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REACTIVE POWER COMPENSATION BY TCR TECHNOL0GY:SIMULATIONFOR LARGE ELECTRICAL LOADS CONTROL

F.Tosato - S.Quaia - G.RabachUniversity of Trieste - Dipartimento di Elettrotecnica, Elettronica ed Informatica

via valerio 10 - 34127 TRIESTE (Italy)

SUMMARYThe large dynamic loads reactive powercompensation in industry power systems (i.e. arc furnaces ) , is very often amandatory action in order to minimizevoltage fluctuation and flicker, as wellas for power factor improving and loadbalancing. All the above are differentaspects of the same type ;f action,basically called " compensation .If the reactive power of the load ischanging rapidly, fast responsecompensators are required. This istypically the case of FC-TCR ( FixedCapacitor - Thyristor Controlled Reactor) ; such a static compensator, expeciallyif used in open loop control strategy,responds with a dynamic adequate to meetthe requirements in most of the industryapplications.The ability of an FC-TCR compensator tochange its reactive power ( even frominductive to capacitive ) , within thetheoretical time of half a period,requires, as a prerequisite, to set up aproper control function. In other wordsthe firing angle a of the thyristors inantiparallel has to be related to properlydetectable input variables, i.e. loadreactive power.A theoretical approach to the problem ispossible, as well as simulation byc o m p u t e r . ~ 1 1 ~ 2 1 ~ 3 1 ~ 4 1 ~ 5 1 ~ 6 1 ~ 7 1In the present papers both approaches areinvestigated and compared. The describedmethodology has a general validity,nevertheless to become straight-forward inthe nature of the problem an example,referred to a two 100 tons arc furnacesplant, is discussed.First they are introduced the equationsdescribing, under some usualapproximations, the law between a and theload reactive power, able to meet thedesign requirements in terms of voltagestabilization. The whole system is thenmodelled and simulated by computer and theresults are compared with the theoreticalones.The comparison offers interestinginformations about goodness and accuracyof the proposed algorithm.

1. THE NATURE OF THE PROBLEM.A power system including a large variableload, like an arc furnace, and a FC-TCRcompensator, is tipically arranged asreported in Fig.1.

U A l N SUPPL"41 I l lI 1 I I

Fig.1 Power system including arc furnacesand FC-TCR compensator; three-phaseequivalent model.The values of the concerned network andloads, as assumed in the present sudy, arereported in Appendix.A three-phase model, if used forsimulation purposes, allows to studyunbalanced situations as well ( this lastcompensator action is not considered inthe present paper, nevetheless themathematical model has been preparedaccording, in order to grant the maximumpossible flexibility ) .Assuming a balanced situation, a singlephase equivalent can be considered; if Rsand Xs are the resistive and reactivecomponents of the net impedance 2s seenfrom the Vx bus bars ( main transformerincluded and we assume to be Xs>>Rs, as

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is usually the case, the followingapproximated linear equation is valid

where Vx is the bus bar voltage, E is theno load voltage, Q is the total reactivepower ( load + compensator ) , PCC is theshort circuit power at the Vx bus bars and1/p is the network answer slope or networkgradient ( negative ) .The total flowing reactive power Q is thealgebric sum of the load reactive power Q1and the compensator one Qy.The compensator reactive power is:

where C is the polarization capacitor andBl(a) is the controlled reactorsusceptance, that is a well known functionof the firing thyristor angle a [ 6 ]U = 2 ( x - a )3) BL(a )=!-I.%!!WLx

The eq. ( 1 ) can then be rewritten as

Eq. (4) represents a family of paraboliccurves in the Vx-Q1 plane, depending by a.the above curves referredig. 2 reportsto the networkAppendix. values mentioned in theII

\

a

t\\Fig.2 Theoretical relations between Vx, Q1and a.

The dotted line in the Fig.2, connectinga=O and a=180 dgrs, represents the "obtained compensating effect 'I . In otherwords this line is the total network +compensator answer that we will achieveinstead of the I' natural " one as per eq.(1). The slope of the compensatedcharacteristic determines the maximumvoltage drop within the compensator workingrange; the max voltage drop must be lowerthat the one selected in the designspecifications. ( In the Fig.2 example themax voltage drop is 1,3/30 kV, or 4.33 %) .The intersections of the compensatedcharacteristic ( dotted line ) , with thesystem curves, offer the theoreticalfunction a = f(Q1), that is required toachieve the target.Such a curve is plotted in Fig.3, where itis called I' theoretical 'I .

t a

I I /

Fig.3 Firing angle a as function of loadreactive power Q1: theoretical,approximated and simulated trends.To impose a linear overall answer meansimplicitly to assume a linear answer forthe compensator too. In other words thecompensator law must be:

where Qy is the reactive power generated (or consumed ) by the FC-TCR and l/r (positive ) is the slope ( or gain ) of thecompensator itself.The overall compensated network answer isthen [ 7 1

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Eq. ( 6 ) is represented by the dotted lineof Fig.2.An analitycal expression of a as functionof Q1 can be written as well. Thefundamental current in the TCR branches is[61 :u - in uIx =-7 ) noL, "x

therefore:

From eq.s ( 5 ) and ( 6 ) :

then:

(10)

consequently:

Expanding sina in series, truncated to thesecond therm and remembering a = n - a/2,we obtain

(12)

The function according to eq.s (12) isalso plotted in Fig.3, where it is called"analytical".A further betterment can be granted simplycorrecting K1 and K2 by a factor 3/2, thatis

Kl = 9 n 0 2 L x C

Such corrected function is also plotted inFig. 3 and called "approx" where appearsapproximating quite good the theoreticalone.The network can be simulated by computer aswell. This have been done writing all thedifferential equations of the Fig.1 netmodel and solving them by computer. TheCSMP ( Continuous System Modelling Program) has been used.[8]The control action of the antiparallelthyristors on the compensator currents,has been simulated by the equations

where the parameters Kij are assumingvalue 0 or 1, according to the firingangle a, to simulate thyristor'sinterdiction or conduction.The load has been assumed as consisting offixed resistances and variable ( step bystep ) reactances in parallel. Due to theno-linearity introduced by the parametersKij, the relevant current and voltagewaves obtained, are of course,no-sinusoidal. The harmonic content and theconsequent filtering problems, have beenalso considered in the simulation, as wellas the unbalanced conditions, neverthelessthe results obtained are not reported inthe present paper.The relation a = f(Q1) has been determinedby this way too. A fixed active power of100 MW has been taken into account. Thereactive power Q1 has been changed bysteps ( 0, 33.3, 66 .6 , and 100 W A R ) .Fig.4 is reporting the voltage answerobtained by simulation, to be comparedwith the theoretical one of Fig.2.The maximum voltage drop, obtained bysimulation at a=180 dgrs, appears to be alittle bit higher than in theoretical case( 1,525/30 kV or 5% ) . One of the mainreasons in the differences between the twosets of curves and consequently in thevoltage drop, is consisting in thecomputing of the resistance Rs effects ,not considered in eq. ( 4 1 , as well as theactive part of the load.Both are in fact contributing to increasethe voltage drop in respect of thetheoretically predicted one.

32

30.

28

26

2

Fig.4 Answer of the network at loadreactive power changes as obtained bysimulation.

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In order to get the function a = f(Ql),,adotted line, similar to the one used inFig.2, has been plotted and the resultreported in Fig.3 toqether with thesimilar theore ical and approximatingfunctions.

2. CONCLUSIONS.Two methodologies, the theoreticalapproach and the computer modelling, havebeen compared.The studied power system proves that thecontrol curves obtained theoretically areconfirmed quite good by the one obtainedby simulation.The two curves do not differ each otherconsistently and the related values ofsusceptance for the controlled reactorsare also not changing more than somepercent point, in the worst cases.We can conclude that the proposedanalytical approximating equation ( 1 2 ) ,used together with parameters (131, offersquite good results for practical purposes.

APPENDIX.

With reference to Fig.1, the studiednetwork, consisting of two 100 tons arcfurnaces plant, has the followingelectrical values:main supply: 130 kV - 50 HZbus bar voltage: 30 kVshort circuit at 130 kV: Pcc=3500 MVAmain transformer: 130/30 kV, 150 MVA,Vcc=14%The remaining values are ( at 30 kV ) :Rs=0.12 ohmxs=1.2 ohmFor the load and compensator side:C=8.75*10-5 FLx=O.1158 HR=9 ohm

3 . REFERENCES.[l] L. Gyugyi - R.A. Otto - T.H. Putman,"PRINCIPLES AND APPLICATIONS OF STATICTHYRISTOR-CONTROLLED SHUNT COMPENSATORS"IEEE-Transactions on P.A.S. Vol-PAS-97, Nr5 Sept./Oct. 1978[21 L. Gyugyi,"REACTIVE POWER GENERATION AND CONTROL BYTHYRISTOR CIRCUITS"IEEE Transactions on I.A. Vol-IA, Nr 5Sept./oct. 1979[3] I. Hosono - M. Yano - M. Takeda -S.Yuya,"SUPPRESSION AND MEASUREMENT OF ARC FURNACEFLICKER WITH A LARGE VAR COMPENSATOR"IEEE-Transactions on P.A.S. Vol-PAS-98, Nr6 Nov./Dic. 1979[4] L. Gyugyi - E.R. Taylor,OF STATICCHARACTERISTICS

SYSTEMOR POWER TRANSMISSIONAPPLICATIONS"IEEE-Transactions on P.A.S. Vol-PAS-99, Nr5 Sept./oct. 1980[5] R.H.Lasseter - S.Y.Lee,"DIGITAL SIMULATION OF STATIC VAR SYSTEMTRANS1 NTS 'IEEE Transactions on P.A.S. Vol-PAS-101,Nr 10 Oct. 1982[ 6 1 T.J. Miller,"REACTIVE POWER CONTROL IN ELECTRICSYSTEMS"New York - 1982;[7] F.Tosato - A.Contin,"LA COMPENSAZIONE DEI CARICHI MEDIANTEREATTORI CONTROLLATI IL'Energia Elettrica n.9-1987[8] F.Speckhart - W.Green,"A GUIDE TO USING CSMP - The ContinuousSystem Modelling Program"Prentice Hall - 1976

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