ACTA TECHNICA CORVINIENSIS - Bulletin of Engineering

ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGsynchronous machines and induction motorscompiled by now and availability of thedeveloped method designed for synthesising theequivalent circuits adequately reflecting theinitial frequency-response characteristics of theAC electrical machines open up freshopportunities for improving and furtherdevelopment of the frequency-responsemethods for investigating the transients inelectrical machines.The objective of the paper is to develop themathematical models of the AC machines basedon the experimental frequency-responsecharacteristics for investigating the transients atshort-circuits and connections of the ACmachines in electrical system taking intoconsideration the occurring speed changes ofthe AC machine rotor.BASIC RELATIONSThe mathematical relations realising thegraphic-analytical approach [1,2 and 3] todetermining the components of the stator phasecurrent and electromagnetic torque at shortcircuitsor connections of the synchronousmachines rotating at the synchronous speed tothe electrical system are obtained in [5, 10, 11and 18]. When the machine with the rotorasymmetry operates at the short-circuit with thespeed changes relative to the synchronousspeed or it is connected to the network at thegiven slip, determining the components of thegeneralised stator current vector is carried outin the following way:We find the average value of the steady-statecurrent I sfor the s at the first instant of the0 avtransient processI = Y (js(1)avwhereYavs 0 av)s0Yd(js) + Yq(js)(js) =2We determine the pulsating component of thesteady-state current− j2δ0Δ Is0= (Re[ ΔY(js)s0] − j.Im[ ΔY(js)s0]).e (2)whereYd (js) + Yq(js)Δ Y (js) =, δ0=angle between2The q-axis of the rotor and the voltage vector atthe infinite bus of an electrical system;We find the changes in the steady-state currentwith time, taking into account the difference inthe rotor parameters on axes of its electrical andmagnetic symmetry,IS 0(t)− j2 st j. ω.t= (IS 0+ ΔIS 0e ). e(3)avWe determine the aperiodic current componentIS 1 avYav(js)−(1−s)= (4)And the periodic current of the frequency closeto the doubled one− j.2. δ0Δ IS1= (Re[ ΔY(js)−(1−s)]j.Im[ ΔY(js)−(1−s)]). e (5)Aperiodic current and the current componentcaused by the rotor asymmetry are changed inaccordance with the following expressionIS1(t)j. ωn. ω.t−j2(1−S−ωn ) ω.t−t / τa= −[IS1.e −ΔIavS1.e]. e (6)The natural angular frequency of the aperiodeccurrent vector, ω and the time constant of itsndecaying, τa, are defined for the averagecomplex admittance Y av(js) at the slips = −(1− s) by equationsω = Im[ Y (js) ]. R(7)navs=−(1−s)1τa=(8)ω = Im[Y (js) ].R ωnavS0s= −(1−s)S0.The initial value of the periodic component ofthe transient current, is determined byrecognizing thatI S 2I0(t)t=0+ IS1(t)t=0+ IS2(t)t=0S=Generally, the initial value of the current vectorI St does not coincide with the d-axis of a2( )t=0rotor (including the connections of thesynchronous machine occurring at theangle ( δ 0= 0)resulting in aperiodic currentcomponents in both axes of the rotor symmetry.Implementation of the method proposed isassociated with representing the initialfrequency-response characteristics in the form ofequivalent circuits in the d- and q-axis of asynchronous machine. The latter ones, e.g., theequivalent circuit in d-axis shown in Figure1may be used for determining the changes in theperiodic current components with time [6].0682010/Fascicule 2/April­June /Tome III