TECHNICAL SIMULATIONS AND MEASUREMENTS OF CAGE-SWITCHING AT THE INDUCTION MACHINE. Tulbure Adrian*, Risteiu Mircea**

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1 TECHNICAL SIMULATIONS AND MEASUREMENTS OF CAGE-SWITCHING AT THE INDUCTION MACHINE Tulbue Adian*, Risteiu Micea** * Univesity of Petosani ** Univesity 1 Decembie 1918 Alba-Iulia Abstact: In the pesent pape the dive system with double-cage induction machine using diffeential equations will be mathematically modelled and simulated. The mathematical models epesent the wavefoms of electomagnetic quantities associated with the stato and oto cicuits as well as coesponding mechanical quantities. Fo examing the chaacteistic pefomance of the induction machine by switching between cages, the simulato softwaes MATLAB and NETASIM have been used. The simulated cuent- and toque-wavefoms will be compaed with the expeimental values. To pactical validation of the esults a mains opeated induction machine with woingcage contolle have been designed and tested in the Institute of Electical Powe Engineeing in Clausthal, Gemany. Keywods: induction machine, dive sistem, cage switching, mathematical model, measuements, wavefom. 1. SIMULATION AND VALIDATION OF THE SINGLE CAGE INDUCTION MACHINE As an electical pat, the Induction Machine (IM) with diect connection to the powe netwo (Fig.1) possesses dampe and sping popeties. The moto attenuation and the moto sping chaacteistics depend on the excitation fequency ωa, speed of otating field ωd, beadown slip sk and beadown toque espectively MK (Bec et al., 1), (Tulbue, 3). The mechanical pat (Fig.1) is assumed to be, with cetain simplifications, a mathematical model of a two-mass-oscillato. This is chaacteised by the following mechanical paametes: masses with inetia (J1,J), damping (b), sping stiffness (c) and the natual (self) fequency (fe) (Richte, 1983). The mathematical model of the dive system with the mains-opeated IM (Fig.1) can be descibed analytically afte lineaization by the following equations: Fig.1 Stuctue of the dive system. 1. load as DCmoto,. flexible shaft, 3. one-cage induction machine, 4. double-cage induction machine

2 ) M M = bm p + cm 1 (1) ( α M = J p 1 α + W () 1 W = b p α α ) + c ( α ) (3) ( 1 1 α W = J p α + L (4) d i d ω i = α p = (5) whee: J 1 moto inetia; J load inetia M M moto toque; M W shaft toque ML load toque p Laplace opeato b attenuation coefficient of the shaft c sping coefficient of the shaft b M attenuation coefficient of the moto c M sping coefficient of the moto ωi otation speed of the system α1, α mechanical angle of the moto espectively load. ω A v = specific excitation fequency s ω d λ = s aveage slip s The moto coefficients c M and b M depend on the excitation fequency ω A, speed of otating field ωd., beadown slip and toque s K espectively M K (Richte, 1983), (Bec et al. 1) and can be calculated as follows: c b M = s K v = (1 + λ ) (1 + v λ ) [(1 + λ v ) + 4 v ] (1 + v 3 λ M [(1 + λ v ) + 4 v ] M M K 1.1. Simulation in the fequency domain ) K (6) (7) Fom the elations pesented above, the diffeent tansfe functions fo the electomechanical system can be calculated. In ode to analyse the dynamic behaviou of the IM in fequency domain, the Bodediagam fo the signal path W L has been simulated with the help of the MATLABsoftwae. The tansfe function F(p) shaft-toque load-toque fluctuation is descibed by the following equation (8). F ( p) = ( J 1 p + b M M [ J p + ( b + b) p + c ]( J 1 p + bp + c) ( bp + c) 1 M M p + c ) ( bp + c) Fig. Bode-diagam of the tansfe function F(p)= M W ( p) L ( p) in coelation with excitation fequency ωa,and the slip value s. The tansfe function (8) will have the following final fom (polinomial function of 7 ode): a p + a6 p a1 p + a F ( p) = (9) b p8 + b p b p + b Fom this, the oscillation magnitude will be obtained: { F} jim{ F} F ( jω A = log Re + (1) db Figue shows the fequency esponse chaacteistic fo the tansfe function F(p) (Matlab, 5) as a function of the stationay opeating point (slip) of the machine. In this diagam a scaling up to the factos =5 db (at no-load opeation, s=%) espectively 3=1dB (at the load opeation mode with s=7%) is to be obseved. 1.. Simulation in the time domain The whole electomechanichal system has been modelled using a new pogammed maco-bloc of the simulation pogam (Netasim, 199). The dynamic model of the induction moto is descibed within a system of coodinates with two ectangula axes α and β. The geneated toque (11) can be expessed in tems of oto cuents and oto flux linages (Schöde, 1). The load toque will be epesented (1) though the Load Input Function: M M M L 3 = Z p ( Ψβ iα + Ψα iβ ) (11) = M + L sin Ω At (1) whee: M = basic load toque L = amplitude of the Load Input Function Ω A = πf A = excitations fequency Ψ α, Ψ β α- and β- components of the oto flux linage i α, i β α- and β-components of the oto cuent Zp numbe of pole pais.

3 Table 1. Paametes of the fist test bench Paamete Value AC-Moto powe, P NAC 3 W Nominal speed, n N 147 min -1 Nominal toque, M N 195 Nm DC-Moto powe, P NDC 3 W Moto inetia, J 1.35 gm Load inetia, J.83 gm Natual fequency of mechanical system, f a 14.7 Hz Shaft damping, b 6.3 Nms Shaft stiffness, c 1 Nmad The efeence values fo the load wee extenally poduced by the signal geneato and given to the evesible dc-convete. This thyisto-convete feeds the excitation cicuit of the dc-machine to geneate in this way the LIF. The shaft-toque MW has been oscillogaphed in the XY Wave-Fom in dependance on the excitation fequency fa (figue 4). Fig.3 Nomalised load-toque ML_No, shaft-toque MW_No and excitation fequency fa_no. Simulation (top) basic load ML=5% and amplit..ml=5%. (bottom) basic load ML=1%and ampl..ml=5%. This moto toque, which is estimated by elation (11), is tansmitted to the mechanical pat. The simulated cuves (figue 3) have been digitally geneated by the NETASIM- Softwae. On the Yaxis ae epesented the values of the load-toque, shafttoque and excitation fequency elated to the nominal values MN=195 Nm espectively fn=5 Hz. The time is shown on the X-axis Expeiments of single cage IM The simulation esults have been validated with measuements at the test bench. The test bench fom fig.1 is available at the Institute fo Electical Powe Engineeing at the Technical Univesity of Clausthal in Gemany (Tulbue, 3). Fo the fist expeiment this bench is composed of single cage induction machine, convete-fed DCmoto to geneate the Load-Input-Function (LIF) and the flexible shaft between the masses. Some impotant paametes of this bench ae contained in the table 1. Fig.4 XY-Fomat of the shaft toque in dependence on the excitation fequency fa. Expeimental esults (top) basic load ML=% and amplitude.ml=5% and (bottom) ML=1% and amplit..ml=5%.

4 In fig. 4 the measuement esults fo the shaft toque in dependence on the stationay opeating points ae pesented. The esults show that the shaft toque magnitude is a function of the stationay opeating point (slip) of the machine (Richte, 1983). Two esonance places ae to be obseved at about f1=4 Hz and f=18 Hz (fig.4), espectively ω1=5.1 1s and ω= s in figue (. s..).. SIMULATION AND VALIDATION OF THE DOUBLE CAGE INDUCTION MACHINE In the second investigations step the fequency esponse of the tansfe function G(p) shaft-toque load-toque fluctuation fo the double cage induction machine (Fig.5) has been simulated. W ( p) G( p) = (13) L ( p) The esults show that lie in the fist step, the shaft toque magnitude is a function of the stationay opeating point (slip) of the machine. Slip is a moto popety which depends on the oto paamete. Fo the mains opeated machine with double cage, two esonance sites (simulation Fig.5 cuve b) and measuement (Fig.6) at about f1=4 Hz and f=17 Hz can be obseved. The measuements (see the wavefoms in Fig.6 top and bottom) confim the afimation, that the damping capacity is much highe fo the induction machine with stating cage only. The poposed combination to adjust the shaft oscillations is based on this statement, as moe oto esistance as little oscillations amplitude. This concept has been applied in the pactice fo the double-cage induction machine (DoCa-IM). In this case the vaiation of oto paametes (R`L and X`L) is achieved by tun-on and -off between the cages with help of the Switching Device (DE) see Fig. 7 Fig.6 Measuement of the shaft-toque M W as function of the excitation fequency f A : a) IM with stating cage only; b) double cage IM. 3. DESIGN OF THE MACHINE WITH SWITCHING CAGES 3.1.Simulation in the time domain By the new machine the seconday cicuit fom Fig. 7 is chaacteised by Ra, La common esistance and inductance fo both cages, LA, LB and RA, RB stating cage and woing cage inductance espectively eactance. The pefomance chaacteistics of the machine depend on the oto cuent distibution in the stating o woing cage (Leonhad,1997). Fig.5 Bode-diagam of G(p) fo the double cage IM a) with stating cage only b) with both cages. Fig.7 Equivalent electical cicuit of the DoCa-IM with switching device (DE).

5 Tab. Chaacteistic data of the double cage induction machine Paamete Symbol Value P.u. Nominal slip s N. Beadown slip S.1 1 Stato esistance Rs (Ω) Stating cage esist. R A ( Ω) Woing cage esist. R B ( Ω) Stato leaage eactance R Sσ (Ω) Stating cage leaage eactance x A ( Ω) Woing cage leaage eactance x B ( Ω).95.1 Roto leaage without sin x S ( Ω) Mutual eactance X H ( Ω) Nominal impedance Z (Ω) In ode to obtain good simulation esults it is necessay to identify the electical paametes of the model (Tab.). The used mathematical model (Leonhad, 1997) of a machine consists of: equations of the electical cicuits, esp. stato and oto windings (eq.14) and (15); equations of the electomagnetic field inside the machine (16, 17); equations of the mechanical motion of the oto (11,1). Will be selected the flux as state vaiable, the equations (14) and (15) can be ewite: dψ1 u1 = 1 i1 + TN + j ω K Ψ1 (14) dψ u = i + TN + j ( ω K ωle ) Ψ (15) Ψ 1 = x1 i1 + xh i (16) Ψ = x h i1 + x i (17) Will be selected the flux as state vaiable, the equations (14) and (15) can be ewite: d & Ψ c c & Ψ1 1 u1 TN = + & Ψ c c & Ψ 1 1 u (18) Fom the complex maticial equation (18) esults the elation (19) with the notations ()...(3): I TN ψ& = B ψ + I u (19) [ ψ1a ψ1b ψ A ψ B ] T [ u ] T 1A u1b u A u B N ψ = () u = (1) 1 1 I = () 1 1 b11 b1 b13 b14 b1 b b3 b4 B = ( bij ) b31 b3 b33 b = 34 b41 b4 b43 b44 (3) The elements of the matices aij, bij, cij ae calculated using the paametes fom the Tab Pactical ealisation The stating cage (top winding), being of highe esistance RA and lowe leaage inductance LA, is placed below the oto suface. In the woing cage (bottom winding) in contast, because the bas ae located deep in the ion, the leaage inductance LB is highe. Because of RA > RB and LB > LA the two cages ae electically complementay. The switching unit (DE) is composed of an electonically powe switch (ES) and a micocontolle (µc). The ES is able to switch the woing cage off and on and consists of a combination of multiphase ectifie with Schottydiodes and an IGBT-beae. The necessay signals fo the command of the semiconducto which is geneated by the micocontolle, ae sent fom the stato to the oto though a tansmission system (Tulbue, 3). Fig.8 Thee phase induction machine with cageswitching. (top) oto with integated powe electonics (bottom) thee phase stato.

6 4. EXPERIMENTS BY MACHINE WITH SWITCHING CAGES 4.1. Measuement infastuctue The induction machine is connected diectly to the thee phase powe supply netwo. With the help of a metteing shaft the signal coesponding to the toque values in the shaft (mw) is acquisited and pocessed. The load toque (ml) is geneated though a dcmachine. The cuent and voltage ae acquisited fom stato side only fo one phase, because the moto is consideed as a symmetic consume. The switching signal on the gate of in oto integated tansistos Upwm, is deliveed on the one micocontolle pot. 4.. Compaison of the simulated and expeimental esults In fig. 1 and 11 the esults in time domain coesponding to the analyzed signals, load toque ml, shaft toque mw, phase cuent i1 and contol signal Upwm ae pesented. In the case of simulation fom fig.1 the esults ae nomalised to the nominal values of toque and phase cuent. Fig.11 Measuements of load-toque m L shaft-toque m W, phase cuent i1,collecto cuent ic and oto time facto τ The wavefoms show a good coespondance of the simulation with the measuements. The switching tas will be caied out by the semiconducto device mounted in the oto of the machine. This switching unit mae possible a dynamic and low-loss adjustment of the chaacteistic cuve of the moto. Compaisons of un tests have been demonstated that the amplitude of the shaft toque oscillations can be adjusted by switching between stating and woing cage of the machine. REFERENCES Fig.9 Peview of the measuements systems Fig. 1 Simulated wavefom of load- m L shaft-toque m W, cuent i l and oto time facto τ Bec, H.-P.; C. Souounis, A. Tulbue (1), Schwingungsdämpfung in Antiebssystemen mit Doppeläfig-Asynchonmaschine. VDI-Beicht N. 166, pp , Düsseldof. Leonhad, W. (1997), Contol of electical dives, pp , 4-65, Ed.Spinge. Belin MATLAB 7.1. (5), Use Manual, The MathWo Inc., USA 5 NETASIM.5 (199), Benutzehandbuch, Daimle- Benz AG, Belin 199 Richte, K. (1983), Vehalten von Antiebssystemen mit Asynchonmotoen bei ezwungenen Schwingungen, Feibege F-Hefte, pp , Leipzig. Schöde, D. (1), Eletische Antiebe. Regelung von Antiebssystemen, pp.4-434,84-81, Ed.Spinge, Heidelbeg. Tulbue, A. (3), Netzgespeiste Asynchonmaschine mit eletonische Käfigumschaltung zu ativen Schwingungsbedämpfung. Doctoal Thesis, Univ. of Technology Clausthal, Gemany