramo opo ge accordg toExample 7-4's defo of Eq 79 a

Ca c A +B 714 order to omre the wo opos available, we take he differece icoss a he measure We thus defe the savigs S as

715This reduces o usig qs. 713 ad 74 t

S A B172B/ 716

Defig the costat

P=1 72

i )

/3 71 z

(�

r 718The Eq. 716 be wie as

SBIpz Z 719ClerlS a tke o egaive values, idicaig a utoff value where the otio is o loger more eoomic ha he coesodg a alteaive.

For illustrio puroses it is more coveie to deal ith he rio

S, eoe here b 8: B 72This has miimum with resect to he variable z, obtaied by setig heeriive equl to zeo. Thus

This ocurs t lue of zm:

2pzzz0

71Here the miimum is give b substutig q. 721 to Eq. 72 Thus,

-_ 4 in P 2

The vritio of & wth he raio lA is obtaied by ubstutg iEq. 722 from q. 717

723


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�

.

- / =1.2

-AlA =1.4

"

/

= 1. 6

Smin = -0.114

Smin=-0.478

- S . =-0 930 - �

min . I Zm= 2951 1 I

I I

Zm= 1435 1

Z= .5 69

Figure · 1 1 . Variaion of wih for Dien A/ Ratos.

Z


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gh Voltage Dict-Curnt Tnmiio

TALE 72

Revnt oints o he S versus Crceriscs/A P Zl Z2 Zm 8 m 1942 .072 1.495 1.95 -0.114 2.153 0.8810 1.865 1.435 -0.478 2.353 0.8033 2.133 1.569 -0.930 2.545 0.7454 367 1.69 -144 .730 0.7021 .580 1.820 -2.015

nspection of Es. .22) and 23) shws that for psitive vales of p:

Smn 0 , forp 1.8899 or

A

; 115 .

�n < 0 forp > 18899 or

A> 1.15 .

The implication o E. (.2) is that S (and conseentl S) is positive forall alues of Z log as (/A) is le than 1.15. From E .15), we canconclude that Cae> dc for all vales of z defined b Eq (18) ifA<1.1.

For alues oA> 1.154, Sm and hence a rane f S are neatieThe alue of S l e zero for two val of z denoted l and 2 and llbe a minimum at m' Table 2 lists a few vales of the rato (A) and thecorresponding alues of Z' 2 , m. and S' The neral sape of the Sves variation is shown in Fire -

7.7 CONVRTER CIRCUITS:CONFGURATIONS AND PROPERTES

Groups o ales can be connected in varos was to frm a converterIn this section e eamine some poible configrations of cnverter circuits

and stud the asic properties that are sefl in the desin of HYDeconerter cici It is instctive to egn with a std of the case of asinglephase ac power suppl The fllwave rectifier circit is stdied rst

Single-Phase FUllWave Rectifier

A singlephase fllwave rectifier circit is shown in Fire 12. Atransfoer with a centertapped secondar windin and two valves 1 and 2are used The cathodes of the valves are connected thoh a lare smoothing reactor to the dc load


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So Solvd Pbs 4

where Xc is the commutating reactance of the rectifier's ac source Theactive po�er aance etween the ac and dc sides gives

Vdd, = VJos (7 165)Using Eqs 7160 and 7 16 1 i n Eq 7165, we get

Vd K1 .cos q . 0i " ,

(7166)

The rectier votage and inverter votage on the dc part of the systema reated y

Vd - Vd . = RdJd • (7 167)

The mode of the inverter is similar to that of the rectifier Thus thefoowing equations appy:

Vd Kcos·= 0j } } y}(7.168)(7169)

The mode deveoped so fa consists of five independent equationsEqs71 62, 71 , 7 167, 718, and 71 9in tes of the foowing ninevaiales:

Vd" Vdj ' j , cos ' cos Yj ' ' j ' and IdTo sove for nine vaes, four equations gvng the contro specificationsa needed Thus,

VJP Vd, = 0cos cos 0cos cos j 0

d .d - = 0J J

Proem 7-A-18 iustrates the per unit system and provides an anaysis of a system in its tes

OME OLVED PROBLEMS

Problem 7·A·1

Consider an estin tephase, dubeiuit, a ine in eation toits onvesion to dc with tee circuits Aume the same insuation eveShw that the ratio of power transmitted y dc to that y ac is given y

Power y d = 1Power y ac


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4 Hih Va icCur amiO

o so tt the ercee os rto sPercetage osses y dc

_ = 0 707Percete osses c

[

.

Slutin

Power transmitted by ac (2)(3)vhIL ' e c ie s conerted totree dc circuits eac ang to coductors t u d us ( Vd/2) toound.

Poer trasitted by dc = 6VddFort te sae insulaton ee o

Vd

[ vh '

e irst required ratio is

e so e

Poer y dc _ 6VddPoer y c - 6vh

_ Vdvh

=

P rc ntag ossesy

c Losses by c oe by ac-� ,

- . Percentage oss s c oer dc Lose c

blem 7-A-2

_ ower y c Losse dcPoer dc oes a1

[

0.707

Aume a ticuar desig criterio seciies that te rato o sulation leel or a dc ioar ie to the iutio leve or te equent acteease ine equa oer trser s o tt te correondingosses are reated y

Assume tat the insutio ee res drect it te e ue o teotge


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Soluion

The nsulaton level rato assumed sV

X

_

d

l�hFor equal power transfer,

Therefore,3�hIL Vd1d

Some Soled Pblems

Elmnatng the voltages from oth sdes usng the nsulaton rato, we get

The lo rato s

Problem 7A3The losses for a proposed ac lne are 0 MW Fnd the coespondng

loes f a dc lne s desgned such that the rato of nsulaton level for the dclne t that for the equvalent ac three-phse lne s 087

oution

We have from Prolem 7Ax 087

It has een shon earler that

Thus,

30)

4(087 )2

=5945 MW


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0 ighVoltage DictCunt Tnsission

blem 7A4

The annual sangs to the utlity due to insulation and loss reductionby using the dc option over the ac option depend on the choice o te ratio x

deined in Probem 7A2Sketch the variation of the total annual savngs wth x Obtain theoptimum value of x for maxmum total annual savng

outon

The total savngs are given by the sum o the reduction in annua costo lo and the reduction in the capital cost o insulation calcuated on ayearly basis

•Cost of the ac insulationrelated euiment = A

• Cost of the dc insulationrelated euipment = x where is asdeined in textThus,

Savngs in insulation cost = A x

Annual savings in loss cost = B (1 � dC )Lac= B ( � 4x2

Thus we have the total annual sangs given byS = A x + l )

42

A setch of the annual savngs is shown in Fire 7-38. To maximize thesavings,

Thus,

as = 0

a

-A - B = 0 3

(-2

)4 xThe optimum value of x is thus x· =

:

r/3

The mamum sang are thus

S = B _ ( 3B + 4A ) mo

4x2

= A + B - 1.72Bl/3/3


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S v i ng s

Figure 7-38. Annual Savings Vration wth x.

Prolem 7A5

So Sold bls 1

High-voltage dc is used for the transmiion of MW power rom remote generating site to the load center. Aume that transmiio loeare 4 percent of total usig the ac alteative and that this lo cts 35mil/kWh. A lo load factor of 0.56 is cmmnly aumed. The line design

is uch tha the es usig dc are80

erce o teir ac cu


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2 HghVoage Dc-Cn Tnsmssn

Assumng s ro s e oml oe u ol nul os oflosses nd nsulon re mmum ue

A Te nnul o of e loes ug e c lee

Te nnul os of e losses usng d The nnu os of nsulon morzed nu

Hint:

Sutin

d f v g pow r losso or - pek power oss

A Fo the c ee we lcue s foowsPek poer loss 0048 3 MW

Aerge ower oss = 05) (3) 79 MWAnnu enegy o ( 79(8700

5979 X 0 kWAnnul cos of loes 5979 X 0 35 X 0

54947 06 /erB Fo he cot of o we he

Thus

pLdC 08ac

Annul cos of d o (0854947 X 06 4 3954 X 06 $/yer

Fo optm desgn we he from exmple 7

Prbem 7-A-6

Cos of c insuon (nnu cos of dc lo )moize nnu

4 3954 X 06 879084 06 $/er

Conie the cscde of wo eephse onew eifie shown inFgre 739 how h

A Aerge e cuen s 0333d•B Pek nee oge on e s 047Vd

C Diectcen oge ippe pek o pek is 04Vd

economic hvdc

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