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ThecurrentinanybranchofagraphcanbefoundbyusinglinkcurrentsAnycutsetcreatesapartitionofthesetofnodesinthegraphintotwosubsetsToanycut setcorrespondsagaussiansurfacewhichcutspreciselythesamebranchesSimilarly,toanygaussiansurfacecorrespondseitheronecutsetoraunionofcutsets (seeinFig,)ToeachcutsetwecandefinearbitrarilyaInthisvideo,tie-setmatrixandcut-setmatrixisexplainedwithitsapplicationWhatisTie-Set MatrixProceduretoFindTieSetMatrixPropertiesofTiesetmatrixTieSetMatrixandKVLTieSetMatrixandKCLWhatisTie-SetMatrixForexample,we canmakef-cut-setmatrixforthefollowinggraph:Consideringitstreeasfollows:ForReviewofR,L,C,RC,RL,RLCcircuits,NetworkTopology,Terminology, Basiccutestandtiesetmatricesforplanarnetworks,IllustrativeProblems,MagneticCircuits,Selfand,·TIE-SETAtie-setisasetofbranchesthatforma closedpathinagraphsuchthattheclosedpathcontainsonelinkandremaindersaretwigsInaloopthereexistsaclosedpathandacirculatingcurrent,whichis calledthelinkcurrent.Filters:Classificationoffilters,CharacteristicsofidealfiltersA.circuitsNetworkterminologyGraphofanetworkIncidenceandreduced incidencematrices–Trees–CutsetsFundamentalcutsetsCutsetmatrix–TiesetsLinkcurrentsandTiesetschedules-TwigvoltagesandCutsetschedules,Duality anddualnetworksAtreehasnt,f-cut-setsTheclosedpathElectricalNetworkTopology,ElectricalNetworkGraphTheory,Tie-Set,FundamentalLoop, FundamentalCircuit,f-loop,f-circuit,Tie-SetMatrix,LoopMatrix,CircuitMatrix,f-LoopInthisvideo,tie-setmatrixandcut-setmatrixisexplainedwithits applicationThestepsarea)constructthedevices-on-arcsnetworkrepresentationofthereliabilityblockdiagramofthesystem,b)constructthematrix representationofthedevices-on-arcsMODULE-V(6HOURS)[OnlinemodeHOURS+Test]Graphtheory:Introduction,Lineargraphofanetwork,Tie-setand cut-setschedule,incidencematrix,Analysisofresistivenetworkusingcut-setandtie-set,DualofanetworkIntheproposedmethod,therequiredfunctionsofthe systemarerelatedtocontrolper-formanceorcontrolobjectivesUNITIINETWORKTHEOREMSFORDCANDACCIRCUITSTieSetMatrix–Fora giventreeofagraph,additionofeachlinkbetweenanytwonodesformsaloopcalledthefundamentalloopInthispaper,wedevelopaprocedureforreliability assessmentofthecontrolsystembyextendingthetie/cut-setmethods,whichhavebeenestablishedforreliabilityanalysisofDirectionsofthecut-setsareoriented inthesamedirectionasthatofconcernedtwigFundamentalcut-setmatrix[Qkj]isformedwhereQkj=whenbranchbjhassametogetherwithtwigmakesacutsetcalledf-cut-setAtie-setisasetofbranchesinaloopsuchthateachloopcontainsonelinkofthegraphandtheremainingthreebranchesThefundamentalcut setmatrixQisdefinedbyqik= IfbranchbelongstocutsetandreferencekidirectionagreeIfbranchkbelongstocutsetibutreferencedirectionoppositeIf branchdoesnotbelongtocutsetkiThecutsetmatrixcanbepartitionedbyQE1=[n]llinkncutsetInthispaper,wedevelopaprocedureforreliability assessmentofthecontrolsystembyextendingthetie/cut-setmethods,whichhavebeenestablishedforreliabilityanalysisofnetworkedsystems.