University of Southern California Dissertations and Theses

The dynamic interaction of synchronous condensers, SVC, STATCOM and superconducting magnetic energy storage on electric vehicles

(USC Thesis Other)

The dynamic interaction of synchronous condensers, SVC, STATCOM and superconducting magnetic energy storage on electric vehicles

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Content I
T h e D y n a m i c I n t e r a c t i o n o f S y n c h r o n o u s C o n d e n s e r s , S V C ,
S T A T C O M a n d S u p e r c o n d u c t i n g M a g n e t i c E n e r g y S t o r a g e o n
E l e c t r i c V e h i c l e s .
B y
A h m e d A l l e h y a n i
T h e s i s S u b m i t t e d T o T h e
U n i v e r s i t y o f S o u t h e r n C a l i f o r n i a
I n P a r t i a l F u l f i l l m e n t o f T h e D e g r e e R e q u i r e m e n t o f
M a s t e r o f S c i e n c e I n E l e c t r i c a l E n g i n e e r i n g
D e c e m b e r 2 0 1 5
D r . M o h a m m e d B e s h i r
I I
T a bl e of C ont e nt s
1. I n t r oduc t i on ...................................................................................................................... 1
1.1 P r obl e m D e f i ni t i on .................................................................................................1
1.2 O bj e c t i ve s .............................................................................................................. 1
1.3 M e t hodol og y .......................................................................................................... 2
1.4 T he s i s O ut l i ne ........................................................................................................ 2
2. L i t e r a t ur e R e vi e w .............................................................................................................3
2.1 P ow e r S y s t e m S t a bi l i t y .......................................................................................... 3
2.1.1 R ot or A ngl e S t a bi l i t y .................................................................................. 4
2.1.2 V o l t a ge S t a bi l i t y ........................................................................................ 10
2.2 E l e c t r i c V e hi c l e s ................................................................................................... 17
2.3 D y n a m i c D e vi c e s ................................................................................................. 20
2.3.1 S y n c hr onous C onde ns e r ............................................................................20
2.3.2 S t a t i c V a r C om pe ns a t or ( S V C ) ................................................................. 27
2.3.3 S t a t i c S y n c hr onous C om pe ns a t or ( S T A T C O M ) ....................................... 35
2.3.4 S upe r c onduc t i ng M a gne t i c E ne r g y S t or a ge ( S M E S ) ............................... 38
3. M ode l i ng ........................................................................................................................ 47
3.1 I n t r oduc t i on .......................................................................................................... 47
3.2 I E E E 14 bus ......................................................................................................... 48
3.3 E V s M ode l i ng ...................................................................................................... 50
3.4 D y n a m i c D e vi c e s ................................................................................................. 52
3.4.1 R ound R ot or S y n c hr onous G e ne r a t or ( G E N R O U ) ...................................52
3.4.2 I E E E t y p e 1 E x c i t a t i on M ode l ( I E E E T 1) ................................................. 54
3.4.3 I E E E G 1 G ove r nor M ode l ......................................................................... 56
3.4.4 S t a t i c V a r C om pe ns a t or ( C S V G N 1) ......................................................... 57
3.4.5 S t a t i c C onde ns e r ( C S T A T T ) ..................................................................... 58
3.4.6 S upe r c onduc t i ng M a gne t i c E ne r g y S t or a ge ( C S M E S T ) .......................... 60
4. R e s ul t s a nd A na l y s i s ...................................................................................................... 62
4.1 D y n a m i c A na l y s i s r e s ul t s f or t he I E E E 14 bus s y s t e m B a s e c a s e ....................... 63
4.2 D y n a m i c A na l y s i s of t he I E E E 14 bus A f t e r I n c r e a s i ng t he A c t i ve L o a d t o 1.4
T i m e s t he B a s e C a s e A c t i ve P ow e r L oa d. ................................................................. 70
4.3 D y n a m i c A na l y s i s of t he I E E E 14 bus A f t e r I n c r e a s i ng t he A c t i ve L o a d t o 1.8
T i m e s t he B a s e C a s e A c t i ve P ow e r L oa d. ................................................................. 77
4.4 D y n a m i c A na l y s i s of t he I E E E 14 bus A f t e r I n c r e a s i ng t he A c t i ve L o a d t o 1.9
T i m e s t he B a s e C a s e A c t i ve P ow e r L oa d. ................................................................. 81
4.5 S um m a r y a nd C om pa r i s on ................................................................................... 97
5. C onc l us i on ................................................................................................................... 104
6. F ut ur e W o r k ................................................................................................................. 104
7. R e f e r e nc e s .................................................................................................................... 105
I I I
A c k n o w l e d g m e n t
F i r s t , t hi s t he s i s , a nd e ve r y ot he r bl e s s i ng I ha ve , w a s done w i t h t he he l p of G od. S e c ond,
I w oul d l i ke t o e x pr e s s m y s i nc e r e g r a t i t ude t o m y pa r e nt s w ho s uppor t e d m e w i t h m y
j our ne y t o c ont i nue m y hi g he r e duc a t i on. W i t hout t he m I w oul d not be w he r e I a m t oda y .
A l s o, I w oul d l i ke t o e xpr e s s m y s i nc e r e g r a t i t ude t o m y s upe r vi s or P r of e s s or M oha m m e d
B e s hi r w ho g ui de d m e t hr ough t he s t e ps of m y t he s i s . H e w a s pa t i e nt a nd e nc our a gi ng
t hr oughout t he pr oc e s s of w r i t i ng t hi s t he s i s .
I V
A b s t r a c t
T he m ode r n a ge ha s be e n know n a s t he i ndus t r i a l a ge . N e w t e c hnol og i e s ha ve be e n
i nve nt e d e ve r y da y a nd ol d t e c hnol ogi e s a r e be i ng i m pr ove d t o g e t t he m a x i m um be ne f i t s
out of t he m . H ow e ve r , t he e nvi r onm e nt i s s uf f e r i ng t he a dve r s e i m pa c t s r e s ul t e d f r om t he
de ve l opm e nt of t he ne w t e c hnol ogi e s . U nw a nt e d e m i s s i ons t ha t c a us e s o m uc h ha r m t o
t he e nvi r onm e nt s uc h a s C a r bon D i oxi de a r e e m i t t e d t o t he a t m os phe r e . T o de c r e a s e t he
r a t e of e m i s s i ons , t he us e of E l e c t r i c V e hi c l e s ( E V ’ s ) i s r e c om m e nde d due t o t he l ow e r
e m i s s i ons r a t e c om pa r e d t o t he g a s - pow e r e d c a r s .
H ow e ve r , s hi f t i ng t o E V ’ s ha s t o be pl a nne d a nd s t udi e d c or r e c t l y . T he E V ’ s ne e d t o be
c ha r g e d f r om t he ut i l i t y pow e r g r i d. T he e l e c t r i c i nf r a s t r uc t ur e m i g ht not be a bl e t o
w i t hs t a nd t he e x c e s s i ve l oa di ng of t he E V s . T he s y s t e m m i g ht l os e i t s s t a bi l i t y c a us i ng a n
unde s i r e d vol t a g e c ol l a ps e . T he r e f or e , a n a c t i on ha s t o be done t o pr e ve nt t he i ns t a bi l i t y
t ha t c oul d oc c ur . I n s t a l l i ng dy n a m i c de vi c e s m i g ht c ont r i but e t o t he vol t a g e c om pe ns a t i on
ne e de d t o s t a bi l i z e t he s y s t e m .
T o s t udy t he i m pa c t of t he S y n c hr onous C onde ns e r s , S t a t i c V a r C om pe ns a t or , S t a t i c
C onde ns e r a nd t he S upe r c onduc t i ng M a g ne t i c E ne r g y S t or a ge on E l e c t r i c V e hi c l e s
c ha r g i ng, t he I E E E 14 bus g r i d i s bui l t i n P S S E . T he dy n a m i c de vi c e s a r e i nt e g r a t e d i nt o
di f f e r e nt ba s e c a s e s w he r e t he i r i m pa c t a l one i s e va l ua t e d. P ow e r f l ow a na l y s i s i s t o be
done f i r s t t o m a ke s ur e t he s y s t e m i s s t a bl e . D i f f e r e nt s c e na r i os a r e t o be e x pl or e d i n t hi s
t hi s t he s i s . T he pe ne t r a t i on of t he E V s a r e t o be i nc r e a s e d t o a c e r t a i n pe r c e nt a ge i n e a c h
s c e na r i o. D y n a m i c a na l y s i s i s a l s o t o be done t o e a c h ba s e c a s e s e pa r a t e l y . T hr e e pha s e
ba l a nc e d f a ul t i s i nt r oduc e d a t s e ve r a l bus ba r s w i t hi n t he s y s t e m f or f i ve c y c l e s . A f t e r
t ha t , t he c a pa bi l i t y of e a c h ba s e c a s e t o r e ga i n s t a bi l i t y a nd t he c ont r i but i on of e a c h
dy n a m i c de vi c e i s e va l ua t e d.
1
1 . I n t r o d u c t i o n
1 . 1 P r o b l e m D e f i n i t i o n
T he qua l i t y of vol t a g e i n a pow e r s y s t e m i s a f f e c t e d by t he a m ount of l oa d c onne c t e d i n
t he s y s t e m . A s t he l oa d i nc r e a s e s t he s y s t e m e x pe r i e nc e a s t r e s s f ul s i t ua t i ons t ha t r e s ul t i n
a di s t or t i on i n t he s y s t e m vol t a g e a nd s om e t i m e s r e s ul t a s y s t e m c ol l a ps e . M or e ove r , i f
t he s y s t e m i s s t r e s s e d out e nough, i t w oul d a f f e c t i t s c a pa bi l i t y of c om i ng ba c k t o s t a bi l i t y
a f t e r a n oc c ur r e nc e of a f a ul t i n t he s y s t e m .
C ha r g i ng e l e c t r i c ve hi c l e s ( E V s ) c a n be a hug e bur de n on t he e l e c t r i c g r i d i nf r a s t r uc t ur e .
I n or de r t o c ha r g e t he e l e c t r i c ve hi c l e s , e ne r g y ha s t o be s uppl i e d t o t he E V f r om t he g r i d.
T he e ne r g y dr a w n f r om t he g r i d t o c ha r g e t he E V s pl a c e s t he e l e c t r i c g r i d unde r s t r e s s .
T he e l e c t r i c gr i d m i ght not be a bl e t o w i t h s t a nd t he i nc r e a s i ng l oa d r e s ul t e d f r om t he E V s .
A s a r e s ul t of t ha t , a n a c t i on i s ne e de d t o be t a ke n t o ove r c om e t he pr obl e m a nd r e duc e
t he s t r e s s on t he e l e c t r i c g r i d.
T he r e f or e , t o s t r e ngt he n t he s y s t e m i n or de r t o c om e ba c k t o s t a bi l i t y , s om e de vi c e s c a n
be i nt r oduc e d. T he de vi c e s a r e i nt r oduc e d t o s t r e ngt he n t he s y s t e m by pr ovi di ng r e a c t i ve
or a c t i ve pow e r t o i m pr ove t he vol t a g e pr of i l e of t he s y s t e m .
1 . 2 O b j e c t i v e s
T he m a i n obj e c t i ve of t hi s t he s i s i s a s s e s s how f e a s i bl e t he “ s t a bi l i z a t i on ” de vi c e s
i nc l udi ng S y n c hr onous C onde ns e r , S t a t i c C onde ns e r , S t a t i c V a r C om pe ns a t or a nd
S upe r c onduc t i ng M a gne t i c E ne r g y S t or a ge on t he vol t a g e be ha vi or of t he I E E E 14 bus
s y s t e m a f t e r i nt r oduc i ng a t hr e e pha s e f a ul t , w hi c h i s t he w or s t t y p e of f a ul t s , on di f f e r e nt
bus e s . T he a ppr oa c h i s t o i nc r e a s e t he pow e r s y s t e m l oa d c ons i de r i ng va r i ous l e ve l of E V
pe ne t r a t i on. T he n, a s s e s s t he pow e r s y s t e m s t a bi l i t y w i t h di f f e r e nt E V pe ne t r a t i on l e ve l
a nd a s s e s s di f f e r e nt pow e r dy n a m i c c om pe ns a t i on de vi c e s a bi l i t y t o s t a bi l i z e t he s y s t e m .
2
1 . 3 M e t h o d o l o g y
D i f f e r e nt ba s e c a s e s a r e bui l t i n P S S E f or e a c h dy n a m i c de vi c e a nd pow e r f l ow a na l y s i s
i s r un. A f t e r t ha t , a dy n a m i c m ode l i s de s i gne d f or e a c h dy n a m i c de vi c e a nd e a c h c a s e i s
pr e pa r e d f or dy n a m i c a na l y s i s . T he s y s t e m i s a s s e s s e d w i t h di f f e r e nt E V s pe ne t r a t i on
l e ve l s t o r e a c h a s t r e s s e d out s y s t e m . N e x t , t he dy n a m i c s t e a dy s t a t e i s r un f or 2 s e c onds
a nd a t hr e e pha s e f a ul t i s i nt r oduc e d a t t hi s poi nt f or f i ve c y c l e s . A f t e r t ha t , t he f a ul t i s
c l e a r e d a nd t he s y s t e m i s r un f or 10 s e c onds . F or s i z i ng , t he a na l y s i s i s r un w i t hout l i m i t s
f or t he dy n a m i c de vi c e s . A f t e r t ha t , t he a na l y s i s i s r e pe a t e d f or t he m i ni m um va l ue of 200
M V A t ha t s t a bi l i z e s t he s y s t e m . T he E V s a r e m ode l e d a s c ons t a nt c ur r e nt l oa d.
1 . 4 T h e s i s O u t l i n e
F i r s t C h ap t e r i s a n i nt r oduc t or y c ha pt e r t ha t or i e nt t he r e a de r t o t he ba s i s of t he t he s i s . I t
s t a r t s w i t h t he pr obl e m de f i ni t i on t ha t t hi s t he s i s i s t r y i ng t o s ol ve c ove r i ng a l l t he f a c t or s
ne e de d t o pr ovi de a f ul l pi c t ur e of t he pr obl e m . A f t e r t ha t , i t t ouc he d on t he e x a c t
obj e c t i ve of t he t he s i s a nd t he m e t hodol og y us e d.
S e c on d C h ap t e r pr ovi de s a f ul l l i t e r a t ur e r e vi e w on t he m os t i m por t a nt a s pe c t s r e l a t e d t o
t he t he s i s t opi c s . T he s e c ond c ha pt e r i s e s s e nt i a l i n or de r t o g a i n a de e p know l e dge of t he
t he s i s t opi c i n or de r t o pr oc e e d t o g e t t a ngi bl e r e s ul t s . I t s t a r t s w i t h a n ove r vi e w of t he
vol t a g e s t a bi l i t y . A f t e r t ha t , i t g i ve s a f ul l ba c kgr ound on e ve r y de vi c e us e d i n t he
a na l y s i s .
T h i r d C h ap t e r c ove r s t he m ode l i ng a s pe c t of t he t he s i s . I t de a l s w i t h e ve r y m ode l us e d
i n t he t he s i s s t a r t i ng w i t h t he pow e r s y s t e m us e d ( I E E E 14 bus m ode l ) c ove r i ng a l l t he
da t a us e d i n t he m ode l . A f t e r t ha t , i t s hi f t s t o t he dy n a m i c m ode l s us e d f or e a c h de vi c e s
by e x pl a i ni ng e a c h m ode l a nd t he c ont r ol bl oc k di a gr a m us e d. A l s o, t he va l ue s e nt e r e d
f or t he dy n a m i c pa r a m e t e r s i n t he P S S E w i l l be s how n.
F ou r t h C h ap t e r a na l y z e s t he r e s ul t s a f t e r pe r f or m i ng t he t e s t s on t he m ode l . I t pr ovi de s
t he t e s t i ng s t r a t e gy i m pl e m e nt e d. A ddi t i ona l l y , i t br e a ks dow n t he c a s e s us e d i n t he
t e s t i ng s t r a t e gy . M or e ove r , t he f our t h c ha pt e r pr ovi de s t he dy n a m i c r e s pons e of e a c h c a s e
a f t e r a ppl y i ng a t hr e e pha s e f a ul t t o de t e r m i ne i f t he s y s t e m c a n w i t hs t a nd a f a ul t a t
c e r t a i n E V s l oa di ng f or e a c h i ns t a l l e d dy n a m i c de vi c e .
F i f t h C h ap t e r pr ovi de s t he c onc l us i on of t he e nt i r e t he s i s .
3
2 . L i t e r a t u r e R e v i e w
2 . 1 P o w e r S y s t e m S t a b i l i t y
T he be s t de f i ni t i on of P ow e r s y s t e m s t a bi l i t y i s ” I t i s t he a bi l i t y of a n e l e c t r i c pow e r
s y s t e m , f or a g i ve n i ni t i a l ope r a t i ng c ondi t i on, t o r e ga i n a s t a t e of ope r a t i ng e qui l i br i um
a f t e r be i ng s ubj e c t e d t o a phy s i c a l di s t ur ba nc e , w i t h m os t s y s t e m va r i a bl e s bounde d s o
t ha t pr a c t i c a l l y t he e nt i r e s y s t e m r e m a i ns i nt a c t [ 1] ” . T he pr e vi ous de f i ni t i on m e nt i ons a
br oa d s pe c t r um of s y s t e m va r i a bl e s . H ow e ve r , t he pow e r s y s t e m s t a bi l i t y c a n be
c l a s s i f i e d t o t hr e e t y p e s : R ot or A ngl e S t a bi l i t y , V o l t a ge S t a bi l i t y a nd F r e que nc y s t a bi l i t y
a s s e e n i n f i g ur e 1.
F i gur e 1 s how s t he c l a s s i f i c a t i on of t he pow e r s y s t e m s t a bi l i t y [ 2]
4
2 . 1 . 1 R o t o r A n g l e S t a b i l i t y
F i gur e 2 s how s a t w o i nt e r c onne c t e d g e ne r a t or s t hr ough a t r a ns m i s s i on l i ne .
T o pr ovi de a n i ns i g ht i nt o t he r ot or a ngul a r s t a bi l i t y , a s y s t e m of t w o i nt e r c onne c t e d
g e ne r a t or s t hr ough a t r a ns m i s s i on l i ne i s t o be s t udi e d [ 3] . T he c ur r e nt I 1 2 i s e x pr e s s e d a s
t he f ol l ow i ng :
j X
V V
I
2 2 1 1
12
    

T he a c t i ve pow e r c a n be f ound by t a ki ng t he r e a l pa r t of t he m ul t i pl i c a t i on of t he
vol t a g e t i m e s t he c onj uga t e of t he c ur r e nt . T he r e f or e ,
) 2 1 s i n(
2 1
12   


X
V V
P
) s i n(
2 1
12 12 
X
V V
P


T he r e f or e , t he r e a l pow e r f l ow i ng i n t he s y s t e m i s de pe nde nt m a i nl y on t he vol t a g e l e ve l
i n t he t w o e nds a nd t he a ng l e di f f e r e nc e be t w e e n t he m . A ddi t i ona l l y , t he m a x i m um pow e r
r e s ul t s w he n t he a ng l e di f f e r e nc e i s 90 de gr e e s .
F i gur e 3 s how s t he r e a l pow e r va r i a t i on w i t h t he a ngl e [ 4]
5
A ) S m al l - D i s t u r b an c e A n gu l ar S t ab i l i t y
T o unde r s t a nd t he s m a l l di s t ur ba nc e a ngul a r s t a bi l i t y , a n a s s um pt i on of onl y one m a c hi ne
i s c onne c t e d t o a bus w i t h f i xe d vol t a g e a nd pha s e c a l l e d i nf i ni t e bus ( S M I B ) [ 5] . T he
i nf i ni t e bus dy n a m i c s i s e x pr e s s e d by t he f ol l ow i ng e qua t i on c a l l e d s w i ng e qua t i on:
dt
d
D P e P m
dt
d
M
 
  
2
2
w
dt
d
 

H M 2 
W he r e , M i s t he a ngul a r m om e nt um w he n t he m a c hi ne i s ope r a t i ng a t t he s y n c hr onous
s pe e d. P m a nd P e a r e t he m e c ha ni c a l a nd e l e c t r i c pow e r r e s pe c t i ve l y . D a nd δ a r e t he
da m pi ng c oe f f i c i e nt a nd t he a ngl e of t he r ot or r e s pe c t i ve l y . T he s w i ng e qua t i on i s not a
l i ne a r e qua t i on. T he r e f or e , i n or de r t o s ol ve i t a ‘ l i ne a r i z a t i on ’ m us t t a ke pl a c e a r ound a
c e r t a i n poi nt c a l l e d δ o.
0
2
2
   




 
K e
dt
d
D
dt
d
M
W he r e , H M 2 
) c os (
2 1
o
X
V V
K e  


A s s um e
o t      ) 0 (
0 ) 0 (    t w
T he r e f or e , t he s w i ng e qua t i on be c om e s :
0
2
  
M
K e
M
D
 
S ol vi ng t o f i nd λ 1 a nd λ 2
M
K e
M
D
M
D
   
2
2 , 1 )
2
(
2

2
2 , 1 )
2
(
2 M
D
M
K e
j
M
D
    
6
D e f i ne t he f ol l ow i ng ne w va r i a bl e s α a nd Ω w hi c h a r e t he da m pi ng c oe f f i c i e nt a nd
a ngul a r f r e que nc y of os c i l l a t i ons .
M
D
2
  
2
)
2
(
M
D
M
K e
  
T he da m pi ng r a t i o i s de f i ne d a s
2 2
 





E x pr e s s i ng t he s w i ng e qua t i on a s a s e c ond or de r di f f e r e nt i a l e qua t i on:
0 2
2
2
2
    

  

 



n
dt
d
n
dt
d
F i ndi ng t he r oot s of t he s e c ond or de r e qua t i on:
      j n   2 , 1
T he t e r m s ξ a nd Ω a r e t he da m pi ng r a t i o a nd t he os c i l l a t i ons ` f r e que nc y r e s pe c t i ve l y .
T he r e f or e , r e l a t i ng t he t w o f or m s of s w i ng e qua t i on t og e t he r g i ve s :
M
K e
n  
M K e
D


2 /

A s s e e n i n t he pr e vi ous a na l y s i s , t he e l e c t r i c a l c ha r a c t e r i s t i c s a nd c om pone nt s of t he
s y s t e m pl a y a m a j or r ol e i n de t e r m i ni ng t he da m pi ng a nd f r e que nc y of t he s m a l l s i g na l
di s t ur ba nc e s i n s y s t e m . A ddi t i ona l l y , t he os c i l l a t i on f r e que nc y de pe nde nt on t he r e a c t a nc e .
I f t he r e a c t a nc e i s l ow , t he f r e que nc y of t he os c i l l a t i ons w oul d i nc r e a s e a nd vi c e ve r s a .
7
B ) T r an s i e n t S t ab i l i t y
F i gur e 4 s how s t he c i r c ui t of t he i nf i ni t e us w he n a s i ng l e m a c hi ne i s c onne c t e d [ 6] .
A s s um e a f a ul t oc c ur r e d i n a ne t w or k t ha t c a n be r e pr e s e nt e d a s a s i ng l e m a c hi ne
c onne c t e d t o a n i nf i ni t e bus . T he f a ul t r e a c t a nc e i s na m e d X f a nd t he t w o r e a c t a nc e s X 1
a nd X 2 a r e t he e qui va l e nt s y s t e m ’ s r e a c t a nc e s . T he va l ue of X 1 a nd X 2 c ha nge s a s t he
f a ul t l oc a t i on c ha nge s . T he f ol l ow i ng e qua t i on w i l l de s c r i be t he dy n a m i c be ha vi or of t he
s y s t e m i f t he da m pi ng i s ne gl e c t e d:
P e P m
dt
d
M  
2
2

T he c ha nge i n t he r ot or s pe e d i s ne gl e c t e d w hi c h g i ve s a c ons t a nt m e c ha ni c a l pow e r P m .
M or e ove r , t he m e c ha ni c a l pow e r i s a s s um e d t o be ha l f t he m a x i m um e l e c t r i c pow e r . T he
e qui va l e nt r e a c t a nc e be f or e t he f a ul t , X nf i s
2 1 X X X nf  
T he e qui va l e nt r e a c t a nc e of t he ne t w or k dur i ng t he f a ul t a f t e r c onve r t i ng t he w y e t o de l t a
X D f c om e s out t o be :
f
D f
X
X X
X X X
2 1
2 1

  
A s s e e n i n t he pr e vi ous e qua t i on, f or a bol t e d t hr e e pha s e f a ul t t ha t ha s no f a ul t r e a c t a nc e ,
t he r e i s no pow e r t r a ns f e r r e d f r om t he m a c hi ne . I n f a c t , t he pow e r i s de l i ve r e d t o t he
g r ound be c a us e of t he z e r o r e a c t a nc e f a ul t . A f t e r t he f a ul t i s c l e a r e d, t he e qui va l e nt
r e a c t a nc e of t he s y s t e m i s a s s um e d t o r e t ur n t o t he pr e - f a ul t c ondi t i on. T he r e f or e , a s s e e n
i n f i gur e 5, t he r e a l pow e r t r a ns f e r r e d i s de pe nde nt on t he a ngl e . T he s t r a i ght l i ne i n t he
m i ddl e of f i g ur e 5 i s t he P m .
8
F i gur e 5 s how s t he de pe nde nc e of t he a c t i ve pow e r on t he a ngl e [ 7] .
T he e l e c t r i c a l pow e r be f or e t he f a ul t i s e qua l t o t he m e c ha ni c a l pow e r . O nc e t he f a ul t
oc c ur , t he e l e c t r i c pow e r dr oppe d t o z e r o. A c c e l e r a t i on t o t he r a t e of P m / M i s t he r e a c t i on
of t he g e ne r a t or t o t he oc c ur r e nc e of t he f a ul t . A f t e r t he f a ul t i s c l e a r e d, t he ope r a t i ng
pow e r r e t ur ns t o t he hy p e r bol i c pow e r c ur ve . A t t hi s poi nt i n t i m e , t he e l e c t r i c a l pow e r i s
l a r g e r t ha n t he m e c ha ni c a l pow e r . A l s o, t he g e ne r a t or w i l l de c e l e r a t i on t o m ove t he
ope r a t i ng pow e r t o poi nt 5. A t poi nt 5, t he e l e c t r i c a l pow e r i s s t i l l l a r g e r t ha n t he
m e c ha ni c a l pow e r . T he r e f or e , de c e l e r a t i on of t he m a c hi ne t o l e s s t ha n t he s y n c hr onous
s pe e d oc c ur s t o r e s t or e t he ope r a t i on t o poi nt one w he r e t he P e = P m . T he s pe e d of t he
m a c hi ne w i l l i nc r e a s e t o a c hi e ve t he s y n c hr onous s pe e d a t poi nt 6. I f da m pi ng t a ke pl a c e ,
t he g e ne r a t or , w i l l ope r a t e a ga i n a t t he e qui l i br i um poi nt w he r e P e = P m . T he g e ne r a t or ’ s
a c c e l e r a t i on i s de pe nde nt on t he e l e c t r i c a l pow e r dr op dur i ng t he f a ul t [ 8] .
C
M
P e P m
dt
d



2
2

W he r e , C i s c ons t a nt .
A ddi t i ona l l y , t he a ngl e c ha nge dur i ng a f a ul t i s de pe nde nt on t he dur a t i on of t he f a ul t .
T he i nt e g r a t i on of t he s w i ng e qua t i on t w o t i m e s g i ve [ 9] :
i ni t t
M
P e P m
t    


2
) (
9
F i gur e 6 s how s t he a r e a of a c c e l e r a t i on a nd de c e l e r a t i on w he n a f a ul t oc c ur s [ 10]
F or a s t a bl e s y s t e m , A 2 ha s t o be l a r g e r t ha n A 1 . O n t he ot he r ha nd, w he n A 1 i s l a r g e r t ha n
A 2 , t he s y s t e m i s not s t a bl e . T he c r i t i c a l a ngl e i n w hi c h t he f a ul t t o be c l e a r e d a t i s
a c hi e ve d by e qua t i ng t he t w o a r e a s A 1 a nd A 2 . T he r e f or e ,
 
    
c r i t
i ni t
c r i t
i ni t
pf f d P m P e d P e P m




  ) ( ) (
P e f a nd P e a f r e pr e s e nt s t he dur i ng f a ul t a nd pos t f a ul t pow e r s . A s s um e P e f = 0:
 
   
c r i t
i ni t
c r i t
d P m
X e q
E V
d P m




  
m a x
) ) s i n( ( ) (
S ol vi ng y i e l ds
) ( ) c os ( ) c os ( m a x m a x i ni t c r i t
E V
X e q P m
    

 
T he c r i t i c a l t i m e c a n be c a l c ul a t e d f r om [ 1 1 ]
) (
2
1   

 c r i t c r i t
P e P m
M
t
1 0
2 . 1 . 2 V o l t a g e S t a b i l i t y
T he dur a t i on of a di s t ur ba nc e t ha t c a us e s vol t a g e i ns t a bi l i t y t o t he e l e c t r i c g r i d i s
c l a s s i f i e d i nt o t w o t y p e s : l ong t e r m s t a bi l i t y a nd s hor t t e r m , t r a ns i e nt , s t a bi l i t y . F or s t r ong
pow e r s y s t e m s , a s hor t t e r m di s t ur ba nc e doe s not c a us e t he s y s t e m t o l os e i t s vol t a g e
s t a bi l i t y . I n f a c t , t he s y s t e m m a na ge t o w i t hs t a nd t he di s t ur ba nc e . V o l t a ge r e gul a t or s a nd
vol t a g e c om pe ns a t i on de vi c e s i nt e r a c t s w i t h t he s y s t e m i n t he s hor t t e r m dur a t i on. O n t he
ot he r ha nd, t he t a p c ha ngi ng t r a ns f or m e r i nt e r a c t s w i t h t he g r i d i n t he l ong t e r m s t a bi l i t y .
F i gur e 7 s how s di f f e r e nt pow e r c om pone nt s a nd c ont r ol s t r a t e gi e s a nd t he i r t i m e
r e s pons e s .
F i gur e 7 s how s t he V o l t a ge s t a bi l i t y r e s pons e t i m e f or di f f e r e nt c om pone nt s a nd c ont r ol
m e t hods [ 12]
1 1
T o g i ve a g e ne r a l i de a a bout vol t a g e s t a bi l i t y , a s i m pl e t w o bus pow e r s y s t e m w i l l be
a na l y z e d[ 13] .
F i gur e 8 s how s t he s i m pl e t w o bus pow e r s y s t e m [ 14] .
T he r e a l pow e r t r a ns f e r r e d be t w e e n t he t w o bus e s i s g i ve n by
 s i n
X
E V
P 
T he r e a c t i ve pow e r t r a ns f e r r e d be t w e e n t he t w o bus e s i s g i ve n by
 c os
2
X
E V
X
V
Q   
W he r e :
  E = T he vol t a g e a nd a ngl e a t bus 1.
  0 V T he vol t a g e a t bus 1.
X = T he i nduc t a nc e of t he t r a ns m i s s i on l i ne
δ = T he pow e r a ngl e
F or t he s a ke of s i m pl i c i t y , a s s um e :
E
V
v  ,
E
X P
p
2
.
 , a nd
E
X Q
q
2
.
 . T he r e f or e ,
 s i n v p 
 c os
2
v
v
q   
B y s qua r i ng a nd r e a r r a ngi ng t he pr e vi ous t w o e qua t i ons
S ol vi ng f or v y i e l ds ,
) (
2
)
c os s i n
(
2
2
2 2 2
v q
p
v 
    
1 2
S ol vi ng t he pr e vi ous e qua t i on r e s ul t s
q p q v     
2
4
1
2
1
A s s e e n i n f i gur e 9, t he t hr e e di m e ns i ona l pl ot of e qua t i on i s pr e s e nt e d. T he nor m a l i z e d
vol t a g e i s a f unc t i on of t w o va r i a bl e s ( p,q) w hi c h a r e t he nor m a l i z e d r e a l pow e r a nd t he
nor m a l i z e d r e a c t i ve pow e r . M or e ove r , f or e a c h poi nt of ( p,q) , t he r e a r e t w o s ol ut i ons f or
t he nor m a l i z e d vol t a g e . O ne s ol ut i on i s l a r g e r t ha n t he ot he r one . T he l a r g e r s ol ut i on
r e pr e s e nt s t he bus vol t a g e i n t he s y s t e m . O ne t he ot he r ha nd, t he s m a l l e r s ol ut i on
r e pr e s e nt s t he uns t a bl e s ol ut i on. T he l i ne i n t he m i ddl e of f i gur e 9 r e pr e s e nt s t he onl y
c a s e w he n t he t w o s ol ut i ons of v c oi nc i de s a nd r e s ul t s a s i ng l e s ol ut i on. T he s i ng l e
s ol ut i on oc c ur s a t t he m a x i m um ( p,q) . I nc r e a s i ng ope r a t i ng ( p,q) i n t he r e gi on a bove t he
c e nt e r l i ne put s t he s y s t e m i n t he r i ght di r e c t i on t o t he m a x i m um pow e r poi nt s . O n t he
ot he r ha nd, i f t he m a x i m um pow e r poi nt i s r e a c he d, i nc r e a s i ng t he nor m a l i z e d r e a l or
r e a c t i ve pow e r r e s ul t s i ns t a bi l i t y i n t he s y s t e m .
F i gur e 9 s how t he p- q- v of t he t w o bus s y s t e m a nd t he va r i a t i on of e a c h e l e m e nt [ 15] .
1 3
T he r e a r e s e ve r a l m e t hods t o s t udy t he s t e a dy s t a t e vol t a g e s t a bi l i t y . E a c h m e t hod s t udi e s
t he vol t a g e l i m i t w he n t he s y s t e m c ol l a ps e .
A ) P - V c u r ve m e t h od [ 16]
P - V c ur ve m e t hod i s a ve r y c om m on m e t hod t o a na l y z e t he vol t a g e s t a bi l i t y of a ny pow e r
s y s t e m . I t pr ovi de s how m uc h r e a l pow e r i s r e m a i ni ng t o hi t t he m a x i m um pow e r poi nt
t ha t i s c ons i de r e d a s t he c e i l i ng be f or e t he i ns t a bi l i t y oc c ur . F or i nt e r c onne c t e d pow e r
s y s t e m s , P i s t he t ot a l r e a l pow e r i n t he l oa d s i de a nd V i s us ua l l y t he c r i t i c a l bus ’ s
vol t a g e .
F or t he s a ke of s i m pl i c i t y , t he t w o bus s y s t e m i s s t udi e d t o i l l us t r a t e t he P - V c ur ve
m e t hod[ 16] .
F r om q p q v     
2
4
1
2
1
F i ndi ng t he r e a l s ol ut i ons of v^ 2
0 ) 4 4 1 (
2
   p q
A s s um e t ha t q/ p= k
) ) 1 ( (
2
1
2 / 1 2
k
k
p   
T he s ol ut i ons of t he l a s t e qua t i on a r e :
) 4 / 1 ( 2 / 1 (
2
1 p pk pk v     
) 4 / 1 ( 2 / 1 (
2
2 p pk pk v     
T o f i nd t he r e a l s ol ut i on of v , t he e x pr e s s i on unde r t he s qua r e r oot ha s t o be l a r g e r t ha n
z e r o:
0 ) 4 / 1 ( 2 / 1 (
2
     p pk pk
R e a r r a ngi ng g i ve s
0 ) 1 (
2 2
  k p
E qua t i on i s a l w a y s t r ue f or a ny va l ue of p a nd q.
1 4
F i gur e 10 s how s t he t w o bus s y s t e m nor m a l i z e d P - V c ur ve [ 17]
1 5
B ) V - Q c u r ve m e t h od
T he c onc e pt of t he Q - V c ur ve i s i l l us t r a t e d on t he t w o bus s y s t e m a s w e l l . H ow e ve r ,
i t i s not a m us t t o e x pr e s s t he s y s t e m i n i t s T he ve ni n e qui va l e nt c i r c ui t . I n f a c t , a t a ny
g i ve n bus , i t i s pos s i bl e t o pl ot t he nor m a l i z e d r e a c t i ve pow e r w i t h r e s pe c t t o t he g i ve n
bus vol t a g e [ 18] .
T o pl ot t he Q - V c ur ve , a n i m a g i na r y r e a c t i ve pow e r s our c e t ha t ha s no r e a l pow e r
out put i s c onne c t e d t o t he de s i r e d bus . T he i m a g i na r y r e a c t i ve pow e r s our c e c oul d be a
s y n c hr onous c onde ns e r or a s y n c hr onous g e ne r a t or w i t hout r e a l out put pow e r . A l s o, t he
i m a g i na r y r e a c t i ve pow e r s our c e ha s t o ha ve no r e a c t i ve pow e r l i m i t . T he pow e r f l ow
a na l y s i s s houl d t a ke pl a c e t o de t e r m i ne t he a m ount of r e a c t i ve pow e r ne e de d w i t h
di f f e r e nt c hoi c e s of vol t a g e s w i t hi n t he de s i r e d r a nge . A f t e r t ha t , t he Q - V c ur ve i s pl ot t e d.
F i g ur e 1 1 s how s t he t w o bus s y s t e m ’ s Q - V c ur ve [ 19]
1 6
2 . 1 . 3 F r e q u e n c y S t a b i l i t y
F i gur e 12 s how s t he f r e que nc y c ont r ol i n t he pow e r g r i d [ 20]
T he f r e que nc y s t a bi l i t y i s r e l a t e d t o how s t a bl e t he f r e que nc y of t he s y s t e m . T he
f r e que nc y of t he s y s t e m us ua l l y c ha nge s w i t h t he va r i a t i on of t he l oa d. I f t he l oa d
i nc r e a s e s , t he f r e que nc y de c r e a s e s a nd vi c e ve r s a . A ddi t i ona l l y , i t c a n be r e l a t e d t o t he
g e ne r a t i on. I f t he g e ne r a t i on i s m or e t ha n t he l oa d t he f r e que nc y i nc r e a s e s a nd vi c e ve r s a .
T he r e f or e , t he f r e que nc y s t a bi l i t y i s r e l a t e d t o s y s t e m ’ s f r e que nc y r e c ove r y i f a
di s t ur ba nc e oc c ur s t o t he s y s t e m . I f t he f r e que nc y of t he s y s t e m i s not s t a bl e , i t w oul d
r e s ul t s g e ne r a t or ’ s t r i ppi ng . P ow e r s y s t e m f r e que nc y i s us ua l l y 60 or 50 H z . T he r e f or e ,
a n i nc r e a s e of t he f r e que nc y m e a ns a de c r e a s e i n l oa d. O n t he ot he r ha nd, a de c r e a s e i n
t he f r e que nc y m e a ns a l os s i n g e ne r a t i on or a n i nc r e a s e i n l oa d.
T he s t a bi l i t y of t he pow e r s y s t e m i s de pe nde nt on t he a ngl e , vol t a g e , a nd f r e que nc y
s t a bi l i t y . A vol t a g e c ol l a ps e of t he s y s t e m a t a c e r t a i n bus c oul d r e s ul t a bl a c kout i n a
r e gi on of a g r i d w hi c h r e s ul t s f r e que nc y or a ngul a r i ns t a bi l i t y .
1 7
2 . 2 E l e c t r i c V e h i c l e s
F i gur e 13 s how s t he 3 t y p e s of ve hi c l e s [ 21] .
T he pr ogr e s s i n t he i nve nt i on of t he t r a ns por t a t i on m e a ns ne ve r s t ops . H um a n be i ngs a r e
de ve l opi ng t he e x i s t i ng t e c hnol ogi e s t o be c om e be t t e r i n e f f i c i e nc y a nd r e duc e t he i r
pot e nt i a l ne g a t i ve i m pa c t s on t he e nvi r onm e nt . O ne e x a m pl e of t he pr ogr e s s i n t he
de ve l opm e nt of t e c hnol og y i s t he i m pr ove m e nt of c a r s . F or m t he i nt e r na l c om bus t i on
e ngi ne ve hi c l e s ( I C E V ) t ha t de pe nds m a i nl y on g a s ol i ne t o pl ug i n hy b r i d e l e c t r i c
ve hi c l e s ( P H E V s ) a s s e e n i n f i gur e 13. T he c onve nt i ona l ve hi c l e i s not t he be s t opt i on i n
t e r m s of e f f i c i e nc y a nd i t c a us e s s o m uc h ha r m t o t he e nvi r onm e nt t hr oug h t he a dve r s e
e m i s s i on t he r e l e a s e i n t he a i r .
T he hy b r i d e l e c t r i c ve hi c l e s ( H E V ) w a s t he i m pr ove m e nt a f t e r t he c onve nt i ona l ve hi c l e
t ha t i t ut i l i z e t he br e a ki ng s y s t e m t o c ha r g e t he ba t t e r y . A f t e r t ha t , t he a dve nt of P H E V s
w a s t he ne x t br e a kt hr ough i n t he ve hi c l e ’ s pr ogr e s s i n w hi c h t he y c a n be c ha r g e d f r om
t he ut i l i t i e s a nd us e g a s ol i ne i f t he ba t t e r y i s not c ha r g e d. T he ne x t pr ogr e s s i s t he E V
w hi c h us e s onl y t he g r i d a s a s our c e of pow e r . T he f oc us of t hi s t he s i s i s on t he ve hi c l e s
t ha t c a n be c ha r g e d f r om t he g r i d ( E V s ) .
1 8
F i gur e 14 s how s t he l a y o ut of ve hi c l e s [ 22]
U nf or t una t e l y a s i g ni f i c a nt a m ount of t he g r e e nhous e g a s e m i s s i ons a r e r e l e a s e d f r om t he
t r a ns por t a t i on f ue l a s s e e n i n f i g ur e 15. T he r e f or e , m a ki ng t he t r a ns por t a t i on m e a ns
e m i s s i ons f r e e i s r e que s t i n or de r t o m a ke t he a i r c l e a n. N ot e onl y t ha t , t he r e duc t i on of
t he us e of s ubs t a nc e s t ha t r e l e a s e ba d e m i s s i ons i s a ddr e s s e d a s one of t he t hi ng s t ha t
m a i nt a i n t he e nvi r onm e nt s us t a i na bl e .
F i gur e 15 s how s t he s our c e s of g r e e n g a s e m i s s i ons [ 23]
A ddi t i ona l l y , i t i s c l e a r f r om f i g ur e 15 t ha t t he g r e e nhous e g a s t ha t a r e e m i t t e d f r om t he
t r a ns por t a t i on m e a ns i s c om pa r a bl e t o t he e m i s s i ons f r om i ndus t r i a l pr oc e s s e s . T he r e f or e ,
t he pr om ot i on of e l e c t r i c ve hi c l e s w i l l m i t i g a t e t he g r e e nhous e e m i s s i ons .
1 9
E V ’ s C h ar gi n g L e ve l s [ 24]
A ) L e ve l 1
L e ve l 1 c ha r g i ng us e s 120 A c - vol t s a nd 15 A C - A m pe r e s . I t c ha r g e s us i ng a hous e hol d
s oc ke t di r e c t l y w i t hout a c ha r g i ng uni t . A ddi t i ona l l y , t he ba t t e r y us e d de t e r m i ne s t he
a m ount of t i m e ne e de d t o be f ul l y c ha r g e d. T y pi c a l l y , t he t i m e r a nge i s be t w e e n f our t o
e l e ve n hour s . S i nc e l e ve l 1 r e qui r e s m a ny hour s t o c ha r g e , i t i s r e c om m e nde d f or
c us t om e r s t o c ha r g e t he i r ve hi c l e s ove r ni ght .
B ) L e ve l 2
L e ve l 2 c ha r g i ng us e s 240 A c - vol t s a nd 32 A C - A m pe r e s . S e pa r a t e c ha r g i ng uni t i s
m a nda t e d t o c ha r g e t hr oug h l e ve l 2. T y pi c a l l y , c ha r g i ng uni t i s i ns t a l l e d i n publ i c or
i ns i de t he hous e . M os t e l e c t r i c ve hi c l e s a r e c ha r g e d t hr ough l e ve l 2 be c a us e i t i s
e c onom i c a nd doe s not r e qui r e a l ot of t i m e t o c ha r g e . T he a ve r a ge c ha r g i ng t i m e i s
be t w e e n t w o t o s i x hour s .
C ) L e ve l 3
L e ve l 3 c ha r g i ng us e s 480 D C - vol t s . T he r e f or e , a r e c t i f i e r i s r e qui r e d t o r e c t i f y t he
vol t a g e f r om A C t o D C . L e ve l 3 c ha r g e s e l e c t r i c ve hi c l e s f a s t e r t ha n l e ve l 2 a nd l e ve l 1.
T he a ve r a ge c ha r g i ng t i m e i s be t w e e n f or t y m i nut e s up t o a n hour . T he m a i n
di s a dva nt a ge of l e ve l 3 i s t he hi g h c os t of t he c ha r g i ng uni t .
2 0
2 . 3 D y n a m i c D e v i c e s
2 . 3 . 1 S y n c h r o n o u s C o n d e n s e r
S y n c hr onous c onde ns e r s a r e de vi c e s t ha t c ons i de r e d t o ope r a t e unde r t he pr i nc i pa l of
s y n c hr onous m a c hi ne . I t i s ba s i c a l l y a s y n c hr onous g e ne r a t or or m ot or t ha t i t s s ha f t s pi ns
f r e e l y a nd i t i s not c onne c t e d t o a ny t hi ng . I t i s not us e d t o pr ovi de a n a c t i ve pow e r f or t he
s y s t e m , i t i s s uppos e d t o i m pr ove t he vol t a g e pr of i l e of t he s y s t e m . S y n c hr onous
c onde ns e r s a dj us t t he vol t a g e pr of i l e of t he s y s t e m by pr ovi di ng r e a c t i ve pow e r . A s a
r e s ul t of t ha t , t he pow e r f a c t or i s i m pr ove d w hi c h r e s ul t a be t t e r vol t a g e pr of i l e .
T he r e a r e di f f e r e nt m ode l s of a s y n c hr onous m a c hi ne . H ow e ve r t he r e a r e t hr e e m a i n
t y p e s w hi c h i nc l ude a s e ve n s t a t e va r i a bl e m ode l , s our c e be hi nd a r e a c t a nc e , a nd a s our c e
be hi nd a s ub- t r a ns i e nt [ 25] . T he pr e vi ous m ode l s di f f e r s i n t e r m of us a ge w i t h r e s pe c t t o
di f f e r e nt a ppl i c a t i ons .
C yl i n d r i c al R ot or [ 26]
T he pr i nc i pa l of ope r a t i on of s y n c hr onous m a c hi ne s l i e s w i t hi n t he r e l a t i ons hi p
di s c ove r e d be t w e e n t he m a gne t i c a nd e l e c t r i c f i e l ds s y n c hr onous m a c hi ne . W he n t he r e i s
a r ot a t i ng m a gne t i c f i e l d, a vol t a g e w i l l be i nduc e d i n t he ot he r e l e c t r i c a l l y i s ol a t e d
c i r c ui t . T he t w o pa r t s of t he c i r c ui t a r e t he s t a t or a nd t he r ot or . T he r e l a t i ons hi p be t w e e n
t he vol t a g e t ha t i s i nduc e d t o t he s t a t or by t he m a g ne t i c f i e l ds i s g i ve n by e qua t i on 1:
dt
as d
i as r s V as

  
T he va l ue of t he f l ux l i nka g e ( l a m bda ) i s de pe nde nt on t he e a c h c oi l ’ s i nduc t a nc e a nd t he
m a gne t i c c ont r i but i on of t he ot he r c oi l s t ha t e x i s t on t he s t a t or a nd r ot or .
2 1
F i gur e 16 s how s a M ode l of C y l i ndr i c a l R ot or S y n c hr onous M a c hi ne [ 27]
F i gur e 16 i s a r e pr e s e nt a t i on of a s e c t i ona l vi e w of a s y n c hr onous m a c hi ne w i t h t hr e e
pha s e . F or t he s a ke of s i m pl i c i t y , f i gur e 16 i s c r os s s e c t i ona l a r e a of a t w o pol e
s y n c hr onous m a c hi ne . F or N num be r of pol e s , t he s a m e a ppr oa c h i s a ppl i e d. C oi l s a s - a s ’ ,
bs - bs ’ , a nd c s - c s ’ r e pr e s e nt s w i ndi ng s t ha t a r e w r a ppe d a r ound t he s t a t or w hi c h
r e s pons i bl e of t he g e ne r a t i on of t he m a gne t o- m ot i ve f or c e ( M M F ) . T he f d- f d ’ a r e a
r e pr e s e nt a t i on of t he w i ndi ng di s t r i but e d on t he r ot or w hi c h i s e s s e nt i a l t o pr oduc e t he
s t a t i one r y m a gne t i c f i e l d f or t he m a c hi ne . M or e ove r , kd- kd ’ a nd kq- kq ’ a r e a
r e pr e s e nt a t i on of t he da m pe r w i ndi ng s w hi c h da m pe n t he m a c hi ne ’ s os c i l l a t i ons .
2 2
F i gur e 17 s how s t he I n duc t a nc e S e e n B y T w o P ol e C y l i ndr i c a l R ot or M a c hi ne [ 28]
F i gur e 17 s how s a n i l l us t r a t i on of t he i nduc t a nc e g e ne r a t e d by t he t w o pol e s y n c hr onous
m a c hi ne w i t h c y l i ndr i c a l r ot or . W he n t he r ot or r ot a t e s i ns i de t he s t a t or , t he ove r a l l
i nduc t a nc e be t w e e n pha s e A a nd t he r ot or i s f i x e d ove r t i m e . T hi s i s a c hi e ve d be c a us e of
t he l a y o ut of t he m a c hi ne . T he s a m e i de a i s a ppl i e d f or a m a c hi ne w i t h a n N num be r of
pol e s .
2 3
T he f l ux l i nka g e of e a c h of t he w i ndi ng s i s de r i ve d us i ng F a r a da y ’ s l a w a s i n
e qua t i on[ 29] :
i f L af i c L ac i b L ab i a L aa a         
i f L bf i c L bc i b L bb i a L ba b         
i f L c f i c L c c i b L c b i a L c a c         
i f L f f i c L f c i b L f b i a L f a f         
T he i nduc t a nc e s w i t h s i m i l a r l e t t e r s a r e t he s e l f - i nduc t a nc e s of t he w i ndi ng . O n t he ot he r
ha nd, t he i nduc t a nc e s w i t h di f f e r e nt l e t t e r s i ndi c a t e s t he m ut ua l i nduc t a nc e s be t w e e n t he
t w o m e nt i one d c oi l s . I n a s y n c hr onous m a c hi ne , t he r e a r e t hr e e t y p e s of i nduc t a nc e s :
r ot or s e l f - i nduc t a nc e , r ot or - t o- s t a t or m ut ua l i nduc t a nc e , a nd s t a t or i nduc t a nc e s .
A ) R ot or S e l f - I n d u c t an c e [ 30]
T he r ot or s e l f i nduc t a nc e i s i nde pe nde nt of t he a ngul a r pos i t i on of t he r ot or be c a us e of
t he g e om e t r y of t he m a c hi ne . A ddi t i ona l l y , t he e f f e c t of t he ha r m oni c s a nd t he ope ni ng s
of t he s t a t or a r e ne g l e c t e d. T he f ol l ow i ng e qua t i on i s t he r e s ul t of t he pr e vi ous
a s s um pt i ons :
L f l L f f L f f   0
L f f o i s a r e pr e s e nt a t i on of t he a i r - g a p f l ux ’ s f unda m e nt a l c om pone nt be t w e e n t he s t a t or
a nd r ot or . M or e ove r , L f l r e pr e s e nt s t he l e a ka ge f l ux of t he f i e l d w i ndi ng t ha t ha ve no
l i nka g e c ont r i but i on t o t he ot he r c oi l s . T he pr e vi ous a s s um pt i ons onl y a ppl y i n t he s t e a dy
s t a t e c ondi t i on. I n c a s e of a t r a ns i e nt i nc i de nt , t he f l ux be ha vi or w i l l c ha nge ove r t i m e
w hi c h c ha nge t he vol t a g e s g e ne r a t e d i n t he c i r c ui t of t he r ot or .
B ) S t at or t o R ot or M u t u al I n d u c t an c e s [ 31]
T he s t a t or t o r ot or i nduc t a nc e s i s not c ons t a nt w i t h r e s pe c t t o t he a ngul a r pos i t i on of t he
r ot or ( Ɵ ) s i m i l a r t o t he r ot or s e l f - i nduc t a nc e . T he y c ha nge ove r t i m e i ns t e a d. A ngl e Ɵ
r e pr e s e nt s t he di f f e r e nc e be t w e e n t he pha s e a r m a t ur e w i ndi ng a nd t he f i e l d w i ndi ng s ’
2 4
m a gne t i c a x i s of t he r ot or .
A s s um e t he di s t r i but i on of t he a i r g a p f l ux, s pa c e m m f a nd t he m ut ua l i nduc t a nc e s
be t w e e n t he s t a t or a nd r ot or i nduc t a nc e s a r e va r y i ng ove r t i m e a s a c os i ne f unc t i on. W i t h
t he pr e vi ous a s s um pt i ons , t he f ol l ow i ng e x pr e s s i on c om e s out :
 c os    L af L f a L af
T he m ut ua l i nduc t a nc e be t w e e n t he ot he r t w o pha s e s B a nd C obe y t he s a m e e qua t i ons
but t a ki ng i nt o c ons i de r a t i on t he 120 de gr e e s pha s e s hi f t be t w e e n t he pha s e s .
0      t
Ɵ o r e pr e s e nt t he pos i t i on of t he r ot or a t t he be gi nni ng ( w he n t = 0) . T he f ol l ow i ng
e qua t i on de s c r i be s t he f l ux l i nka g e be t w e e n t he r ot or a nd P ha s e A w he n a D C e x c i t a t i on
( I f ) i s a ppl i e d:
) c os ( 0        t I f L af af
C ) S t at or I n d u c t an c e s [ 32]
I n a c y l i ndr i c a l r ot or m a c hi ne , t he a i r - g a p i s not de pe nde nt on t he a ngul a r pos i t i on s i nc e
t he di s t a nc e be t w e e n a ny poi nt i n t he c i r c um f e r e nc e of t he r ot or i s f i xe d. C ons e que nt l y ,
a l l s e l f i nduc t a nc e s of t he s t a t or a r e e qua l i n m a gni t ude a nd do not c ha nge ove r t i m e . T he
f ol l ow i ng e qua t i on r e pr e s e nt s t he s e l f i nduc t a nc e s of t he s t a t or :
L al L aa L aa L c c L bb L aa      0
L a a o i s t he c om pone nt of t he s e l f i nduc t a nc e c a us e d by t he a i r g a p. L a l i s t he a r m a t ur e ’ s
l e a ka ge f l ux . T he f ol l ow i ng e qua t i on r e pr e s e nt s t he pha s e t o pha s e m ut ua l i nduc t a nc e s :
0
2
1
L aa L c b L bc L c a L ac L ba L ab       
2 5
P ha s e A ’ s f l ux l i nka g e i s g i ve n by :
af i c i b L aa i a L al L aa a         ) (
2
1
) ( 0 0 ( 2)
F or a ba l a nc e d t hr e e pha s e s y s t e m :
0    i c i b i a
S ubs t i t ut i ng i n ( 2) y i e l ds
af i a L aa i a L al L aa a        0 0
2
1
) (
af i a L al L aa a      )
2
3
( 0 ( 3)
T he r e i s a n i m por t a nt pa r a m e t e r t o be i nt r oduc e d a t t hi s poi nt c a l l e d t he s y n c hr onous
i nduc t a nc e ( L s ) . I t i s g i ve n by t he f ol l ow i ng e qua t i on:
L al L aa L s   0
2
3
A ppl y i ng s y n c hr onous i nduc t a nc e e qua t i on t o e qua t i on ( 3) y i e l ds
af i a L s a     
A t t hi s poi nt , t he e qua t i ons of t he f l ux l i nka g e f or e a c h pha s e ha s be e n de r i ve d. N ow , i t i s
t i m e t o r e a c h t he a i m of t he a l l t he pr e vi ous de r i va t i on w hi c h i s f i ndi ng t he s y n c hr onous
g e ne r a t or ’ s t e r m i na l vol t a g e e qua t i on w hi c h i s :
dt
as d
i as r s V T

  
I t c a n be e x pr e s s e d a s :
dt
af d
dt
di
L s i as r s V
as
T

   
R e c a l l t ha t
) s i n( 0   

       t I f L af
dt
af d
E af
2 6
E a f i s t he e x c i t a t i on vol t a g e t ha t i s c r e a t e d f r om t he r ot or ’ s f l ux . U s i ng t he f ol l ow i ng
t r i g onom e t r i c i de nt i t y :
)
2
c os ( s i n

    
T o r e w r i t e e x c i t a t i on vol t a g e e qua t i on y i e l ds
)
2
c os ( 0

          t I f L af E af
D i vi di ng t he a m pl i t ude of E a f by t he s qua r e r oot of 2 t o g e t t he r m s va l ue y i e l ds :
2
I f L af
E af
 


T he r e f or e , t he e qua t i on of t he e x c i t a t i on vol t a g e c a n be r e w r i t t e n a s
E af
dt
di
L s I a R a V
a
T     
T hus ,
E af I a j X s I a R a V T      ( 4)
E qua t i on 4 r e pr e s e nt e d t he pa r a m e t e r s ne e de d t o e x pr e s s a m ode l of t he s y n c hr onous
m a c hi ne . T he r e f or e , a c i r c ui t m ode l c oul d be dr a w n t o e x pr e s s t he m a t he m a t i c a l f or m of
t he s y n c hr onous m a c hi ne i n a c i r c ui t m ode l .
F i gur e 18 s how s t he s y n c hr onous m a c hi ne s ’ s s t e a dy s t a t e m ode l [ 33] .
2 7
2 . 3 . 2 S t a t i c V a r C o m p e n s a t o r ( S V C )
T he s t a t i c va r c om pe ns a t or i s one of t he de vi c e s i n t he F A C T S ( f l e x i bl e a l t e r na t i ng
c ur r e nt t r a ns m i s s i on s y s t e m s ) [ 34] . T he m a i n g oa l of t hi s s y s t e m i s be a bl e t o s uppl y t he
ne e de d a m ount of r e a c t i ve pow e r t o t he pow e r s y s t e m a s f a s t a s pos s i bl e . T he f a s t s uppl y
of r e a c t i ve pow e r ne e de d i s a c hi e ve d by t he s w i t c hi ng of t he t hy r i s t or - s w i t c he d
c a pa c i t or s i n a nd out . A l s o, by c ont r ol l i ng t he t hy r i s t or - c ont r ol l e d r e a c t or ’ s f i r i ng a ngl e .
F i gur e 19 s how s how t he s hunt - c a pa c i t or ba nks a nd S V C c onne c t e d i n a t r a ns m i s s i on
l i ne [ 35] .
S V C s a r e s om e t i m e s i ns t a l l e d i ns t e a d of c a pa c i t or ba nks i n t he r e c e i vi ng e nd of t he
t r a ns m i s s i on l i ne i n or de r t o pr ovi de a vol t a g e c om pe ns a t i on. T he y a r e us e d i ns t e a d of
s hunt c a pa c i t or s f or s e ve r a l r e a s ons s uc h a s t he be t t e r c ont r ol of t he vol t a g e
c om pe ns a t i on. A ddi t i ona l l y , S V C s a r e w i de l y us e d t o i m pr ove t he dy n a m i c s t a bi l i t y of
t he s y s t e m by pr ovi di ng r e a c t i ve pow e r t o s t a bi l i z e t he s y s t e m .
T o a c hi e ve a be t t e r vol t a g e c om pe ns a t i on f or pow e r s y s t e m s , S V C s s houl d r e pl a c e t he
s hunt c a pa c i t or ba nks . H ow e ve r , r e pl a c i ng t he c a pa c i t or ba nks w i t h S V C s i s be t t e r i n
t e r m s of pe r f or m a nc e but t he pr i c e of S V C s i s ve r y hi g h c om pa r e d t o c a pa c i t or ba nks . I n
f a c t , s om e t i m e s S V C pr i c e c oul d r e a c h f i ve t i m e s t he pr i c e of s hunt c a pa c i t or ba nks [ 36] .
T he r e f or e , m os t ut i l i t y c om pa ni e s do not r e pl a c e s hunt c a pa c i t or ba nks w i t h S V C s
be c a us e of t he pr i c e , e ve n t houg h t he pe r f or m a nc e i s be t t e r . A ddi t i ona l l y , a not he r r e a s on
f or t he ut i l i t y c om pa ni e s not t o r e pl a c e t he s hunt c a pa c i t or ba nks w i t h S V C s i s t ha t t he
vol t a g e c om pe ns a t i on r e s ul t e d f r om s hunt c a pa c i t or ba nks i s ve r y a c c e pt a bl e a nd i s not
w or t h t he a m ount of m one y ne e de d t o r e pl a c e i t .
2 8
S V C s c a n be g e ne r a l l y c l a s s i f i e d i nt o t w o t y p e s : t he f i r s t t y p e i s t he t hy r i s t or - c ont r ol l e d
r e a c t or w i t h f i x e d c a pa c i t or ( T C R - F C ) a nd t he s e c ond t y p e i s t he t hy r i s t or - c ont r ol l e d
r e a c t or w i t h t hy r i s t or s w i t c he d c a pa c i t or ( T C R - T S C ) .
1) T C R - F C t yp e S V C
T he t hy r i s t or - c ont r ol l e d r e a c t or w i t h f i x e d c a pa c i t or ( T C R - F C ) ha s a t hy r i s t or - c ont r ol l e d
r e a c t or t ha t i s pl a c e d t o a bs or b t he e x c e s s i ve r e a c t i ve pow e r f r om t he s y s t e m t ha t ha s t he
S V C . A l s o, i t i nc l ude s a c a pa c i t or ba nk t ha t ha s a f i x e d c a pa c i t a nc e va l ue t ha t s uppl i e s a n
a m ount of r e a c t i ve pow e r t o t he pow e r s y s t e m w hi c h t he S V C i s c onne c t e d t o.
F i gur e 20 s how s t he l a y o ut of t he T C R - F C t y p e S V C [ 37] .
A s s e e n i n f i gur e 20, t he c a pa c i t a nc e of t he f i x e d c a pa c i t or s a r e c ons t a nt a nd c a n not va r y
w i t h r e s pe c t t o t he r e a c t i ve pow e r ne e de d by t he s y s t e m . A l s o, s w i t c hi ng t he c a pa c i t or s i n
a nd out c a nnot be done .
O n t he ot he r ha nd, t he r e a c t i ve pow e r a bs or be d by t he r e a c t or c a n be c ont r ol l e d by t he
t hy r i s t or s . B y m odi f y i ng t he f i r i ng a ngl e of t he t hy r i s t or s , t he r e a c t i ve pow e r a bs or be d
c ha nge s .
2 9
F i gur e 21 s how s a s i m pl i f i e d one pha s e di a gr a m of T C R - F C t y p e S V C [ 38] .
F i gur e 21 s how s a s i m pl i f i e d ve r s i on of one pha s e of t he T C R - F C t y p e S V C . T he a m ount
of r e a c t i ve pow e r ne e de d by t he s y s t e m t o s t a bi l i z e va r y w i t h r e s pe c t t o t he c ondi t i ons of
t he pow e r s y s t e m . T he r e f or e , t he f i r i ng a ngl e of t he t hy r i s t or s i s a dj us t e d t o m a ke t he
t ot a l r e a c t i ve pow e r a bs or be d or s uppl i e d by t he S V C s ui t a bl e f or t he s y s t e m . F or
e x a m pl e , i f t he r e i s no r e a c t i ve pow e r ne e de d t o be s uppl i e d t o t he pow e r s y s t e m or
a bs or be d by t he S V C , t he t hy r i s t or ’ s f i r i ng a ngl e ha s t o be a dj us t e d t o a bs or b a l l t he
r e a c t i ve pow e r s uppl i e d by t he f i x e d c a pa c i t or s .
M or e ove r , i f t he r e i s a l a c k of r e a c t i ve pow e r i n t he s y s t e m , t he S V C c a n pr ovi de t he
a m ount ne e de d. T hi s c a n be a c hi e ve d by t he a dj us t i ng t he f i r i ng a ngl e of t he t hy r i s t or s . I f
t he f i r i ng a ngl e i nc r e a s e s t he c ons um e d r e a c t i ve pow e r by t he S V C de c r e a s e s . T he l e s s
r e a c t i ve pow e r c ons um e d by t he S V C , t he m or e s uppl i e d r e a c t i ve pow e r t o t he s y s t e m .
A ddi t i ona l l y , i f t he f i r i ng a ngl e of t he t hy r i s t or w a s not t ur ne d on, t he m a x i m um a m ount
of r e a c t i ve pow e r i s s uppl i e d t o t he s y s t e m . T hi s m e a ns t ha t t he S V C i s a c t i ng a s a pur e
f i x e d c a pa c i t or w i t h a s pe c i f i c r a t i ng .
3 0
O n t he c ont r a r y , w he n t he pow e r s y s t e m ha s e x c e s s i ve r e a c t i ve pow e r , t he S V C c a n
a bs or b i t t o m a i nt a i n t he vol t a g e a t a n a c c e pt a bl e l e ve l . T he T C R ha s t o a bs or b a n
e qui va l e nt a m ount of r e a c t i ve pow e r g e ne r a t e d by t he c a pa c i t or s f i r s t a nd t he n a bs or b t he
e x c e s s i ve r e a c t i ve pow e r s uppl i e d by t he pow e r s y s t e m . I t i s not a bl e , i n t he T C R - F C , t ha t
t he r e a c t i ve r a t i ng of t he r e a c t or ha s t o be s uf f i c i e nt l y l a r g e r t ha n t he r a t i ng of t he f i x e d
c a pa c i t or s i n or de r f or t he e x c e s s i ve r e a c t i ve pow e r i n t he s y s t e m t o be a bs or be d.
F i gur e 21 s how s t he c ha r a c t e r i s t i c of T C R - F C ’ s r e a c t i ve pow e r e x c ha nge [ 39]
T o c ont r ol t he T C R - F C , t he a m ount of r e a c t i ve a bs or be d or s uppl i e d by t he T C R ha s t o
m a t c h w ha t i s ne e de d by t he s y s t e m a nd t o c oor di na t e t he f i r i ng a ngl e t o pr oduc e a n
e qui va l e nt va l ue .
3 1
T he m a j or di s a dva nt a ge of t he T C R - F C l i e s i n t he r a t i ng ne e de d f or t he r e a c t or . T he
r e a c t or ne e ds t o ha ve a l a r g e r pow e r r a t i ng t ha n t he f i x e d c a pa c i t or . A s a r e s ul t of t ha t , t he
s i z e of t he r e a c t or w i l l be l a r g e w hi c h c oul d r e s ul t pr obl e m s i n pl a c i ng i t t he s ubs t a t i on.
F or i ns t a nc e , i f t he T C R - F C S V C i s de s i gne d t o pr ovi de a va r i a bl e a m ount of r e a c t i ve
pow e r be t w e e n - 200 M va r a nd + 70 M va r , t he r e a c t or r e a c t i ve pow e r r a t i ng ha s t o be 270
M va r . T hi s i s be c a us e t he r e a c t or ha s t o pr ovi de r e a c t i ve pow e r t ha t i s e qui va l e nt t o t he
r e a c t i ve pow e r c a pa c i t y of t he c a pa c i t or s pl us t he r e a c t i ve pow e r ne e de d by t he s y s t e m .
2 ) T C R - T S C t yp e S V C
T C R - T S C ( T hy r i s t or - c ont r ol l e d r e a c t or w i t h t hy r i s t or s w i t c he d c a pa c i t or ) ha s t w o m a i n
m a i n c om pone nt s : t he f i r s t one i s t he t hy r i s t or - c ont r ol l e d r e a c t or a nd t he s e c ond one i s
t hy r i s t or s w i t c he d c a pa c i t or . T he t hy r i s t or - c ont r ol l e d r e a c t or i s pl a c e d t o a bs or b t he
r e a c t i ve pow e r f r om t he pow e r s y s t e m . O n t he ot he r ha nd, t he t hy r i s t or s w i t c he d
c a pa c i t or ba nks a r e pl a c e d i n or de r t o s uppl y r e a c t i ve pow e r t o t he s y s t e m i f t he s y s t e m
r e qui r e s r e a c t i ve pow e r . I t i s i m por t a nt t o know t ha t T C R - T S C m i g ht ha ve f i xe d
c a pa c i t or s i n s om e c a s e t o ope r a t e a s a ha r m oni c f i l t e r .
F i gur e 23 s how s t he l a y o ut of t he T C R - T S C [ 40]
3 2
A s s e e n i n f i gur e 23, i t i s pos s i bl e t o s w i t c h t he c a pa c i t or ba nks i n t hi s c onf i gur a t i on on
or of f . T he a m ount of r e a c t i ve pow e r s uppl i e d t o t he s y s t e m c a n be c ont r ol l e d by
s w i t c hi ng t he s hunt c a pa c i t or s out a nd i n s e r vi c e . I f a hi g h a m ount of r e a c t i ve pow e r i s
ne e de d t o be s uppl i e d t o t he s y s t e m , m or e c a pa c i t or ba nks ha ve t o be s w i t c he d i n. O n t he
ot he r ha nd, t he l ow e r t he r e a c t i ve pow e r ne e de d t o be s uppl i e d t he m or e c a pa c i t or s a r e
r e qui r e d t o be s w i t c he d of f .
O n t he ot he r ha nd, t he t hy r i s t or - c ont r ol l e d r e a c t or c a n be c ont r ol l e d t o c oor di na t e w i t h
t he T S C s i n or de r t o a c hi e ve t he de s i r e d r e a c t i ve pow e r out put . T hi s i s a c hi e ve d by
c ha ngi ng t he va l ue of t he f i r i ng a ngl e f r om 90 de gr e e s , w hi c h r e pr e s e nt s t he c onduc t i on
s t a t e , a nd 180 de gr e e s , w hi c h r e pr e s e nt s t he i s ol a t i on s t a t e .
F i gur e 24 s how s a one pha s e s i m pl i f i e d ve r s i on of t he T C R - T S C [ 41]
F i gur e 24 r e pr e s e nt s a s i m pl i f i e d ve r s i on of t he t hy r i s t or - c ont r ol l e d r e a c t or w i t h t hy r i s t or
s w i t c he d c a pa c i t or . F or t he s a ke of s i m pl i c i t y , onl y one pha s e i s t a ki ng i nt o c ons i de r a t i on
be c a us e i f t he s i ng l e pha s e i s unde r s t ood, t he s a m e c onc e pt w i l l be a ppl i e d f or t he ot he r
t w o pha s e s . F i gur e 24 di s pl a y s t he ba s i c e l e c t r i c a l va l ue s s uc h a s t he vol t a g e a c r os s t he
S V C , c ur r e nt i n t he T S C a nd t he c ur r e nt i n t he T C R .
3 3
F or e a c h r e a c t i ve pow e r r e qui r e m e nt , t he r e i s a w a y t o g e t t he de s i r e d out c om e . F or
e x a m pl e , i f t he r e i s no r e a c t i ve pow e r i s ne e de d t o be s uppl i e d or c ons um e d by t he
s y s t e m , t he T S C s a r e r e qui r e d t o be s w i t c he d out . I n a ddi t i on t o t he t hy r i s t or s t o ope r a t e
a t t he 180 de gr e e s a ng l e w hi c h r e pr e s e nt s t he nonc onduc t i ng s t a t e .
M or e ove r , i f t he r e a c t i ve pow e r i s ne e de d by t he pow e r s y s t e m , t he r i g ht num be r of t he
T S C s a r e t o be s w i t c he d i n i n or de r t o m a t c h or us ua l l y e x c e e ds t he a m ount of r e a c t i ve
pow e r r e qui r e d by t he s y s t e m . I f t he r e a c t i ve pow e r g e ne r a t e d by t he T S C s e x c e e d t he
r e qui r e d r e a c t i ve pow e r by t he s y s t e m , t he f i r i ng a ngl e of t he T C R ha s t o be a dj us t e d t o a
va l ue t ha t c a nc e l s out t he e x t r a r e a c t i ve pow e r s uppl i e d by t he T S C s s o t ha t t he ove r a l l
s uppl i e d r e a c t i ve pow e r m a t c he s t he r e qui r e d r e a c t i ve pow e r by t he s y s t e m .
A ddi t i ona l l y , i f t he r e a c t i ve pow e r ne e de d by t he pow e r s y s t e m t o c om pe ns a t e t he ove r a l l
vol t a g e pr of i l e of t he s y s t e m , a T S C c a n be i nt r oduc e d t o t he s y s t e m by s w i t c hi ng i t on.
C onve r s e l y , one or m or e T S C c a n be t a ke n out of s e r vi c e i f t he r e a c t i ve pow e r r e qui r e d
by t he s y s t e m de c r e a s e s i n or de r t o m e e t t he r e a c t i ve de m a nd. W he t he r t he r e a c t i ve
pow e r ne e de d by t he s y s t e m i nc r e a s e s or de c r e a s e s , t he f i r i ng a ngl e of t he T C R ha s t o be
c oor di na t e d i n or de r t o g e t t he f i na l de s i r e d out put .
I n t he oppos i t e of t ha t , t he r e a c t i ve pow e r i n t he pow e r s y s t e m c a n e x c e e d w ha t i s ne e de d
a nd c a us e s pr obl e m s t o t he vol t a g e pr of i l e of t he s y s t e m . T he r e f or e , t he T C R - T S C c a n
pr ovi de a w a y t o da m p or c ons um e t he e x t r a r e a c t i ve pow e r .
T he c ons um pt i on of t he r e a c t i ve pow e r i s a c hi e ve d by s w i t c hi ng of f a l l t he T S C i n or de r
t o g e t z e r o s uppl i e d r e a c t i ve pow e r . I n a ddi t i on of t ha t , t he f i r i ng a ngl e of t he T C R ha s t o
be c ha nge d t o c ons um e t he s uppl i e d r e a c t i ve pow e r by t he pow e r s y s t e m .
3 4
F i gur e 25 s how s t he c ha r a c ht e r s i t c of r e a c t i ve pow e r e x c ha ng e i n t he T C R - T S C S V C
t y p e [ 42] .
A s s e e n i n f i gur e 25, t he ove r a l l c ons um e d or s uppl i e d r e a c t i ve pow e r Q L by t he
T C R - T S C e qua l s t o t he t ot a l r e a c t i ve pow e r s uppl i e d by t he T S C Q c s ubt r a c t e d f r om t he
t ot a l r e a c t i ve pow e r c ons um e d by t he T C R Q L .
I n or de r t o ha ve a n e f f i c i e nt T C R - T S C , t he c ont r ol of t he T C R - T S C ha s t o t a ke s e ve r a l
e s s e nt i a l t a s ks i nt o c ons i de r a t i on. F i r s t , t he c ont r ol l e r ha s t o be a bl e t o de t e r m i ne how
m a ny T S C s a r e r e qui r e d t o s uppl y r e a c t i ve pow e r a nd how m uc h r e a c t i ve pow e r i s
ne e de d t o be c ons um e d by t he T C R by c ont r ol l i ng t he f i r i ng a ngl e . S e c ond, t o s w i t c h t he
T S C a nd c oor di na t e be t w e e n i t a nd t he f i r i ng a ngl e .
3 5
2 . 3 . 3 S t a t i c S y n c h r o n o u s C o m p e n s a t o r ( S T A T C O M )
F i gur e 26 s how s t he S T A T C O M c onne c t e d t o t he r e c e i ve r e nd[ 43]
T he S t a t i c S y n c hr onous C om pe ns a t or i s a f l e x i bl e A C t r a ns m i s s i on de vi c e . T he m a i n
c om pone nt s of t he S T A T C O M i s a t hr e e pha s e P ul s e W i d t h M odul a t or ( P W M ) .
S T A T C O M i s c onne c t e d i n pa r a l l e l w i t h a poi nt i n t he g r i d, s uc h a s t he r e c e i ve r e nd a s
s e e n i n f i gur e 26, w he r e r e a c t i ve pow e r i s ne e de d. T he r e a c t i ve pow e r i s i nj e c t e d f or
s e ve r a l pur pos e s s uc h a s c om pe ns a t i ng t he vol t a g e i n t he g r i d.
A ddi t i ona l l y , S T A T C O M c a n be vi e w e d a s a vol t a g e s our c e c onve r t e r t ha t pr oduc e s a n
A C pow e r w i t h c ont r ol l a bl e a m pl i t ude a nd a ngl e f r om a D C pow e r . C ont r ol l i ng t he A C
pow e r ’ a m pl i t ude a nd pha s e c ont r i but e i n t he out put r e a c t i ve pow e r pr ovi de d t o t he
e l e c t r i c a l g r i d. T he pr i m a r y pur pos e of S T A T C O M s i s s i m i l a r t o t he pur pos e of c a pa c i t or
ba nks w hi c h i s i nc r e a s i ng t he vol t a g e l e ve l of t he s y s t e m .
M or e ove r , S T A T C O M s pr ovi de a be t t e r c ont r ol of vol t a g e l e ve l i n t he s y s t e m c om pa r e d
t o c a pa c i t or ba nks . A ddi t i ona l l y , S T A T C O M s a r e c ons i de r e d one of t he be s t opt i ons t o
i m pr ove t r a ns i e nt s t a bi l i t y of t he pow e r s y s t e m . T he s upe r i or i t y of S T A T C O M s r e s ul t e d
f r om t he f a c t t ha t t he y dy n a m i c f a s t dy n a m i c r e s pons e t o t r a ns i e nt phe nom e non.
3 6
F i gur e 27 s how s t he l a y o ut of t he S T A T C O M [ 44]
A s s e e n i n f i gur e 27, t he l a y o ut of S T A T C O M s c ons i s t of a t hr e e pha s e s t e p- dow n
t r a ns f or m e r i n t he A C s i de a c c om pa ni e d w i t h a t hr e e pha s e f i l t e r . T he c a pa c i t or i n t he D C
s i de C i s l a r g e e nough t o pr ovi de t he r e qui r e d r e a c t i ve pow e r t o t he A C s y s t e m . T he A C
a nd D C s i de s a r e i nt e r c onne c t e d t hr oug h P W M . W he n t he pow e r i s f l ow i ng f r om t he A C
t o t he D C s i de , t he vol t a g e a t t he D C s i de l a gs t he c ur r e nt by 90 de gr e e s . T he r e f or e , t he
S T A T C O M i s a t t he i nduc t or ope r a t i on m ode w hi c h a bs or bs r e a c t i ve pow e r . O n t he ot he r
ha nd, i f t he pow e r i s f l ow i ng f r om t he D C t o A C s i de , t he c ur r e nt a t t he A C s i de l e a ds t he
vol t a g e w i t h 90 de gr e e s . T he r e f or e , t he S T A T C O M ope r a t e s i n t he c a pa c i t i ve m ode a nd
pr ovi de r e a c t i ve pow e r t o t he g r i d.
F i gur e 28 s how s t he ope r a t i ng r e gi ons of S T A T C O M [ 45]
3 7
R e pl a c i ng t he s hunt c a pa c i t or ba nks i n t he pow e r g r i d w i t h S T A T C O M s r e s ul t a be t t e r
t e c hni c a l pe r f or m a nc e . H ow e ve r , r e pl a c i ng t he c a pa c i t or ba nks w i t h S T A T C O M s i s be t t e r
i n t e r m s of pe r f or m a nc e but t he pr i c e of S T A T C O M s i s ve r y hi g h c om pa r e d t o c a pa c i t or
ba nks . T he r e f or e , m os t ut i l i t y c om pa ni e s do not r e pl a c e s hunt c a pa c i t or ba nks w i t h
S T A T C O M s be c a us e of t he pr i c e , e ve n t houg h t he pe r f or m a nc e i s be t t e r . A ddi t i ona l l y ,
a not he r r e a s on f or t he ut i l i t y c om pa ni e s not t o r e pl a c e t he s hunt c a pa c i t or ba nks w i t h
S T A T C O M s i s t ha t t he vol t a g e c om pe ns a t i on r e s ul t e d f r om s hunt c a pa c i t or ba nks i s ve r y
a c c e pt a bl e a nd i s not w or t h t he a m ount of m one y ne e de d t o r e pl a c e i t . T he c ont r ol of t he
S T A T C O M i s done vi a a f e e dba c k l oop t ha t m e a s ur e s t he vol t a g e l e ve l a c r os s t he
S T A T C O M . I f t he vol t a g e l e ve l i s not a c c e pt a bl e , t he c ont r ol l oop de t e r m i ne s t he a m ount
of r e a c t i ve pow e r ne e de d t o m a ke t he vol t a g e l e ve l a c c e pt a bl e .
F i gur e 29 s how s t he c ont r ol of S T A T C O M S [ 46]
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2 . 3 . 4 S u p e r c o n d u c t i n g M a g n e t i c E n e r g y S t o r a g e ( S M E S )
S M E S i s a de vi c e t ha t t a ke s t he e x t r a e ne r g y f r om t he pow e r s y s t e m a nd s t or e s i t i n t he
m a gne t i c f i e l d r e s ul t e d by t he f l ow D C c ur r e nt r ot a t i ng i n s upe r c onduc t i ng c oi l . T he r e a r e
t hr e e t y p e s of S M E S : C S C , V S C a nd t hy r i s t or - ba s e d S M E S [ 47] .
1) C S C b as e d S M E S
F i g ur e 30 s how s a g e ne r a l s c he m e of t he S C R C S C ba s e d S M E S [ 48]
C ur r e nt s our c e c onve r t e r ( C S C ) us e d t o be r e ga r de d a s one of t he g r e a t e s t opt i ons t o
t r a ns f e r a c t i ve a nd r e a c t i ve pow e r t o t he g r i d. C S C c a n be S C R - ba s e d or G T O - ba s e d.
A s s e e n i n f i g ur e 30, t he c ur r e nt I ha s t o be c ont i nuous . T he r e f or e , a c l os e d r out e i s
ne e de d i n or de r t o ope r a t e . T he c l os e d r out e i s e s t a bl i s he d by t ur ni ng on t he uppe r t hr e e
s w i t c he s na m e d S 1, S 3, S 5 or t ur ni ng on t he l ow e r t hr e e s w i t c he s S 2,S 4,S 6. B y doi ng t hi s
a r out e f or t he c ur r e nt t o pa s s i s ope n. M or e ove r , i f t he l ow e r s e t of s w i t c he s i s t ur ne d on,
t he uppe r s e t of s w i t c he s ha s t o be t ur ne d of f a nd vi c e ve r s a . T hi s c ondi t i on pr e ve nt s
s hor t i ng t he l i ne - l i ne t hr e e pha s e vol t a g e s .
T he s i x- pul s e C S C a l l ow s t he D C c ur r e nt t o be pa s s e d t o t he A C l i ne s f or onl y 60 de gr e e s
f or a s i ng l e pul s e . G i ve n t ha t t he pe r i od i s c ons t a nt , t he t ot a l a ppa r e nt pow e r i s not
c ont r ol l e d. H ow e ve r , t he t ot a l pow e r c a n be c ont r ol l e d by c onne c t i ng t w o S C R C S C s i n
s e r i e s . A ddi t i ona l l y , G T O s c a n be us e d i ns t e a d t o c ont r ol t he pow e r by s hor t i ng a s i ng l e
l e g i n t he 60 de gr e e s pe r i od w hi c h r e s ul t s a l ow e r c onne c t i on t i m e be t w e e n t he A C l i ne s
a nd t he S M E S i nduc t or . T he pr e vi ous m e t hod i s know n a s “ pa r t i a l s hor t i ng c ont r ol . ” [ 49] .
3 9
F i gur e 31 s how s t he c ur r e nt w a ve f or m s of t he s i x pul s e C S C [ 50]
F i gur e 32 s how s t he s i x pul s e G T O C S C t y p e S M E S [ 51]
4 0
2) V S C b as e d S M E S
F i gur e 33 s how s a g e ne r a l s c he m e of t he s i x pul s e C S C ba s e d S M E S [ 52]
T he V S C ba s e d S M E S i s ve r y di f f e r e nt t ha n t he C S C l a y o ut [ 53] . I t ut i l i z e d a c hoppe r
w i t h t w o qua dr a nt a nd a D C vol t a g e V S C l i nke d. T he D C c ur r e nt f l ow i ng f r om t he
i nduc t or of t he S M E S i s c ha nge d t o a D C vol t a g e by t he c hoppe r . A ddi t i ona l l y , t he D C
vol t a g e a c r os s t he S M E S c oi l i s c ha nge d t o a t hr e e pha s e A C c ur r e nt by t he V S C . T he
G T O s a r e e s s e nt i a l f or t he V S C a nd t he c hoppe r .
T o m i ni m i z e t he out put r i ppl e of t he S M E S , a t w e nt y - f our pul s e V S C i s us e d. T he
t w e nt y - f our pul s e V S C i s bui l t by us i ng f our s i x pul s e V S C a nd a ddi ng t he out put of t he
t he f our s i x pul s e V S C . C ont r ol l i ng t he f i r i ng a ng l e s of t he G T O s c a n r e s ul t a f l e x i bl e
c ont r ol of t he a c t i ve a nd r e a c t i ve pow e r . A l s o, c ont r ol l i ng t he dut y r a t i o of t he c hoppe r
c ont r ol s t he D C vol t a g e w hi c h pl a y s a r ol e i n c ont r ol l i ng t he a c t i ve a nd r e a c t i ve pow e r i n
t he s y s t e m .
T he V S C ha s s e ve r a l a dva nt a ge s ove r t he C S C l a y o ut . I n t he V S C c onf i gur a t i on, t he
c ur r e nt of t he S M E S i nduc t or pa s s e s i n t he D C c hoppe r onl y a nd g e t s c onve r t e d t o D C
vol t a g e . T hi s r e duc e s t he s t r e s s of t he c ur r e nt pa s s i ng t hr oug h t he V S C t o a l ow va l ue
w hi c h r e duc e s t he S M E S pow e r r a t i ng. T he t r a ns f or m e r ’ s l e a ka ge i nduc t a nc e i s us e d t o
f i l t e r t he ha r m oni c s c a us e d by t he V S C .
4 1
T he m a i n g oa l of t he D C c hoppe r i s t o c ont r ol t he S M E S i nduc t or ’ s e ne r g y . I f t he S M E S
i s t o be us e d t o s t or e e ne r g y , t he D C c hoppe r a c t s a s a l i nk a nd pr ovi de a D C vol t a g e t o
t he S M E S w hi c h c a us e s t he i nduc t or t o c ha r g e . O n t he ot he r ha nd, i f e ne r g y i s ne e de d t o
be s uppl i e d t o t he s y s t e m f r om t he S M E S , t he oppos i t e vol t a g e i s c onne c t e d t hr ough t he
c hoppe r .
F i gur e 34 s how s t he c onf i gur a t i on of t he t w o- qua dr a nt c hoppe r [ 54] .
A s s e e n i n f i gur e 34, c ha r g i ng t he c oi l s i s a c hi e ve d by a ppl y i ng a pul s e t o t ur n on t he t w o
G T O s a t t he s a m e t i m e w hi l e ke e pi ng t he t w o di ode s r e ve r s e bi a s e d. O n t he ot he r ha nd,
by t ur ni ng t he G T O s of f , t he di ode s c onduc t w hi c h a l l ow s t he S M E S i nduc t or t o
di s c ha r g e t o t he s y s t e m . B y c ha ngi ng t he c onduc t i on t i m e w i t h r e s pe c t t o t he e nt i r e
pe r i od, t he i nduc t or ’ s vol t a g e i s c ont r ol l e d. I f t he c onduc t i on t i m e ( dut y c y c l e ) i s % 50 t he
pe r i od, t he D C c ur r e nt a nd t he a ve r a ge vol t a g e of t he V S C a r e z e r o. A s a r e s ul t of t ha t ,
t he t r a ns f e r r e d ne t pow e r i s z e r o i n a s i ng l e s w i t c hi ng c y c l e . A ddi t i ona l l y , 0.5 dut y c y c l e
i s t he bounda r y be t w e e n c ha r g i ng a nd di s c ha r g i ng t he c oi l . F or dut y c y c l e ove r 0.5, t he
i nduc t or s t or e s e ne r g y . O n t he ot he r ha nd, t he i nduc t or i s di s c ha r g i ng f or dut y c y c l e unde r
0.5.
T he pr e vi ous m e t hod i s t he c om m on w a y of ope r a t i on. H ow e ve r , S M E S c a n be ope r a t e d
i n a not he r w a y t o m i ni m i z e t he r i ppl e a nd t he s w i t c hi ng i nvol ve d i n t he pr oc e s s by
ope r a t i ng one G T O i n t he of f t i m e .
4 2
F i gur e 35 s how s t he 24- pul s e V S C [ 55]
A s s e e n i n f i gur e 35, a f t e r t he V S C t he r e i s a D C c hoppe r i n or de r t o pr ovi de a g ood
pow e r s y s t e m c ondi t i oni ng . T he V S C i s of a 24 pul s e t ha t c ons i s t s of f our s i x- pul s e V S C
c onne c t e d t og e t he r t o pr ovi de a t ot a l of 24 pul s e . T o m a ke t he s i x- pul s e vol t a g e r a t i ng
one - f our t h t he l i ne vol t a g e , t he pr i m a r y s i de of e a c h t r a ns f or m e r i s c onne c t e d i n s e r i e s
a nd t he n t o t he ut i l i t y .
4 3
U s i ng onl y s i x pul s e c onf i gur a t i on i s not t he be s t w a y t o pr oduc e a g ood r e s ul t . T he
s i x- pul s e c onf i gur a t i on r e s ul t s a hi g h a m ount of ha r m oni c s by pr oduc i ng a D C c ur r e nt or
vol t a g e t ha t ha s a l a r g e r i ppl e . I n or de r f or t he ut i l i t y t o f i l t e r out t he ha r m oni c s , l a r g e
f i l t e r m us t be pr e s e nt or c onne c t i ng s e ve r a l s i x- pul s e t og e t he r . M or e ove r , i t c oul d be done
by c onne c t i ng a m a t c hi ng t r a ns f or m e r a t e a c h s i x- pul s e m odul e .
F i gur e 36 s how s t he m a t c hi ng t r a ns f or m e r f or e a c h s i x- pul s e uni t [ 56]
A s s e e n i n f i gur e 36, t he ha r m oni c s r e s ul t e d f r om e a c h V S C c onf i gur a t i on i s pr e s e nt e d.
F i gur e 36 i nc l ude s t he ha r m oni c s r e s ul t e d f r om t he 6,12 a nd 24 pul s e V S C . T he m or e
pul s e s t he V S C ha s , t he l e s s ha r m oni c s r e s ul t s . T he s i x pul s e V S C r e s ul t s t he hi g he s t
a m ount of ha r m oni c s . T he t w e l ve pul s e V S C i s c r e a t e d by us i ng t w o s i x- pul s e V S C s w i t h
w y e - w y e a nd de l t a - w y e c onne c t i on. I t i s i m por t a nt t o m e nt i on t ha t t he m or e pul s e s us e d,
t he hi g he r t he c os t .
4 4
F i gur e 37 s how s t he ha r m oni c s w he n us i ng e a c h c onf i gur a t i on[ 57]
4 5
3) T h yr i s t or b as e d S M E S
F i gur e 38 s how s t he 6- pul s e t hy r i s t or ba s e d S M E S [ 58]
F i gur e 38 s how s a s i m pl e l a y o ut of t he t hy r i s t or ba s e d S M E S . I t c ons i s t s of t he m a i n
s upe r c onduc t i ng c oi l t ha t i s f e d a D C c ur r e nt f r om a t hy r i s t or c onve r t e r t ha t c onve r t s t he
A C pow e r r e c e i ve d f r om t he W y e - D e l t a t r a ns f or m e r .
T he t hy r i s t or c onve r t e r a ppl i e s ne ga t i ve or pos i t i ve vol t a g e on t he s upe r c onduc t i ng
i nduc t or . T he pr oc e s s of di s c ha r g i ng a nd c ha r g i ng i s c ont r ol by m odi f y i ng t he f i r i ng a ngl e
of t he t hy r i s t or s . I f t he f i r i ng a ngl e i s be l ow 90 de gr e e s , t he c onve r t e r c ha r g e s t he
s upe r c onduc t i ng c oi l . O n t he ot he r ha nd, i f t he f i r i ng a ngl e a bove 90 de gr e e s , t he
s upe r c onduc t i ng c oi l di s c ha r g e s . A s a r e s ul t of t ha t , pow e r i s s uppl i e d or a bs or be d.
T he D C vol t a g e a t t he c onve r t e r s i de i s r e pr e s e nt e d a s V s m
 c os . 0 V s m V s m 
T he V s m 0 i s t he m a x i m um D C no l oa d vol t a g e of t he c onve r t e r . T he f ol l ow i ng e qua t i on
r e l a t e s t he vol t a g e a nd c ur r e nt of t he S M E S :

  
t
t
I s m d V s m
L s m
I s m
0
0
1

W he r e I s m r e pr e s e nt s t he c oi l i ni t i a l c ur r e nt .
T he f ol l ow i ng e qua t i on g i ve s t he pow e r i n t he c oi l a s de r i ve d i n[ 59] .
I s m V s m P s m  
4 6
T a bl e 1 s how s c om pa r i s on be t w e e n di f f e r e nt S M E c onf i gur a t i ons [ 60]
C r i t e r i a S M E c onf i gur a t i on
T hy r i s t or ba s e d
S M E
V S C ba s e d S M E C S C ba s e d S M E
R e a c t i ve a nd a c t i ve
pow e r c ont r ol a bi l i t y
I t ha s a l a ggi ng
pow e r f a c t or
c om pa r e d t o t he
s y s t e m a nd e xhi bi t s
ha r m oni c s of l ow
or de r r e s ul t e d f r om
t he f i r i ng pa t t e r n.
T he r e f or e , i t c a n
c ont r ol a c t i ve pow e r
m a i nl y a nd ha s a
w e a k a bi l i t y t o
c ont r ol r e a c t i ve
pow e r .
A c t i ve a nd r e a c t i ve
pow e r a r e c ont r ol l e d
i nde pe nde nt l y .
M or e ove r , V S C
ba s e d S M E
c onf i gur a t i on ha s
t he a bi l i t y t o
pr ovi de c ont i nuous
r e a c t i ve pow e r r a t e d
s uppor t e ve n i n t he
a bs e nc e of a ny c oi l
c ur r e nt .
A c t i ve a nd r e a c t i ve
pow e r a r e c ont r ol l e d
i nde pe nde nt l y .
H ow e ve r , C S C
c onf i gur a t i on ha s
t he a bi l i t y t o
pr ovi de a l a r g e
a m ount of l e a di ng
r e a c t i ve pow e r .
A ddi t i ona l l y , C S C
S M E de pe nds on t he
c oi l w he n s uppl y i ng
V A R .
C ont r ol U ni t I t ha s s i ng l e A C / D C
c ont r ol uni t .
T he r e f or e , i t i s ve r y
e a s y t o c ont r ol .
I t ha s bot h a D C / D C
c hoppe r a nd A C / D C
uni t w hi c h m a ke t he
c ont r ol m or e
c om pl e x .
I t ha s s i ng l e A C / D C
c ont r ol uni t .
T he r e f or e , i t i s ve r y
e a s y t o c ont r ol .
T o t a l ha r m oni c
di s t or t i on ( T H D )
I t ha s t he hi g he s t
va l ue of t ot a l
ha r m oni c di s t or t i on
c om pa r e d t o t he
ot he r c onf i gur a t i ons
T he t ot a l ha r m oni c
di s t or t i on of t he
V S C ba s e d S M E i s
l ow .
T he t ot a l ha r m oni c
di s t or t i on of t he
C S C ba s e d S M E i s
l ow .
S e l f - C om m ut a t i on P oor
s e l f - c om m ut a t i on
a bi l i t y
G ood
s e l f - c om m ut a t i on
a bi l i t y
P oor
s e l f - c om m ut a t i on
a bi l i t y
4 7
3 . M o d e l i n g
3 . 1 I n t r o d u c t i o n
T hi s c ha pt e r i s w r i t t e n t o g i ve a de t a i l e d ove r vi e w of t he m ode l i ng us e d t hr oughout t he
pr e pa r a t i on of t he di s s e r t a t i on. T he I E E E 14 bus s y s t e m i s us e d a s t he ba s e c a s e of t he
s t udy [ 61] . F or t he de vi c e s t ha t c ont r i but e s t o t he t r a ns i e nt be ha vi or of t he I E E E 14 bus
s y s t e m , t he r e i s a dy n a m i c m ode l [ 62] t o t a ke a s m a ny dy n a m i c pa r a m e t e r s a s pos s i bl e .
S om e e l e m e nt s i n t he s y s t e m ha ve m ul t i pl e dy n a m i c m ode l s f or e a c h pa r t of t he e l e m e nt .
M ode l i ng a l l g e ne r a t or s i n t hi s t he s i s i s c om pos e d of t hr e e dy n a m i c m ode l s w hi c h a r e
g e ne r a t or , t ur bi ne a nd e x c i t a t i on s y s t e m . T he m ode l us e d f or t he g e ne r a t or i s R ound
R ot or G e ne r a t or M ode l ( G E N R O U ) . F or t he e x c i t e r , t he I E E E t y p e 1 e x c i t a t i on m ode l
( I E E E T 1) i s us e d. A ddi t i ona l l y , t he I E E E t y p e 1 t ur bi ne - gove r nor m ode l i s us e d f or t he
t ur bi ne m ode l .
T he s y n c hr onous c onde ns e r s a r e m ode l e d t he s a m e a s t he g e ne r a t or s but w i t hout a
dy n a m i c m ode l f or t he t ur bi ne s i nc e i t i s s pi nni ng f r e e l y . A l s o, t he out put pow e r of t he
s y n c hr onous c onde ns e r s i s z e r o. T he m ode l us e d f or t he g e ne r a t or i s R ound R ot or
G e ne r a t or M ode l ( G E N R O U ) . F o r t he e x c i t e r , t he I E E E t y p e 1 e x c i t a t i on m ode l ( I E E E T 1)
i s us e d.
T o s i m ul a t e t he S t a t i c c onde ns e r dy n a m i c a l l y , t he m ode l C S T C N T i s us e d. A l s o, t he
S t a t i c V a r C om pe ns a t or ( S V C ) i s s i m ul a t e d us i ng t he bui l t - i n dy n a m i c m ode l f or S t a t i c
V a r C om pe ns a t or s c a l l e d C S V G N 1.
T he f ol l ow i ng pa r t of t he t he s i s w i l l pr ovi de a n ove r vi e w of a l l t he da t a us e d i n t he I E E E
14 bus m ode l s uc h a s t r a ns m i s s i on l i ne pa r a m e t e r s a nd t he l oa d c onne c t e d t o e a c h bus . I n
a ddi t i on t o t he dy n a m i c m ode l us e d i n t he I E E E 14 bus m ode l bui l t us i ng P S S / E .
4 8
3 . 2 I E E E 1 4 b u s
T he I E E E 14 bus s y s t e m i s a s t a nda r d s y s t e m us e d f or r e s e a r c h s t udi e s pr e pa r e d by
t he I n s t i t ut e of E l e c t r i c a l a nd E l e c t r oni c s E ngi ne e r s ( I E E E ) . T he s y s t e m i s m a de up of
f i ve di f f e r e nt s y n c hr onous m a c hi ne s . T w o of t he m a r e g e ne r a t i on s our c e s a nd t he ot he r s
a r e us e d t o pr ovi de r e a c t i ve c om pe ns a t i on t o t he s y s t e m . T he t ot a l num be r of l oa ds
c onne c t e d t o t he s y s t e m i s e l e ve n.
F i gur e 39 s how s t he s i ng l e l i ne di a gr a m f or t he I E E E 14 bus
4 9
T he f ol l ow i ng t a bl e s pr ovi de a de t a i l e d e x pl a na t i on of t he s t a t i c pa r a m e t e r s e nt e r e d
i n t he I E E E 14 bus s uc h a s t he l i ne s r e s i s t a nc e , i nduc t a nc e a nd s us c e pt a nc e . A l s o, i t g i ve s
t he a m ount of l oa d c onne c t e d t o a s pe c i f i c bus num be r .
T a bl e 2 s how s t he l i ne s pa r a m e t e r s i n t he I E E E 14 bus s y s t e m
F r o m B u s T o B u s
L i n e R
( p u )
L i n e X
( p u )
C h a r g i n g
B ( p u )
1 2 0 . 0 1 9 3 8 0 . 0 5 9 1 7 0 . 0 5 2 8
1 5 0 . 0 5 4 0 3 0 . 2 2 3 0 4 0 . 0 4 9 2
2 3 0 . 0 4 6 9 9 0 . 1 9 7 9 7 0 . 0 4 3 8
2 4 0 . 0 5 8 1 1 0 . 1 7 6 3 2 0 . 0 3 4
2 5 0 . 0 5 6 9 5 0 . 1 7 3 8 8 0 . 0 3 4 6
3 4 0 . 0 6 7 0 1 0 . 1 7 1 0 3 0 . 0 1 2 8
4 5 0 . 0 1 3 3 5 0 . 0 4 2 1 1 0
6 1 1 0 . 0 9 4 9 8 0 . 1 9 8 9 0
6 1 2 0 . 1 2 2 9 1 0 . 2 5 5 8 1 0
6 1 3 0 . 0 6 6 1 5 0 . 1 3 0 2 7 0
7 8 0 0 . 1 7 6 1 5 0
7 9 0 0 . 1 1 0 0 1 0
9 1 0 0 . 0 3 1 8 1 0 . 0 8 4 5 0
9 1 4 0 . 1 2 7 1 1 0 . 2 7 0 3 8 0
1 0 1 1 0 . 0 8 2 0 5 0 . 1 9 2 0 7 0
1 2 1 3 0 . 2 2 0 9 2 0 . 1 9 9 8 8 0
1 3 1 4 0 . 1 7 0 9 3 0 . 3 4 8 0 2 0
T a bl e 3 s how s t he l oa ds i n t he I E E E 14 bus s y s t e m
B u s
N u m b e r
P l o a d
( M W )
Q l o a d
( M v a r )
2 2 1 . 7 1 2 . 7
3 9 4 . 2 1 9
4 4 7 . 8 - 3 . 9
5 7 . 6 1 . 6
6 1 1 . 2 7 . 5
9 2 9 . 5 1 6 . 6
1 0 9 5 . 8
1 1 3 . 5 1 . 8
1 2 6 . 1 1 . 6
1 3 1 3 . 5 5 . 8
1 4 1 4 . 9 5
5 0
3 . 3 E V s M o d e l i n g
E l e c t r i c a l ve hi c l e s c ha r g i ng m ode l s c a n be c l a s s i f i e d i nt o t hr e e t y p e s : C ons t a nt C ur r e nt
C ha r g i ng M ode l , C ons t a nt V o l t a ge C ha r g i ng M ode l a nd a c om bi na t i on of bot h[ 63] .
F i gur e 40 s how s t he c ur r e nt vol t a g e r e l a t i ons hi p i n e a c h l oa d t y p e s
T he c ons t a nt c ur r e nt l oa d, t he vol t a g e a ppl i e d i n or de r t o c ha r g e t he ba t t e r y i s a l l ow e d t o
c ha nge t o ke e p t he f l ow i ng c ur r e nt c ons t a nt . I f t he ba t t e r y ha s z e r o e ne r g y , t he f l ow i ng
c ur r e nt t o c ha r g e t he ba t t e r y i s t o be c ons t a nt a s t he vol t a g e r i s e a c r os s t he ba t t e r y . T he
s t a t e of c ha r g e ( S O C ) i n t he c ons t a nt c ur r e nt m ode , de f i ne d a s t he r e m a i ni ng c a pa c i t y
di vi de d by t he r a t e d c a pa c i t y , i s a l i ne a r f unc t i on w i t h t i m e . I n t hi s t y p e of l oa d, t he
de t e r m i na t i on of t he c om pl e t e c ha r g i ng i s a c ha l l e nge i n t hi s c ha r g i ng m ode l . T hi s t he s i s
w i l l a s s um e t ha t t he E V s a r e c ha r g e d i n t he c ons t a nt c ha r g i ng m ode l [ 64] .
T he C ons t a nt V o l t a ge M ode l c ha r g e s t he E V by va r y i ng t he c ha r g i ng c ur r e nt w hi l e
ke e pi ng t he vol t a g e c ons t a nt . T hi s m e t hod c a n be us e d not onl y t o E V s but t o a l l t y p e s of
ba t t e r i e s . I n t hi s c ha r g i ng m ode l , t he c ur r e nt c ha nge s w i t h t i m e a s t he ba t t e r y i s be i ng
c ha r g e d. T he c ha l l e nge i n t hi s c ha r g i ng m ode l i s t he hi g h pow e r c ons um pt i on i n t he
be gi nni ng of t he c ha r g i ng pr oc e s s [ 65] .
5 1
F i gur e 41 s how s t he c ha r g i ng c ha r a c t e r i s t i c s of L i - i on c e l l [ 66]
F i gur e 41 s how s t he L i - i on c ha r g i ng pr oc e s s t ha t us e s c om bi na t i on of t he c ons t a nt
c ur r e nt a nd vol t a g e c ha r g i ng m ode l s . I n t he be gi nni ng of t he c ha r g i ng pr oc e s s , pr e
c ha r g i ng pe r i od, t he c ha r g i ng m ode l i s l ow vol t a g e c ons t a nt c ur r e nt . A f t e r t ha t , i t
c ont i nue s a s c ons t a nt c ur r e nt but w i t h a hi g he r pow e r . A f t e r t ha t , t he c ons t a nt c ha r g e
t a ke s pl a c e .
5 2
3 . 4 D y n a m i c D e v i c e s
3 . 4 . 1 R o u n d R o t o r S y n c h r o n o u s G e n e r a t o r ( G E N R O U )
G E N R O U m ode l i s a r e pr e s e nt a t i on of t he R ound R ot or S y n c hr onous G e ne r a t or . T he
e x pone nt i a l s a t ur a t i on of t he g e ne r a t or i s i n bot h a x i s . F i gur e 42 s how s t he bl oc k di a gr a m
of t he R ound R ot or S y n c hr onous G e ne r a t or ( G E N R O U ) .
F i gur e 42 s how s t he bl oc k di a g r a m of G E N R O U
5 3
T a bl e 4 s how s t he c hos e n dy n a m i c pa r a m e t e r s f or a l l s y n c hr onous m a c hi ne s
G e n e r a t o r B u s S y n c h r o n o u s B u s
P a r a m e t e r 1 2 3 6 8
T ' d o 7 . 4 6 . 1 6 . 1 4 . 7 5 4 . 7 5
T " d o 0 . 0 3 0 . 0 3 0 . 0 3 0 . 0 3 0 . 0 3
T ' q o 0 . 3 1 0 . 3 1 0 . 3 1 0 . 3 1 0 . 3 1
T " q o 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5 0 . 0 5
H 5 . 1 8 4 6 . 5 2 8 1 . 5 1 . 5 1 . 5
D 2 2 2 2 2
X d 0 . 8 3 0 . 7 3 0 . 7 3 0 . 7 3 0 . 7 3
X q 0 . 6 8 4 5 0 . 6 0 . 6 0 . 6 0 . 6
X ' d 0 . 3 0 4 0 . 3 0 4 0 . 3 0 4 0 . 3 0 4 0 . 3 0 4
X ' q 0 . 4 8 4 5 0 . 4 8 4 5 0 . 4 8 4 5 0 . 4 8 4 5 0 . 4 8 4 5
X " d = X " q 0 . 2 0 . 2 0 . 2 0 . 2 0 . 2
X l 0 . 1 5 0 . 1 5 0 . 1 5 0 . 1 5 0 . 1 5
S ( 1 , 0 ) 0 0 0 0 0
S ( 1 , 2 ) 0 0 0 0 0
5 4
3 . 4 . 2 I E E E t y p e 1 E x c i t a t i o n M o d e l ( I E E E T 1 )
T he vol t a g e r e gul a t i on of t he pow e r s y s t e m i s t he m a i n r e s pons i bi l i t y of t he e x c i t a t i on
c ont r ol s y s t e m s . T he y e x i s t i n or de r t o ke e p t he t e r m i na l vol t a g e s w i t hi n a s pe c i f i e d l i m i t
c hos e n by t he de s i g n e ngi ne e r . I f t he vol t a g e e x c e e d t he s pe c i f i e d l i m i t f or a l ong pe r i od
of t i m e , t he g e ne r a t or ’ s pe r f or m a nc e be c om e s a f f e c t e d a nd i n s om e c a s e s i t m i g ht r e s ul t s
ha r m t o t he g e ne r a t or .
F i gur e 43 s how s a bl oc k di a gr a m of t he I E E E T 1
F i gur e 43 s how s t he bl oc k di a gr a m of t he I E E E T 1 e x c i t a t i on m ode l . T he g e ne r a t or ’ s
t e r m i na l vol t a g e , E c , r e pr e s e nt s t he i nput vol t a g e t o t he t r a ns duc e r , w hi c h i s a de vi c e f or
vol t a g e m e a s ur e m e nt , w hi c h pl a y s a r ol e of f i l t e r t ha t ha s t he t i m e c ons t a nt T R .
S om e t i m e s T R i s s m a l l e nough t ha t i s a s s um e d t o be z e r o.
T he f i r s t s um m a t i on a i m s t o f i nd t he di f f e r e nc e be t w e e n t he V R e f ( r e f e r e nc e vol t a g e ) a nd
t he out put of t he vol t a g e m e a s ur e m e nt de vi c e . T he vol t a g e di f f e r e nc e i s c a l l e d t he e r r or
vol t a g e . V R e f doe s not c ha nge i n t he s y s t e m , i t i s s pe c i f i e d f r om t he be gi nni ng a nd i t w i l l
r e m a i n c ons t a nt .
5 5
T he s e c ond s um m a t i on a i m s t o c om bi ne t he s t a bi l i z i ng e x c i t a t i on f e e dba c k vol t a g e a nd
t he vol t a g e e r r or t o g e ne r a t e t he i nput f or t he r e gul a t or . T he a m pl i f i e r ’ s vol t a g e r e gul a t or
ha s a t i m e c ons t a nt a nd a g a i n r e pr e s e nt e d a s T A a nd K A r e s pe c t i ve l y . T he r e gul a t or ’ s
out put , V R , i s ut i l i z e d f or t he e x c i t e r ’ s c ont r ol .
T he vol t a g e e xc i t a t i on s y s t e m i s a ve r y f a s t de vi c e . I t us ua l l y ha s a ve r y s m a l l t i m e
c ons t a nt i n or de r t o m a ke t he c ont r ol a s f a s t a s pos s i bl e . T he f ol l ow i ng t a bl e s pe c i f i e s a l l
t he dy n a m i c da t a us e d i n t he f i ve e x c i t a t i on m ode l s a t di f f e r e nt bus e s .
T a bl e 5 s how s t he dy n a m i c pa r a m e t e r s f or t he e x c i t e r a t e a c h s y n c hr onous m a c hi ne i n t he
s y s t e m
E x c i t e r a t
bus no.
1 2 3 4 5
K
A
200 20 20 20 20
T
A
0.02 0.02 0.02 0.02 0.02
T
B
0 0 0 0 0
T
c
0 0 0 0 0
V
R m a x
7.32 4.38 4.38 6.81 6.81
V
R m i n
0 0 0 1.395 1.395
K
E
1 1 1 1 1
T
E
0.19 1.98 1.98 0.7 0.7
K
F
0.0012 0.001 0.001 0.001 0.001
T
F
1 1 1 1 1
5 6
3 . 4 . 3 I E E E G 1 G o v e r n o r M o d e l
F i gur e 44 s how s t he bl oc k di a gr a m of t he I E E E G 1 m ode l
F i gur e 44 s how s t he bl oc k di a gr a m of t he dy n a m i c m ode l us e d f or t he t ur bi ne . T he
I E E E G 1 i s t he dy n a m i c m ode l r e c om m e nde d by t he I E E E . B y c hoos i ng t he pa r a m e t e r s
pr ope r l y , t he I E E E G 1 c a n r e pr e s e nt di f f e r e nt t y p e s of t ur bi ne s y s t e m s s uc h a s t a nde m
c om pound a nd nonr e he a t t y p e s . M or e ove r , t he I E E E G 1 i s c a pa bl e of r e pr e s e nt i ng t he
dy n a m i c s of t he hy d r o t ur bi ne g ove r nor s . T he f ol l ow i ng t a bl e i l l us t r a t e t he da t a us e d i n
t he I E E E G 1 dy n a m i c m ode l .
T a bl e 6 s how s t he dy n a m i c pa r a m e t e r of t he I E E E G 1 of g e ne r a t or 1 a nd 2
P a r a m e t e r V a l u e
K 2 5
T 1 0
T 2 0
T 3 ( > 0 ) 0 . 1
U o 0 . 1
U c ( < 0 . ) - 0 . 3
P M A X 1
P M I N 0
T 4 0 . 1
K 1 1
K 2 0
T 5 0
K 3 0
K 4 0
T 6 0
K 5 0
K 6 0
T 7 0
K 7 0
K 8 0
5 7
3 . 4 . 4 S t a t i c V a r C o m p e n s a t o r ( C S V G N 1 )
F i gur e 45 s how s t he bl oc k di a gr a m of t he C S V G N 1 m ode l
F i gur e 45 s how s t he bl oc k di a gr a m of t he S t a t i c V a r C om pe ns a t e r . I t i s a r e pr e s e nt a t i on of
a n e l e c t r i c c i r c ui t c om pos e d of a c a pa c i t or c onne c t e d i n pa r a l l e l w i t h s hunt r e a c t or
c ont r ol l e d by a n S C R c i r c ui t . T he g a t e of t he S C R i s c ont r ol l e d by t he vol t a g e e r r or i n
a ddi t i on t o a n a uxi l i a r y s i g na l . T he M V A a nd M B A S E i n t he pow e r f l ow da t a r e pr e s e nt
t he a c t ua l s i z e of t he r e a c t or , w he r e a s C B A S E i n t he dy n a m i c f i l e r e pr e s e nt t he phy s i c a l
s i z e of t he c a pa c i t or .
T he l ow e r a nd uppe r vol t a g e c ont r ol l oop ’ s a c t i ve r a nge i s r e pr e s e nt e d by t he va r i a bl e s
V M I N a nd V M A X r e s pe c t i ve l y w hi c h a r e z e r o a nd uni t y i n m os t of t he c a s e s . R M I N i s a
r e pr e s e nt a t i on of t he a dm i t t a nc e ’ s m i ni m um l i m i t w hi c h i ndi c a t e s t he r e a c t or ’ s e f f e c t i ve
a dm i t t a nc e i f t he S C R c i r c ui t i s t ur ne d of f .
T 5 i ndi c a t e s t he t i m e c ons t a nt t ha t g i ve s a n a ppr ox i m a t i on r e a c t or ’ s r e s pons e ’ s de l a y .
A ddi t i ona l l y , t he r e s t of t he t i m e c ons t a nt s f r om T 1 t o T 4 pr ovi de c ont r ol l oop ’ s t r a ns i e nt
g a i n r e duc t i on w hi c h a l l ow t he vol t a g e c ont r ol g a i n of t he s t e a dy s t a t e , K , t o be hi g h.
5 8
T a bl e 7 s how s t he dy n a m i c pa r a m e t e r s of t he S V C dy n a m i c m ode l
B u s N u m b e r
P a r a m e t e r 3 6 8
K 1 0 0 1 0 0 1 0 0
T 1 1 1 1
T 2 0 0 0
T 3 ( > 0 ) 1 0 1 0 1 0
T 4 0 0 0
T 5 0 . 6 0 . 6 0 . 6
R M I N 0 0 0
V M A X 1 1 1
V M I N 0 0 0
C B A S E 1 0 0 1 0 0 1 0 0
3 . 4 . 5 S t a t i c C o n d e n s e r ( C S T A T T )
F i gur e 46 s how s t he bl oc k di a gr a m of t he C S T A T T m ode l
C S T A T T dy n a m i c m ode l i s a D C c a pa c i t or c onne c t e d t o a pow e r s y s t e m us i ng a
pow e r - e l e c t r oni c ba s e d s w i t c he s . T he m ode l a s s um e s t ha t a c t i ve pow e r i s z e r o be c a us e i t
i s s o s m a l l t ha t i t c oul d be ne gl e c t e d. A s s e e n i n f i gur e 46, t he m ode l i s c om pos e d of a
vol t a g e r e gul a t or t ha t ha s a t r a ns i e nt g a i n. T he t r a ns i e nt g a i n i s de pe nde nt of t he t i m e
c ons t a nt T 1, T 2, T 3 a nd T 4. T he f ol l ow i ng t a bl e s how s t he va l ue s of a l l t he dy n a m i c
pa r a m e t e r s us e d i n t he m ode l .
5 9
T a bl e 8 s how s t he dy n a m i c pa r a m e t e r s of t he C S T C N T m ode l
P a r a m e t e r B u s N u m b e r
T 1 ( > 0 ) 0 . 2 0 . 2 0 . 2
T 2 ( > 0 ) 0 . 2 0 . 2 0 . 2
T 3 ( > 0 ) 0 . 2 0 . 2 0 . 2
T 4 ( > 0 ) 0 . 2 0 . 2 0 . 2
K 2 4 2 4 2 4
D r o o p 0 . 0 3 0 . 0 3 0 . 0 3
V M A X 9 9 9 9 9 9 9 9 9
V M I N - 9 9 9 - 9 9 9 - 9 9 9
I C M A X 1 . 2 5 1 . 2 5 1 . 2 5
I L M A X 1 . 2 5 1 . 2 5 1 . 2 5
V C U T O U T 0 . 2 0 . 2 0 . 2
E L I M I T 1 . 2 1 . 2 1 . 2
X T 0 . 1 0 . 1 0 . 1
A C C 0 . 0 5 0 . 0 5 0 . 0 5
S T B A S E
( > 0 )
1 0 0 1 0 0 1 0 0
6 0
3 . 4 . 6 S u p e r c o n d u c t i n g M a g n e t i c E n e r g y S t o r a g e ( C S M E S T )
F i gur e 47 s how s t he bl oc k di a gr a m of t he C S M E S T M ode l
T he s upe r c onduc t i ng m a gne t i c s t or a ge us e d i s t he vol t a g e - s our c e ba s e d S M E . I D C O
r e pr e s e nt s t he i ni t i a l di r e c t c ur r e nt a nd P m a x i s t he uppe r pow e r l i m i t s pe c i f i e d by t he
de s i gne r . V D C M I N a nd V D M A X r e pr e s e nt t he l ow e r a nd uppe r vol t a g e l i m i t t ha t t he
c oi l a nd c onve r t e r c a n w i t hs t a nd. I d c m i n1, I d c m a x 1, I d c m i n2 a nd I d c m a x 2 a r e t he l ow e r
a nd uppe r l i m i t s f or t he c oi l c ur r e nt i n or de r t o pr e ve nt t he c oi l f r om be i ng unde r c ha r g e d
or ove r c ha r g e d. I a c m a x r e pr e s e nt s t he l i m i t a t i on on t he c onve r t e r c ur r e nt . K xV a c xI d c i s
pr e s e nt t o de s c r i be t he i na bi l i t y t o w i t hs t a nd m a x dc vol t a g e w he n a l ow vol t a g e i s
a ppl i e d.
6 1
T o obt a i n t he dy n a m i c da t a f or t he S M E S , s om e e qua t i ons a r e t o be us e d. T he i nduc t a nc e
of t he c oi l c a n be de r i ve d f r om t he r a t i ng of t he S M E S . T he f ol l ow i ng ba s i c i nduc t a nc e
e ne r g y e qua t i on i s us e d t o de t e r m i ne t he i nduc t a nc e :
U s i ng t he ba s e s of t he pe r uni t va l ue s , V D C M I N a nd V D M A X a r e - 1 a nd 1. A l s o,
I d c m i n1, I d c m a x 1, I d c m i n2 a nd I d c m a x 2 a r e 0.01, 1, 0.01, a nd 1.01 r e s pe c t i ve l y . I a c m a x
e qua l s t o P m a x/ P ow e r F a c t or a nd K x i s c ons i de r e d 1. M or e ove r , I D C O i s de r i ve d f r om
t he f ol l ow i ng e qua t i on:
T he f ol l ow i ng t a bl e g i ve s a l l t he us e d va l ue s f or e a c h dy n a m i c pa r a m e t e r r e l a t e d t o t he
dy n a m i c m ode l of t he S upe r c onduc t i ng M a gne t i c E ne r g y S t or a g e .
T a bl e 9 s how s t he dy n a m i c pa r a m e t e r s f or C S M E S T m ode l
P a r a m e t e r V a l u e
L , C o i l
I n d u c t a n c e
0 . 2 6 5
P M A X 9 0
V D C M A X 1
V D C M I N - 1
I D C M A X 1 1
I D C M A X 2 1 . 0 1
I D C M I N 1 0 . 0 2
I D C M I N 2 0 . 0 1
I A C M A X 1 0 0
L i m i t e r K
F a c t o r
1
I D C O 1
K R 0
K A V R 2 5
T 1 0 . 5
T 2 0 . 5
T 3 0 . 5
T 4 0 . 5
V M A X 9 9 9 9
V M I N - 9 9 9 9
A V R D r o o p 0 . 0 3
6 2
4 . R e s u l t s a n d A n a l y s i s
A f t e r t he I E E E 14 bus m ode l ha s be e n c ons t r uc t e d us i ng P S S / E , i t i s t i m e t o r un i t t o
ha ve a n i de a of t he s y s t e m be ha vi or . T he s a m e pa r a m e t e r s of t he I E E E 14 bus s y s t e m a r e
us e d w i t hout a ny m odi f i c a t i ons O t he r t ha n a ddi ng s w i t c he d c a pa c i t or t o t he
c om pe ns a t i on bus e s . F i gur e 48 s how s t he pow e r f l ow l i ne l oa di ng pe r c e nt a ge .
F i gur e 48 s how s t he pow e r f l ow r e s ul t s of t he I E E E 14 bus
6 3
4 . 1 D y n a m i c A n a l y s i s r e s u l t s f o r t h e I E E E 1 4 b u s s y s t e m B a s e
c a s e
T he f i r s t s t e p i n t he a na l y s i s t o e va l ua t e t he dy n a m i c i m pa c t of t he c om pe ns a t i on de vi c e s
i s t o r e m ove a ny c om pe ns a t i on de vi c e t ha t m a y c ont r i but e t o t he dy n a m i c s t a bi l i t y of t he
s y s t e m . I n t he c a s e of t he I E E E 14 bus s y s t e m , s y n c hr onous c onde ns e r s ha ve dy n a m i c
c a pa bi l i t i e s . T he r e f or e , t he y w i l l be r e m ove f r om t he I E E E 14 bus s y s t e m . A f t e r t ha t , a
t hr e e pha s e f a ul t i s t o be a ppl i e d t o di f f e r e nt bus e s i n t he s y s t e m t o de t e r m i ne i f t he
s y s t e m i s a bl e t o r e ga i n i t s s t a bi l i t y ba c k a f t e r a s e ve r e di s t ur ba nc e . T he t hr e e pha s e t y p e
f a ul t i s c hos e n be c a us e i t i s t he w or s t t y p e of f a ul t .
S y s t e m ’ s D y n a m i c R e s pons e W i t hout S y n c hr onous C onde ns e r s
F a ul t a t bus 1
F i g ur e 49 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
6 4
F a ul t a t bus 2
F i g ur e 50 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
F a ul t a t bus 3
F i g ur e 51 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
6 5
F a ul t a t bus 4
F i g ur e 52 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
F a ul t a t bus 5
F i g ur e 53 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
6 6
F a ul t a t bus 6
F i g ur e 54 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
6 7
S y s t e m ’ s D y n a m i c R e s pons e W i t h S y n c hr onous C onde ns e r s
F a ul t a t bus 1
F i g ur e 55 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 56 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
6 8
F a ul t a t bus 3
F i g ur e 57 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 58 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
6 9
F a ul t a t bus 5
F i g ur e 59 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 60 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
7 0
F r om t he pr e vi ous a na l y s i s , t he I E E E 14 bus ba s e c a s e w a s ve r y s t a bl e a nd r e ga i ne d i t s
s t a bi l i t y a f t e r a ppl y i ng di f f e r e nt t hr e e pha s e ba l a nc e d f a ul t s t o di f f e r e nt bus e s t hr oughout
t he s y s t e m . T he ne x t s t e p i s t o c onne c t t he E l e c t r i c V e hi c l e s t o t he s y s t e m i n or de r t o
s t r e s s t he s y s t e m out . T he E l e c t r i c V e hi c l e s a r e m ode l e d a s pur e 8 kW a c t i ve pow e r l oa d.
T hi s i s done t o f i nd t he poi nt w he r e t he s y s t e m i s s t r e s s e d out e nough w i t h t he c ha r g i ng
of e l e c t r i c ve hi c l e s t ha t i t r e a c he s t he bor de r poi nt of c ol l a ps e .
4 . 2 D y n a m i c A n a l y s i s o f t h e I E E E 1 4 b u s A f t e r I n c r e a s i n g t h e
A c t i v e L o a d t o 1 . 4 T i m e s t h e B a s e C a s e A c t i v e P o w e r L o a d .
S y s t e m ’ s D y n a m i c R e s pons e W i t hout S y n c hr onous C onde ns e r
F a ul t a t bus 1
F i g ur e 61 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
7 1
F a ul t a t bus 2
F i g ur e 62 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
F a ul t a t bus 3
F i g ur e 63 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
7 2
F a ul t a t bus 4
F i g ur e 64 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
F a ul t a t bus 5
F i g ur e 65 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
7 3
F a ul t a t bus 6
F i g ur e 66 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
7 4
S y s t e m ’ s D y n a m i c R e s pons e W i t h S y n c hr onous C onde ns e r
F a ul t a t bus 1
F i g ur e 67 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 68 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
7 5
F a ul t a t bus 3
F i g ur e 69 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 70 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
7 6
F a ul t a t bus 5
F i g ur e 71 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 72 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
7 7
A s s e e n i n t he pr e vi ous f i gur e s , i nc r e a s i ng t he a c t i ve pow e r of t he s y s t e m by c onne c t i ng
E l e c t r i c V e hi c l e s t o 1.4 t i m e s t he r e a l pow e r of t he I E E E 14 bus s y s t e m di d not r e s ul t a
c a s e of i ns t a bi l i t y . I n f a c t , t he s y s t e m r e ga i ne d i t s s t a bi l i t y a f t e r a ppl y i ng di f f e r e nt t hr e e
pha s e f a ul t s t o di f f e r e nt bus e s i n t he pr e s e nc e a nd a bs e nc e s of t he s y n c hr onous
c onde ns e r s . T he r e f or e , m or e E l e c t r i c ve hi c l e s a r e ne e de d t o be c onne c t e d t o r e a c h t he
l i m i t w he r e t he s y s t e m i s a bout t o c ol l a ps e .
4 . 3 D y n a m i c A n a l y s i s o f t h e I E E E 1 4 b u s A f t e r I n c r e a s i n g t h e
A c t i v e L o a d t o 1 . 8 T i m e s t h e B a s e C a s e A c t i v e P o w e r L o a d .
S y s t e m ’ s D y n a m i c R e s pons e W i t hout S y n c hr onous C onde ns e r s
F a ul t a t bus 1
F i g ur e 73 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
7 8
F a ul t a t bus 2
F i g ur e 74 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
F a ul t a t bus 3
F i g ur e 75 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
7 9
F a ul t a t bus 4
F i g ur e 76 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
F a ul t a t bus 5
F i g ur e 77 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
8 0
F a ul t a t bus 6
F i g ur e 78 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
A s s e e n i n t he pr e vi ous f i gur e s , i nc r e a s i ng t he a c t i ve pow e r of t he s y s t e m by c onne c t i ng
E l e c t r i c V e hi c l e s t o 1.8 t i m e s t he r e a l pow e r of t he I E E E 14 bus s y s t e m di d not r e s ul t a
c a s e of i ns t a bi l i t y . I n f a c t , t he s y s t e m r e ga i ne d i t s s t a bi l i t y a f t e r a ppl y i ng di f f e r e nt t hr e e
pha s e f a ul t s t o di f f e r e nt bus e s i n t he pr e s e nc e a nd a bs e nc e s of t he s y n c hr onous
c onde ns e r s . T he r e f or e , m or e E l e c t r i c ve hi c l e s a r e ne e de d t o be c onne c t e d t o r e a c h t he
l i m i t w he r e t he s y s t e m i s a bout t o c ol l a ps e .
8 1
4 . 4 D y n a m i c A n a l y s i s o f t h e I E E E 1 4 b u s A f t e r I n c r e a s i n g t h e
A c t i v e L o a d t o 1 . 9 T i m e s t h e B a s e C a s e A c t i v e P o w e r L o a d .
S y s t e m ’ s D y n a m i c R e s pons e W i t hout S y n c hr onous C onde ns e r s
F a ul t a t bus 1
F i g ur e 79 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 80 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
8 2
F a ul t a t bus 3
F i g ur e 81 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 82 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
8 3
F a ul t a t bus 5
F i g ur e 83 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 84 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
8 4
T he pr e vi ous g r a phs s how t he s y s t e m ’ s dy n a m i c r e s pons e of t he I E E E 14 bus s y s t e m
w i t hout t he s y n c hr onous c onde ns e r s c l e a r l y i ndi c a t e t ha t t he s y s t e m i s not s t a bl e . A f t e r
a ppl y i ng t hr e e pha s e ba l a nc e d f a ul t s t o di f f e r e nt bus e s ( 1, 2, 4, a nd 5) i n t he s y s t e m , t he
pow e r s y s t e m di d not r e t ur n t o t he nor m a l ope r a t i ng c ondi t i ons . I n f a c t , t he s y s t e m
r e a c he d a l e ve l of c ol l a ps e . T he r e f or e , t he de s i r e d bounda r y w he r e t he s y s t e m i s on t he
e dge of i ns t a bi l i t y i s r e a c he d w i t h c onne c t i ng E l e c t r i c V e hi c l e s t ha t a r e e qui va l e nt of
doubl e t he r e a l pow e r l oa d c onne c t e d t o t he I E E E 14 bus s y s t e m . T he e x pl a na t i on of
i ns t a bi l i t y i s t ha t w he n s y n c hr onous c onde ns e r s a r e r e m ove d, r e a c t i ve pow e r w a s
r e m ove d a s w e l l . T he r e f or e , a de vi c e i s ne e de d t o r e i m bur s e t he s y s t e m ’ s l os t r e a c t i ve
pow e r .
S y s t e m ’ s D y n a m i c R e s pons e W i t h t he S y n c hr onous C onde ns e r s
F a ul t a t bus 1
F i g ur e 85 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
8 5
F a ul t a t bus 2
F i g ur e 86 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
F a ul t a t bus 3
F i g ur e 87 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
8 6
F a ul t a t bus 4
F i g ur e 88 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
F a ul t a t bus 5
F i g ur e 89 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
8 7
F a ul t a t bus 6
F i g ur e 90 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
8 8
S y s t e m ’ s D y n a m i c R e s pons e W i t h t he S t a t i c V a r C om pe ns a t or
F a ul t a t bus 1
F i g ur e 91 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 92 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
8 9
F a ul t a t bus 3
F i g ur e 93 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 94 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
9 0
F a ul t a t bus 5
F i g ur e 95 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 96 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
9 1
S y s t e m ’ s D y n a m i c R e s pons e W i t h t he S T A T C O M
F a ul t a t bus 1
F i g ur e 97 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 98 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
9 2
F a ul t a t bus 3
F i g ur e 99 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 100 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
9 3
F a ul t a t bus 5
F i g ur e 101 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 102 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
9 4
S y s t e m ’ s D y n a m i c R e s pons e W i t h t he S upe r c onduc t i ng M a g ne t i c E ne r g y S t or a ge
F a ul t a t bus 1
F i g ur e 103 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 1
F a ul t a t bus 2
F i g ur e 104 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 2
9 5
F a ul t a t bus 3
F i g ur e 105 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 3
F a ul t a t bus 4
F i g ur e 106 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 4
9 6
F a ul t a t bus 5
F i g ur e 107 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 5
F a ul t a t bus 6
F i g ur e 108 s how s t he vol t a g e r e s pons e a f t e r a ppl y i ng a f a ul t a t bus 6
9 7
4 . 5 S u m m a r y a n d C o m p a r i s o n
A f t e r r unni ng t he a na l y s i s , t he s y s t e m s how s s t a bi l i t y a f t e r c l e a r i ng t he f a ul t a t e a c h bus
w i t h or w i t hout t he dy n a m i c de vi c e s unt i l % 80 E V s a s s e e n i n t a bl e 10- 14.
T a bl e 10 s um m a r i z e s t he r e s ul t s w he n t he r e i s no E V s c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E s S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
T a bl e 1 1 s um m a r i z e s t he r e s ul t s w he n t he r e i s % 20 E V s a r e c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E s S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
9 8
T a bl e 12 s um m a r i z e s t he r e s ul t s w he n t he r e i s % 40 E V s a r e c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E s S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
T a bl e 13 s um m a r i z e s t he r e s ul t s w he n t he r e i s % 60 E V s a r e c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E s S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
9 9
T a bl e 14 s um m a r i z e s t he r e s ul t s w he n t he r e i s % 80 E V s a r e c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E s S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
T a bl e 15 s um m a r i z e s t he r e s ul t s w he n t he r e i s % 90 E V s a r e c onne c t e d
F a ul t a t B us N um be r
D e vi c e 1 2 3 4 5 6
N one N ot
S t a bl e
N ot
S t a bl e
S t a bl e N ot
S t a bl e
N ot
S t a bl e
S t a bl e
S C N ot
S t a bl e
S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S V C N ot
S t a bl e
S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S T A T C O M S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
S M E S S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e S t a bl e
1 0 0
W he n i nc r e a s i ng t he E V s c onne c t e d t o t he s y s t e m t o % 90 t he a c t ua l r e a l l oa d, t he s y s t e m
e x pe r i e nc e a s t a t e of vol t a g e c ol l a ps e a f t e r a ppl y i ng f a ul t s a t bus 1,2,4, a nd 5. T he
s y n c hr onous c onde ns e r s a nd S V C s ol ve d t he s t a t e of i ns t a bi l i t y e x c e pt a f t e r a ppl y i ng a
f a ul t a t bus 1. O n t he O t he r ha nd, S M E S a nd S T A T C O M w e r e a bl e t o m a ke t he s y s t e m
s t a bl e a t a ny g i ve n f a ul t .
T he f ol l ow i ng t a bl e s g i ve a de t a i l e d pi c t ur e of t he l a s t s i t ua t i on w he n t he E V s a r e
c onne c t e d t o a n a m ount of % 90 of t he e x i s t i ng a c t i ve pow e r l oa d i n t he I E E E 14 bus
s y s t e m . T a bl e s how s t he t ot a l a c t i ve pow e r c onne c t e d a t e a c h l oa d bus i n t he s y s t e m
i nc l udi ng E V s a nd ot he r r e a l pow e r l oa ds . A f t e r t ha t , t a bl e s how s t he t ot a l a m ount of r e a l
pow e r c onne c t e d t o t he s y s t e m i n t he f or m of E V .
T a bl e 16 s how s t he a c t i ve pow e r c onne c t e d a t e a c h bus i n t he c onne c t i on of % 90 E V
B u s # P ( M W ) 1 . 2 P ( M W ) 1 . 4 P ( M W ) 1 . 6 P ( M W ) 1 . 8 P ( M W ) 1 . 9 P ( M W )
2 2 1 . 7 2 6 . 0 4 3 0 . 3 8 3 4 . 7 2 3 9 . 0 6 4 1 . 2 3
3 9 4 . 2 1 1 3 . 0 4 1 3 1 . 8 8 1 5 0 . 7 2 1 6 9 . 5 6 1 7 8 . 9 8
4 4 7 . 8 5 7 . 3 6 6 6 . 9 2 7 6 . 4 8 8 6 . 0 4 9 0 . 8 2
5 7 . 6 9 . 1 2 1 0 . 6 4 1 2 . 1 6 1 3 . 6 8 1 4 . 4 4
6 1 1 . 2 1 3 . 4 4 1 5 . 6 8 1 7 . 9 2 2 0 . 1 6 2 1 . 2 8
9 2 9 . 5 3 5 . 4 4 1 . 3 4 7 . 2 5 3 . 1 5 6 . 0 5
1 0 9 1 0 . 8 1 2 . 6 1 4 . 4 1 6 . 2 1 7 . 1
1 1 3 . 5 4 . 2 4 . 9 5 . 6 6 . 3 6 . 6 5
1 2 6 . 1 7 . 3 2 8 . 5 4 9 . 7 6 1 0 . 9 8 1 1 . 5 9
1 3 1 3 . 5 1 6 . 2 1 8 . 9 2 1 . 6 2 4 . 3 2 5 . 6 5
1 4 1 4 . 9 1 7 . 8 8 2 0 . 8 6 2 3 . 8 4 2 6 . 8 2 2 8 . 3 1
1 0 1
T a bl e 17 s how s t he t ot a l a c t i ve pow e r of E V s i s c onne c t e d a t e a c h bus
E V l o a d ( M W )
B u s # 1 . 2 P 1 . 4 P 1 . 6 P 1 . 8 P 1 . 9 P
2 4 . 3 4 8 . 6 8 1 3 . 0 2 1 7 . 3 6 1 9 . 5 3
3 1 8 . 8 4 3 7 . 6 8 5 6 . 5 2 7 5 . 3 6 8 4 . 7 8
4 9 . 5 6 1 9 . 1 2 2 8 . 6 8 3 8 . 2 4 4 3 . 0 2
5 1 . 5 2 3 . 0 4 4 . 5 6 6 . 0 8 6 . 8 4
6 2 . 2 4 4 . 4 8 6 . 7 2 8 . 9 6 1 0 . 0 8
9 5 . 9 1 1 . 8 1 7 . 7 2 3 . 6 2 6 . 5 5
1 0 1 . 8 3 . 6 5 . 4 7 . 2 8 . 1
1 1 0 . 7 1 . 4 2 . 1 2 . 8 3 . 1 5
1 2 1 . 2 2 2 . 4 4 3 . 6 6 4 . 8 8 5 . 4 9
1 3 2 . 7 5 . 4 8 . 1 1 0 . 8 1 2 . 1 5
1 4 2 . 9 8 5 . 9 6 8 . 9 4 1 1 . 9 2 1 3 . 4 1
T he a m ount of r e a l pow e r c onne c t e d t o e a c h bus i s c a l c ul a t e d i n t a bl e i n or de r t o e va l ua t e
how a ny E V s c a n be c onne c t e d t o t he s y s t e m i n t he pr e s e nc e of c om pe ns a t i on de vi c e s . A
s i ng l e E V i s a s s um e d t o be a r e a l pow e r l oa d of 8 kW . T he r e f or e , t he t ot a l E V ’ s r e a l
pow e r i s di vi de d by 8 t o g i ve t he num be r of E V s c onne c t e d a t e a c h bus a s i l l us t r a t e d i n
t a bl e .
T a bl e 18 s how s t he N um be r of E V s c onne c t e d a t e a c h bus
N u m b e r o f E V s
B u s # 1 . 2 P 1 . 4 P 1 . 6 P 1 . 8 P 1 . 9 P
2 5 4 2 . 5 1 0 8 5 1 6 2 7 . 5 2 1 7 0 2 4 4 1 . 2 5
3 2 3 5 5 4 7 1 0 7 0 6 5 9 4 2 0 1 0 5 9 7 . 5
4 1 1 9 5 2 3 9 0 3 5 8 5 4 7 8 0 5 3 7 7 . 5
5 1 9 0 3 8 0 5 7 0 7 6 0 8 5 5
6 2 8 0 5 6 0 8 4 0 1 1 2 0 1 2 6 0
9 7 3 7 . 5 1 4 7 5 2 2 1 2 . 5 2 9 5 0 3 3 1 8 . 7 5
1 0 2 2 5 4 5 0 6 7 5 9 0 0 1 0 1 2 . 5
1 1 8 7 . 5 1 7 5 2 6 2 . 5 3 5 0 3 9 3 . 7 5
1 2 1 5 2 . 5 3 0 5 4 5 7 . 5 6 1 0 6 8 6 . 2 5
1 3 3 3 7 . 5 6 7 5 1 0 1 2 . 5 1 3 5 0 1 5 1 8 . 7 5
1 4 3 7 2 . 5 7 4 5 1 1 1 7 . 5 1 4 9 0 1 6 7 6 . 2 5
1 0 2
F r om t he t e c hni c a l poi nt of vi e w t he s y s t e m di s pl a y s a be t t e r pe r f or m a nc e a ga i ns t
di s t ur ba nc e s w he n t he dy n a m i c de vi c e s ( S y n c hr onous C onde ns e r s , S t a t i c V a r
C om pe ns a t or , S t a t i c S y n c hr onous C om pe ns a t or a nd S upe r c onduc t i ng M a gne t i c E ne r g y
S t or a ge ) w e r e c onne c t e d t o t he s y s t e m . T hi s i s due t o t he a bi l i t i e s of t he dy n a m i c de vi c e s
t o s uppl y r e a c t i ve pow e r t ha t he l pe d t he s y s t e m m a i nt a i n a g ood vol t a g e l e ve l a f t e r t he
di s t ur ba nc e .
H ow e ve r , t he dy n a m i c c ont r i but i on i s not t he onl y f a c t or a f f e c t i ng t he de c i s i on of
i ns t a l l i ng t he dy n a m i c de vi c e s . T he de c i s i on i s f unc t i on of s e ve r a l f a c t or s s uc h a s
phy s i c a l s i z e , c os t , m a i nt e na nc e a nd r e a c t i ve pow e r c a pa bi l i t y .
F or e x a m pl e , i n t e r m s of t he r e a c t i ve pow e r c a pa bi l i t y , t he s y n c hr onous c onde ns e r c a n
s uppl y c a pa c i t i ve r e a c t i ve pow e r t ha n i nduc t i ve . T he S V C r e a c t i ve pow e r s uppl y de pe nds
on how m a ny r e a c t or s a nd c a pa c i t or s t he S V C ha s . A l s o, i t de pe nds on t he c ont r ol of t he
t hy r i s t or ’ s a ngl e . F or i ns t a nc e , i f 500 M V A R of i nduc t or s a nd 200 M V A R of c a pa c i t or s
a r e i ns t a l l e d, t he m a r g i n of i nduc t i ve r e a c t i ve of t he S V C i s m or e t ha n t he c a pa c i t i ve . F or
t he S T A T C O M , i t ha s t he a bi l i t y of s uppl y i ng a n e qua l a m ount of i nduc t i ve or c a pa c i t i ve
r e a c t i ve pow e r .
I n t e r m s of s i z e , T he S M E S r e qui r e s t he l a r g e s t s pa c e of a l l t he m e nt i one d dy n a m i c
de vi c e s . T hi s due t o t he f a c t t ha t t he c oi l i s ve r y l a r g e . T he s e c ond l a r g e s t de vi c e s i n s i z e
i s t he S V C . T he s y n c hr onous c onde ns e r c om e s t hi r d i n t he s pa c e r e qui r e m e nt . T he
s m a l l e s t de vi c e i n t e r m s of s i z e i s t he S T A T C O M .
T he c os t c om pa r i s on[ 67] i s one t he m os t f a c t or i n m a ki ng t he de c i s i on of i ns t a l l i ng t he
dy n a m i c de vi c e s or not . T he s y n c hr onous c onde ns e r s i s t he c he a pe s t w i t h a c os t of
a r ound 10- 40 $/ K V A . A f t e r t ha t , t he S V C i s s e c ond i n t he r ow w i t h a pr i c e of 40- 60
$/ K V A . T he t hi r d de vi c e i s t he S T A T C O M w i t h a c os t of 55- 70 $/ K V A due t o t he hi g h
c os t of t he P W M m odul e s . T he m os t e x pe ns i ve de vi c e i s t he S M E S be c a us e of i t s a bi l i t y
t o s t or e r e a l pow e r a nd de l i ve r i t t o t he s y s t e m w he n ne e de d. T he pr i c e of S M E S i s
a r ound 690$/ K W .
1 0 3
T he c hoi c e of t he de vi c e de pe nds on t he s i t ua t i on. F or e x a m pl e , i f t he s pa c e of t he
s ubs t a t i on i s l i m i t e d a nd t he t e c hni c a l pe r f or m a nc e i s ve r y i m por t a nt , t he be s t opt i on i s
t he S T A T C O M . O n t he ot he r ha nd, i f t he r e i s a n a bunda nc e of s pa c e a nd t he s t or a ge
c a pa bi l i t y i s ne e de d, i n c a s e of t he e x i s t e nc e of r e ne w a bl e e ne r g y r e s our c e s , a nd t he c os t
i s not a n i s s ue , S M E S i s t he be s t opt i on. T a bl e 19 s um m a r i z e s t he c om pa r i s on of t he f our
de vi c e s .
T a bl e 19 s how s di f f e r e nt c om pa r i s on f a c t or s f or e a c h de vi c e
F ac t or / D e vi c e S C S V C S T A T C O M S M E S
L e ad i n g &
L aggi n g
R e ac t i ve
P ow e r
M or e c a pa c i t i ve
m a r g i n t ha n
i nduc t i ve
D e pe nds on t he
r a t i ng of T C R
& T S C
E qua l L a ggi ng
a nd l e a di ng
B ot h L a g a nd
l e a di ng[ 68]
P h ys i c al S i z e L e s s t ha n S V C L e s s t ha n
S M E S
S m a l l V e r y L a r g e
R e al P ow e r Z e r o Z e r o Z e r o w i t hout
s t or a ge
D e pe nds on t he
r a t i ng
C os t C he a pe s t L e s s e x pe ns i ve
t ha n
S T A T C O M
L e s s e x pe ns i ve
t ha n S M E S
E xpe ns i ve
M ai n t e n an c e L i t t l e
m a i nt e na nc e
be c a us e t he
m ovi ng pa r t s
A l m os t no
m a i nt e na nc e
A l m os t no
m a i nt e na nc e
V e r y l i t t l e
m a i nt e na nc e
O ve r l oad [ 69] V e r y g ood N ot g ood
c om pa r e d t o S C
N ot g ood
c om pa r e d t o S C
N ot g ood
c om pa r e d t o S C
[ 70]
1 0 4
5 . C o n c l u s i o n
T he s y s t e m i s s t a bl e w he n ope r a t e d a t one t i m e t he or i gi na l l oa d. I f t he s y s t e m i s s t r e s s e d
out , t he i m pa c t of c om pe ns a t i on de vi c e s oc c ur . W i t hout t he dy n a m i c de vi c e s , t he s y s t e m
c ol l a ps e s w he n s ubj e c t e d t o c e r t a i n bus f a ul t s . W i t h t he a ddi t i on of S y n c hr onous
C onde ns e r s , S T A T C O M , S V C a nd S M E t he s y s t e m s t a bi l i z e s . H ow e ve r , t he dy n a m i c
c ont r i but i on i s not t he onl y f a c t or a f f e c t i ng t he de c i s i on of i ns t a l l i ng t he dy n a m i c de vi c e s .
T he de c i s i on i s a f unc t i on of s e ve r a l f a c t or s s uc h a s phy s i c a l s i z e , c os t , m a i nt e na nc e a nd
r e a c t i ve pow e r c a pa bi l i t y .
6 . F u t u r e W o r k
1- I n t e gr a t i ng r e ne w a bl e e ne r g y r e s our c e s s uc h a s w i nd a nd s ol a r t o t he s y s t e m a nd
e va l ua t i ng t he i m pa c t of t he dy n a m i c de vi c e t o s t a bi l i z e t he s y s t e m .
2- E va l ua t i ng t he i m pa c t of dy n a m i c de vi c e s on t w o i nt e r c onne c t e d A C ne t w or k vi a
H V D C .
3- C r e a t i ng ne w c ont r ol m e t hods f or e a c h c om pe ns a t i on de vi c e a nd t e s t t he i r
pe r f or m a nc e i n or de r t o s t a bi l i z e t he g r i d.
4- I n ve s t i ga t i ng t he hi g h vol t a g e s pi ke i n t he r e s pons e of t he S M E S a f t e r c l e a r i ng t he
f a ul t s .
5- D e ve l opi ng t he dy n a m i c m ode l s t o a c c om m oda t e t he ne w i m pr ove m e nt s i n t he
t e c hnol ogy of dy n a m i c de vi c e s s uc h a s s upe r c onduc t i ng or pow e r e l e c t r oni c c ont r ol l e d
S y n c hr onous C onde ns e r s .
1 0 5
7 . R e f e r e n c e s
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" D e f i ni t i on a nd c l a s s i f i c a t i on of pow e r s y s t e m s t a bi l i t y I E E E / C I G R E j oi nt t a s k f or c e on
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" D e f i ni t i on a nd c l a s s i f i c a t i on of pow e r s y s t e m s t a bi l i t y I E E E / C I G R E j oi nt t a s k f or c e on
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1 0 7
[ 22] L o r f , C l e m e ns F r i e dr i c h. " O pt i m um B a t t e r y C a pa c i t y f or E l e c t r i c V e hi c l e s w i t h
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Abstract (if available)

Abstract The modern age has been known as the industrial age. New technologies have been invented everyday and old technologies are being improved to get the maximum benefits out of them. However, the environment is suffering the adverse impacts resulted from the development of the new technologies. Unwanted emissions that cause so much harm to the environment such as Carbon Dioxide are emitted to the atmosphere. To decrease the rate of emissions, the use of Electric Vehicles (EVs) is recommended due to the lower emissions rate compared to the gas-powered cars. ❧ However, shifting to EVs has to be planned and studied correctly. The EVs need to be charged from the utility power grid. The electric infrastructure might not be able to withstand the excessive loading of the EVs. The system might lose its stability causing an undesired voltage collapse. Therefore, an action has to be done to prevent the instability that could occur. Installing dynamic devices might contribute to the voltage compensation needed to stabilize the system. ❧ To study the impact of the Synchronous Condensers, Static Var Compensator, Static Condenser and the Superconducting Magnetic Energy Storage on Electric Vehicles charging, the IEEE 14 bus grid is built in PSSE. The dynamic devices are integrated into different base cases where their impact alone is evaluated. Power flow analysis is to be done first to make sure the system is stable. Different scenarios are to be explored in this this thesis. The penetration of the EVs are to be increased to a certain percentage in each scenario. Dynamic analysis is also to be done to each base case separately. Three phase balanced fault is introduced at several busbars within the system for five cycles. After that, the capability of each base case to regain stability and the contribution of each dynamic device is evaluated.

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Asset Metadata

Creator Allehyani, Ahmed (author)

Core Title The dynamic interaction of synchronous condensers, SVC, STATCOM and superconducting magnetic energy storage on electric vehicles

School Viterbi School of Engineering

Degree Master of Science

Degree Program Electrical Engineering

Publication Date 10/27/2015

Defense Date 10/14/2015

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag Electric vehicles,OAI-PMH Harvest,power system dynamics,SMES,STATCOM,SVC,synchronous condenser

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Beshir, Mohammed (committee chair), Bogdan, Paul (committee member), Maby, Edward (committee member)

Creator Email ahmed5a@hotmail.com,allehyaa@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-191892

Unique identifier UC11276468

Identifier etd-AllehyaniA-3991.pdf (filename),usctheses-c40-191892 (legacy record id)

Legacy Identifier etd-AllehyaniA-3991.pdf

Dmrecord 191892

Document Type Thesis

Format application/pdf (imt)

Rights Allehyani, Ahmed

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA