shmeivseis 3 facts

7/25/2019 Shmeivseis 3 Facts

1/79

.

9, 157 73

, 2007


2/79

2

1 ......................................................................................................................................... 3

1.1 .............................................................................................................................................. 31.2 ................................................................ 31.3 .................................................. 41.4 ............................................................................ 7

1.5 ........................................................................................... 10

2 (FACTS) .............................. 12

2.1 ............................................................................................................................................ 122.2 ............................................................................................................. 132.2.1 ............................................................................................... 132.2.2 (STATIC VAR COMPENSATOR) ............................. 182.3 .................................................................................................................. 242.3.1 (TCSC)........................ 242.3.2 TCSC ................................ 262.3.3 TCSC...................................................................................... 282.4 ............................................................................................................... 362.4.1 .......................................................................................................................................... 362.4.2 ............................................... 362.4.3 PHASE SHIFTER..................................... 392.4.4 STATIC PHASE SHIFTER (SPSS).............................................................................................................................................. 412.5 FACTS .............................................................. 43

3 FACTS ........................................................ 45

3.1 /(SVS/SCS).................................... 45

3.1.1 SVS ............................................................................................................................. 463.2 ..................................................... 463.3 SVS .................................................................................................. 483.4 ............................................................................................................. 493.4.1 STATCOM............................................................................. 493.4.2 V-ISTATCOM.............................................................. 503.4.3 STATCOM ................................................................................. 523.5 .................................................................................................................. 543.5.1 ............................................................................ 543.5.2 ............................................ 553.5.3 SSSC ............................................................................... 563.5.4 V-ISSSC ....................................................................... 63

3.5.5 P-TCSCSSSC........................................................... 643.6 (UNIFIED POWER FLOW CONTROLLER-UPFC) ... 653.6.1 ...................................................................................................................................... 653.6.2 UPFC................................................... 653.6.3 UPFC ........................................................................... 67

4 .......................................................................................... 73

4.1 (HVDC).............................................. 73

5 ............................................................................................................................... 77


3/79

3

1

1.1

, (..),

,

, ,

,

. ,

,

.

,

/ ,

, ,

.

,

, ,

,

. ,

, ,

,

. ,

, ,

,

.

1.2

, .

,

, , .

. ,


4/79

4

,

,

,

.

. -

,

.

,

.

. ,

.

,

,

, .

,

PRI (Electric Power Research Institute) 1980. - FACTS (Flexible AC Transmission Systems) -

..,

.

1.3

, .

,

, 1.1.


5/79

5

1.1

(a)

(b)

X. RV~

,

. , :

=+= IVjQPS~~

.

(.. ):

=+= IVjQPS RRRR~~

(1.1)

sinmaxPPR = (1.2)

X

VPQ RR

2

max cos = (1.3)

:

sinmaxPPS = (1.4)

cosmax

2

PX

VQ SS = (1.5)

RS VV , ,

X

VVP RS=max . ( SP )

( RP ) , .

1.1b maxP ,

=900. ,


6/79

6

.

d

dP. maxP

d

dP

.

.

, ,

() (-

).

1.1b, ,

,

:

.

900

. ,

.

,

.

IEEE ..

,

..

, (, )

.

300. ,

450.

(1.2) (1.4)

. (1.3) (1.5)

.

, ,

.

(1.2)-(1.5)


7/79

7

, ,

.

FACTS,

. ,

, ,

.

, ,

(1.2) (1.4),

maxP . ,

X.

, SV RV ,

. ,

, 0,95 1,05 ..

. (1.3) (1.5)

,

.

,

. ,

.

...

1.4

,

, 1.2.

(1.2b). s , r

.(per unit) .


8/79

8

1.2:

()

(b)

(c)

(d) ()

:

, 0~ 0=II

( sV~

) ( rV~

) V ,

VVV r ==~~

s

sV~

rV~

2/~

2/~

== VVVV rs

1.2

IjXVX~~

= . XV~

I~

. 1.2c.

1.2c ,

BOA . 1.2b :

mX

ms VV

VIX

jV~

2

~~~

2

~+=+= (1.6)

2 2

Xm r r

VXV j I V V = + = +

%% % % % (1.7)


9/79

9

(1.6) (1.7)

:

m cos2 2

s rV VV V +

= =% %

% (1.8)

irchhoff 1.2a, s rV jXI V = +% % %

,

:

2sin

2~~

~

X

V

jX

VVI rs =

= (1.9)

,

(1.8) (1.9) :

sin2

m

X

VIVPPPP mrs ===== (1.10)

, sQ rQ

, LQ (

).

Im{ }s sQ V I= % % (1.11)

Im{ }r r

Q V I= % % (1.12)

L s rQ Q Q= (1.13)

:=+=

sssss IVjQPS~~~

+=+== 2

sin2

2cos

2sin

2

2sin

2}

2sin

2{cos

~~~ 222

X

Vj

X

V

X

VjVIVS ss

)cos1(sin~~~

22

+== X

Vj

X

VIVS ss (1.14)

=+=

rrrrr IVjQPS~~~

=== 2

sin2

2cos

2sin2

2sin2}

2sin

2{cos~~~ 2

22

X

VjX

V

X

VjVIVS rr

)cos1(sin~~~

22

== X

Vj

X

VIVS rr (1.15)

:

)cos1(2

=X

VQs (1.16)

)cos1(2

=

X

VQr (1.17)

22(1 cos )L S r

VQ Q Q

X= = (1.18)


10/79

10

1.2d

. 2

=

X

VPP

2

max == .

.

1.5

..

" "

.

, , '90,

,

.

(

MVA) "

" FACTS (Flexible AC Transmission Systems).

:

.

.

:

M , .

(Static Var Compensators, SVC),

(hyristor Controlled Series Capacitors, TCSC)

(Phase Shifters, PS).

(

)

.


11/79

11

GTO (Gate Turn Off thyristors)

.

(STATic synchronous COMpensators, STATCOM),

(Static Synchronous Series Compensators, SSSC),

(Unified Power Flow Controllers, UPFC)

(Interline Power Flow

Controllers, IPFC).

.

FACTS.

1.2: FACTS


12/79

12

2 (FACTS)

2.1

(, , ).

, SVC , TCSC

PS .

, .

FACTS

K


13/79

13

2.2

2.2.1

1.1a,

( ),

,

.

.

2.1.

2.1

(a)

.

(b) .

, 2.1,

2.2a 2.2b.


14/79

14

() (b)

2.2:

(a) (b)

2.3:

mV~

2.1a

sV~

rV~

,

:

00~

= VVm (2.1)

{cos / 2 sin / 2}2

sV V V j

= = +% (2.2)

}2/sin2/{cos2

~

jVVVr == (2.3)

2.2a 2.3a

smV~

mrV~

,

2.2b 2.3b.

2.2b 2.3b :


15/79

15

/ 4sm smV V = % ; / 4mr mr V V =

% ; cos / 4sm mrV V V = = (2.4)

2

~~~

Xj

VVI mssm

= (2.5)

+

=+

=

2

2sin

2

}2

{cos

2

}2

sin2

{cos~

X

j

jV

Xj

VV

Xj

VjV

Ism

+

=+

=X

V

jX

V

X

V

jX

VIsm

)4

2sin(2}1)4

2{cos(22

sin2}12

{cos2~

+=+

=X

V

X

Vj

X

V

jX

VIsm 4

cos4

sin44

sin44

cos4

sin22}4

sin2{2~

22

4

j

smsm eX

VI

X

jVI 4

sin4~

)4

sin4

(cos4

sin4~

=+

= (2.6)

+

=

=

=

2

2sin

2

2cos

2

}2

sin2

{cos

2

~~~

X

j

jV

X

j

VV

X

j

jVV

X

j

VVI rmmr

+

=+

=X

V

jX

V

X

V

jX

VImr

)4

2sin(2)}4

2cos(1{22

sin2}2

cos1{2~

=

=

+=+=

)4sin4(cos4

sin4~

)

4

sin

4

(cos

4

sin4~

4cos

4sin4

4sin4

4cos

4sin22}

4sin2{2

~22

jX

V

IX

jV

I

X

V

X

Vj

X

V

jX

VI

mrmr

mr

44sin4

~

j

mr eX

VI

= 4

sin4

4sin

2

2~~

X

V

X

VIII mrsm ==== (2.7)

qI~

:

smmrq III~~~

= =

44sin4~

j

q eX

VI 4

j

e4sin4

X

V


16/79

16

===

}4

sin2{4

}4

sin2{4sin4

}{4sin4

~ 244

X

Vjj

X

Vee

X

VI

jj

q

}2

cos1{4~

=X

VjIq (2.8)

qI~ ,

( 0=pP ).

, :

)~~

Im(

= qmp IVQ = = )}2

cos1(4

Im{)]}2

cos1(4

[Im{2

X

Vj

X

VjV

)2

cos1(4 2

=X

VQp (2.9)

() ,

, . 2.2b 2.3b:

2 2* 4 4 2Re( ) cos ( sin ) cos sin sin

4 4 4 4 2sm sm sm sm mr mr

V V VP V I V I V I V

X X X

= = = = = =% % (2.10)

:

s s s s s s ssmS P jQ V I V I = + = =% % % % % (2.10)

(2.11), sV~

sI~

, :

2 2

2 4 2 4 4

4 sin 4 sin 4 sin4 4 4j j j j j

s

V V V

S Ve e e e eX X X

= = = %

24 sin4 {cos sin }

4 4s

VS j

X

= + %

2 24 sin 4 sin4 4cos sin

4 4s

V VS j

X X

= + %

+=4

sin4

4sin

4cos

4~ 222

X

Vj

X

VSs )

2cos1(

2

2sin

2~ 22 +=

X

Vj

X

VSs

:

2sin

2 2

X

VPs = (2.11)

)2

cos1(2 2

=X

VQs (2.12)

:

r r r r r r rmS P jQ V I V I

= + = =% % % % % (2.13)

(2.13), rV~

rI~

, :


17/79

17

=rS~

2

j

Ve

44sin4

j

eX

V

= 42

2

4sin4

jj

eeX

V

= 4

2

4sin4

j

eX

V

=

=+=)}4sin()4{cos(

4sin4 2

jX

V

}4sin4{cos

4sin4 2

jX

V

=rS~

4cos4

sin4 2

X

V

=4

sin4

4sin

4cos

4

4sin4

sin42

222

X

Vj

X

V

X

V

j

)12

(cos2

2sin

2~ 22+=

X

Vj

X

VSr

:

22sin 2

r

VP X

= (2.14)22

(1 cos )2

r

VQ

X

= (2.15)

2.4: PpQp

2.4 , :

P :

Pp :

Qp : rs QQ =

P- ,

, ,

(dP/d>0)

1800

.


18/79

18

2.2.2 (Static Var Compensator)

SVC ( )

. SVC

.

.

(TSCs-Thyristor Switched Capacitors)

(TCRs-Thyristor Control Reactors),

2.5.

2.5: ETSCs/TCRs

, SVCs

, .


19/79

19

2.2.2.1 SVC

.

2.6:

SVC .

:

VVV rs ==~~

, }2/sin2/{cos2

~

jVVVS +== , }2/sin2/{cos

2

~

jVVVr == ,

sV% rV

~.

:

Cmmm

jBI

CjIV

1~1~~==

mCm VjBI

~~= (2.16)

smms IX

jVV~

2

~~= (2.17)

mrrm IX

jVV~

2

~~= (2.18)

mrmsm

~~~III += (2.19)

(2.17), (2.18) (2.19) :

mmrsmmrs IX

jIIX

jVVV~

2)

~~(

2

~2

~~==+ (2.20)

(2.16) (2.20) :

)4

1(~

2

~~

Cmrs B

XV

VV=

+ (2.21)

)2

sin2

(cos~

jVVs += (cos sin )2 2

rV V j

= % , :

2cos

2

~~

VVV rs =+

(2.22)


20/79

20

(2.21) (2.22) :

C

m

Cm

BX

V

V

BX

VV

41

2

cos

~

)4

1(~

2cos

=

=

(2.23)

sm:

2 2

cos2sin sin 2sin cos sin

2 2 2 2(1 ) 1 1

2 2 4 4 4

S m

sm

CC C

V VVVV V

X XPX X X X X

B B B

= = = =

% %

mr

C

P

BXX

V

P =

= sin

41

2

sm (2.24)

,2.7.

2.7: Bcmax SVC (Bcmax1


21/79

21

SVC

BCmax ( , , ).

(

)

() .

2.2.2.2 V-I SVC

, Thevenin

, .

00th thV V= % .

:th M th S V V jX I = +

% % % (2.25)

, :

th M th S M th S M th th S V V jX jI V X I V V X I = + = = +% % % % % (2.26)

, :

( )th M th S M th S M th th S V V jX jI V X I V V X I = + = + = % % % % % (2.27)

() () , .


22/79

22

V-I SVC, (

) .

2.8.

2.8: V-I SVC

minL

maxL

maxC


23/79

23

SVC

.

,

SVC.

( )

SVC

.

V-I SVC

2.9. 0V .

( 1V ), SVC

3V . SVC 4V

( 2V ).

2.9: V-I SVC


24/79

24

2.3

2.3.1 (TCSC)

-

2.10.

2.10

(a)

(b)

2.10a ,

.

() .

2.10b TCR

( L C L CB B X X< > ),

() () TCR.

TCR (OFF).


25/79

25

, LX .

2.11:

Kirchhoff :

s rs r L L

L

V VV V jIX V I

jX

= = =

% %% % % % % (2.28)

.

2.12: -

-, 2.12, :

( )( )

s rs r L C L C L C

L C

V VV V jI X X jI X jI X V V I

j X X

= = = + =

% %% % % % % % % % (2.29)

'~

I sV%

, rV%

,

(2.28) (2.29) | '~

I |>|I~

|, ( )L C LX X X < .

-2.13.

2.13: -

, :

( )

( ) ( )1 1

C L C L C L C L C C C

C CC L L C L C L C

L L

Z Z jX jX X X X X X ZZ j j

X XZ Z j X X j X X X X

X X

= = = = = =+

(2.30)

10 .

TCR . TCR :


26/79

26

0CL C CL

XX Z Z

X (2.31)

2.3.2 TCSC

.

2.14

(a)

-

(b)

(c)

k=X

XC, 10 k

. ,

:

I~

( 00~

=II )

VVV rs ==~~

,2

SV V

= % ,2

rV V

= % , SV~

rV~

.

XV jIX =% % , LX = CXC /1= , XV

~

I

~

.

Vx


27/79

27

, XV~

I~

mV~

.

2.14:

=

==

2sin

)1(2

2sin2

)(

~~

~ Xk

VXXV

XXjVVI

CC

rs

2sin

)1(2~

XkVI

= (2.32)

2 2 2 2 2

C C CXs s m m

jX jX jXVjXV V I V I I V I

= = + = +

%% % % % % % % % (2.33)

2 2 2 2 2

C C CXr r m m

jX jX jXVjXV V I V I I V I

= + = + = +

%% % % % % % % % (2.34)

(2.33) (2.34) :

cos2 2

s rm

V VV V

+= =% %

% (2.35)

:

2

Re( ) sin(1 )

m m

VP V I V I

k X= = =

% % (2.36)

SCQ :

=SCQ )cos1()1(

2~

2

22

=

k

k

X

V

XI C (2.37)

,

:

2

sin(1 )

s r m m

VP P P P V I

k X= = = = =

(2.38)

:

2 22

2 2

2{cos sin } sin

2 2 (1 ) 22 2

cos sin (sin )(1 ) 2 2 (1 ) 2

sin (1 cos )(1 ) (1 )

s s s s

s

VS P jQ V I V j

k XV V

jk X k X

V VS j

k X k X

= + = = + =

= +

= +

% % %

%

:

sin)1(

2

Xk

VPS

= (2.39)

)cos1()1(

2

=Xk

VQS (2.40)


28/79

28

:

2 2 2 22

2{cos sin } sin

2 2 (1 ) 2

2 2cos sin (sin ) sin (1 cos )

(1 ) 2 2 (1 ) 2 (1 ) (1 )

r r r r

r

VS P jQ V I V j

k X

V V V V j S j

k X k X k X k X

= + = = =

= =

% % %

%

:

2

sin(1 )

r

VP

k X=

(2.41)

)cos1()1(

2

=Xk

VQr (2.42)

2.14c s rP P=

SCQ .

:

k ( k = 1 )

( maxP ) .

kTCSC

.

TCSC ,

, .

, .

2.3.3 TCSC

2.15: TCSC


29/79

29

TCSC ()

2.15.

10 30,

1500 3000.

.

kV.

mH.

(MOV Metal Oxide Varistor)

.

TCSC

(), CX =Cn

1 , , =nL.

LC :

X

X

LC

CnR

==

1 (2.43)

:

X

XC

n

R == (2.44)

2 4.

. TCSC

( appX ),

:

}~

~

Im{1

1

L

Capp

I

UX = (2.45)

, BK ,

TCSC,C

app

BX

XK = . , TCSC

:

)1( BCappCTCSC KXXXX +=+= (2.46)


30/79

30

,

- .

. LCC IjXU ~~ =

CX


31/79

31

2.17:

2.17,

() () .

,

.

TCSC ,

(capacitor stress) .

,

,

().

2.18.

()

(). ,

.

. .


32/79

32

, , 2.19

.

2.18:

, :

}2sin

)tan)tan((1

cos2{

1

21

2

2

2

2

+=BK (2.47)

, tan(),

2= . TCSC


33/79

33

2.19

() =2,5

(b)


34/79

34

TCSC ,

.

,

2.20.

2.20:

2.20,

, max, ,

. , KB


35/79

35

2.21:

.

.

, TCSC

.


36/79

36

2.4

2.4.1

,

, (phase shifting)

, , ,

2.22.

2.22:

2.4.2

2.23

.


37/79

37

2.23

(a) phase shifter

(b)

. , SV~

RV~ SZ RZ .

:

()

()

phase shifter,

, .

/ .

2.23 / PV~

,

BV~

, .

PV~

BV~

.

/ , |~

| BV ,

P

. :


38/79

38

)sin(

~~

PRS

eq

RS

X

VVP

= (2.48)

eqX S , R

S

V~

R

V~

.

(2.48) P

. phase shifter

P ,

.

phase shifter

,

, . phase shifter P 30

0

300 1 2 . 2.24

phase shifter .

2.24

(a) phase shifter

(b)

phase shifter :

.

1 1 2 2P c a a a a eV V k V k V V k V k V = + + % % % % % % %


39/79

39

.

phase shifter

.

,

.

phase shifter ,

,

.

2.4.3

phase shifter

2.25a 2.25b phase

shifter .

S (R) SZ

( RZ ). EZ BZ

. , BV BT.

, ,

:

. ,

EZ BZ .

.

.

:

)exp(~~

jVkV EB = (2.49)

E

B

V

Vk ~

~

= BV~ EV

~.

,

. :

== BBEEBE IVIVSS~~~~~~

(2.50)


40/79

40

(2.49) (2.50) :

=

BEEE IjVkIV~

)exp(~~~

)exp(~~

jIkI BE = (2.51)

BEBBEEBE PPjQPjQPSS =+=+=~~

(2.52)

BEQQ = (2.53)

2.25

() phase shifter

(b) phase shifter

, / , (2.49)

.

(2.49) (2.53) phase shifter

, 2.26.


41/79

41

2.26: phase shifter

2.4.4 Static Phase Shifter (SPSs)

SPS ,

. 2.27

SPS.

2.27: phase shifter

SPS . SPS

,

:

)exp(~

jkVV EB = (2.54)


42/79

42

)exp(~~

jIkI BE = (2.55)

S B EI I I= +% % % BR II

~~= (2.56)

SSSEESSS XIjVVVXIjV~~~

0~~~

== (2.57)

0~~~~

=+RRRBE

VXIjVV (2.58)

E

B

V

Vk ~

~

= =900.

2.28

(2.50) (2.58)

k0 0,3.

.

() (b)

2.28:

2.28 BV~ , 900,

0 0,26 .., 0< k


43/79

43

2.29:

,

phase shifter .

2.30

, ,

. , phase shifters

.

(.. bcV )

k (.. bckV ) (.. aV ).

(. bcV )

(.. aV ).2.31.

2.5 FACTS

(50Hz), (3, 5, 7)

SVC . ,

(50Hz),

.

LC SVC

TCSC.


44/79

44

2.30

(a)

.

(b)

(c)

2.31: phase shifter

s seffV V V= +% % %


45/79

45

3 FACTS

3.1 /(SVS/SCS)

(SVS/SCS-Synchronous Voltage/Current Sources).

, ,

,

.

,

,

. ,

,

().

,

SVS . 3.1

SVS. refQ refP

V

AC.

( 0=refP ), SVS

. SVS

, DC

DC .

3.1: SVS


46/79

46

3.1.1 SVS

SVS (

)

, SVS

(, , )

.

SVS

. SVS

.

AC

DC SVS, DC SVSs

3.2

.

.

3.2,

, bV , eV

eX .

be VV < , ,

. ,

3.2b.

be VV > ,

, 3.2c.

.

eV bV . ,

,

3.2d 3.2e.


47/79

47

3.2

()

(b)

(c)

(d)

(e)

: sine

ebLoss

XVVP = .


48/79

48

3.3 SVS

To STATCOM(SVC)

.

SSSC (TCSC) , .

UPFCFACTS,

(, , )

.

3.3 FACTS

.

3.3: FACTS


49/79

49

3.4

3.4.1 STATCOM

STATCOM SVC dc-ac , () ()

SPWM. 3.4 STATCOM.

3.4: STATCOM

STATCOM

. STATCOM

, STATCOM

. STATCOM

, ,

STATCOM .

. ,

.

, AC ,

.

,

. DC

-


50/79

50

. SVS

STATic synchronous COMpensator.

3.4.2 V-I STATCOM

3.5 V- STATCOM,

eV eX .

3.5: V-I STATCOM

, eX 10% 20%.

, , 10-

20% STATCOM.

GTO, IGBT IGCT

. (),

STATCOM.

1,1..,

STATCOM . , STATCOM

-()

, .

, dc

, STATCOM

dc .


51/79

51

STATCOM ,

2% 5%,

. ,

, 3.6.

3.6: V-I STATCOM

higheV, ,

. , loweV, ,

.

,

, , dc . 3.7

V-I STATCOM.

3.7: V-I STATCOM


52/79

52

, STATCOM

,

( )

. STATCOM

,

.

maxCI , ,

. , , ,

,

, GTOs ,

.

,

GTO.

3.4.3 STATCOM

STATCOM

:

00

~=

mm VV ()

0000 90~

== IjII ()

2/~

= VVS , 2/~

= VVr

:

mrsm00

~~~

~~~IIIIII mrsm =+= (3.1)

sms

~

2

~~I

XjVV m = (3.2)

mrrm IX

jVV~

2

~~= (3.3)


53/79

53

(3.2) (3.3) :

)~~

(2

~2

~~mrsmmrs II

XjVVV =+ (3.4)

(3.1) (3.4) :

22

~

2

~2

~~000

XIjI

XjI

XjVVV mrs ===+ (3.5)

2cos22/2/

~~ VVVVV rs =+=+ (3.6)

, (3.6) (3.5), :

42cos

~

2

~2

2cos2 00

XIVV

XIVV mm +==

(3.7)

(s m) :

mrsmsm

ms

sm

PVI

X

VP

XI

X

V

X

VP

X

XIVV

X

VVP

=+=+=

+

=

=

2sin

2sin

2sin

4

2

2cos

2sin

2

2sin

2

}42

cos{

2sin

2

~~

0

2

0

2

0

3.7 .

3.8: ,

max(max1


54/79

54

STATCOM

o

max,0I (, , ). SVC STATCOM,

3.8, 02

)( = OSTATCOMVI

P , SVC

0)( =SVCP . , STATCOM, (MARGIN)

SVC.

3.9: STATCOM SVC

3.5

3.5.1

()

, ,

,

. , -

, .

, -

900

,


55/79

55

. 3.10

.

3.10:

, :

IjkXVC~~

= (3.8)

:

CV~

:

I~

:

X :

k : (X

Xk C= , )10


56/79

56

:

)(qV : ( max)(0 qq VV )

:

I I = % :

(3.9) :

0( 90 )( ) ( ) jq q qV jV V e

= =%

0( 90 )

( ) ( )j

q q qV jV V e

+= + =%

SSSC 3.11.

3.11: SSSC

3.5.3 SSSC

,

() ,

3.11.

, IIII ==~

0~ 0

1

~

=I

I.

I

IVjVq

~

)(~

q = m , qV~

I~

. :

}2

sin2

V{cos2/~

jVVs +== (3.10)

}2

sin2

{cos2/~ jVVVr == (3.11)


57/79

57

rS~

.

, Kirchhoff

:

rxqs VVVV~~~~

= }2

sin2

{cos~

}

~

)({}2

sin2

{cos

jVIjXI

IjVjV q =+ m

( ){cos sin } {cos sin } { }

2 2 2 2

2 sin( ) 22 sin { }2 ( )

q

q

q

VV j V j j X I

I

VVjV j X I I I

I V

X I

+ =

= = =

%m

% %m%

m

(3.12)

:

2 2 2 2 2 2

2 2

2 sin / 2cos sin

( )2 2

2 sin cos 2 sin (2sin cos ) (2sin )2 2 2 2 2 2

( ) ( ) ( ) ( )

sin (1 cos )( ) ( )

r r r r q

q q q q

q q

VS P jQ V I V j

VX

I

V V V V

j j

V V V V X X X XI I I I

V Vj

V VX X

I I

= + = =

= =

=

% % %

m

m m m m

m m

(3.13)

:

sin)(

2

I

VX

VP

qr

m

= (3.14a)

)cos1()(

2

=

I

VX

VQ

qr

m

(3.14b)

() 3.14a 3.14b , ()

.

Kirchhoff

:


58/79

58

}2

sin2

{cos~

})({}2

sin2

{cos~~~~

jVIjXjVjVVVVV qrxqs =+= m

X

VVI

jVjVIjX

jVjVjVIjX

q

q

q

)(2

sin2~

)}({2/sin2~

)}({}2

sin2

{cos}2

sin2

{cos~

=

=

+=

m

m

(3.15)

o

=+= rrr jQPS~

}2

sin2

{cos~~

jVIVr =

X

VV q )(2

sin2

X

VVVjVVV qq }

2

sin)(

2

sin2{

2

cos)(

2

cos

2

sin2 222

=

X

VVVjVVV qq }2

sin)()2

sin2({2

cos)()2

cos2

sin2( 222

=

X

VVVjVVV qq }2

sin)()cos1({2

cos)(sin 22

=

XVVVj

XVVVS

qq

r2sin)()cos1(2cos)(sin~

22

= (3.16)

:

2cos

)(sin

2

X

VV

X

VP

q

r

= (3.17)

2sin

)()cos1(

2

X

VV

X

VQ

q

r

= m (3.18)

() 3.17 3.18 , ().

3.5.3.1 SSSC

SSSC (Voltage Source

Converter VSC) , GTO thyristors,

(.. ), .

SSSC

. -


59/79

59

.

PWM (Pulse Width Modulation).

, VSC -

.

SSSC

.

,

900,

SSSC .

,

,

.

SSSC ,

,

. ,

, ,

. SSSC ,

.

, SSSC

. , SSSC

STATCOM .

3.12 SSSC,

, ,

.


60/79

60

3.12: SSSC

. pqV~

lineI~

. 3.13 SSSC ,

SSSC. lineI~ ,

max

~pqV .

3.13: SSSC


61/79

61

,900.

, SSSC -

C

kX , lineCpq

IjkXV~~

= 10 k .

,

,

. 3.14. ,

() 1800 ( lineCpq IjkXV~~

= ),

,

.

pqV~ ,

,

SSSC

. 3.14

SSSC

900.

SSSC ,

.

.

,

pqV~

LineV~

, .

SSSC LineV~

, pqV~

LineV~

,

. , SSSC,

0,95 ..-1,05 ..,

.


62/79

62

3.14: SSSC

SSSC , ,

SSSC.

SSSC .

SSSC ,

SSSC. ()

SSSC

.

pqV~

SSSC

,

LinetrSSSCpq IXVV~~~

m= (3.19)

() , (+)

trX

.


63/79

63

, pqV~

SSSCV~

,

,

. SSSC

:

cosLinepqpq IVP = (3.20)

sinLinepqpq IVQ = (3.21)

SSSC

.

(3.20) (3.21)

SSSC 900,

SSSC . ,

SSSC

, :

lossesdcpq PPP += (3.22)

SSSC

.

3.5.4

V-I SSSC

3.15: V-I SSSC


64/79

64

3.15, SSSC ,

, ( max,lineI ). SSSC

,

. ,

. ,

,

V-I .

3.5.5 P-TCSC SSSC

3.16

(TCSC) (SSSC).

3.16:

TCSC .

SSSC

, ,

2

0

.

TCSC P-,

SSSC, ,

SSSC .


65/79

65

3.6 (Unified Power Flow Controller-UPFC)

3.6.1

UPFC .

, UPFC

. , UPFC

(.,

, ). ,

.

3.6.2 UPFC

UPFC

, .

UPFC ,

pqV~

, pqV , 0 max~

pqV ,

(0 ) , ,

3.17.

3.17: UPFC

, UPFC

. , , UPFC (SVS)


66/79

66

,

, .

,

. UPFC back to back ,

3.18.

3.18: UPFC back to back

"Converter 1" "Converter 2" DC

().

AC-AC ,

.

2 UPFC,

pqV~ .

,

.

.

DC DC

.

1

2 DC . DC


67/79

67

. 1

, ,

.

,

, -, 1

2 ,

2

. 1

2.

UPFC.

3.6.3 UPFC

To UPFC -

, pqV~

sV%

. , UPFC, , 3.19.

3.19(a)

pqV~

, V ( =0)pqV = % .

.

-3.19(b), q qV V=% %

900 .

, , -.

- UPFC , ,

,

- ( ),

.


68/79


69/79

69

UPFC

3.11.

P rQ :

( )s pq rr rV V V

P jQ VjX

+

=

% % %

% (3.23)

0~

=pqV , ,

:

( )S rr rV V

P jQ VjX

= % %

% (3.24)

0~

pqV , , (3.23) :

( )r pqS r

r r

V VV VP jQ V

jX jX

= +

% %% %% (3.25)

:

/ 2 {cos sin }2 2

sV V V j

= = +% (3.26)

}2

sin2

{cos2/~

jVVVr == (3.27)

2 sin2

s rV V j V

=% % (3.28)

)2

(~

+

=j

pqpq eVV )}2

sin()2

{cos(

+++= jVpq (3.29)

:

( )r pqs r

r r

V VV VP jQ V

jX jX

= + =

% %% %%

=

+++=

jX

jVjV

jX

Vj

jVpq )}

2sin()

2{cos(}

2sin

2{cos

}2sin2

}{2

sin2

{cos

=+++++

+

=X

jVV

jX

j

Vpq )]}

2sin(

2cos)

2cos(

2[sin)

2sin(

2sin)

2cos(

2{cos

}2sin2

2sin

2cos2

{

2

2

2 sin (1 cos ) cos( ) sin( )pq pqV jV jVV VV

X X X X + += + + =

)}cos()cos1({)sin(sin22

+++=X

VV

X

Vj

X

VV

X

V pqpq

:2 2

sin sin( ) { (1 cos ) cos( )pq pq

r

VV VV V VP jQ j

X X X X = + + + } (3.30)

)sin(sin2

++=X

VVXVP pq ; )cos()cos1(

2

+=X

VVXVQ pqr (3.31)


70/79


71/79

71

UPFC, 3.17.

pqV .

:

sinsin)(2

0 ==X

VP (3.40)

cos1)cos1()()()(2

000 ====X

VQQQ rs (3.41)

, 12

=X

V.

:

=2

00 )}({11)( PQ r =+2

00 )}({11)( PQ r =+2

02

0 )}({1}1)({ PQ r

1)}({}1)({ 202

0 =++ PQ r (3.42)

(3.42)

0=P 1=rQ {P, rQ }, 3.21.

3.21

0P 0rQ

., :

0= o 0 0P = , 0 0rQ =

30= o 0 0,5P = , 0 0,134rQ =

90= o 0 1P = , 0 1rQ =

180= o 0 0P = , 0 2rQ =


72/79

72

3.17, pqV 0 .

pqV . 0 ,

),( P ),( rQ

pqV~

maxpqV .

,

)(0 P )(0 rQ X

VV pqr

X

VV pqr max,

VVV rs == . :

2max2

0

2

0 }{)}(),({)}(),({X

VVQQPP

pq

rr =+ (3.43)


73/79

73

4

.

50 km.

( back to back)

.

(

).

4.1 (HVdc)

9.

.

4.1

()

AC

6

DC


74/79

74

:

)]cos([cos2

1uVV cd ++= (4.1)

dc

cd IXVV

3cos = (4.2)

)]cos([cos2

uX

VI

c

dd += (4.3)

Vd Id Vc

,

u .

4.2.

:

dc

cd IX

VV

3

cos = (4.4)

4.3.

:

ddc IVIVP == cos3 (4.5)

:

)]cos([cos2

1cos u++= (4.6)

H :

tanPQ= (4.7)

)22cos(2cos

)22sin()22sin(tan

u

uu

+

+=

(4.8)


75/79

75

4.2

a) b) 1c), d) e)R


76/79

76

4.3

a) b) 1c), d) e)R


77/79

77

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42.

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45.

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