Ba 11gal o rc I 11(1 i a.
1I iini bai. India
~
like nliriirllizikt,ionof losscs, rniixirnizat,ion of Q reserves:
mininiization of reactive power loss [l]etc. However,
ttoric of tl~esc!ohjcc:t,ivc! functions iLrc trlily sat,isfbct,ory
from t,lic systtm poiiit of viciw. For exalnplc, MW loss
iiiiriiitiizatioii CUI lcati to over volt,ages; rnaxirriixatioii
of “eserves may lead to low voltage profile.
The objective that correc1,s the voltage profile to a
desired ra.ilge may a.void problems of Jtnder voltage or
I\XY
r l t.iigc. l;i i r1.1ior , i t I:&i ii i ; i 1 1
of I
11.1 i y vol t.;rgc*
profile under stressed conditions, requires reduction in
rc:iic:t,iv(lpowel Hows, thcrcby rcdiicirig the losstis i i t t h e
syst,eni. In liglitly loiidcd systoitis t.lre problern of loss
rcidiict.ion is :lot iis significant. its t,llitt of ovw volt,iig(!s.
Thus, we conclude that for real life operation, it is
desiraSlc to select rnaintenancc of voltiqe witliui a desired band ~5 an objective for react,ive powcr/voltage
control.
(
l i t n y ~or& Reactivt. power coiitrol. Voltage control, OPF
I. INTRODUCTION
Rrzactiw power plays a significant role in tleterminatioii of system security. For esainplc, low voltage at
nodes n:ay irican proximity to the nose of P - b’ curve,
thereb:. making system susceptible t o voltage collapse.
.4h.poor reactive power flow profile (low voltage and
high voltage). may imply excessive M W power loss. If
r!:r g t u m r o r s are ciycrating IICW t,lieir rcwrvc’ limitas,
ttirtrt.
riot hc sufficient MM\.;-iR rcsc:rws i~viiilahle
t l J c q ~ ti!.)
c ~ ~ i t eniergencies.
h
Further, geiic’rators inay
have sii:all
absorption limits (under excited condit i o n s ~ and
.
this may lead to generator tripping. Some
system !oa& can be sensitive to voltage. Thus it becomes essential to have proper reactive power manageiiiriit i n ii systrtti. Thr*sc. problenis tliiticr s t ~ a d yst,i\te
conditions can be formulated as the Optimal Power
Flow (OPF) problem with various objective functions
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(,(vi
(YL
i ( s i i
A ddit i on a1 cvns t ruint in r w l tin1c ope vu t i v ri is th(At
m a n y controllers cu~nnot be used. Fursther the amount
of control used should he realisticully matched with the
gain accrued. For example, if initially 10 MVAR compcnsatioii irnprovcs \,oltag(! iLt i k I I O ~ ( ?by 0.05 )).U,(i t .
from 0.89 to 0.94) arid rz fiirthcbr 10 MVAR by say.
;inothor 0.01 p.u; then, eve11 if tlic-: dcsirc:ti rnirii~~tuni
voltage is 0.95 p.u. it, rniiy h c t atlvisablc to IISF only
10 MVAR compensation. These issues have been discussed in [2,3] . Somari et. al. (41 propose a niethod
to achieve this realistic curtailed nurnber and reduced
colitrollcr Inovctiiixit. idgorit.liiii using sc!risit.ivit.y i L I t ; L l ysis and Singular Vulue Decomposition. However, the
computational effort, rcquircd is significant, and requires coitiitiiiiiicatioit supporf,. Instead, in tliis paper we propose a Iiic:thodology t,h;ir, ck\~~
hantllo thc
curtailcrl tiuilitwl i L t i ( 1 rcdiicxd c:ontroller inoveiri(!rit,s
for the reactive power/ volta.ge control in local control
inode with two tier hiclrarc1iic:;d control strategy for Q
cornperisation and til13 control. Further, the proposcd
inethod does not, rcquire convorgctd Load Flow (LF)
sc>liition ;is ;I lwgiiitiin:!, i l . r i d I i ~ ~ i i is
~ . oniorv si.iit.;il)!vf o r
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11 CLASS DEFINITIONS..AND
MODELLING
Object Oriented Programming (OOP) has been accppted by the pov.-cr indust.ry as a viable altcniativc to
traditional procedural programming, with C++ as the
utliversill choice for implementation. OOP language
iike CT+ exhibits following features which arc not supported by procedural languages [ 5 ] .
0 Definition of classes and their methods : This inVij1vt.s designing classes by encapsulating data and
niehods. Seycr et. al. IS] discuss definition of classes
for ~ ( J W W system apparatus like lines, transformers,
tal
1'
Operator overloading : Methods for arithmetic and
Ic~gicliloperations such as addition, subtraction?etc on
u w defined classrs like niatris. vt?ct,or can bc iinplenieritrd by overloading the corresponding arithmetic
ol)c'rat(trs . 1'1ie. iiiput mid output opcwitoi's ritii also
be overloaded to increase the readability of the pro-
gram.
Inlierirancr : Zhou [7] has defined a network coiitainer base c l a s Ivhich contains classes for power sys~ e i i iapparatus. i-irtual functions are defined 011 the
tiisijt. c1a.j~..4C Load Flow is then a derived class which
n i b load fiou as: a method. Derived classes and use of
virtual functions improve flesibility of a large program.
0
Thta proposcd work coriibines tlic alww iii(!iit.iorwd
features of OOP, along with the sparse rriatrix corriputstion tecliniques. OOP for sparse ttiatriu cortiputations is discussed in 181. This section defines classes
for the Pi.' nodes and PQ nodes. Steady state models of P\' nodes for modelling governor control and
AGC characteristics, steady state load modelling are
discussed i n brief.
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Three possible ways of AGC controls have been ~011sidered, namely ( i ) flat- frequcncy coiitrol (FFC) ( i i )
flat tie-line control (FTC) (iii) flat tic-line frequency
bias control (TBC). The constants defined by generator capability C U ~ V Care xnodclled by lirniting Qmiri
and Qmax.
These attributes are modelled by class node-PV.
The input and output (iostream) operators >>, <<
are overloaded making the program more readable.
Modelling of PQ node : Active arid reartivc power
loilds ii.r<'itlod(:llt:cl ~ L f1iiic:tioiis
S
of ifolt,iig:1!;it. tlic, l)lls
and system frequency deviation. The functions considered are
PL, = PL,,;(~+ P i A F ) ( A l , + A2,b;
Ql,,
= QLOi (1 -t. b;AF)(.!tI;
+ &;Vi2)
+ 112, r: + I t ,172)
(6)
(7)
The coefficient. F, arid F2 represent the frequency senarid
sitive coinpoileiit of the loi-ids. Constants A I !
ilZ,
R.2 and A3, fl3 rcfer to the constant powcr. cunstarit current arid the constant impedance coriiyorients
of the loads with 6'4i = CRi = 1.
The attributes are modelled by class node-PQ with
overloaded iostrearri operators. The cornpcnsatiori at
;I Iioric? is ~ n o c l ~ l l (by
d I,Iio i r i i n i r r i i i r i t ;tt\d ltiilxittltttli
liiiiits of (.2 iiritl sct. v;rlucs.
Modclling of cliisses for transforrnctr, transmission
lines etc follow tho tl(:sigri j)ritic:iplcs alrc;idy discussod
.in literature [6,7].
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T!w philosopiiy follon.cd i n this work for curtailing
aiid :c~dricirtg c u r t ~ i h dr~ir~~;ernr~~ts
for r ( d the! Or>erarion is t h a t such a sulj-optimal solution is better
reahmi rhrough reactive power arid voltage control
w I L r ~ : : ! ~intr:gratetl i n LF solution. At the saiiic: tirw.
! c d i > i k sc,c.uriry asessiiieiit is possible by niodelliilg
io:&. L;,.!.c m o r characteristics and !iC;C features [I 1).
15 c1iust.i: sriiall enough so that it satisLL+uriiprioii implicit i n liiieariz,ition involved
i n LF. Typically. 1.25 1II’hR step has been found satIsfacIorv. .\ rnntrol is affmed only il‘ () c,oriipcinsntioi!
sei is n.iKillr1 limits df the apparatus. ’Tlic control strucrurt? ca:; be aiigmrilted to consider a tier of node voltage3 a d j . ~ ~ i * itlot t Iir coritrollrr bus ;U: w t ~ l l . H o w t * v ~ ~ r .
for the system studied, this was not found necessary.
In fact. by t.spcrlriict!. niiiiimum and niaxinium deskaide limit:: fi,I voltages at controller buses may bc set
such that t tip controller rrsporids (or is iriliibited for
response 1 ro adjacent node voltages.
S i c
ci
(..:.p
~1t.srhc
Fine control of voltage profile is achieved using on
!,-,,;.ti
r h : m q i p y fmn.cfomPrs. This cont.ro1 is ;if-
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FDLF
i l k
ii:ipleiiieiitatioii with govcrnor control can
whew A =
Sixiiihr equatiun ciiii be w i t t e n for FFC with h ( S F )
repiacci! by LL'.
\\liile iuodcllirig FTC or TBC, in addition to slack bus
injectim. net tit-line exchange or ACE is modelled in
a similar way it5 follows.
V FACTORIZATION OF AUGMENTED B'
MATRIX
req7Llircso n l y one additional equation A P, with one
.widit ivlial variable 1F or AG.
Lcr
B'
TIN!backward substitution is completed as follows
:
= LDL'' where L is a unit lower tri;tngular
D is a diagonal matrix. Also let
iiia:ris and
~
Similar multi stcp forwar d - h c h w d r d (FB) substitution can be derived for cases pertaining to FTC /
TBC.
T1iu.i the i i t ? ~L D C factorization of augrnelited B'
can hi. coniputvd froin misting sparse L D L ~ fnctor'
izatim of B' hy t w o forward substitutions. The vector
and 3 Cali bc ow"ritten on CI c2 and scalar d,, can
be overu-ritren on a .
~
Augnieiited U' niatris in c u e of FTC or ?'BC
be decomposed into LDU factors as follows. Let
caii
VI OVERALL REAL AND REACTIVE
POWER CONTROL ALGORITHM
An important requircriicnt, for i i i i dgorithtn to be used
in energy control center is to have good speed characteristic. The proposcltl algorit,hrri is essentially Ixiwd
o t i FDLF cxcept, Cor i ~ d d i t , i ~ i iIicuristics
i~l
1.0 griitic
the solution and localized urisyrrlrrietricity in the augmented B'. As such stat,e of art methods for sparsity
exploita.tior1in FDLF like stat.ic data st,ructiire, miiiirriiiiri tlcgroci nlgorit,lirir for fill i . c ! t l i i t t i o r i , scq>ar:itc! a r i a l p c illid factorize p11;~sc:
etc ha.vc: bccii used in tlw irw
plerrit:rita!.iori of ~ ~ O ! N J S tiic:t.liod.
C ~
A separii.tc class
, .
!<[;:li'54!.. : i ; : i 1 i ' l S
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5iti;ip
c!ia::;rnr;i of a 2.4
!ii:f:
110&
arc+:; i;; !f
nect,ed by tie-lines connecting nodes 5- 19 arid nodes
5-24 respectively. System base frequex~cyis $0 Hz. Jt
is assumed that the real pon-er load decreases by 3 %
for 1 Hz. decrease in the frequency. and rcactive power
load is frequency independent. Other load modelling
factors are A , = RI = 0.5, A 2 = RZ = 0.3 ;13 = R3 =
0.2. Generator droop characteristic is 5 % on its own
rating for all the generators. Generator 1 i s treated
as the regulating generator for hoth the areas, which
part.icipat,e i n the secondary control [ U ; = 1). For the
give11 operating conditions thr net scheduled real interchange from area 1 to 2 is 83.75 Mli-. Table 1shows
f.lw wsr1ft.s o n f.110 folfcnr.iiig 2 cii.ws :
! ~ ~ I J I 1.
~ C.r]ic:yt; ; ) I [ ! i i y i j
The proposed voltage and reactrivepower control algorithm is as follows :
Initialize (Flat Start,).
Foririulate B', B" and compute LDL' factorization
using sparse m;rt,ris t.cc:hiiiqucs.
Sclect, the control strat,egy GC: FFC, FTC or TBC.
Forrni~lat~c
t,hc ;iiqyicrit,cxi I?' a n d factorize as pcr
equa.t,ions (13) or (14).
M'hilc (mas-misrriat~cli> e or tderance) do .
-- - Solve liricarizcd cquittioii corrc:sponding to 3 update and update
( ~ A1 F ; i r i t l /or A C v;ii~i;i.i)f~!s.
-- Solve for AV update in identical manner to FDT,F
- - Effect Q-control.
-- If maximum mismatch < 10 1: 6 , effect tap-control.
It can be seen that as tap-control is affected only in
later stages, iln implicit, reduction and curtailmcnt; in
t i l p riiovcmcnt becomcs possible. The 'methodology
(;;in ti;rndlc with (!as(:
discrete nature of controllers.
The load inodel described in section I1 is used duri n K mismatch c:otnpllt,iit,inIis. As t,hc Q compensators
IISC' locd coti6rol pliilosopliy, t h e y also implicitly follow curtailcd riuuiber i~11tl rcduccd coutroilcr niovcrncnt. philosophl..
vrr RESULTS
.4 computer program was developed based on the proposcil rnct hod and ilp1)lictl t.0 scvcrd int,crconncrted
power systems The results W C I C obtained on Intel
Pwtium Pro Processor at 200 M H a with 32 MB RAM
running a Linux kernel (version 2.0.34), using a gnu
C + -t compilcr (version 1.0.2-8) The convergence for
all systems was obt,ained in approximately 10 msec.
Case A : Load Change in Area 1 : In this case.
load at bus 9 in area 1 is changed from 30 A l i i - . 10
MVAR. to 90 L4W, 30 MVAR. At the end of the primary control(generator) action, the frequency computed in the system is 49.9199 Hz. The net tim-line
interchange is 68.816 M W .If the tie-linc real poncr
is to remain constant, and the frequency is to remain
normal, the generation at the bus 1 is 615.26 l l i i - .
(Refer Table 1).
Case B : Tie-Line Trip : This stud:, corxsprx;&
to tripping of tsic-linr 5- 19 from the base ctmdir iors
(restoring load of bus 9), which results in change of
system frequency to 50.0023 Hz. Tie-line 5-24 esports
80 MW from area 1 to area 2 with consequent rrduction of voltage profile in area 2. The reduced voit.age
decreases the actual load due t.o the voltage dependent
nature of the load. The resulting new generation and
load balance reflect:; in improved system frequeucy.
Casc
1
2
Node
---t-mNO.
BUS-3
BUS-4
BUS-2
nus-4
II I
Table 1
Node
- -.- Svstam
~"- - - - ~ P-inj
I P-tie 1 Frequency
MW
1 MIV ] H z
!
588.360 I
i
i
129.326 68.816 49.9199
199.614
393.459
-
556.089
124.875
189.722
379.612
80.133
I 50.0023
i
Voltage Control
For voltage control, the desired voltage range at load
buses was fixed from 0.95 to 1.05 p.u. A system having 514 nodes was tested, whirh h m initially 1300 SlIY
..................................................................
of scheduled load with a demand of 4273 Ally and a
j
in[ A
&--.!
generation of 4505 MW t o meet loss of 232 >ITV The
I
-!
-4
nuniber of voltage violations are 145 with absolute sum
of voltage violated as 5.1 p U . With governor control
the quantities rhanged to a demand of 4380 11lY and
a generation of 4497 MW to meet 216 >{If' a5 the loss.
Thc n u m t i c ~ rof voltage violatiolls arc 86 W I T h absn111tc
:I
a
4
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PIw<.r.S ~ \ > t , ~ ~ \ ~I:,> !I,:,~,::,
i~~!;
rtivv
Effcct of load niodcllirlg W:LSt.c:stc!d or1 a systc!nl wit,h
81)noclcs. T l i ~results iirc t.al)ulai.cdin Talh: 2.
nbie 2
89 Node System Without Load Modelling
citsc .4 : FDLF without. control
case B : I T C with c:ontrol
case C : GC with corltrol
Resulting Quantity
IA
IB
C
Net Demand MW
I 20.19 I 2049 2049
2154
108
9
0.087
262
57
~-50
'
i'i:..:r.r
,\*,
n o . 10. Cjctober 1983. PP 3481-3487:
[z! W. F. Tinney, J. M. Bright, K. D. Demaree. B. -4.
Hughes, ''Some Deficiencies In Optima] Power Flow", Pro,.
ccc?din@of the IEEE-PICA Conference. Xlontrr& Canada,
May 1987, pp. 164-169.
[3] Hans C h i t s & , m n e r Bacher, "Optimal POW= F l m
Algorithms", Control and Dynamic Systems - Advances in
theory and applications. Vol 41, Analysis and control
tem tecllniques for electric power systems. Academic Prac.
1991, pp. 135-206.
[4]
A . Soman, K . Parthsarathy, D. Thukaram. ?Curtailed Number And Reduced CoritroIIer hIovet1it.nt Optimization .4lgorithms For Real Time \:oltage/Reactir-e
Poww Control". l E E E 'Trans on Power Systerus vol.
9, 1 1 0 . -I,N ~ l \ r l l l b c ~1994.
r
1111. L'();{&?().i
1
s.
21 72
117
14
11.307
:I32
57
-19.897
--
[5]Bjiirne Stroustrup, "The C++ Programming Language
-third ditiori'* .~ddisotl-\\'cslr,vPublishing Coiilpp.ny.
t T Bell, 1997.
[6] Andreas F. Never arid Felix F. \Vu and Karl Imhof.
89 Node System With Load Modellixig
R.esulting CJiiantity
IA
j R
I C
Ker. Dcrmnd hlW
1 1940 I 2007 1 2009
Net Ccncration M W
2054 2119
2116
Ncst Loss hlW
113
107
109.5
KO of VoIt,agr Violiitiol1s
14
---___I_
"Object Oricnt.ed Programming for Flexible Software Exaniple Of A Load Flow" IEEE Trans. on Power S y s t r "
~01.5,no.3, August 1990, pp.689-695.
[7] E.Z.Zliou, "Object Oriented Programming. C++ anti
Power System Sirnulation". IEEE Trans. 011 Powr Syst,enis, ~01.11,110.1.February 1995, pp.206-2!5.
[SI l3.Nakavik and A.T.Holcn, Power System I\iodelling
And Sparse Matrix Operations Vsing Clhject Oriented Programming", IEEE Trans. on Power Systems. vol. 9. no 2.
]
240
57
49.937
L
'lil
'l'l..~!l:-
From the ahow results it can bc o1,served tha.t
0 In comparison with no-loatl-niodelling, when the syst.cIt1 10;lds ar(! r i i ~ d ~ : l ilt s~ a
~ lfuncttion of voltikgc
- murc ( ~ C I I I ~ I isI I ~Inct,.\rit,h voli,ikgc coiitrol.
- the arnouiit of compensation rcquircd rcduces.
- frequency of operation improves.
The proposed algorithm reduces voltage violations
significantly.
0 Propcr rrilctivr powcr nianappiicnt 1ca.d~
to roductiori in lossrs. Howovcr as load ai.t.c!nuat,cs with volt,iigf.!s. thr: gaiiis arc r i o t signific:iuit as in ttir 110-loadniodelliiig c a w .
0 Almost. 43% (:oiit.rols iLr(' (;iirt,ii,il(:d and this is inclrI)(*JldClll.of t,llc control st.ri1t.cgy ~ s r r l .
May 1994, pp. 1045-1052.
[9]M. A . El-Kady, B. D. Bell. 1'. F. Cdrvalho. K. C.
Rurchett, H. H. Happ, D. R. Vierath. '' Assessment Of
Real-timc Optimal Voltage Control:', IEEE Trans. 0 1 1
Power'Systertis. vol.1, no.2, May 1986. pp.98-107.
(101 Milan Bjelogrlic, Milan S. Calovic. Borivoje S. Babic.
P. Ristanovic, " Application Of Sewton's Optimal Power
Flow In Voltage/Reactive power Control", IEEE Trans.
on Power Systems, vol.5, no.4, Xovember 1990. pp.11171454.
111.1 M. Okainiirn, Y. 0-ura. S. Hayashi. I\: Ucnirita.
F. Ishiguro. " A New Power Flow hlodcl And Sidutirrri
Method- Including Load And Generator Characteristics
And Effects Of System Control Devices''. IEEE Trans.
on Power Apparatus arid Systcms. vol.P.4S-94. nn.3.
h l a v /.Ju III- 1975.
X BIOGRAPHIES
VI I1 C; 0N CL US 1 0NS
Thc paper proposed an integrated niethodology for LF
a r i d reactive power / voltsagecontrol for power systems.
'rile FDLI; like iirlplcrncntat,ion coiisidcrs r e d life constraints like curtailed number o f coiit.ro1 actions, modelling governor action, AGC control st,rategies, load
modclling etc. It, tias twc!n t,cst,cct on various syst.cms
Ilpt,o 51.3 riotlcis. The tlcvclop~didgoritilxn is suitable
fur 11se iri Eiie.rgy Control Centcr for realistic voltage
control and security asscssment.
Ili REFERENCES
Shubtia Pandit is pursuing her Ph. D. within the area of
implementation of object oriented program dejlgn wirh efficient numerical techniques to polver system ana1:isis problems.
S. A . Soman is .Assist.ant Professor at. I.I.T.Eiomba!-. His
research interest include sparse matrix computaticns. object, l>ripntrd Prograrwning nppl.ications in p o \ w s w c m .
s. A. KhapRrde is Professor at 1.I.T. Bombay. HIS r e
interests include power system analysis, neural networks and power system automation.
A. Pandjan received his fh.D. in Electrical Enginming from 11s~. Bangalore. Presently he is working a a
software specialist with Wipro Infotech, Bangalore.
[I] L.Fra.Ilchi,M.InnorLa, P. Mararinino, C. Sabelli, "Evalu;ltioii Of Econoriiy And/Or Security Oriented Objective
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