ACTA TECHNICA CORVINIENSIS - Bulletin of Engineering

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ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGAt researching the electromechanical transientsconnected with the speed variations of ACmachine rotor one should consider thesimultaneous solution of the equations deducedabove and the supplementary equation of therotor relative motion. The latter one can bewritten in the following form:dsM = T − T mech(17)dtWhere T mech=shaft torque developed by theprime mover; M =inertia constant.THE PARAMETERS OF THE ALGORITHMIf the influence of the rotor acceleration is nottaken into account the following problemalgorithm considering the rotor speed changescan be suggested:• The transient process is divided into smalluniform intervals of time ;• The speed increment over the given intervalis determined by solving the equation (17) asfollows :T − TΔ s =mech Δt;M• The sustained component of the IS0currentis calculated at the constant speed obtainedfor the given time interval ;• The amplitude of the IS1current componentdecaying with the time constant τaiscalculated at the initial value of the rotorspeed (at the beginning of the first interval) ;• The natural angular frequency, ωn, and thetime constant, τ a, of the aperiodic currantcomponent are re-counted using equation(7),(8) in relation to the slip changes of arotor ;• The amplitude of the IS2current componentcaused by the transient currents in the rotorcircuits is determined at the rotor slipcorresponding to the first instant of theprocess.• It should be pointed out that the angularspeed of the I S2current being taken intoaccount in (10) varies with the slip changes.The rotor slip dependence of the naturalangular frequency and the time constant ofdecaying the magnetic flux ψS1are takeninto account by equation (16).ESTIMATION OF MODEL VALIDITYThe efficiency of application of the frequencyresponsecharacteristics for calculating thetransient process can be demonstrated with thefollowing examples:1. Short-circuit at the terminals of the statorwinding and connection to the network withoutexcitation of the model turbo generator of theMT-3type:(Sxdn=30KVA , V= 1.453; xqn= 414 V, I= 1.394;RS0n= 41.8A,= 0.00624 p.u.)In the case being considered the influence of thesign and initial slip value at connecting thegenerator to the network as well as the influenceof the rotor speed changes at the transientconditions were analyzed.2. Connection to the network of the unexcitedturbo generator of the ТГВ-200 type:Sxnd= 235MVA , V= 1.9; xqn= 1.89;R= 15.75KV, IS0n= 0.0012p.u.= 8635 A,When calculating the electromechanicaltransients the errors being brought about bysimplifying the complicated equivalent circuits,reflecting the electromagnetic of the solid rotor,were considered.3. Starting of the induction motor of the ДАЗО-1914-10/12А type:Pn = 1500Kw;In= 204A; Vn= 6000V from the noloadcondition, and three-phase short-circuit atits terminals.Estimation of the results obtained, when usingthe techniques proposed above, was carried outby comparison with the appropriate calculationsmade by the use of algorithms based onnumerical integrating the system of thedifferential Parc-Gorev equations. Thefrequency-response characteristics reflecting thedynamic properties of the AC machines beingstudied were obtained experimentally from theDC decay in the armature winding at standstilltest [8, 7, 17].Computer programs realizing the abovementioned algorithms for calculating theelectromechanical transients in AC machineswere elaborated within the framework of theMathCAD 7.0.The time-dependence of changing thegeneralized stator current vector and theelectromagnetic running torque at connection702010/Fascicule 2/AprilJune /Tome III
ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGthe unexcited model generator to the networkunder the various initial rotor slips were carriedout without the account and in view ofchanging the rotor speed at transient .Theinvariable rotor speed was simulated by way ofsetting the great value of the inertia constant [9].As follows from comparison of the resultsobtained for the given slip values, equal to 0 ;0.01 ; 0.03 ; 0.05 and 0.1 put., the changes in thetime-dependence of the generalized statorcurrent vector and electromagnetic torquepractically does not differ from the analogouscalculations made on the basis of the Parc-Gorev equations. In these cases the difference inthe maximum values of the similar operatingvariables being compared did not exceed 10.4%.The typical changes in the transients differ not atall. So, when making use of the static frequencyresponsecharacteristics, one can infer that theelectromagnetic processes may be identifiedwith a sufficiently high degree of accuracy.The analysis of the transients calculated withtaking into consideration the rotor speedchanges, following the connection of the modelgenerator, points to some differences in thetime-dependent variables. By way of example, inthe Figure 2 are shown the results of calculatingthe transients at connection the unexcitedmodel machine to the network with the fieldwinding short-circuited.The calculations carried out in compliance withthe system of Parc-Gorev equations (see dottedline) reflect the features connected with changesin the current, I s ,and electromagnetic torque,T , with the rotor speed changes. The timedependence of the slip in the case underconsideration has the oscillatory character.Mathematical simulation based on the staticcharacteristics (see solid line) brings about themonotonous changes in the rotor slip under thetransient process. Meanwhile, the resultant timeof approaching the rotor speed to thesynchronous one, being estimated at the instanta rotor slip for the second time passes throughzero, practically agrees with the time beingdetermined from the solid line obtained atsimulating the transients by means of themethod proposed. As may be seen from theFigure 2.Distinguishing features of the variables beingconsidered are in close agreement; theirmaximum values appearing at the initial stage ofthe transient process correlate well with the datagot without regard for speed changes of therotor. In the Figure 3 are given the curvesreflecting the changes in the variables at theshort-circuit on the terminals of the inductionmotor ДАЗО-1914-10/12А type.Figure 2 Connection to the network of the unexcitedmodel turbo generatorThe quantities of the motor equivalent circuitssynthesized in accordance with [4,10] havingthree parallel branches and the magnetizing one,separated in the manner as is shown in theFigure 1, are as follows (in per unit on machinebase) :RXδ+ Xγ= 2.19 ; X = 0.271 ; X2X3= 0 .717 ;R0 .6241== 0 .0055;R3 12=1.1790 .1139The comparative analysis of the results obtainedby calculating the generalized stator currentvector, Isand electromagnetic torque, T ,calculated by various methods points to theirclose agreement because of the maximumvalues of the mentioned variables differ less than7,8%.The analysis of the electromechanical transientsat starting the non-loaded motor also indicatesto the satisfactory coinciding of the resultsobtained by using the mentioned calculationtechniques. In particular, the starting timedetermined by the technique proposed differsfrom the same parameter obtained through theuse of the Parc Gorev equations less than 9, 2%.2010/Fascicule 2/AprilJune /Tome III 71
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