IEEE Transactions on Power Delivery, Vol. 4,No.4,October 1989
2171
STUDY OF HVDC CONTROLS THROUGH EFFICIENT DYNAMIC DIGITAL SIMULATION OF CONVERTERS
K.R.PADIYAR
Member
1.1.S~. Bangalore
INDIA
SACHCHIDANAND
Non-member
1.I.T.KanDUr
INDIA
A.G.KOTHAR1
Non-member
VRCE. Naqpur
INDIA
ABSTRACT
T h i s p a p r d e s c r i t x s t h e c o n v e r t e r m d e l f o r 6/12
p u l s e o p e r a t i o n and p r e s e n t s i t s a p p l i c a t i o n s f o r t h e
s t u d y of t h e performance o f c o n v e r t e r c o n t r o l s . The
s i m u l a t i o n i s s i m p l i f i e d by r e p r e s e n t i n g t h e c o n v e r t e r
a s a time v a r y i n g e q u i v a l e n t circuit on t h e DC s i d e
which i s d e r i v e d on t h e b a s i s o f g r a p h t h e o r y .
E l i m i n a t i o n o f t h e need t o store c o n n e c t i o n matrices
a n d a n e f f i c i e n t way of g e n e r a t i n g t h e c o n v e r t e r
e q u a t i o n s are f u r t h e r i n n o v a t i o n s i n t r o d u c e d h e r e .
The c o n v e r t e r c o n t r o l based on d i g i t a l t e c h n i q u e s
h a s been c o n s i d e r e d a l o n g w i t h r e p r e s e n t a t i o n of
v o l t a g e dependent c u r r e n t o r d e r l i m i t . The results o f
v a r i o u s test s i m u l a t i o n s c o n s i d e r i n g b o t h weak and
s t r o n g ac system c h a r a c t e r i s t i c s are r e p r e s e n t e d t o
i l l u s t r a t e t h e simulation capability.
Keywords : HVdc, D i g i t a l S i m u l a t i o n , C o n v e r t e r ,
Digital Control
A s t h e a p p l i c a t i o n s o f t h e HVdc systems grow, t h e
need f o r a d e t a i l e d i n v e s t i g a t i o n of t h e p o t e n t i a l
problems i n c r e a s e s . A s a n example, one c o u l d c o n s i d e r
t h e problems of system o p e r a t i o n w i t h d c l i n k s f e e d i n g
weak a c s y s t e m s . T h e r e a r e v a r i o u s a s p e c t s o f t h e
problem such a s v o l t a g e dependent c u r r e n t o r d e r l i m i t ,
v a r ccmpensation etc. B u t i t i s well recognized t h a t a
s u i t a b l e c o n v e r t e r c o n t r o l is t h e most s i g n i f i c a n t
f a c t o r i n t h e optimum a n d s e c u r e o p e r a t i o n o f t h e
system.
While c o n v e r t e r c o n t r o l and o p t i m i z a t i o n a r e
u s u a l l y c a r i e d out u s i n g HVdc simulators, t h e reduced
cost and i n c r e a s e d a v a i l a b i l i t y of d i g i t a l computers
m k e s it a t t r a c t i v e t o use d i g i t a l s i m u l a t i o n . The
s i m u l a t i o n of HVdc c o n v e r t e r s is c h a r a c t e r i z e d by t h e
f a c t t h a t t h e network t o be s o l v e d changes with t h e
commencement and c e s s a t i o n of v a l v e conduction. To
h a n d l e t h i s time v a r y i n g t o p o l o g y o f t h e n e t w o r k
v a r i o u s a p p r o a c h e s h a v e b e e n r e p o r t e d [ 1 - 7 1 . The
system models t h u s d e r i v e d a r e well s u i t e d f o r dynamic
s t u d i e s i n t h e f r e q u e n c y r a n g e u p t o lkHz which i s
appropriate t o investigate the converter control
r e s p o n s e . However f o r h i g h f r e q u e n c y t r a n s i e n t
s t u d i e s , EMTP t y p e s i m u l a t i o n is n e c e s s a r y (81.
This paper d e s c r i b e s a c o n v e r t e r model f o r 6/12
p u l s e o p e r a t i o n and p r e s e n t s i t s a p p l i c a t i o n f o r t h e
s t u d y o f p e r f o r m a n c e o f c o n v e r t e r c o n t r o l s . The
s i m u l a t i o n i s s i m p l i f i e d by c o n s i d e r i n g a time v a r y i n g
e q u i v a l e n t circuit on t h e d c s i d e , which is d e r i v e d on
t h e b a s i s of graph t h e o r y . E l i m i n a t i o n o f t h e need t o
store c o n n e c t i o n matrices and a f a s t and e f f i c i e n t way
of g e n e r a t i n g t h e c o n v e r t e r e q u a t i o n s a r e f u r t h e r
i n n o v a t i o n s i n t r o d u c e d h e r e . For t h e s i m u l a t i o n of t h e
89 WM 113-2 PWRD
A paper recommended and approved
by the IEEE Transmission and Distribution Committee
of the IEEE Power Engineering Society for presentation
at the IEEE/PES 1989 Winter Meeting, New York, New
York, January 29 - February 3, 1989. Manuscript
submitted August 25, 1987; made available for printing
January 16, 1989.
S.BHATTACBARYYA
Member
Univ.of British Columbia
Vancouver, CANADA
A .SRIVASTAVA
Non-member
1.I.T Kanpur
INDIA
HVdc system t h e approach employed is t o mdel each
canponent s e p e r a t e l y and i n a modular f a s h i o n . These
models a r e i n t e r c o n n e c t e d u s i n g a p p r o p r i a t e i n t e r f a c e
v a r i a b l e s . The c o n t r o l of c o n v e r t e r s based on d i g i t a l
scheme h a s b e e n c o n s i d e r e d a l o n g w i t h v o l t a g e
dependent c u r r e n t o r d e r l i m i t (VDCOL). Results f o r a
two t e r m i n a l HVdc system under normal o p e r a t i o n and a
few abnormal c o n d i t i o n s l i k e s e v e r e AC s i d e v o l t a g e
d i p s , are presented p r i m a r i l y t o i l l u s t r a t e t h e
c a p a b i l i t y of t h e s i m u l a t i o n method.
ccRwERTER~
A t h r e e phase b r i d g e c o n v e r t e r system is shown i n
Fig. 1. T h i s i n c l u d e s t h e r e s i s t a n c e s and i n d u c t a n c e s
Rc and La, Lt,
of t h e converter transformer ( R ,
Lc)
and d c smoothing r e a c t o r $%?id).
Both t h e ac
and d c v o l t a g e sources a r e n o t c o n s t a n t a n d are
a c t u a l l y o u t p u t o f a c a n d d c n e t w o r k m o d e l s . The
e f f e c t of t h e c o n v e r t e r on t h e ac and d c networks is
r e p r e s e n t e d by t h e i n j e c t i o n o f c u r r e n t s i n t o t h e
r e s p e c t i v e network. The g r a p h o f t h e c o n v e r t e r system
is shown i n F i g . 2. I n t o t a l t h e r e a r e Y e l e m n t s , of
Nhich t h e f i r s t 6 r e p r e s e n t t h e v a l v e s . Elements 7 and
Y correspond t o t h e e q u i v a l e n t circuit r e p r e s e n t a t i o n
o f t h e a c s y s t e m f e e d i n g t h e c o n v e r t e r [Y]. The
element 8 i n c l u d e s t h e series c a n b i n a t i o n of Rd,
From t h e graph i t i s clear t h a t t h e r e areL$
t:zevk;anches
and 5 l i n k s . A tree is so chosen such
t h a t i t i n c l u d e s e l e m e n t s 7 , 9 a n d a n y two o f t h e
conducting v a l v e s . Consequently, t h e tree branches a r e
p a r t i t i o n e d i n t o two sets, one set (T1) c o n s i s t i n g of
elements 7 and 9 and t h e o t h e r ( T 2 ) c o n s i s t i n g of t h e
two c o n d u c t i n g v a l v e s . T h e l i n k e l e m e n t s a r e
p a r t i t i o n e d i n t o 3 sets. The first set (L1)
corresponds t o element 8 and t h e o t h e r two sets ( L 2
and L3! c o n s i s t of c o n d u c t i n g a n d n o n - c o n d u c t i n g
valves i n t h e l i n k s respectively.
The v o l t a g e ( v ) a c r o s s and c u r r e n t ( i ) through
t h e branch and l i n k e l e m e n t s are r e l a t e d a s
w h e r e , t d e n o t e s t h e t r a n s p o s e and BL is t h e
f u n d a m e n t a l cutset m a t r i x c o r r e s p o n d i n g t o l i n k
e l e m e n t s . B a s e d o n t h e s u b d i v i s i o n o f t h e set of
branch and l i n k e l e m e n t s d e s c r i b e d e a r l i e r , BL c a n be
p a r t i t i o n e d as
L1
L2
L3
--.
c
[BLl=
For e l e m n t s 7 and 9, t h e circuit e q u a t i o n i s
=
LT1 e
and t h a t f o r element 8
'
where,
xTl =
e = [ (ec
-
0885-8977/89/0700-2171$01.00
-
It
[ v 7 v9
eb) (ea
0 1989 IEEE
-
;
iT1
= [i7
(3)
i9 I t ; z = R ( 1 t c p )
eb)] ; c = L ~ / R= ~$ / R ~ = L,/R,
2172
r-------i
I
1
DC
CONVERT E R
FIG. 1
CONVERTER
NETWORK
FIG.4 12PULSE EQUIVALENT ClRCUlT
SYSTEM
vd
I
A
N
I
- 1-
I
,.I
J
vc?
L------J
C
FIG.3 6 PULSE EQUIVALENT CIRCUIT
0
FIG.2
(5)
&
L2 ; set of nonconducting valves
It i s , t h e r e f o r e , evident t h a t L~~ =O;
yT2 =O;
xL2 = 0
Substituting t h i s i n (1) t o ( 4 )
gives
i T 2 = -BL21 iL1 - BL22 iL2
YL3 = (BL13 )
vL1 =
(ltcp)
where,
(6)
(7)
YT1
- R l ( l + c p ) iL1- R 2 ( l + c p ) i L 2+ ( B L l l ) t
AL2
= -R4-IR3 ( l t c p ) iL1t R4 -1 (BL12)t
R1 = ( B L l l ) t
R BLll
(8)
(9)
BL12
; R2 =
R3 = ( B L 1 2 I t R B L l l ; R4 = ( B L l z )
e
e
t
R BL12
Eqn. ( 8 ) can be f u r t h e r s i m p l i f i e d by using ( 9 ) t o g e t
V L ~= -zeq ' ~ 1 eeq
(10)
'
where,
Zeq
= ( R ~ - R ~ R ~ - (~ l R
t c~p )) = req ( l t c p )
eeq
= [ ( B , ~ I )-~ R2R4-1(BL12)tl
ell
vL i s t h e voltage a c r o s s element 8 which is t h e dc
voltage b e f o r e s m o t h i n g r e a c t o r of t h e bridge. Eqn.
( 1 0 ) c a n be viewed a s a e q u a t i o n f o r a n e q u i v a l e n t
circuit having voltage source e
behind a n irrpedance
Ze
The c o m p l e t e model of a %'pulse c o n v e r t e r i s ,
t h g s , a s shown i n Fig.3. The dynamic equation which
gives t h e dc c u r r e n t ( i L l )of t h e converter i s
.
Id
FIG. 5
GRAPH O F F I G . l
c , t h e t i m e c o n s t a n t o f t r a n s f o r m e r impedance i s
assumed t o be t h e same i n a l l t h e phases. Assuming t h e
v a l v e s t o be i d e a l s w i t c h e s with z e r o forward
impedance and i n f i n i t e r e v e r s e impedance, t h e elements
1 to 6 are
governed by t h e following
equations
vk = 0 , k E K ; set of conducting valves
m
M
i!
DC NETWORK
EQUIVALENT CIRCUIT
i, = 0,
0
piLl = -(Rt/Lt)
where, Rt = reqtRd
iL1 +
VDCOL CHARACTERISTICS
(eeq - Vc)/Lt
(11)
; Lt = c req t Ld
In a d d i t i o n t o ( l l ) , (9) has t o be solved f o r t h e c a s e
of t h r e e and f o u r valve conduction made. The c u r r e n t s
i n t h e conducting valves i n t h e branches and l i n k s a r e
given by ( 6 ) and ( 9 ) r e s p e c t i v e l y , whereas t h e voltage
across t h e non-conducting valves is given by ( 7 ) .
-Twelve Pulse Converter
Representation
A 1 2 p u l s e converter c m p r i s e s of two s i x p u l s e
b r i d g e s connected i n series w i t h one s i x p u l s e
converter fed by a wye/wye transformer and t h e o t h e r
by a d e l t a / wye transformer so a s t o produce a 30°.
phase s h i f t between t h e corresponding phase voltages.
Each 6 p u l s e b r i d g e c a n b e r e p r e s e n t e d by t h e
equivalent circuit of Fig.3 (eqn.10) and t h e series
c o n n e c t i o n of two s u c h c i r c u i t s w i t h R ~ Ld
, and vc
g i v e s t h e model f o r 12 p u l s e c o n v e r t e r a s shown i n
Fig.4.
The c i r c u i t of F i g . 4 c a n be r e d u c e d t o t h e
form of Fig. 3 with t h e equivalent circuit parameters
given by
2
2
2
E~~ =
eesj ; R~~ = c r q j : L~~ = c c,reqj
]=1
j=l
j=l
where eeqj and reqj a r e equivalent circuit parameters
f o r t h e bridge j . The d c c u r r e n t equation for t h e 12
p u l s e converter is i d e n t i c a l t o (11) with t h e following s u b s t i t u t i o n
% = Req+Rdr L t = LeqtLdr eeq - Eeq
The r e s u l t i n g dynamic e q u a t i o n i s s o l v e d a t e v e r y
i n t e g r a t i o n time s t e p f o r t h e d c c u r r e n t of 1 2 p u l s e
converter. I n a d d i t i o n , ( 9 ) is solved f o r each of t h e
6 p u l s e b r i d g e s which c o n s t i t u t e t h e 1 2 p u l s e
converter, t o obtain t h e current through t h e
2173
c o n d u c t i n g v a l v e s n o t i n c l u d e d i n t h e tree.
The
change i n t h e s t a t u s of valves i n t h e l i n k can be
c o n s i d e r e d by r e a r r a n g i n g t h e columns of m a t r i x BL.
The m a t r i x BL h a s t o b e c h a n g e d w h e n e v e r a n y v a l v e
ceases
t o conduct.
included i n
t h e tree
The s i x p u l s e c o n v e r t e r model p r e s e n t e d h e r e is
c o n c e p t u a l l y s i m p l e and a s i l l u s t r a t e d can b e e a s i l y
e x t e n d e d t o r e p r e s e n t c o n v e r t e r s h a v i n g series
connected 6 p u l s e bridges.
T h e number o f s t a t e
e q u a t i o n s p e r c o n v e r t e r t e r m i n a l w i l l v a r y depending
on t h e number o f c o n d u c t i n g v a l v e s p e r b r i d g e ( N i ) and
b
i s g i v e n by 1 t C ( N i - 2 ) , where, b is t h e number of
i=l
b r i d g e s p e r c o n v e r t e r t e r m i n a l . The model i s f l e x i b l e
enough t o i n c l u d e a ) forward v o l t a g e d r o p a c r o s s a
v a l v e , b ) unequal t i m e c o n s t a n t s o f t h e t r a n s f o r m e r
p h a s e s and c ) g r a d i n g and damping c i r c u i t across a
valve.
CONlROL REPRESENTATION
HVdc c o n v e r t e r s a r e g e n e r a l l y e q u i p p e d w i t h
c o n s t a n t c u r r e n t and c o n s t a n t e x t i n c t i o n a n g l e (CEA)
controllers.
Analog t e c h n i q u e s have t r a d i t i o n a l l y
b e e n u s e d f o r t h i s p u r p o s e . However , d i g i t a l
t e c h n i q u e s have become quite p o p u l a r because o f t h e
f l e x i b i l i t y , accuracy and r e l i a b i l i t y . The c o n t r o l of
t h e c o n v e r t e r s c o n s i d e r e d h e r e i s based on t h e d i g i t a l
t e c h n i q u e s [ l o , 111. The f i r i n g scheme i s e s s e n t i a l l y
a n E q u i d i s t a n t P u l s e C o n t r o l Scheme w i t h P u l s e
Frequency C o n t r o l .
T h e i n t e r v a l b e t w e e n two
successive f i r i n g instants, called t h e I n t e r Firing
P e r i o d ( I F P ) , i s c a l c u l a t e d as
IFP = 60' + Q
(12)
where, Q is t h e f i r i n g c o r r e c t i o n o b t a i n e d a s t h e
o u t p u t of e i t h e r t h e c u r r e n t or e x t i n c t i o n a n g l e
c o n t r o l l e r s . I n s t e a d y state, Q = 0 and f i r i n g t a k e s
p l a c e a t e v e r y 60' i n t e r v a l f o r a s i x p u l s e c o n v e r t e r .
For a 1 2 p u l s e c o n v e r t e r , both t h e b r i d g e s have a n
independent c a l c u l a t i o n of t h e i r r e s p e c t i v e IFP 's and,
i n s t e a d y s t a t e , f i r i n g occurs a l t e r n a t e l y i n each
I n case o f c u r r e n t
b r i d g e s p a c e d a p a r t b y 30'.
c o n t r o l l e r , Q is determined a s
Q=KEc,
(13)
w h e r e , K i s t h e g a i n a n d Ec i s t h e c o n t r o l s i g n a l
obtained a s
Ec = K 1 ( l d - I r e f ) t Kz.did/dt
(14)
I n case o f CEA o p e r a t i o n , t h e c o n t r o l l e r a c t i o n t a k e s
p l a c e t h r o u g h two c o m p l e t e l y i n d e p e n d e n t l o o p s ,
I n v e r t e r S a f e t y C o n t r o l (ISC) and I n v e r t e r Optimum
Control (IOC). ISC acts when t h e measured e x t i n c t i o n
a n g l e ( 7 ) i s less t h a n r e f e r e n c e a n d i t c a n o n l y
reduce t h e f i r i n g angle.The f i r i n g c o r r e c t i o n i s g i v e n
bY
(15)
Q = K3 ( 7 - r r e f )
IOC a t t e m p t s t o b r i n g back t h e system t o its optimum
operating condition.
However, i t a c t s o n l y when
s a f e t y i s g u a r a n t e e d . To f a c i l i t a t e t h i s , a r e c o r d is
k e p t o f t h e measured e x t i n c t i o n a n g l e s i n a c y c l e and
i f t h e minimum o f t h e s e measured v a l u e s i s g r e a t e r
than t h e 7 reference, t h e f i r i n g angle is increased.
Thus, t h e IOC o p e r a t e s o n l y once p e r c y c l e and t h e
f i r i n g c o r r e c t i o n is
Q=K ( 7
- 7
1
(16)
4
min
ref
I f 7 , 7,
i n ISC and ymi < rref i n IOC, Q=O. I n
( 1 4 ) t o ( 7 6 ) , K1 t o K 4 are & & c o n t r o l l e r g a i n s whose
v a l u e s are j u d i c i o u s l y chosen [ l l ] .
The r e c t i f i e r c o n t r o l comprises o f b o t h minimum
a l p h a a n d c o n s t a n t c u r r e n t c o n t r o l . F o r minimum
a l p h a o p r a t i o n t h e v a l v e conduction i s p r e v e n t e d t i l l
t h e v o l t a g e a c r o s s it rises t o a r e q u i r e d l e v e l . F o r
t h e constant current control, Q is derived a t every
time step based o n t h e c o n v e r t e r d c c u r r e n t and i t s
d e r i v a t i v e (eqn. 1 1 ) . T h i s i s used f o r c a l c u l a t i n g
IFP and t h e v a l v e i s f i r e d when t h e e l a p s e d time a f t e r
T h i s procedure
t h e l a s t f i r i n g i n s t a n t equals IFP.
o f f e r s t h e d i s t i n c t advantage t h a t t h e f i r i n g p u l s e is
g e n e r a t e d based on t h e latest a v a i l a b l e sample o f t h e
control variable.
H m e v e r , i n [ l o ] , t h e use of t h e
c o n t r o l v a r i a b l e i n f o r m a t i o n a v a i l a b l e immediately
a f t e r each f i r i n g i s recommended. I n t h e above f i r i n g
scheme w i t h p u l s e frequency c o n t r o l , as t h e phase of
the f i r i n g continues t o increase, it m y cause t h e
r e c t i f i e r t o move i n t o t h e i n v e r t e r r e g i o n of
o p e r a t i o n . I n o r d e r t o a v o i d t h i s , or worse s t i l l , a
commutation f a i l u r e a t r e c t i f i e r , a n end s t o p i s
i n c o r p o r a t e d a t a l p h a e q u a l t o 120'.
The e x a c t
mechanism i s t o f i r e v a l v e i immediately a f t e r t h e
commutation v o l t a g e of v a l v e i t 2 g o e s p o s i t i v e .
F o r t h e i m p l e m e n t a i o n o f CEA c o n t r o l , t h e
e x t i n c t i o n a n g l e i s m e a s u r e d a s t h e time i n t e r v a l
between c u r r e n t zero i n s t a n t and t h e i n s t a n t a t which
t h e v o l t a g e across t h e v a l v e goes p o s i t i v e a g a i n . The
i n s t a n t i s a c t u a l l y measured a s t h e commutation
v o l t a g e z e r o c r o s s i n g i n s t a n t of t h e v a l v e which has
c e a s e d c o n d u c t i o n p r i o r t o t h e v a l v e f o r which
e x t i n c t i o n a n g l e i s b e i n g measured. T h i s approach h a s
t h e advantage t h a t even i f a v a l v e c o n t i n u e s t o
conduct due t o f a u l t , s a y commutation f a i l u r e , a
v o l t a g e z e r o c r o s s i n g i n s t a n t would s t i l l b e o b t a i n e d
and t h e occurence of t h e f a u l t w i l l b e d e t e c t e d . For
example, i n t h e c o n v e r t e r circuit of Fig. 1 , suppose
v a l v e s 2 and 3 are c o n d u c t i n g and v a l v e 4 is f i r e d . I n
normal o p r a t i o n t h i s would canmutate v a l v e 2 , t h e
v o l t a g e across w h i c h w i l l now b e (e, This
valve
v o l t a g e i s same a s t h e c u r n u t a t i o n v o l t a g e
1. N o w i f v a l v e 4 f a i l s t o c o m m u t a t e v a l v e 2 , t h e
latter c o n t i n u e s t o conduct and t h e v o l t a g e a c r o s s it
c o n t i n u e s t o b e z e r o . However, t h e commutation v o l t a g e
for v a l v e 1 would s t i l l g i v e a z e r o c r o s s i n g i n s t a n t
t h e r e b y i n d i c a t i n g t h e occurence o f a f a u l t . B u t as
t h e v a l v e 2 c u r r e n t d o e s n o t go t o z e r o , e x t i n c t i o n
a n g l e cannot be measured.
A t t h e i n v e r t e r , t h e d c current is a l s o
c o n t i n u o u s l y monitored and t h e o p e r a t i o n i s changed t o
c o n s t a n t c u r r e n t c o n t r o l mcde i f t h e d c c u r r e n t f a l l s
below t h e r e f e r e n c e s e t t i n g . The r e v e r s e t r a n s i t i o n
from c o n s t a n t c u r r e n t t o Cw c o n t r o l t a k e s p l a c e when
e x t i n c t i o n a n g l e f o r a n y v a l v e i s less t h a n t h e
reference value.
'fo);
VDCOL R e p r e s e n t a t i o n : A s a p a r t o f t h e c o n v e r t e r
c o n t r o l system, v o l t a g e dependent c u r r e n t o r d e r l i m i t
nas also been c o n s i d e r e d t o modify t h e c u r r e n t
r e f e r e n c e s e t t i n g as a f u n c t i o n o f d c v o l t a g e d u r i n g
f a u l t . A t y p i c a l VDCOL c h a r a c t e r i s t i c i s shown i n Fig.
5 . The c h a r a c t e r i s t i c i s r e p r e s e n t e d a s series o f
p o i n t s which are t h e n connected t h r o u g h s t r a i g h t
l i n e s . V K O L d o e s n o t operate u n l e s s t h e c o n v e r t e r is
o p e r a t i n g i n c o n s t a n t c u r r e n t c o n t r o l mode. Once
o p e r a t i o n i n c o n s t a n t c o n t r o l m d e b e g i n s , t h e VDCOL
samples t h e d c v o l t a g e a f t e r t h e smoothing reactor
through a f i r s t o r d e r time d e l a y element. When t h i s
sampled v a l u e r e a c h e s a v a l u e below t h a t s p e c i f i e d by
t h e f i r s t c o r n e r p o i n t ( C and 0 i n F19.5), t h e VDCOL
o p e r a t i o n begins and c u r r e n t r e f e r e n c e a t each
s u b s e q u e n t i n s t a n t i s c a l c u l a t e d by i n t e r p o l a t i n g
between t h e corner p o i n t s ( C , D and 0 , P ) . The i n c r e a s e
and d e c r e a s e i n c u r r e n t s e t t i n g i s r e s p e c t i v e l y
governed by TUP and TDN time c o n s t a n t s o f t h e d e l a y
element.
Ac AM] Dc IvEIviDm MODEL
A t h r e e phase s c h e m t i c r e p r e s e n t a t i o n o f t h e ac
system and harmonic f i l t e r s , a s s o c i a t e d with a
p a r t i c u l a r terminal is shown i n Fig. 6. The ac system
is r e p r e s e n t e d by i d e a l v o l t a g e sources ( e l , e
e )
behind a T- equivalent c i r c u i t o f t h e a c networz' [I??].
F d e n o t e s t u n e d f i l t e r s f o r 5 t h , 7 t h , 1 1 t h and 1 3 t h
harmonics a l o n g w i t h a second o r d e r high p a s s f i l t e r .
2174
AC
:a
/ b
F : FILTER
Fcg. 7
FIG. 6
A C SYSTEM
REPRESENTATION
(C,)
i s c h o s e n based on t h e
The s h u n t c a p a c i t o r
r e a c t i v e power r e q u i r e m e n t of t h e c o n v e r t e r . The
inductance ( L s ) i s determined a t fundamental frequency
from t h e knowledge of t h e e f f e c t i v e s h o r t c i r c u i t
r a t i o (ESCR) t a k i n g i n t o a c c o u n t t h e p a r a l l e l
c o m b i n a t i o n of t h e a c network and harmonic f i l t e r
impedance a l o n g w i t h s h u n t c a p a c i t o r a d m i t t a n c e .
Resistance Rs r e p r e s e n t s t h e e f f e c t of damping due t o
l o a d s w i t h i n t h e a c s y s t e m and i s c h o s e n t o g i v e a
d e s i r e d impedance angle. The e f f e c t of converter on
t h e a c s y s t e m i s r e p r e s e n t e d by c u r r e n t s o u r c e s
(IA,,I) . The s t a t e and o u t p u t e q u a t i o n s f o r t h e
eauiva5ent circuit of Fia.6 can be w r i t t e n i n t h e form
where, t h e
output
input
xtAC =
tlAc =
[ eA
[ el e2 e3 IA Ic
eB
eC
1 tand
1
The matrices AAC and BAc a r e dependent on t h e network
t o p o l o g y and p a r a m e t e r s . Although a s i m p l i f i e d
e q u i v a l e n t r e p r e s e n t a t i o n of t h e AC network has been
considered h e r e , any d e t a i l e d r e p r e s e n t a t i o n can be
h a n d l e d which may b e n e c e s s a r y f o r s t u d i e s l i k e
harmonic a n a l y s i s e t c .
The d c network comprises of dc f i l t e r , s m o t h i n g
r e a c t o r and t r a n s m i s s i o n l i n e s . The l i n e i s
represented by pi- equivalent circuits. S t a t e equations
f o r t h e d c s y s t e m can be e a s i l y w r i t t e n down choosing
i n d u c t o r c u r r e n t s and c a p a c i t o r v o l t a g e s a s s t a t e
v a r i a b l e s . The d c network s t a t e equations a r e solved
considering t h e d c c u r r e n t of each c o n v e r t e r a s t h e
input. The converter and t h e d c network models a r e
t h u s i n t e r f a c e d t h r o u g h t h e d c c u r r e n t which i s
o b t a i n e d a s t h e s o l u t i o n of t h e c o n v e r t e r s t a t e
equations. The o u t p u t from t h e d c network mcdel is t h e
d c bus v o l t a g e shown a s Vc i n Fig. 1. The l a t t e r is
used i n t h e s o l u t i o n of t h e c o n v e r t e r system
equations.
I n t e r f a c e between 12-pulse Converter and AC System
Models
Power from t h e a c bus i s fed t o t h e bridges of 1 2
p u l s e converter through two transformers each having
an o f f nominal t a p s e t t i n g ( a ) . One transformer has YY connection and t h e o t h e r has A -Y connection with
t u r n s r a t i o of l : a and l:a/<3
r e s p e c t i v e l y . The
t r a n s f o r m r connection diagram is shown is Fig. 7 . It
i s assumed t h a t n e u t r a l of Y- Y t r a n s f o r m e r i s n o t
grounded. The v o l t a g e s and c u r r e n t s on t h e two s i d e s
of t h e Y-Y connected transformer a r e r e l a t e d a s
TRANSFORMER
CONNECTIONS
FOR
A 12- PULSE
CONVERTER
eYa = aeA, eYb = a e B r e Y c = aeC
i YA - aiYg, i Y c = aiY,
(19)
(20)
The v o l t a g e s arid c u r r e n t s on t h e two s i d e s of
connected t r a n s f o r m r a r e r e l a t e d a s
A/Y
T h e a c c u r r e n t s iy iy i7 and ig a r e obtained from
wglch i n t u r n d e t e r m i n e s t h e
t h e c o n v e r t e r mm?;l
source c u r r e n t s IA and Ic ( F i g . 6 ) a s
=
i Y A t iA,
A
= iyc t ic
A
(23)
From t h e knowledge of source c u r r e n t s IAand Ic, ( 1 7 )
can be solved a t each i n t e g r a t i o n t i m e s t e p t o update
t h e v o l t a g e e s t i m a t e s ( e A , e B , e C ) .T h i s , i n t u r n ,
e s t a b l i s h e s transformer secondary v o l t a g e s (ea,e , e )
which a r e used subsequently f o r t h e s o l u t i o n oP tge
converter dynamic equations. I f need be t h e converter
t r a n s f o r m e r c a n b e r e p r e s e n t e d by t h e s t a n d a r d
equivalent circuit c o n s i s t i n g of an i d e a l transformer
i n c o n j u n c t i o n w i t h series and s h u n t impedances
representing t h e leakage f l u x , series r e s i s t a n c e and
m a g n e t i z i n g c u r r e n t . The s e r i e s impedance of t h e
p r i m a r y s i d e and t h e m a g n e t i z i n g c i r c u i t c a n be
considered a s a p a r t of t h e a c system. The secondary
s i d e o f t h e t r a n s f o r m e r c a n b e r e p r e s e n t e d by
dependent voltage sources ( p r o p o r t i o n a l t o t h e v o l t a g e
of t h e primary s i d e ) i n series with i t s a s s o c i a t e d
series impedance.
SIMUMTION PROGRAM
I n c o r p o r a t i n g t h e v a r i o u s s u b s y s t e m models
o u t l i n e d i n t h e previous s e c t i o n s , a computer program
is developed t o s i m u l a t e H V d c s y s t e n k , both point t o
point and multiterminal c o n f i g u r a t i o n s c o n t a i n i n g upto
10 monopolar t e r m i n a l s , with 6/12 p u l s e converters.
The structure of t h e program i s extremely m d u l a r with
each subsystem described i n i n d i v i d u a l subroutine.
T h i s f a c i l i t a t e s f u r t h e r program a u g m e n t a t i o n t o
include d e t a i l e d r e p r e s e n t a t i o n of any subsystem l i k e
AC or DC network, implementation of d i f f e r e n t c o n t r o l
schemes and o t h e r advanced f e a t u r e s n e c e s s a r y t o
simulate a p r a c t i c a l system. A t a p a r t i c u l a r i n s t a n t
of t i m e , t h e s t a t e s of a l l t h e c o n v e r t e r s a r e defined
and t h e e q u a t i o n s a r e f o r m u l a t e d by a p p r o p r i a t e l y
calculating the converter equivalent circuit
parameters which depend on t h e converter conduction
s t a t u s . The l a t t e r changes whenever a v a l v e begins or
2175
ceases conduction. The exact i n s t a n t of c e s s a t i o n is
determined by l i n e a r i n t e r p o l a t i o n using t h e valve
c u r r e n t measurement. A t each i n t e g r a t i o n t i m e s t e p ,
t h e c o n v e r t e r s t a t e i s checked and t h e dynamic
equations corresponding t o t h e various subsystems a r e
solved using modified E u l e r ' s i n t e g r a t i o n method. Some
of t h e s a l i e n t f e a t u r e s of t h e program a r e :
Both 6 D u l s e and 1 2 pulse oceration of converter
can be simulated.
A t present, t h e r e a r e t h r e e choices of converter
c o n t r o l s v i z . , constant alpha, c u r r e n t control
and CEA c o n t r o l . The f i r i n g p u l s e g e n e r a t i o n
s c h e m e i s b a s e d o n IPC a n d EPC ( a n a l o g a n d
d i g i t a l techniques).
The simulation can begin e i t h e r from zero i n i t i a l
c o n d i t i o n or from s t e a d y s t a t e o p e r a t i n g
condition derived using A C / E load flow.
RES
mT
SOF SIMUJATION
_
_
_
various t e s t s i m u l a t i o n s of a two t e r m i n a l d c
l i n k a r e c a r r i e d out both with and without d e t a i l e d a c
system r e p r e s e n t a t i o n t o i n v e s t i g a t e t h e system
r e s p o n s e and c o n t r o l performance f o l l o w i n g a
d i s t u r b a n c e . The system p a r a m e t e r s and o p e r a t i n g
conditions a r e given i n t h e Appendix.
Fig. 8 shows t h e steady s t a t e waveforms for a two
terminal d c system with 12 pulse converter operation.
The r e c t i f i e r end a c system SCR is 15 and i n v e r t e r end
SCR i s 3. Fig. 9 shows t h e r e s u l t i n g waveforms of t h e
ac system voltages and c u r r e n t s t o demonstrate t h e
s a t i s f a c t o r y o p e r a t i o n of t h e system w i t h weak a c
system a t t h e i n v e r t e r .
Transient Response with Strong AC System
Reduction i n t h e a c voltage a t t h e i n v e r t e r end
has a predcminant e f f e c t on t h e performance of t h e
HVdc l i n k . To i n v e s t i g a t e t h e e f f e c t i v e n e s s of t h e
control under such conditions, results of t h e various
test simulations a r e given i n Figs.10 t o 1 2 . A t both
2.0
2.01-
10
1.5
0.75
vBR I
0
05
- n" 7 5-
15
VBR2
0.5
1.5
2.0c
~ E C T
..
-.O
' r---
(a)
-
3 01
0
b R 2
-30
'IN,
-
3 60*
-3.0
05.
0
1
FIG 9
I2 P U L S E STEADY WAVEFORM WITH AC
S Y S T E M SCR 15 AT RECTIFIER SCR 3 AT
STEADY STATE AC WAVEFORMSAT
INVERTER
SCR 3
-J
t-
CYCLES
I
(c)
F1G 8
d/dt
30
VlNV
-1.5.
15.
FIRST S A M P L E , n o
FIG.
10
LATEST S A M P L E , d l d t
'
CURRENT WAVEFORM O N RECOVERY
F R O M COMMUTATION FAILURE
INVERTER
20
1.5'
'
-1.5
01
-1.sL
0
0
t u
- 2.0t
- 1.5
I
I
I
-1.E.L
"INV
1
I
-1
2176
t
-1.5
t
1.5
t
-1.5
t
O L - -
i
1'5[
VINV
2.0;
01
0-
, - - - l . I
5
'0 c y c i e s '5
FIG 15
F I G 14
A
5
25
20
Z O I , S I N G L E PHASE,10 CYCLE DIP AT
INVERTER
SCR 15 at R o c t i t , e r , S C R 3 at I n v e r t e r
.
I
I
-2
lo
cycles
15
20
25
20%.SINGLE PHASE.10 CYCLE D I P AT
I NVERTER
I
'REc:oi-vJ---
L_.-.-L
-_i-i__
F I G 16
5
'"cycles
50'/.,3PHASE.
15
20
25
5CYCLE DIP AT
RECTIFIER
SCR 15 a t R e c t i f i e r , S C R 15 at I n v e r t e r
- 1.5 1
o i
SCR 15 a t R e c t i f i e r , S C R
3 at I n v e r t e r
c a p a b i l i t y i n simulating 1 2 p u l s e converter o p e r a t i o n ,
a 50%, 3 phase, 10 c y c l e a c voltage d i p a t i n v e r t e r
end has been considered. The results a r e shown i n Fig.
13. A s i s evident t h e c o n t r o l a c t i o n helps t h e system
t o r e c o v e r r a p i d l y and t h e d u r a t i o n of t h e s h o r t
c i r c u i t i s l i m i t e d t o only 3 c y c l e s . In 12 pulse
operation t h e d c v o l t a g e l e v e l is higher and so, t h e
s e v e r i t y of t h e f a u l t is a l s o increased. I n t h i s c a s e
study, a 1 2 t h harmonic double tuned f i l t e r has a l s o
been considered on t h e d c s i d e a t both ends.
'IYansient Responce with Weak AC System
V"V1'ib- 15
The e f f e c t i v e n e s s of t h e c o n t r o l system can be
thoroughly examined only by d e t a i l e d r e p r e s e n t a t i o n of
t h e a c system c h a r a c t e r i s t i c s . I n t h e following
s t u d i e s , two d i f f e r e n t a c s y s t e m c h a r a c t e r i s t i c s
having SCR 15 and 3 have been considered. The various
voltaqe d i s t u r b a n c e c a s e s simulated a r e
5 0 % d i p i n p h a s e A v o l t a g e a t i n v e r t e r f o r 10
cycles. AC System SCR = 15 a t r e c t i f i e r and 3 a t
inverter.
20% d i p i n p h a s e A v o l t a g e a t i n v e r t e r f o r 1 0
c y c l e s . AC system SCR = 15 a t both r e c t i f i e r and
inverter.
50% d i p i n a l l t h e 3 phases a t r e c t i f i e r f o r 5
c y c l e s . AC system SCR = 15 a t r e c t i f i e r and 3 a t
i n v e r t e r . VDCOL not considered.
Same a s c a s e ( c ) b u t w i t h VDCOL a t b o t h e n d s
having c h a r a c t e r i s t i c s a s given i n Appendix.
r e s u l t s f o r t h e c a s e s ( a ) t o I d ) a r e shown i n
F i g s . 1 4 t o 1 7 . From t h e c o m p a r i s o n o f v a r i o u s
responses (cases a , b ) i t is observed t h a t t h e recovery
i n c a s e of s t r o n g a c system ( S C R 1 5 ) i s mrch f a s t e r
14N
0
5
FIG17
10
15
50%,3PHASE,5CYCLE
20
25 Cycles
D i p AT RECTIFIER
SCR 15 o t R e c t i f j e r , S C R 3 a t I n v e r t e r
ends of t h e d c l i n k , t h e ac s y s t e m i s assurnsd t o be
s t r o n g and h e n c e i t s d e t a i l e d r e p r e s e n t a t i o n i s
i g n o r e d . The s i x p u l s e c o n v e r t e r o p e r a t i o n i s
considered. Fig. 10 shows t h e c u r r e n t waveforms on
recovery from canmutation f a i l u r e following a 20% d i p
i n phase A voltage f o r 10 c y c l e s . The f i r s t and t h e
l a t e s t sample r e f e r t o t h e sampling of t h e d c c u r r e n t
immediately follcwing t h e previous f i r i n g [ l o ] and the
l a t e s t p o s s i b l e i n s t a n t r e s p e c t i v e l y . It 1s seen t h a t
i n c l u s i o n of a d e r i v a t i v e term i n c u r r e n t c o n t r o l
(eqn. 1 4 ) l e a d s t o a s u b s t a n t i a l reduction i n c u r r e n t
o s c i l l a t i o n s . Pdvancing t h e sampling i n s t a n t t o t h e
l a t e s t p o s s i b l e i n s t a n t causes a f u r t h e r improvement.
To f u r t h e r i l l u s t r a t e t h e e f f e c t of t h e d e r i v a t i v e
term i n t h e current c o n t r o l , t h e computed waveforms of
t h e r e c t i f i e r and i n v e r t e r end average d c voltage and
following a
c u r r e n t (average taken over every 30')
s i n g l e phase voltage c o l l a p s e (99% d i p ) a t t h e
i n v e r t e r f o r one cycle, a r e s h m n i n F i g s . 11 and 1 2 .
With a view t o demonstrate t h e v e r s a t i l e n a t u r e
of t h e c o n t r o l scheme and i l l u s t r a t e t h e program
t h a n f o r w e a k a c s y s t e m ( S C R 3 ) w h i c h h a s many
successive canmutation f a i l u r e s and t h e system dces
not recover u n t i l t h e voltage d i p i s removed. It may
be n o t i c e d i n F i g . 1 4 t h a t r e c t i f i e r v o l t a g e g o e s
negative which is i n d i c a t i v e of i t s operation i n t h e
i n v e r t e r region. The r e c t i f i e r , however, is equipped
with end s t o p limit on i t s f i r i n g angle (=120° ) .
From responses shown i n Figs. 16 and 17 ( c a s e s c
and d), i t i s e v i d e n t t h a t t h e i n t r o d u c t i o n of VEOL
causes a d r a s t i c improvement i n t h e p e r f o r m n c e and
t h e c u r r e n t peak i s c o n s i d e r a b l y r e d u c e d c a u s i n g
smaller o s c i l l a t i o n s and quicker r e s t o r a t i o n of steady
o p e r a t i n g c o n d i t i o n s . Also, presence of V E O L avoids
undesirable excursion of r e c t i f i e r i n t o i n v e r t e r
region and v i c e versa.
2177
The various case studies primarily illustrate the
capability of the program in properly simulating
the behaviour of HVdc system. As an indication of the
program efficiency, it may be mentioned that to
simulate lms of real time, the program takes around
0.6 to 1.0 sec of computation time on MicroVAX I1
computer depending upon the details considered.
CONCLUSIQNS
The converter equivalent circuit based on graph
theory approach is developed. The converter mdel has
a modular structure and hence can be used to simulate
a converter terminal with any nunber of 6 pulse/l2
pulse bridges in series. Elimination of the need to
store connection matrices and a fast and efficient way
of generating the converter equations are s m of the
advantages of this method. Based on this converter
model, a computer program has been developed
incorporating the detailed representation of the ac
system, digital converter control scheme and voltage
dependent current order limit. Results of various test
simulations are presented to illustrate the program
capability for studying the controller response under
severe disturbances.
T h e financial support received from the
Department of Electronics, Government of India under
National HVdc R and D programme is gratefully
acknowledged.
AJ?PrnIX
SYSW DATA
-
Rated power of DC link = 240 MW for 12 pulse and 120
for 6 pulse system. AC system frequency = 50 Hz.
MW
Converter Transformer :
Resistance Rcl =Rc2 = 0.5 O h m
Carmutating Reactance Xcl = Xc2 = 6.283 O h m
Smoothing Reactor :
Resistance Q1=Rd2=O.1 Ohm, Inductance Ldl=+,2=1.0
H
Transmission Line :
Resistance = 8.64 O h m , Total inductance = 0.50148 H
Eta1 capacitance = 54.1645 micro farads
Digital controller (adapted from ref. [Ill) :
a) Constant Current Controller :
K1 = 0.4 rad/p.u. current, K2 = 0.4 rad2/p.u. current
b) CEA Controller : K3 = 1.0 ; K4 = 0.25
AC system Details :
RMS AC Voltage (L-N) : E = 42.78 kV, E2 = 38.51 kV
Valve turn off time = 3 iegrees
AC system impedance angle = 85 degrees
VrOL Time Constants :
Rectifier : TDN = 0.00008 sec; TUP = 0.03 sec
Inverter : TDN = 0.00008 s e c ; TUP = 0.04 sec
VDCOL Characterigtics (Fig. 5) :
Rectifier : C = (1.0, 0.21, D = (0.4, 0.2)
Inverter : 0 = (0.9, 0.61, P = (0.3, 0.2)
DC Filter Parameters :
R = 15.0 Ohm,L1 = 0.084 mH, L2 = 246.5 mH
C1 = 0.801 micro farads, C2 = 2.31 micro farads
Operating conditions:
a) 12 pulse :
= iooo Amps
rmin=5O, ldl~c=ldfOo, al = 21.46’,
b ) 6 pulse : I
7 min
. = 50,
8:
- 1000 Amps
= =Idto;,a,
a2 = 148.39’
= i2.880,a2
= 148.38O
REPWENCES
N.G.Hingorani, J.L.Hay and R.E.Crosbie, ‘Dynamic
Sirmlation of HVDC system on a digital computer‘,
Proc.IEE, ~01.113, pp 793-802, May 1966.
J.S.C.Htsui and W.Shepherd, ‘Method of digital
computation of thyristor circuits’, Proc.IEE,
~01.118,pp 990-998, Aug. 1971.
N.G.Hingorani, R.H.Kitchin and J.L.Hay, ’Dynamic
simulation of HVDC power transmission systems on
digital computer’, IEEE Transaction gn
Apparatus and Systems, vol. PAS-87, pp 989-996,
April 1968.
S.Williams and I.R.Smith, ‘Fast digital
computation of 3-phase thyristor bridge
circuits’, Proc. IEE, vol. 120, pp 791-795, July
1973.
J .Mil ias-Argitis and G.Galano.9, .Dynamic
simulation of HVdc transmission systems’,
Transactions on Power Apparatus @ Systems, vol.
PAS- 97, pp 587-593, March/April 1978.
M.M.Muda1iar and H.S.Chandrasekharaiah, ‘Dynamic
Digital simulation of Hydc systems using novel
modular converter model , IEEE Transactions 2
Power Apparatus and Systems, vol. PAS-104, No.10,
pp 2852-2856, Oct.1985.
K.R.Padiyar and Sachchidanand, ‘Digital
simulation of multiterminal HVdc systems using a
novel converter model ’, IEEE Transactions
Power Apparatus and systems, vol. PAS-102, pp
1624-1632, June 1983.
D.A.Woodford, A.M.Gole and R.W.Menzies, ’Digital
Simulation of DC links and AC machines‘, EE
Transactions on Power Apparatus and Systems’,
vol. PAS-102, pp 1616-1623, June 1983.
G.Kron, ’Tensor for Circuits’, Dover, 1959.
C.M.Alegria, L.L.Freris
and J.P. Sucena-Paiva,
‘Microcomputer control of power converters’, IEEE
Transactions on Power Apparatus and Systems’,
vol. PAS-103, pp 2011-2017, Auq. 1984.
J. Arri 1 laga anh D.G. Baldwin ‘ Direct digital
closed loop control of HVdc converters’, Proc.
IEE, VOl. 121, N0.12, pp 1567-1571, Dec. 1974.
J.P.Bowles, ‘AC systems and transformer
reDresentation for HVdc transmission studies ’,
Systems,
Transactions on Power Apparatus
vol. PAS- 89, pp 1603-1608, Sept./Oct. 1970.
IEEE
BIOGRAPBY
K.R.Padiyar received the BE degree in Electrical
Engineering from Poona University in 1962, ME and Ph.D
degrees from 1.1.S~. Bangalore and University of
waterloo in 1964 and 1972 respectively.
He worked with the Department of Electrical
Engineering, IIT Kanpur initially as Assistant
Professor (1976-1980) and later as Professor (1980July 1987). Since August 1987 he has joined Indian
Institute of Science Bangalore where he is currently
Professor of Electrical Engineering. His teaching and
research interests include HVdc Transmission,
Reliability, System Stability and Control.
Sachcbidanand received the B.Tech. degree in
Electrical Engineering from Banaras Hindu University,
Varanasi in 1975, M.Tech. and Ph.D degrees from IIT
Kanpur in 1978 and 1983 respectively.
After working as Lecturer at BHU, Varanasi from
April 1983, he joined Department of Electrical
Engineering , IIT Kanpur in Dec. 1983 where he is
currently an Assistant Professor. His teaching and
research interests include HVdc transmission, Real
Time Control and Power System Analysis.
2178
Discussion
Ake Ekstrom, A 0 0 Power Systems AB, Sweden
S-721 69 Vasteras,
The authors present an interesting paper about the simulation
of a converter in a digital computer program and how the program
is used for the study of the performance of the converter control.
a complex system should be, i n our opinion, t o use
s i m p l i f i c a t i o n s wherever p o s s i b l e without s a c r i f i c i n g
accuracy. Actually, t h i s philosophy is a l r e a d y being
used i n AC system simulation. For example, although
EMTP can be used f o r t r a n s i e n t s t a b i l i t y s t u d i e s , a
transients
are
separate
program, where network
neglected is used.
The major o b j e c t i v e of t h e simulation program
r e p o r t e d i n t h e paper is t o carry o u t s t u d i e s on
controller
performance
under
various
system
However, as a number of different digital computer programs
We b e l i e v e that t h e r e is a need f o r a
conditions.
for the simulations of converters have been presented during
s p e c i a l purpose program vhich can supplement t h e H V E
the last years, i t should be of great value, if the authors also
could give some comparison t o other similar computer simulations simulator ( a p h y s i c a l model). The major emphasis i n
our paper is t h e use of graph- theoretic a n a l y s i s f o r
e.g. comparisons with simulations in t h e EMTP and t h e EMTDC
t h e development of converter model. The concept of a n
programs.
e q u i v a l e n t c i r c u i t given i n t h e paper is, i n our
more e f f i c i e n t than
the
time- varying
opinion,
With regard t o the simulation of t h e control i t must be stressed
As
that t h e performed simulation by necessary is very much simplified. impedance model of a valve used i n EMTP or EMTDC.
a matter of f a c t , t h i s r e p r e s e n t a t i o n of a valve can
The results have because of that to be treated with some caution.
The presented control principles give basically a non-linear system, l e a d t o numerical problems u n l e s s snubber c i r c u i t s are
represented (although they d o n ' t p l a y any role i n t h e
as the adjustment in delay angle at each firing instant is propordetermination of t h e c o n t r o l l e r r e s p o n s e ) .
tionai to rhe control signal. By including a derivative term in
the control signal a proportional term will also be included in
While i t is t r u e that t h e c o n t r o l l e r models given
the current control loop, which explains that the constant K 2
i n t h e paper a r e s i m p l i s t i c , t h i s has t h e advantage of
has t o be non-zero in order t o obtain an acceptable damping of
h i g h l i g h t i n g t h e f a c t o r s that determine t h e response
the control response.
f o r d i f f e r e n t types of d i s t u r b a n c e s . A s t h e example
considered i n t h e paper is n o t based on a s p e c i f i c DC
I t would be of interest t o know if the authors have made some
l i n k , t h e optimization of t h e c o n t r o l l e r parameter is
comparisons with other computer programs, if it is planned t o
n o t attempted.
I n t h i s c o n t e x t , we would l i k e t o
further develop the program and if some comparisons have been
stress t h e importance of e s t a b l i s h i n g a benchmark
made with oscillograms from real HVDC plants or from HVDC
model and s t a n d a r d i z a t i o n of DC l i n k c o n t r o l l e r blocks
simulator test
which w i l l then enable t h e v a r i o u s computer programs
Manuscript received February 21, 1989.
t o be t e s t e d i n terms of accuracy, computing times,
etc.
In t h e absence of such t e s t systems, t h e
the d i f f e r e n t programs
is n o t
comparison
of
a
meaningful.
However, we have also developed
K.R. PADIYAR, SACHCHIDANAND, A.G.KOTHAR1,
simulation program along t h e l i n e s of EMTP
for
S.BRATTACHARYYA, A. SRIVASTAVA
comparison.
W e hope t o p u b l i s h t h e
comparisons
between d i f f e r e n t modelling approaches i n f u t u r e .
W e wish t o thank M r . Ake E k s t r o m f o r t h e i n t e r e s t
A l s o w i t h t h e a v a i l a b i l i t y of a HVDC simulator and t h e
shown i n t h e paper. H e has r a i s e d some p e r t i n e n t
conunissioning of HVDC p r o j e c t s i n India, we i n t e n d t o
p o i n t s t o which our response is given below.
do d e t a i l e d comparisons w i t h t h e d i g i t a l programs and
updating of c o n t r o l l e r models.
Although t h e r e are s e v e r a l computer programs that
have been r e p o r t e d i n t h e l i t e r a t u r e f o r converter
F i n a l l y , w e wish t o s t a t e t h a t t h e development of
most of
t h e m are
based
on t h e
simulation,
a r e l i a b l e and f a s t simulation t o o l i n t h e form of a n
modifications of EMTP which was p r i m a r i l y developed
inexpensive computer program, w i l l remove much of t h e
f o r t h e study of network t r a n s i e n t s i n AC systems.
mystery surrounding t h e HVDC c o n t r o l l e r s and s t i m u l a t e
While t h e r e are some advantages i n having a g e n e r a l
innovations i n c o n t r o l s t r a t e g i e s which can b e n e f i t
purpose program, w i t h d e t a i l e d subsystem models, which
t h e u t i l i t i e s who wish t o optimize t h e performance of
can be used f o r a l l types of s t u d i e s , w e f e e l t h a t
HVIX systems.
t h i s approach is computationally more complex and
i n e f f i c i e n t . The general philosophy of simulation of
Manuscript received April 14, 1989.