Generator Dynamics Influence on Currents Distribution in Fault Condition - D. Stojanovic

7/30/2019 Generator Dynamics Influence on Currents Distribution in Fault Condition - D. Stojanovic

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Generator Dynamics Influence on Currents Distribution in Fault ConditionD. Stojanovic

Faculty of Electronic EngineeringUniversity ofNis

18000 Nis, [email protected]

J. NahmanFaculty of Electrical Engineering

University of Belgrade11000 Belgrade, [email protected]

M. VeselinovicFaculty of Electronic Engineering

University ofNis18000 Nis, Yugoslavia

[email protected]

Abstract Current now calculation results along theelements of complex power system are analyzed in thiswork, during three-phase short-circuit taking intoaccount relative rntor swing. Analysis is implementedon the examples when, heside infinite bus fault point issupplied by one or more generators. It is sbown, thatgenerator swing neglect ing during short-circuits,essentially changing current distribution in the system,which can bring to not permissible mistakes incalculation results.Keywords: short-circuit, generator, oscillations

I. INTRODUCTIONShort-circuit calculation results are the base for choice

and checking of the equipment in power plants andprotective relay setting. Great number of papers arededicated to short-circuit calculation problem in the world[1 4 ] and in Yugoslavia [5 - 8]. These papers developedthe theory of processes during short-circuits, where themethods are different, from approximately analyticalcalculations to complex computer calculations. Electricalvalue's calculations in a moment of fault occurrence do notgive answer how particular values are changing in time.

Mathematical formulation of short-circuit problem hascommon with dynamic stability calculation, but sometimescan be more complex. Electromagnetic andelectromechanical transient process has been usuallyconsidered separately in practice, although they areessentially the same process.At short-circuit currents calculation and theircharacteristic values calculation, as a rule, electromagnetictransient process is taken into account only. But as a resultof fault, balance of torques at turbine-generator shaft isdisturbed, so it causes electromechanical transient processwhich is expressed through rotor angle changing and anglechanging between electromotive forces (emf) of eachgenerator. Oscillations of these angles, caused by any rotorswing, affect to character and current distribution duringshort-circuit.

Entire influence of described factors produces intensivechanging of electric values in transient processes caused byshort-circuits, that is shown in [6, 7, 8]. This problem isespecially emphasized at faults very near to power station.Relative rotor moving influence to symmetrical andnonsyirunetrical short-circuit current is considered on theexample of single-machine system in [6]. The sameproblem is analyzed in [7], when a few different generatorsare connected to common bus-bars.

Practical interest is to make qual itative analysis ofelectromechanical transient process influence to morecomplex power system, that was implemented in this work.Total short-circuit current and currents along systemelements are analyzed, and in that way the results achievedin [6 - 8] are complemented. Result analysis isimplemented for three-pole short-circuit, when thisphenomenon is most expressed. Generator dynamicscalculation and calculation of currents along systemelements is implemented by special software for dynamicstability calculation of complex multimachine powersystem. All factors, which are usually neglected attraditional calculations, are fully taken into account here.As mathematical model of synchronous generator the fifthorder model is used based on Park's equations. In thismodel, electromagnetic process in stator windings isneglected, so RMS value of alternating component ofshort-circuit current is attended only. Software is speciallyadapted for result printing and drawing of currents alongsystem elements.Calculation results could be practically useful forchoice and checking of switching equipment and forprotective relay setting.

II. MATHEMATICAL MODELINGA. The model ofsynchronous genera/or

Standard Park's model of synchronous generator [7 - 9]with one damper contour along each axis, is described byfollowing system of equations:Electromagnetic balance equations are:- for stator

IPST'99-International Conference on Power Systems Transients June2()-24, 1999, Budapest - Hungary185


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4difld . U . e---OJ!f/q


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,1.4.2

Ineglecting rotor swing

0,2 0.4 0,6 0,8 1.0time [s]

Fig. 6 Current of branch 1-4

taking into account rotor swing\I\.

1f-

a '0.0

4

3~::l~...J- 2

Generator swing influence on some currents one cansee on Fig, 6, to II . which show paral le l values of faultcur rent in the case with ( - ) and without (---) taking intoaccount relative rotor moving.5 r - - - - - - - - - - - - - ~

Ik=143+153neglecting rotor swing

aki . , Imgmto ac unt. . \otor swing \" ' j ' , ,I " ," ".. '43 /',:.'I .. ,53 C. ,o'o.\. 1'0

0\ o'i'"0,0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

time [s]Fig. 3 Currents coming to fault point 3. from left sid6 , - - - - - - - - - - - - - - - ,

::l 65 5~ u 4t:::lU 32

swing influence on branch currents, inertia constants aretaken Tn TJ2 1010 in calculations.10.--------------- ,

987

1 =' f-- ' ,_ /145 -------_.--------

taking intoaccountrotor swing, IIneglecting rotor swing

5

4". 0' .. ... , ,. . . . .

:,"-/125"" .I , . T'. "'., / '43\.. . ',-

5

3 taking intoaccountrotor swing\ ....

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4time [s]

Fig. 7 Current of branch 2-5

~ e g / c t i n g rolor SWing\

2 -

1098 ~ "I neglecting rotor swing

~ 6=! ki I , -5 ta mgmtoaccount rotor swmg~ , / 1434 -::l 0 , U 3 ~ i " " " ..

2 53

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4time [s]

Fig. 4 Network currents during the fault in node 3 whenrotor swing is neglected

a , '; ,a ,0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.0 0.2 0.4 06 08 1.0time [s] time Is]Fig. 5 Currents coming to fault point (3) from left side Fig. 8 Current of branch 4-5when rotor swing is neglected

. ,1.2 1.4

IPST'99- International Conference on PowerSystems Transients June 20--24, 1999, Budapest- Hungary187


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10,.----------------- ,

It is interesting that generator currents 114 and 125 andcurrent I" also have oscilatorilly character; after beginningfall, their values are increasing again due to rotor swing,after certain time they accept the values near to beginningones (Fig. 6 and 7) or even gra ter, tha t is the case with I"(Fig. 8). In concrete example, current I " gets it's repeatedmaximum in t=0.64s, which accounts I " 3.905pu, that isvery near to beginning subtransient value 114' = 3.9324pu.In the same instant, this current is 16.6% grater thancorresponding one when rotor swing is neglected. Currentincreasing is more expressed at linking line 4-5, wheremaximal value, achieving in t=0.66s, is even 3.14 timesgreater than beginning one. All these can be interestingfrom protective relaying standpoint. Certainly, a questionarises is the fault lasting so long in real conditions.Otherwise, in conditions when rotor swing is neglected,generators currents are damping continually. For adifference of generator currents, currents 143 and 153 havesmaller values in conditions of rotor swing neglecting.Also, their sum current Ik I" + 153 is rapidly decreasing,so in t=0.68s it is only 3.58% of the value obtained whenrotor swing is neglected (Fig. 11).

There are s imilar dependencies for fault in any othernode. Fig. 12 shows network branch currents for threephase fault in node 5, and Fig. 13 shows total fault current.Total fault current has oscilstoril ly character here and theirvalues are always less than current sum of each branches.As it was told before, oscilatorilly character of fault currentis a consequence of generator swing, relatively to anglechanging between generator Gland G2, and anglesbetween each generator and system. Total fault current israpidly decreasing, and already in t ~ 0 . 5 6 s has fallen to thevalue Ik = 18.204pu, that is 68.92% of current valueobtained when rotor swing is neglected. Generallyspeaking, total fault current is always less than the sum ofcurrents coming to fault point, because it is evaluated asvector sum of these currents. This is convenientcircumstance from equipment standpoint, because the realthermal and dynamic strains are less than ones obtained byusual calculation.15 , . - - - - - - - - - - - - - - - ,

1.4

,1.4.2

/ .. 'taking into account rotor swing'

neglecting rotor swingI

~ neglecting rotor swing


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V.REFERENCES

VI. APPENDIX

Pel/II ;;:; 580kW- lines:I" =60km, I" =80km, I" =100km,r = 0.080/ km, x = 0.410/ km

- generator G] :P" =200 MW. U" =15.75kV , coup" =0.85.n=3000 min-I . =0.19. =0.295. Xd = 1.84.'Ida =6.8s, 7;; = Us, r; =0.l35s. 7;, =0.5465,GD 2 = 25tm

cos tp" ;;:; 0.85 ,Xd =0.915,

~ = 0.955.

231/15.75kV,

231 /15.75kV ,k =11.3% ,

Uk = 10.3% ,

- transformer 1; :S" = 240MVA,Pc,," = 650kW- generator G2 :P" =171 MW. U" =15.75kV,n =1000min-' , =0..205, =0.345 ,x; = 0.20 , Xq = 0.65 , 'Ido = 8s, 2'Id =0.035s, 7;, =0.205, GD = 68tm- transformer T2 :S" = 200 MVA.

[I] R. Roeper, Short-circuit currents in three-phasesystems, Wiley, New York, 1985.

[2] A. P. Bergen, Power system analysis, Prentice Hall,New Jersey, 1986.[3]. IEC 909-1 "Technical report: Short-circuit currents

calculation in three-phasea.c. systems", IEC, 199I.[4] IEC 865-1 "Technical report: Short-circuit currents calculation of effects", IEC, 1993.[5] J. Nahman, Short circuit currents and their breaking(in Serbian), ETF Belgrade, 1995.[6] D. Stojanovic, N. Mitrovic, M. Veselinovic, "Influence

of Relative Rotor Swing to Short-Circuit Currents", (inSerbian), Conference Juko-Cigre, R23-05, VrnjackaBanja, May 1995.[7] D. Stojanovic, M. Veselinovic, "Influence of RelativeSwing to Short-Circuit Currents", UPEC'96, Iraklio,Crete, Greece, Vol. 3, pp. 1016-1019.

[8]. D. Stojanovic, J. Nahman, M. Veselinovic,"Calculation and analysis of generator dynamicsinfluence on short-circuit", MELECON '98, May 18-20,1998, Tel-Aviv, Israel.

[9] P, C. Krause, Analysis of Electric Machinery, MeGraw-Hill Book Company, New York, 1986.

35neglecting rotor swing30 ~ I

=! 25""") 20e

/"0e.5 15 taking intoaccountrotor swing") 10=>o-=" 5'",0

IV. CONCLUSION

Long-lasting faults cause electromechanical transientprocess in real multimachine system where all machinesparticipate more or less. The process is versatile,deterrninated by all mutual rotor angle changing. The sameis process of angle changing between vectors of generator'semf, and as a consequence of it, angles changing betweenshort-circuit current vectors. With fault occurrence,generators is downloaded and accelerate independently, sotheir mutual angle is changing and as a consequence of it,currents coming from generator side are changing also.Intensity of electromechanical process and it's influence onfault current is depends on fault location, the type of faultand on initial conditions. So it is necessary create themethod for simple modeling of generator dynamics.

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4time [s]

Fig. 13 Fault current at three-phase short-circuit in node 5

This work shows calculation results of current flowalong system elements and of total fault current. Qualitativeanalysis of rotor swing influence to aforementionedcurrents changing intime is given.

It is established that at longer faults (t i >0.15s), rotorswing neglecting can bring to significant mistake in faultcurrent evaluation. Fault current value, with taking intoaccount rotor swing, is always less than one obtained bystandard calculations, that is convenient from equipmentstandpoint. In same cases, currents along system elementsget the values grater than expected. RMS values of currenthas oscilatorilly character, that can cause malfunction ofprotective relays.Calculation results can be practically useful not only forequipment checking but for choice and setting of protectiverelays.

IPST'99- Inlemational Conference on Power Systems Transients June 2(}-24, 1999, Budapest - Hungary189


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Generator Dynamics Influence on Currents Distribution in Fault Condition - D. Stojanovic