44 - ipc power flow

7/28/2019 44 - IPC Power Flow

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IEEE Transactionson Power Delivery. Vol. 9, No. 2, Api l 1994 833The Interphase Power ControllerA New Concept for Managing Power Flow Within AC Networks

Jacques BrochuMember Pierre Pelletier Fr an pi s BeauregardMember MemberVarennes, Quebec, CanadaCITEQ

Abstract - The paper presents a new concept for controllingthe flow of power within AC networks. The application isbased on the series connection of impedances between dif-ferent phases of the two (synchronous) subnetworks to beinterconnected, hence its name: the Interphase Power Con-troller (IPC).The IPC acts as a current source with the followingcharacteristics:

the power flow is nearly constant (within 10%)for a wide range (f259 of angle between the twosubnetworks;there is no significant short-circuit contributionfrom one network to the other;severe contingencies on one side of the IPC havenegligible impact on the voltage of the other side;no harmonics are generated (because there is nocontrol action).Other operating conditions (reduced power, reactivepower generation or absorption) are possible by switchingimpedance components.In all cases, the IPC comprises only conventional ele-ments (transformer, capacitors, reactors and circuit break-ers).

Keywords: F ACTS, current Limiter, Interphase PowerController, Loop Flow, W heeling, Interconnection.1. INTRODUCTIONThe acronym FACTS (Flexible AC Transmission Sys-tem) most often designates thyristor-based systems charac-terized by static and dynamic control of the power flow and/or voltage. They comprise static var compensators, thyris-tor-controlled series capacitors, thyristor-switched phase

CITEQ (Centre dInnovation sur le Transport dfinagie duQuebec) is a R& D company foimed by Asea Brown Boveii andHydro-QuCbec.1501Mont& Ste-Julie, Varennes, Qc, Cana da J3X 1P9

93 SM 435-8 PWRD A paper recommended and approvedby the IEEE Transmission and Distribution Committeeof the IEEE Power Engineering Society for presenta-tion at the IEEE/PES 1993 Summer Meeting, Vancouver,

Gaston MorinMember

shifte rs, and even generalized phase-shifterholtage regula-tors [l - 31.The purpose of these technologies is to facilitate thesupply of loads in flexible and rapid fashion, wh ile providingoptimal management of electrical networks. In most cases,they allow a controlled flow thus removing some of theconstraints of the free flow of power [4 - 51.Under the current free flow mode, some problemsencountered essentially involve regulating the pow er flow insteady state. However, certain networks may be sensitive todaily or seasonal load variations and may require additionalreactive pow er to adjust their voltages. Othe r networks may

require fast control of voltage and power a t different pointsin the network in order to maintain stability. The conceptpresented in this paper -- the Interphase Power Controller(IPC)- deals mainly with the first of these situations.Many types of IPCs are possible and each type canhave different configurations. An in itial paper presented anIPC equipped with thyristor switches used to interconnectnon synchronous networks [6]. In the present paper and inreference [7], the most basic type of IPC is described forapplications where a fixed quantity of active power must becarried between two subnetworks without increasing theshort-circuit level in either network.The IPC ensures reliable and predictable operationunder normal as well as contingency conditions. In addition,

it is shown that in the case of contingencies, the IPC can pm-vide reactive power support for the adjustment of voltages.Subsequent generations of IPCs equipped with thyris-tors and appropriate control circuits also present interestingprospects for network applications where fast control actionis required.

2. IPC TECHNOLOGY2.1 Operating principle

The IPC uses a group of three-phase reactors and capac-itors each installed in series between two networks or sub-networks (Figure 1). What distinguishes this new class ofequipment from other series compensation equipment is theway in which the series components are connected to the net-works.For instance, the phase A reactor and capacitor of thefirst network could be connected to phases B and C of thesecond network..C., Canada, July 18-22, 1993. Manuscript sub-mitted December 28, 1992; made available for printingMay 3, 1993. Thus, whatever the angle 6 at the IPC terminals, some ofthe components are always subjected to a certain voltage.By adjusting the value of these components, it is always pos-RINTED IN USA

0885-8977/94/$04.00@ 1993 IEEE

Authorized licensed use limited to: UNIVERSIDADE DO PORTO. Downloaded on April 28,2010 at 14:06:46 UTC from IEEE Xplore. Restrictions apply.


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83 4Transform ation and/orphase shifting+W I L

C+ + 6 -Figure 1: IPC operating principle.

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W I tCr

sible to force a current in each of the networks even if theangle at the terminals is nil. When all com ponents are ener-gized, the amplitude and phase angle of the current are set inone of the two buses to which the IPC is connected. Thiscurrent control thus enables the power carried by the IPC tobe set, as well as the reactive power absorbed or generated atone of the buses.2.2Susceptances

In this paper, reactors and capacitors are always consid-ered to be ideal without any losses. The impedances of theseseries componen ts are then reduced to their imaginary part,i.e. reactance. Within the context of the IPC where theseseries componencs are laid out in parallel with respect to oneanother, the term susce ptmce is used instead of reactance forpractical reasons (B = -l/X). We have generally done sothroughout the paper.2.3 Sample applications

From the principle described above, an entire family ofIPCs using two susceptances can be designed. Only twoconfigurationsare shown.ZPC 240

A first IPC appears in Figure 2. The simplified diagramshows only two out of the total six susceptances. The sus-ceptances are connec ted to a set of switches which enable thedirection of the active power flow P to be inverted.

The active power P is defined as positive when the flowoccurs from the S-side (sending) towards the R-side (receiv-ing). Reactive powers Q, and Q, are positive when the IPCgenerates reactive power to the buses to which it is con-nected.Where the flow is positive, susceptances B 1 and B2 areconnected to voltage points ks nd &, respectively, asshown in Figure 2. Power flow inversion is simply done byreconnecting the susceptances on the S-side so that Bl takesthe position of B2 and vice versa. This method of invertingthe direction of the pow er flow is used for all IPCs.The IPC in Figure 2 is designated as 240 type since theB1 and B2 susceptances are respectively connected to voltagepointsE,andb,. hich are phase shifted by an angle y of240".The phase currenth, s equal to the sum of the cur rentsbl and 102 in the susceptances. Since these currents have

, . , - I -

Q. Q,

Figure2 IPC 240 equipped with switches to invertangles of +60 and -60"with respect to the voltage&,, theirpower factor is low.IPC 12 0

To improve the power factor of these currents, a Y-y6(180" phase shift) tran sformer can be used, as shown inFig-ure 3.

the direction of the ac tive power flow.

Figure 3: IPC 120.Susceptances B 1 an d B2 are now connected on theS- side to the& andLsoltages, respectively. Since thesevoltages form an angle yof 120" with respect to each other,the IPC is said to be of the 12 0 type. The three-phase dia-gram of the IPC 120 is shown in the Appendix along with afew additional notes concerning its mode of operation.For the same power level (i.e. the same current hr n

Figures 2 and 3), the currents in the susceptances are nowmuch smaller. The phase shifts of currents and 182 withrespect to the voltage hr re +30" and -30" respectively,which results in a better power factor.



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835The connection of the susceptances between differentphases of the two networks can be represented by the simpli-fied equivalent circuit shown in Figure 5 , provided that thesusceptances are conjugated, transformer leakage impedanceand all losses can be neglected. Under these conditions, theIPC behaves as two controlled current sources. In p.u of therating, the amplitude of each cu rrent source is proportionalto the terminal voltage on the opposite side of the IPC.

The installed reactive power is significantly lower thanthat of the IPC 240, which compensates for the additionaltransformer. The total losses are about the same in bothcases.This paper describes the IPC 120, which is considered abetter overall configuration [7].

3. IPC 120 PERFORMANCE3.1 Ideal characteristics

As shown in the Appendix, if susceptances B1 and B2are variable, the IPC can directly control the active power Pand reactive power Q, or Q , as long as there are voltagesapplied on the susceptances. With a regulating system, it isalso possible to control other variables such as the voltagesVh or V, at the IPC terminals.

In the case of an application where only the activepower flow has to be controlled over a limited angle rangecentered about 6 =0", the susceptances can be set to fixedvalues.Figure 4 shows the characteristics of the active andreactive power on the R-side of the Bl and B2 susceptancesas a function of the angle 6 when the IPC 120 is connected totwo infinite buses. The characteristics of susceptances B ,and B2 are shifted by the angles w1 =-60" nd w2=+60",respectively. The transformer is considered to be ideal.

50' angle rangeFigure 4:Active and reactive power characteristicsThe characteristics of the active power P and reactivepower Q, result from adding the characteristics of each ofthe susceptances. Operation at unity power factor of the IPCwith 6=0" is obtained by assuming that B , =-B2 (the sus-ceptances are conjugated). The power flow P is then a func-tion of the cos(&, while the reactive power Q , variesaccording to -sin(@.The Q, characteristic (notshownin Figure4) s identicalto that of Q,. Equation A.8 shows that Q, =Q, whatever V,and V,when the susceptances are conjugated.

of the IPC 120.

- IIAs =yA rIPC6 6Figure 5 : Simplified equivalent circuit for IPCs

using conjugated susceptances.According to Figure4, he power factor onboth sides ofthe IPC is equal to cos(6).Thus, for a k25" angle range centered at 6=O", theactive power flow remains nearly constant even with fixed-value susceptances. The reactive power varies almost in lin-ear fashion with a curve equal to -1 p d r a d . aroundo".Moreover, the IPCs does not produce any harmonicssince there is no phase control adjustment.

3.2 Influence of different param etersThis section demonstrates that the IPC 120 controls theactive power in reliable and predictable fashion using sus-

ceptances with fixed values.As long as the 6 ngle at the IPC terminals is maintainedwithin a range of fl5". it is not necessary to subdivide andswitch the susceptances to regulate power flow. Switchingis necessary for changing the power level and for generatingor absorbing a desired amount of reactive power.The IPC is first studied between two infin ite buses inorder to show the effects on the power characteristics ofleakage impedance, terminal voltage and sw itching of thesusceptances. T hen, the IPC is connected to two buses withtypical ThCvenin-equivalent impedances in order to showthat the IPC characteristics are virtually not affected by theshort-circuit levels of the networks.The following Characteristics are calculated for nominal

voltage on each side and a transformer ratio n=l(Figure 3). 1.0p.u power is the rating of the IPC. The maxi-mum values for the B1 and B2 susceptances for all of thecharacteristics are -57.7% and +57.7%, respectively. Trans-former leakage impedance is se t at 10%.



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836

-0.42

1.51- . . . . I 1

I . . . . J-i o 0 10 20data (dag.)

i . , . . - . I I

I I-10 0 10 20

ddf a (dag.)1.1 1 I

-10 0 10 201. -20ddf8 dag.)

0-Ek-oPC -Figure 6: Power characteristics of the IPC 120.

Nominal operationThe characteristics of the IPC 120 are shown inFigure6 . The angle range retained extends f25' about6=0" (Figure 4). The ope rating range is sufficient for mostapplications of power exchange between two neighboringsubsystems,The solid and broken curves are plotted for the suscep-tances at their maximum value and at 2/3 of this value.The susceptancesB , and B2 remain conjugated. The flow isthus directly proportional to the values of the susceptancesand the shap e of the power characteristics is not changed.The power flow decreases by 9.37% at 6 =+25" and3.4% at 6=+ 1 5 O . The reactive power on each side varieswith a slope of -0.0169 p.u./deg.

Transformer leakage imp edanceThe angular displacement between the sources is nowshared between the se ries impedances and the transformer'sleakage impedance. Since the direction of the flow is fromthe S-side to the R-s ide, the angle directly located at the sus-

0

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-1.

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-0.5

-1.

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-0.5

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I-20 -10 0 10 20

dens (dag.)

dena ( d e g )

-6.32 I . . . . .-20 -10 0 10 20

d el fa ( d w )nP.IPC -

Figure 7: Power Characteristics of the IPC 120when the power flow is inverted.ceptance terminals decreases, which causes the susceptancesto generate more reactive power. This increase is visible onthe R-side (Figure 6) where there is no msformer . The Q ,characteristic is displaced to the right. On the S-side, theaansfonn er leakage impedance absorbs the reactive powergenerated by the susceptances.Power inversion

Figure 7 hows the power characteristics for the powerflow inverted and for the maximum absolute values of thesusceptances. The power inversion is obtained by recon-necting the susceptances. The Q, characteristic is now dis-placed by the transformer leakage impedance towards theleft.The power flow at 6 =0 and the slopes of reactivepower curves are the same but of opposite sign. The sensi-

tivity of tlie power flow to 6 oes not change.Voltage at the IPC terminalsIn Figure 8 , the characteristics are calculated for maxi-mum power. Curve sets0,Q nd 0 are plotted for voltages



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837

0 V d . 11 . ' - -------c f3.5l$;,-----l-l\.o I o.81 1IO L -20 -10 0 10 20

M a W)1. 0.51

I I-20 -10 0 10 20&/fa (deg.)

-1.

1.

0.5-8 0a-0.5-1. I I-20 -10 0 10 20

&He (dag.)+-El-+PC -Figure 8: Changes in power flow resulting fromsimultaneous variations in voltages oneach side of the IPC120.

on each side of the IPC of 1.1 , 1.0 and 0.9 P.u., respectively.In accordance with (A.3), the variation in the power flow Pis given by the product of two voltages. For instance, curveo shows apower increase of21 %, (1.1)*=1.21.The variations in Q, and Q, are similar for an equalchange in voltage on both sides.However, if the voltage increases by 10% on the R-sideonly (not shown), the maximum reactive power increase ofQ, is 4% and occurs at 6=-25". This demonstrates thatvoltage variations on one sid e of the IPC have no significanteffect on the other side .

Suscepbnce switchingThe power characteristics have a different shape when

susceptances B1 and B2 are not conjugated. Figure 9 showsthe extreme case when one of the susceptances becomes nil.Here, susceptance B2 (capacitive) remains fixed while su s-ceptance B1 (inductive) is maximum and then zero, (solidand broken curves, respectively).

1.5

1.-aQ0.5

0 I I-20 -10 0 10 20dene (dog.)

I-20 -10 10 201 . ' . . - ' ' ' . .dens de^

I I-20 .I O 0 10 201.dene (dog.)-

Figure 9: Sensitivity of the IPC 120 characteristicsto switching of susceptance B1 (L).When B1 is nil, ac tive power decreases almost in linearfashion from -25" to +25', passing from 0.61 to 0.35 p.u.The reactive power generated on each side by the IPC is 0.31p.u. at 6=0"when only the capacitors ( B 2 ) are in the circuit.

Under these conditions, the power flow is more sensi-tive to changes in the angle 6. However, this is an unusualmode of operation for the IPC hat should only be used whenthe subnetworksare in a contingency situation.If susceptance B2 is switched while susceptance B1remains futed, similar results can be inferred. The lowestactive power transfer capability is a t -25' rather than +25Oand reactive power is absorbed instead of generated by theIPC Q, and Q, are shifted by approximately -0.6P.u.).Table 1 gives a summary of the operating points avail-

able from the IPC 120 at nominal conditions.



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838

34

1.5 I

0.53 0.31 0.311.0 0.1 0

Active &Reactiveb Power atSusceptance in nominal conditions(k1.0 p.u. &&o")

2 0.47 -0.28 -0.28

Table 1: Operating points of an IPC 120a. The same number of operating points can be obtained withb.Reactive power i s defined aspositive when generated by

the power inverted.the IPC.

Subnetwork short-circuit impedanceThe two subnetworks are represented by Theveninequivalents in order to demonstrate the influence of theirshort-circuit impedance on the characteristics of the IPC.The rated power of the IPC at 6=0" is set at 1P.u ., while the

corresponding subnetwork short-circuit power is 15 p.u.This is a short-ci rcuit level which is representat ive of anurban area system. The susceptances used by the IPC are thesame as those used previously.Under these conditions, the inductive and capacitiveimpedances of the IPC 120 are each 25 times greater than thesubnetwork short-circuit impedance Zu2o een on each sideof the device . The corresponding charac teristics are plottedin Figure 10 as a solid curve.

If the Thevenin impedance on the S-side only isincreased by loo%, he active and reactive power character-istic are only slightly affectedas shown by the broken curvesin Figure 10.This 100% increase represents a severe contingency

since the short-circu it level decreases by half. Thus, thedaily and seasonal load variations in the subnetw orks as wellas changes during maintenance periods or in contingency sit-uations should not affect the behavior of the IPC.It should be noted that during contingencies of suchmagnitude, the IPC can help to maintain the voltage by gen-erating or absorbing reactive power while reducing theactive power flow between the subnetworks.

3.3 Installed reactive power and lossesThe installed reactive power of the IPC 120 is 2.1 p.u.This amount of reactors and capacitors enables the IPC tomaintain the power flow between 0.91 and 1.0p.u. over anangle range of + 2 5 O when the voltages at its terminals areboth at 1O p.u.Losses are mainly located in the transformer and reac-tors. Under the above condit ions, the transformer losses are0.34%and constant for the entire angle range. The reactor

I I0 10deha (&Q.)

I I0 i o1. ' -30 -20 -10dene (de@)

1.1 I . I

I0 10.g l -30 -20 -10d d l a ( d e g )

1.1 I

I . . IO.g ' -30 -20 . - io 0 10dens (de@)n@/IPC -

Figure 10: Sensitivity of the IPC 120 characteristicsto short-circuit level variations.

losses vary between 0.05% (6=-2 5O) and 0.26%(6=+25"). Losses are calculated using values that are typi-cal for these types of apparatus.The total osses of the IPC 120 thus vary approximatelybetween 0.4 and 0.6%.

4. BEHAVIOR OF TH E IPC IN OPERATIONBased on the power characteristics shown for theIPC 120, two basic observations can be made as to thebehavior of the device compared to transmission lines, withor without series compensation, and a phase-shifting trans-formers.These observations summarized in Table 2 are generaland apply to all IPC configurations:

the sensitivity of the power flow with respect tothe angle at its terminals is low, while it is veryhigh for transmission lines and phase-shiftingtransformers;



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inversely, the sensitivity of the reactive powerwith respect to the angle at its terminals is rela-tively substantial, whereas transmission lines andphase-shifting transformers are not highlyaffected.Equipment

IPCSeries or non-seriescompensated linePhase-shifting transformer

Sensitivity to 6P Qlow high

high lowhigh low

Table 2: Relative sensitivity of certain equipment withrespect to the angle a t their terminals.Thus, following a change in angle, the IPC maintains anearly constant active power transfer between the subnet-works. If the disturbance is accompanied by a voltagechange within the perturbed subnetwork, the error in theactive power flow is also dictated by the amplitude of the

voltage change. Meanw hile the voltage of the healthy sub-network is not affected.In addition, the inversion of the direction of the powerflow due to angular displacement s for all practical purposesprevented.The IPC exhibits this type of behavior in w holly passivefashion without generating any harmonics. Traditional orrecent technologies require mechanical or electronicswitches as well as a clo sed-loop controller in order to per-form equivalent functions.

4.1 Short-circuit current limitation by the IPCAs shown above, the IPC series impedances are substan-tially higher than the subnetwork short-circuit impedances.Considering a short-circuit on either side of the IPC, theseries impedances limit the fault current.In the case of a three-phase short-circuit, each phase ofthe healthy subnetwork feeds a parallel LC circuit with a res-onance frequency of 60 Hz, since the susceptances are con-jugated. The net result is that the contribution to the short-circuit remains at the prefault current level (see Figure 5 ) .An in teresting point regarding the IPC 120 is that duringa fault, the voltages applied to the susceptancesare the sameas during normal operation. "lie faults therefore do not cre-ate any particular voltage constraints to the IPC 120 .

4.2 Open-circuit conditionsShould the circuit breaker on one side of the IPC open,the subnetwork still connected to the IPC supplies three

series LC circuits with a resonance frequency of 60 Hz. Inorder to avoid that the voltages at the midpoint of the LCseries circuits become dangerously high, varistors areinstalled on each side of the susceptances 171.

8394.3 Resonance with the networks

With the IPC operating under normal conditions, aseries resonance phenomenon canoccur with the equivalentreactance of the subnetworks.To illustrate this phenomenon, it is possible to replacethe IPC by its frequency equivalent. This equivalent simplyconsists in a series capacitor which is identical to the one inthe IPC. An eigenvalue study has shown that this equivalent

adequately represents the resonance frequencies with anaccuracy of 10% providing that the IPC impedances are atleast 10 times that of the interconnected networks.Based on this equivalent, it can be deduced that wherethe IPC 120 impedances are equal to 15 times the subnet-work impedances, the resonance frequency is approxi-mately:

f P 604- = 6 0 f i =232Hz (1)Since this value is not close to 60Hz, it does not presentoperational problems sim ilar to those found with series com-pensation where subsynchronousresonances may occur.

5. FUTURE PROSPECTSThis paper has presented the operating principle of dual-susceptance IPCs within the context of power flow controlbetween two subnetworks. It has been shown that if theangle between the subnetworks remains within f25', thesusceptance values do not need to be adjusted.However, if the susceptances are made variable, itbecomes possible, using a regulating system, to directly con-trol any two of the follow ing parameters:e Q,, Q, V, V,IPCs are thus in no way lim ited to passive control of thepower flow between two subnetw orks. The IPC technologybased on two or three susceptances constitutes a new class ofapparatus for the control of power and voltage in networks.As such, it can potentially be used for network applicationswhere a flexible adjustment of the power flow is required

along with voltage support, both in steady and dynamicstates.6. CONCLUSIONS

The Interphase Power C ontroller (IPC) is a new conceptfor controlling the flow of power within AC networks. It is apassive device constructed from conventional elements(transformer, capacitors, reactors and circuit-breaker).For the subnetw orks on each side, the IPC appears as acurrent source with the following characteristics:

the active power flow is nearly constant(within 10%) over a wide range (+25') of angleacross the IPC;there is no significant short-circuit contributionfrom one network to the other;severe contingencies on one side of the IPC havenegligible impact on the voltage of the other side;no harmon ics are generated.

Other operating conditions (reduced power, reactivepower generation or absorption) are possible by switching



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840impedance components within the IPC. This is done withconventional circuit breakers.

ACKNOWLEDGMENTSThe authors would like to convey their thanks to DagRenborg (ABB ower Systems, Sweden ) for contributing tothe first part of the project. Thanks also go to Lennarthg qu is t, Michel Chamia, Tore Petersson (ABB Power Sys-

tems, Sweden), to Jean Depelteau, Andre Dupont, KamalHabashi, Hans Ake Jtjnsson (ABB Canada Inc), and toJacques Allaire, Julien Gagnon, Jacques Lemay and GuySt-Jean (Hydro-Quc5bec) for their collaboration and theiruseful comments.

PQsVYILc-XE6wY

GLOSSARYActive power, positive when flowing from the S-side tothe R-side of the IPCReactive power, positive when flowing out of the IPCApparent powerVoltage amplitudeVoltage phasorCurrent phasorInductorCapacitorImpedanceReactanceSusceptancePhase angle difference between the terminals of the IPCIntemalphase shift in series with a susceptance (Figure 1)Sumof absolute internal phase shift, formally y =y2-w1(Figure 2 and 3)

Subscripts:Sending network side of IPCReceiving network side of IPC

REFERENCESN.G. Hingorani, Flexible AC Transmission Systems(FACTS) - Overview , Panel Session on FACTS, IEEEWinter Power Meeting, Atlanta, 1990.L. Gyugyi, Solid-State Control of AC transmission,Panel Session on F A n S , IEEE Winter Power Meeting,Atlanta, 1990.R. M. Maliszewski et al. Power Flow Control in aHighly Integrated Transmission Network, CIGRE 1990session 37-303C. A. Falcone, Electric Utility Industry Structure in theUnited S tates, IEEE Power Engineering Review, April1992.B . M. P asternack, Flex ible AC Transmissionsystem:Transmission Limitations - A Planners Viewpoint onthe Needs , Panel Session on FACTS, IEEE WinterPower Meeting, Atlanta, 1990.

M. Gavrilovic, G. Roberge, P. Pelletier, J.-C. S oumagn e,Reactive- and Active-Power Control by Means of Vari-able Reactances, COPIMERA 1987, Montreal, 1987K. Habashi et al.,The Design of a 200MW InterphasePower Controller Prototype, Paper No. 93 SM 436-6PWRD, IEEEPES 1993 Summ er Meeting, Vancouver,BC.APPENDIX

Figure 3shows the three-phase diagram of the IPC 120,which comprises 3 reactors and 3 capacitors grouped two bytwo on each of the phases located on the R-side of thedevice. Susceptances El and B2 on phase A, R-side, are con-nected to phases b and c, respectively, on the s-side wherethe Y-y6 transformer is located.XI n : l

Figure A.l : Three-ph ase diagram of the IPC 120.Voltages bl nd J,$Q applied to susceptances B , and E2generate currents b1 and &Q, respectively, that form anangle of 60 between them (Figure 3) . The current &,. ofphase A on the R-side is directly equal to the sum of thesecurrents. Since the IPC is symmetrical, the current isequal, with respect to transformation ratio n, to the sum ofcurrents and &Q. phase shifted by -60 nd +60,respec-tively.By adjusting the value of the susceptances, the IPC thusprovides full control over the amplitude and phase angle ofcurren t with respect to the voltage& r, sim ilarly, fullcontrol of krwith respect to the voltagebr.t is thus possi-ble to set the power $, or &. These powers are defined aspointing towards the S-side and the R-side, respectively(towards the outer side of the IPC ):

- s = - V I *s - s = - P + j Q s

The active power P is positive when the power flowoccurs from the S-side to the R-side. Reactive powers Q,and Q, arepositive when the IPC generates react ive power tothe buses to which it is connected.



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841(M'87) received his B.A.Sc. degree inelectrical engineering from Universie de Sherbrooke in1969. He joined H ydro-Quebec's system testing departmen tin 1969 where he was more specifically involved with theanalysis of 735 -kV transmission system performances.

He has performed simulations and site measurementsfor the commissioningof the Churchill Falls Labrador powersystem in the province of N ewfoundland and for the generat-ing plants fo r the M anic-Outardes complex.He was responsible for testing, integration and acceptance tests of the first 3 15-kV Rimouski static var compensa-tor and the 735-kV static var compensators for James Baysystem. He was also involved in the acceptance tests for theChateauguay, Madawaska and Des C antons HVDC projects.

He holds Canadian and U.S. patents on the interconnec-tion of syncl~ronousnd asynchronous AC networks.He joined CITEQ in October 1990as Project Leader forthe development of a new power flow control device forpower systems.

(S'83,M'86) received hisB.A.Sc. and M.A.Sc. degrees in electrical engineering fromMontreal's Ecole Polytechnique in 1984 and 1987 respec-tively. He joined H ydro-Quebec n 1986, and began workingas a researcher at the utility's research institute (REQ) in thefields of telephone interference related to HVDC convertersand motor drive modeling. In 1990 he joined CITEQ, wherehe is currently involved in control systems and networkmodeling.

Gaston Moriq (M'85) received his B.A.Sc. degree inelectrical engineering from Universite de Sherbrooke in1978 and his M.A.Sc. degree from Montreal's Ecole Poly-technique in 1983. He has been with Hydro-Q uebec since1978 and with the power systems operation department until1991. In January 1992, he joined the CITEQ team as aresearcher.He specializes in harmonics, DC systems and power

system transients. He has authored papers on power systemrestoration, harmonics and DC modeling. He is currently amember of the IEEE Power System Restoration Task Force,System Overvoltage Working Group, Modelling and Analy-sis Techniques using Electromagnetic Transient ProgramsWG, and FACTS WG. He is currently chairm an of the Fre-quency Dependent Network Equivalents TF.

Where the transformer is ideal and n =1, the values forP, Q, and Q, are given by:- , V, sin 6, - , Vrsh 6

The angles 6B1 nd SB Z are the phase shifts appearingbetween the voltages on the S-side and the R-side of suscep-tances B1 and Bz, espectively. Thus:= (A.4)

(A.5)The angle 6 represents the phase shift between voltages& nd &, (figure 2). The angular displacements~1 and y12of the IPC 120 are -60' and +60, respectively.Equation (A.3) is a system of 3 equations with twounknown quantities. The IPC 120 may therefore control anytwo of the three powers provided that the two susceptancescan be varied. Using a regulating system, it is possible toconvert the control of Q, or Q, into a regulation of V, or V,.Other regulation strategies may also be devised. Moreover,with a third susceptance three variables can be controlled.Where the P and Q, values are controlled, the suscep-tance values are given by:

P 2 ~ , v,cos ~-Jllv, in 6)- Q,V, ( & c o s 6- ins)(A.6)

B , = & v , v r ( v , - 2 v r c o s 6 )

-P 2Vr- Vscos6 +&VSsin6) - QrVs ( & co s6 +s in6)8 , = &V,V,(V,- 2Vrcos6)(A.7)

The following equation deducted from (A.3) shows thatQ, =Q, whatever V, and V when the susceptances are con-jugated:Q, = ( B , + B , ) (V:-V;) +Q , (A.8)

BIOGRAPHIESJacaues Brocb "86) obtained his B.A.Sc. andM.A.Sc. degrees in electrical engineering from UniversiteLaval in 1981 and 1986 respectively. From 1981 to 1983, hewas production engineer for Canadian General Electric. Hehas been with the electrical apparatus department at Hydro-Quebec's research institute (IREQ) since 1985. In 1990 he

joined CITEQ, where he is currently involved in main circuitdevelopment.His research has mainly revolved around transistorizeddrives, induction heating inverters and power flow controldevices for power systems.

44 - ipc power flow

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