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A Novel Concept for Stabilization of AC DC Network with UPFCR K andey
Department of Electrical EngineeringInstitute of TechnologyBanaras Hindu University Varanasi INDIA
Abstract: This paper presents a novel concept for stabilization of ACIDC network with Unified Power FlowController (UPFC). The svstem considered has the structure of two areas connected bv HVD C link. Theinvestigation for perturbation in a c bus voltages has been carried ou t and the effect on the stability deterioration hasbeen analvzed. The new conceot of control has been orovosed bv embeddine UPFC and then eeneratine the controldecisions adequately which stabilizes the earlier one. The concept o f including the Unified Power Flow Controller(I. 'PFC, i n \c DC'nctsorh eipccially vhcrc a DC linl, is cmbiddcd 10 connect ihc 1 \ 9 0 \C Sjsrcms is proposed.The ~ ro no sc d ontrol desien has hem donc utilizing a Novel Diicrcte -Time niodcl or'AC'DC s\sle m. Thc coninletcsystem stability has beenstudied in which the individual controller such as HVDC-SVC ~ ~ ~ H V D C - S V C - F Cperformance under varying perturbation of ac system voltage has been widely analyzed. The results show that insituations the HVDC-SVC alone is unable to reject the perturbation, the UPFC along with the HVDC SVC dampsthe oscillations, thus matchi ng the real and reactive powe r dema nds adequately. Thi s novel combination caneffectively be utilized in situations when the ac system b us voltage undergoes the fluctua tions due to changing P andQ requirements. Copyright 006 IFACKeywords: -HV DC, SVC, W F C , Discrete-time, continuous time, multirate sampling
I. INTRODUCTIONThe HVDC transmission technology is wellestablished nowadays. So, many schemes all over theworld are running well including back-to-back, point-to-point and multi-terminal. The basic operationalrequirement of the HVDC schemes is adequatecontrol action, depending upon the power order fordamping the power network oscillations. Sometimes,the inadequate control action such as, absence ofadequate control of Static VAR Compensator (SVC)at the converter bus, might result in unstable systembehaviour. So far, no remedy has been reported inliterature, where there is a variation of the ACswitchyard line-to-line voltage because of externalreasons, which might ultimately affect the operationof converter. A new approach has been proposed forthe network in which DC link is embedded. When ACbus voltages of converter station fluctuate, the SVCmay not be in a position to help to damp this and sothe converter may land to control instability. This isvery detrimental for the system. To alleviate thisnovel concept of Unified Power Flow Controller(UPF C) in between the AC switchyard has beenproposed which acts as a supplementary controllerfor the AC network and thus regulates the systemdynamics adequately in situations of perturbations inAC switchyard voltages either side, which in turnimproves the overall system stability as desired.In the poasr system nrtaork. t n t ~egional gridscan hz interconnected h\ HVDC hack-lo-h3cl\. Thetwo converte r stations connected through the DClink and the converters have their individual controls.
In case of power oscillations, the converters willfunction by their firing angle controls. As the firingangle can vary w ithin a certain limit a s directed by thecontrol, the Static VAR Compensator will also actaccordingly. But, when the HVDC converter controlsalong with SVC are not sufficient enough to damp theoscillations, i.e., reactive power mismatch is not met,and then the AC system voltage will come down fromnormal 1 p.u. value. As this is noticed by the network,it will first land to converter control instability andassociated afterwards failure and then may enter toACI DC system interaction.Moreover, if the voltage in the AC side ofthe corridor becomes low, then DC link voltage, aswell as the power transfer through the DC link willcome down undesirably.Now, providing an UPFC block, in betweenthe AC switchyards, parallel to the AC tie line, andthe DC link, the real and reactive power both can bemodulated adequately, by their multifunctional andcoordinated control. The capability of UPFC has beendemonstrated (Hingorani Narain G, 1999; Wa ng H.F.,2000) in damping oscillations. In case, there isreactive power drop in the network, which cannot bemet by SVS, etc. then, the UPFC will pump thatpower to the AC corridor, immediately, and thusstability of the power network can be maintained.Depending on the rating of UPFC and SVS, the realand reactive power can be modulated and the wholenetwork can be made stable, up to a certain extent.Thus, chances of network tripping, due to large,sudden and sustained power mismatch can beminimized a lot and stability of the ACIDC systemcan adequately be enhanced.
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From the results shown in this work, it can besaid that this proposed HVDC-SVC-UPFC compactsystem Fig.1) is far better to design the effectivecontrol strategy for HVDC link, suited to restorestability in a very short time, which is essential toensure better stability for a dynamically varyingpower network. But, W F C also cannot sustain a verylarge amount of power oscillations because its DClink capacitor has a maximum limit to support therequired VAR. So, this proposed model may notguaranty power network stabilization for a very highamount of perturbation, but it can definitely give ahigher level of confidence to the power systemresearchers, In earlier research studies, no suchconcept has been proposed yet, so this proposedconcept will be interesting to power engineers andresearchers worldwide.
Fig.1 HVDC-SVC-UPFC system representationI1 DISCRETE-TIME MO DEL OFHVDC-SVC-UPFC
In standard practice stability investigations areperformed using linearized perturbation models inwhich the system is linearized around a nominaloperating point. To achieve this objective, it isimportant that the behaviour of various componentsof the HVDC system be appropriately represented ina linear domain.2. Discrete-time HVDC System ModelContinuous-time Carrol and Krause, 1970) anddiscretetime system representation have beendescribed in the literatures Pandey, et a/. . 1990).Discrete-time equations for converters in HVDCsystem Pandey. et al., 1990) are given below:Rectitier Side
AVdr2 kT+T1) A, Aa, kT+T,) + AS [ Aa,
kT+T3)-Ald, kT+T,)]AVdF, kT+T,) =A [ Aa, kT+ T, ) AU,] + A , ,
Aa, kT+T,) +Al2 A/,,, k+l)T
Inverter Side
AVdj4 kT+T3) = BioAa, kT+TJ) Bl , [Aa,
where A to A and B to B,, are linearized scalarconstants. The relation ship between the DC currentId and the overlap angle U are derived for both thecases of rectifier and inverter Pandey, et a1.,1990).The linearized values of the overlap angles U and Ujin terms of DC currents and firing angles are given as,AU, = [Ald, kT+T2)+ Id k 7 ) d , A a , k 7 ) ] / d 2
Combining the transmission line and currentcontroller model, state space expression is obtainedSince it has been assumed that, the predictive typecontrol at inverter end, the variable Aa, has beenrepresented in terms o f the variable AldfAx = A d r + B A V ,where, dr = [ A a , did A l d j AVCi,1
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This state space model represents continuous- timenature of the both transmission line and thecontrollers. To combine the continuous-time modelsof the transmission line and controllers with thediscrete-time model of converter, the theory ofmultirate sampling has been applied Pandey, et a l1990).dx kT+Tl) q T ,) dx k7) @ TI)AVd kT)Ax kT+T2) qT,-T ,) Ax kT +TI) + 6 TrT,)AVd kTtT,)
.. -where Q T,), Q T,-T,), Q T3-T,), Q T-T3) are thestate transition matrices evaluated a t the fou r discreteinstants, while @ TI) , T2-T I), O T1-T2), 0 T-T,) arethe corresponding input matrices.Therefore, combined equation:d x [ k + l ) q = @ TI @ TrT ,) @ T,-T,) @ T-T,Ax k n +@ T2-TI)qT3.T2) qT -T3 ) O Tl) AVAkT)+@ TrT,) qT -T 3) KT2-TI) AVd k T+Tl +@ T-T j@TrT2) AVd kT+T2 +0 T-T 3) AVd kT+T 3) 4)The vector AVd in this expression can besubstituted by the appropriate average expressionsderived at different time instants s given in I and 2).After simplification 4), can be converted into thefollowing homogen eous state eqn.A x k+ I) q M-cAx k7) 5 )This expression represents the combined DC linkmodel . Where Mc is the closed loop matrix of theentire two terminal HVDC system.HVDC-SVC System ModelIn the model of HVDC-SVC, the linearized stateequations of the HVDC are taken from above. Theabove closed loop equation of HVDC is combinedwith the linearized state equations of SVC, which aredeveloped in the following part.Calculation of Reactive Power 0 )n Static VARComoensatorThe standard Static VAR Compensator SVC) circuitcan be represented s in figure below,
Fig.][ Static var compen satorThe equation for the equivalent reactance for astandard SVC circuit is given below,
Susceptance,
Puttine the value of B. in 18 followine results
Now, linearizing 9) the perturbation equation isobtained as
Therefore, the reactive power equation for Static VarCompen sator, connected in the rectifier side, is
Rectifier Reactive Power EquationFor the rectifier, the reactive power equation is,Q = =1.35VL,.I,,,Sin a,) 12 )Linearizing equation 12)
4 ~ R , , A ~ , ) + R , M ~ , , , ) + R , , A C ; ~ )I3)Reactive power injectedlwithdrawn in case of powerimbalance in the network can be expressed as belowfor suitable controller design,AQ- = AQ, -AQ.5Jr,
= R c ~ , ) + R ~ ~ ~ ~ ) + R ~ A ~ L , ) - S , I ~ Y , , ~ )14)At steady state, reactive power perturbation mustbe zero, i.e. 4 ~ , ~ * =
Therefore, from 14)
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R,,(A~,)=~,,(A~s,~,)-R,~(~~,)-R,,~AV,.~,)At instant KT,i\a,(K7)= ,&.,lK7)-8>&,cO-%dY,,AK7)and, A a j ( K T +7 ) d , . N , ( K T + T , )where, s , .~ '=I / s ,~ R ~ ? ' = /Rr2.R,, I/Rr,Putting the values in I), the equations areobtained sW~ KO= ;~a,cL10)+ ;dl~ X7+?;)+C,dldl K~+CCWb K~+GU", (KT+T)Similarly, for other voltage expressions fordiscrete-time instants are obtained for rectifierand inverter both from I) and 2).State eauations in HVDC-SVC model
1 KAa, =--Aa. +-Al,*r rcR 1Aid, = (- -N d , --AVc,, +-AV,)L L L: V,,, = % 3 5 ~ d ,, (35i~.d,+~Vc,.i_)
- -Equations mentioned above are combined andlinearized to result in3 r ~ i Y , ) 4 ~ c r + ~ ~ d r < - ~ , 3 ~ ~ * + ~ 4 ~ J . + 4 4 L r +&~ ,
15)Finally, the combined HV DC-SVC state-spacemodel can be represented as,
The multirate sampling theory (Pandey, e t a / , 1990)is applied and the state transition matrices areevaluated at the four discrete instants, s it is done incase of HVDC model alone. Finally, thehomogen eous state equation is found in the form of[ (k+l )71 Mxvoc-svc N k T )
where, AX= Aasvr,dld, AVi,r, AV,I T
This expression represents the complete HVDC-SVCmodel. Where, MHM~.TVCs the closed loop matrix ofthis system. Here also the eigen values of matrixMH MC - S , ndicate the system stability, i.e., for thestable system operation, the eigen values must liewithin the unit circle.
A =
HVDC-SVC-UPFC Com~act odelThe UPFC block is connected in between two ACswitchyards and the overall compact modelling isdone. Here, for the purpose of simplicity the detailmodelling of AC network has not been attempted.However, perturbing the AC line-to-line voltage canaccommodate the AC side variations.To study the overall model, the UPFC model isstudied first. Steady state model of UPFC bas been
1 1 x -1/ (1 .35C) X , X -0 - R I L 0 - l l L 00 0 I I I L 00 X , - l / ( l 3 5 C ) 0 -R1(135L)0 l l C - l lC 0 0
given in Fig. Il lThe dynamic equations of the UPFC are given Wang ,(2000) asV,=m,v,,J2. ,(r )Vb = mb. dC/2. la)d vdJ/dt=3.m,il4.CdJ[cos ~ s in(JJI .[ i f i~ iEJ
3.md(4.Cd.[cos(&J sin(6J].[iRd iRJrNeglecting UPFC losses, during steady-stateoperation it neither absorbs nor injects real powerwith respect to system.It means, d/dt (Vdc)=O
Fig.111 W F C in two-machine systemThe equations for two-machine system are obtainedas (Pa nde y and Tripath i, ZOOS),ild= D,.E Iq'+ DI . m,.sin(S.), vd, D3.(Ei,'.cos(G)-i2dx2dS+ b.sin(Sb).vdc 12)is Q,. m,cos(G,). vdc Q2.( ~ ~ c o s ( & ) .dc/2+Ez q sin (d ) i>,.x?#)i2d=D,.(E2q .cos(S)-i~d.~id +mh.sin(Sh).d, /2)+D3
. m,.sin(S,). vdc+D6.Elq'i = Q3. m,.cos(S,). vdc Q,( rngco s(Sh). d,/2+E2q'sin(S)+i2,.xi,)where,Dl xnr/xes ,DI - x d ( 2 . x d M )D3 = X ~ J X ~ ~ ~ ,0 xd/xd Up. 5 = xdJxdepLD6 -xdxddQi =x ad(2 .xqeJ Qz = xq& ,Q3 =xq/(2 .x,,).Qr - x,Jxq8Those direct axis current equations and quadratureaxis current equations are linearized and merged w iththe linearized equations of the dynamics of the twogenerators Gyugyi,, et al., 1995).For the first generator,(D,+ M,.s). Aw , =-AT,, = -A (i,,. E,,'+(x,~-xld').i,d. i,J = i,R A Er gr - lq i,,-(x,,-xld').[ i , A i , d + i , d . A i , q ]=- i t rAEl , ' - [E l , '+ly-xldl). ldl.A i,,, - [ ( X I ~ - X I ~ I ~ .lql.A ild=mi. Elq'+n12. irq nil. A i,ds.AG, wsAw/
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(I+s.T1d07AElq'= AEIII)-(xIcxI~~).i,d( I +s TIA).AEN:I>=KIA(-AV,,)Similarly, the second generator equations are alsotaken into account. The final linearized state spacemodel of the two-machine system is given asAx = A d r + B A Uwhere,Ax = M6 Awl do AE,,' AE lm A EJ q' AEdFD Avd,iJA U [Am, A6, Ama A & ] ~The final state equation of UPFC connected in a twomachine system can be written asx = MUPFCThe diagram of the proposed compact model, whereUPFC is combined with the HVDC-SVC system is
7.Fig.lV Proposed HVDC-SVC-UPFC system
The state equation for the HVDC-SVC and W F Ccompact model can be written as
where.Idu, ,,,,,~R-lIAasvtr Ah Ah, AVLL AV, A 8 Aw, Aw2 AE,,'EIF ia Ern AvdclThus. the HVDC-SVC-UPFC comDact model isdeveloped in a discrete time framework and stabilitystudy has been performed using this model througheigen-value analysis.
Il l SIMULATION OF SAMPLE SYSTEMThe simulation study is carried out usingMATLAB software package. The parameters of thesample system are given below,No load rectitier direct voltage, V h = l p.u.No load inverter direct voltage, V h s l p.u.Frequency = 50 Hz.Direct Current, Id,=ld,=0.25 p.u.Link length=500 meterCommutating inductance, Lr 4.9 9e -0 4 p.u.Line inductance, L=0.0399 p.u.Line resistance, R=0.25 p.u.
Line capacitance, C=0.0405 p.u.Rectifier firing angle, a =I p.u.Constant extinction angle, y=l p.uThe SV C block parameters are given below,Capacitance in the SVC, CC = 0.40528 p.u.Firing angle of the SVC thyristor (connected inrectifier side), asvc 130'AC L-L Voltage, VLL:= 0.74074 P UTransfo rmer : ~ ,~=0 .03 ,x~=0 .3Transmission line: x,=0.3, xb,=0.03Operating condition: Vb=l.O p.u., 6 = 20.23 ,UPFC parameter: m,=0.5, nzh=0.5, S,=O.5p.u.,
&=0.5 p.u.DC link parameter: Cdc=7pF, ~ ~ ~ ~ 1 . 0.uGenerator 1 M,=0.0255 MJIMVA ,D,=0.0 sec., T',d0=5.044 sec., x 1 ~ 1 . 0 ,x1,,=0.6, x , ~ 0 . 0 7 6 5 , ,,'=1.024 p.u.Excitation system 1: K,,=10.0, T,~= 0.01secs.Gen erator 2: M.eO.0255 M J M V A , D.eO.0sec., TVzdo=5.9ec., x 2 ~ 0 .9 ,x2 =0.163 . ' ~ ~ 0 . 0 7 6 5 ,E2q 1 .0 p.u.Excitation system 2: K,~ =20 .0, Tu=0.Ol secs.I11 PERFO RMA NCE EVA LUAT IONThe perturhation of A C line-line voltage is increasedfrom 0.074074 p.u. to p.u.(i.e., approxima tely 25%).In this case. as the perturhation is increasedconsiderably, the SVC will not able to sustain it andfinally it will lead to system collapse (Fig. V). Someof the states have been shown below: The detailedstudy h as been g iven in T able 1.
O I . , , -o
0005 0 0 U ? 5 002 om 0 1 003 O M 5 5Tune rec )(a)
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, , , , , , , ,> O oo 00 nos5 2 om on o a l s ow oorr sTime 3ec.)(c)Fig.V Response of state variables for HVDC-SVCmodel by making initial perturbation of 25 ;
(a) A ,, (b) A ldr,(c) A V I LTable : Cornoarison between HVD C-SVC model andMVDC-SVC-UPFC comoact model for 10perturbation and relatively laree oerturbation. (25 )
IV. CONCLUSIONAn investigation has been carried out of a networkwhere HVDC is having back to back link and also thestability characteristics has been found deterioratingwhen the line-to-line voltage of the AC system isvaried. because of some system disturbance. TheHVDC-SVC alone could not handle the perturbationof line to line voltage change afler a certain value andthis is because of the fact that SVC can not supportfor the external reactive power variation as this ismeant to regulate the Var requirements during the
converter control. Under this situation, the concep t ofemploying UPFC as supplementary controller fordamping the oscillations has been thoroughlyexamined and it has been found that the induction ofUPFC drastically improves the overall systemstability that too in minimum time. The completesystem model of HVD C-SV C-W FC 'amework hasbeen developed in the discrete time domain and thesystem stability has been examined, where it has beenobserved that the variation of AC line-to-line busvoltage does not deteriorate the overall systemstability. This has been reflected so because the ba sicfeature of UPFC in the AC network is to control thepower flow dynam ics very fast using VSC technologyhaving very fast control of both real and reactivepower. UPFC has been incorporated at the back toback H VDC link to demonstrate the con cept? where ithas been intentionally presumed that the DC linklength and the AC transmission line length (thedistance between the two AC switchyards has beenassumed to be 500 meters).
REFERENCESPandey R. K., Ghosh A and Sachchidanand(1999), Development of Novel HVDC System Modelfor Control Design, Electric Machines and PowerSystem Research, 27, pp.3243-1257.Carrol D.P. and Krause P.C. (1970), Stability analysisof a DC power system, PAS-89 pp.1112-1119.Hingorani Narain G (1999) Gyugyi Laszlo,Understanding FACTS- Concepts and Technologv ofFlexible AC Transmission Sy st em , I Press, NewYork.Wang H.F.,Swift F.J. and Li M (1998) A unifrdmodel for the analysls of FACTS devices in dampingpowersystems,lEEE Trans. on Powe Del ivev , No. 4.Claudio A. Canizares and Zeno T Faur (1999),Analysis of SVC and TCSC Controllers in VoltageCollapse, IEEE Trans.on Power Systems, Vo1.14,pp58-65.Pandey R. K. and Tripathi S. B Mani 2005), Designof Unified Power Flow Controller with StalePredominant Approach, Sixth InternationalConference on Power Electronics Drives Systems.Kuala Lumpur, Malaysia.Wang H.F. (2000), A unified model for the analysis ofFACTS devices in damping out system oscillationsPart Ill. UnifiedPow er Flow Controller, IEEE Trans.on PWRD, No. 3Saeed Arabi. Prabhashankar Kundur and RambabuAdapa (2000). Innovative techniques in modellingUPFC for power system analysis. IEEE Trans. onPow er Systems, Vo1.15, pp.336-340.Wang H.F. (1999) Selection of robust installinglocations and feedback signals of FACTS -basedstabilizers in multi-machine power systems, lEEETrans. on PWRS , No. 2,.Gyu gyi, L. Scha uder C.D. William s S.L.Reitman T.R. orgerson D.R. Edris A. (1995)The U nified Power Flow C ontroller: A NewApproach to Power Transmission Co nb ol, IEEETrans. Power Delivery. Vol.10, pp.1085-1093.
