Transient Stability Analysis of Synchronous Generator In Multi Machine System Using Time Domain Meth

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 13 Issue: 06 | Jun 2026 www.irjet.net p-ISSN: 2395-0072

Transient Stability Analysis of Synchronous Generator In Multi Machine System Using Time

Domain Method, Direct Method and AI Method

Dipkumar S. Trivedi1 , Arpit R. Joshi2

1, 2Lecturer, Department of Electrical Engineering, K. D. Polytechnic, Patan, Gujarat,India***

Abstract – This paper presents transient stability analysis of synchronous generator in multi machine system using time domain method, direct method and artificial intelligence method in MATLAB. A Multi Machine, two generator and nine bus system is used for this analysis. A three line to ground fault is considered for this analysis. Transient stability of multi machine system is analyzed by Critical Clearing Time (CCT) then CCTs of the system are compared for different methods in this paper.

Key words: Transient stability analysis, Critical Clearing Time, Synchronous Generator, Multi machine system, Direct method, AI method

1. INTRODUCTION

Electricityhasimportantroleinthehumanlife.Thatiswhy powersystemshouldbereliableandstable.Stabilityofthe powersystemaffectsdirectlytothehumanlife,industries productionandeconomyofthecountry.Thatiswhystability of power system becomes very important. Power system stabilitycanbedefinedastheabilityofapowersystemto remaininsynchronismbefore,duringandafterthefaulton thesystem[1][2].Intransientstabilitypointofview,during normal operating conditions of the power systems, synchronism of the system should be maintained and frequencyoftheallsystembusesshouldbesame[4].During steady state condition, input mechanical power and electricalpowerofeachgeneratorshouldbeinbalance.But duetooccurrenceoffaultonthesystem,thispowerbalance is disturbed and system start to accelerate or decelerate. Thisunbalanceofmechanicalandelectricalpowerprovides theconceptofswingequation.Ifdisturbanceissmallthen analysisisknownassmallsignalanalysisandifdisturbance islargethenanalysisisknownastransientanalysis.Power systemmusthaveabilitytorecoverandmaintainstability afterdisturbance.Theabilityofapowersystemtorecover andmaintainsynchronismiscalledrotoranglestability.[2] Small signal stability is the ability of the power system to maintain synchronism under small disturbances.[2] Transient stability is the ability of the power system to maintainsynchronismunderlargedisturbances.[2]

In literature, for transient stability analysis, mainly four methodsaregiven.Thesemethodsare:

(i)Timedomainmethod,

(ii)Directmethod,

(iii)Approximationmethodand (iv)Artificialintelligencemethod.

Time domain method is a traditional method of transient stability analysis based on time domain numerical integration[3].Importantconclusionsanddecisionsdepend onthestabilityanalysisresults,Sothatthestabilityanalysis resultsshouldbeaccurateandwithintimelimitaspossible [7].Thestabilityofthepostfaultsystemisanalysedbased onsimulatedpostfaulttrajectories.Thetypicalsimulation periodforthepostfaultsystemisabout10to15second.

Systemsimulationtakesapprox.10to20second[7].Intime domain method, detail modelling is required of the whole components of the power system for more accuracy. Advantagesoftimedomainmethodare:thisisanaccurate method.Itcanbeuseddirectlyforanylevelofmodelling.For transient and steady state, all type of information can be determined using this method. This method can provide dynamicparametersofthesystemusingswingcurveslike rotorangles(δ),speeds(N);accelerations;powersetc[3][7]. Disadvantages of time domain method are: It is a time consumingmethod(10to20second)Nomeasureofdegree of stability and degree of instability are provided by time domain method. No information for preventive control is given.Itscostishigherthandirectmethod[3][7].

Main disadvantage of time domain method is more time consumptionintransientstabilityanalysis.Toovercomethis problem, direct method had come into picture. Direct method is energy based method. This is the extensions of equal area criterion for multi machine system which is shownbytheclassicalmodel.AdvantagesofDirectmethods are: direct methods without the solution of differential equationscanbeusedtodeterminethetransientstability analysis of power system. It is a faster method than time domainmethods.Itgivesthemeasurementofthedegreeof the stability of system. It provides important information relatedtoderivationofpreventivecontrolandenhancement actionofcontrol.Challengesofdirectmethodaremodeling andreliability.Limitationofdirectmethodisaccuracyofthe analysis[3][7]

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 13 Issue: 06 | Jun 2026 www.irjet.net p-ISSN: 2395-0072

ApproximationmethodisthefastmethodandAImethodis fastest method than other methods. Critical clearing time willbecomparedforallfourmethods.

2. SYSTEM MODEL

This section presents the system which is considered for transientstabilityanalysis.Twogenerators,ninebussystem is considered here, in which one bus is considered as an infinitebus.Threelinestogroundfaultisconsiderednear7 buses on 5-7 line, then after clearing the fault, 5-7 line is removed.Alldataforgenerators,linesandpowerfloware givenin[3].Ybusmatrixofinitialnetworkforgivensystem isof9×9matrix.Twogeneratorsconnectedinnetworkand one infinite bus are the main nodes of system that is why system is converted into 3×3 Y bus matrix using Kron’s transformation.

After conversion the system into three node system, generatorsareconsideredasclassicalmodel.

3. TIME DOMAIN METHOD

A. Classical Model:

Equationforclassicalgeneratormodelisgivenby

Kron’stransformationtoreducekthbusisgiveby,

B. Mathematical System Model:

AfterKrontransformation,reduceddataforprefault,fault onandpostfaultaregiveninnexttonextsection.

C. MATLAB Model

Usingabovemathematicalequations(3–5),MATLABmodel canbepreparedforgivensystemwhichcanbeusedintime domainfortransientstabilityanalysis.[5]

In given system two generators are there that is why two differentswingequationsareusedforeachgeneratorwhich isshownbyequation(3).Equation(4)showsthepowerflow insystemlines.Relationbetweengeneratorrotorspeedand rotorangleisshownbyequation(5).

In above system MATLAB model, two sub systems are used.Thesesubsystemsprovideelectricalpowergenerated byeachgeneratorasperloadandcircuitcondition.During faultandafterfaultclearing electrical network ischanged and its data is given in [3], According to these variable networksduetofault,subsystemsinMATLABaremodeled whichareshowninnextfigures.

Fig. 2:MATLABmodelofconsideredsystem.

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SIMULATION RESULTS:

Classical(0.0)modelofsynchronousgeneratorisusedfor Transientstabilityanalysis.CriticalClearingTime(CCT)can bedeterminedusingsystemsimulation.

In below table system network data is given for three differentconditions(i)PrefaultYbusdata,(ii)FaultonY bussystem,and(iii)PostfaultYbussystemdata.Prefault, fault on, and post fault are considered as steady state condition, during fault condition and after fault clearing conditionrespectively.

These Y bus matrix for pre fault, fault on and post fault conditioncan beobtain usingKron;s transformation from consideredsystem.

UsingEquation(2),MATLABprogrammingcanbeprepared todeterminebelowYbus.

INPUT DATA [3]

Table 1:YBusSystemResultsOfSystemSimulation

DIRECT METHOD

Stepsfortransientstabilityanalysisusingdirectmethod:

1. Usingpostfaultsystem,criticalenergy(Ec)is determined.CriticalEnergyformulaisgivenby,

2. Criticalenergyisdeterminedwithrespecttostable equilibriumpoint(SEP)ofpostfaultsystem,thatis why first stable equilibrium point of post fault system is determined. Formula of critical energy withrespecttoSEPisgivenby,

3. Critical energy is the total energy at Unstable Equilibrium Point (UEP). Speed of synchronous generator rotor at unstable equilibrium point is zeromeanskineticenergyofthesystemiszeroat UEP.CriticalenergyatUEPisgivenby

4. UsingFaultonsystem,Totalenergy(Es)justafter thefaultclearingtimeisdetermined.

5. Total energy (Es) and Critical energy (Ec) is compared,

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 13 Issue: 06 | Jun 2026 www.irjet.net p-ISSN: 2395-0072

5. ARTIFICIAL INTELLGENCE- NEURAL NETWORK (ANN) METHOD

Artificial Neural Network (ANN) is a data-driven approachthatcanbeusedfortransientstabilityassessment and Critical Clearing Time (CCT) prediction. Unlike conventional methods, ANN does not require repeated numericalintegrationofswingequationsaftertraining.The ANN learns the relationship between system operating conditions and stability status from previously generated simulationdata.

In the present work, a Feed-Forward Neural Network (FFNN)isemployedtoestimatethetransientstabilityofthe consideredtwo-machinenine-bussystem.Trainingdataare generated using the Time-Domain Simulation Method. Differentfaultclearingtimesareappliedtothesystem,and the corresponding stability status is recorded. The fault clearingtimeisvariedfrom0.01sto0.25swithastepsize of0.01s.

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056

Volume: 13 Issue: 06 | Jun 2026 www.irjet.net p-ISSN: 2395-0072

6. Comparison of methods

7. CONCLUSION

Transientstabilityanalysisofmultimachinesystemusing timedomainmethodismoreaccurateandslowerthandirect method.ArtificialIntelligencemethodresultshowsnearto time domain method which is more accurate. This comparison becomes possible using Critical Clearing Time (CCT)forthesystem.

REFERENCES

[1] IEEE/CIGRE Joint Task Force on Stability Terms and Definitions, “Definition and classification of power systemstability,”IEEETrans.PowerSyst.,vol.19,no.2, pp.1387–1401,May2004.

[2] P. Kundur, “Power System Stability and Control” New York:McGraw-Hill,1994.

[3]P.M.AndersonandA.A.Fouad,“PowerSystemControl and Stability” 2nd ed. Piscataway, NJ, USA: IEEE Press 2003.

[4]SinaYamacCaliskanandPauloTabuada,“Compositional Transient Stability Analysis of Multi machine Power Networks”, IEEE transactions on control of network systems,vol.1,no.1,march2014.

[5] Ramnarayan Patel, T. S. Bhatti and D. P. Kothari, “MATLAB/Simulink-basedtransientstabilityanalysisof a multimachine power system” IJEEE, vol.39, no.4, October2002.

[6] Dr. S. Kalyani, M. Prakash, G. Angeline Ezhilarasi, “TransientStabilityStudiesinSMIBSystemwithDetailed MachineModels”,IEEEConferenceRecentAdvancements inElectrical,ElectronicsandControlEngineering,2011.

[7]Hsiao-DongChiang,“DirectMethodsforStabilityAnalysis ofElectricPowerSystemsTheoreticalFoundation,BCU Methodologies,andApplications”,AJohnWiley&Sons, Inc.,Publication,2011.

[8]LewisG.W.Roberts,AlanR.Champneys,KeithR.W.Bell, and Mario di Bernardo, “Analytical Approximations of CriticalClearingTimeforParametricAnalysisofPower System Transient Stability”, IEEE journal on emerging andselectedtopicsincircuitsandsystems,vol.5,no.3, September2015.