DYNAMIC PERFORMANCE OF RELUCTANCE SYNCHRONOUS MACHINES

Transcription

1 Annals of the University of Craiova, Electrical Engineering series, No 33, 9; ISSN TH INTERNATIONAL CONFERENCE ON ELECTROMECHANICAL AN POWER SYSTEMS October 8-9, 9 - Iaşi, Romania YNAMIC PERFORMANCE OF RELUCTANCE SYNCHRONOUS MACHINES Aurel CAMPEANU, Ion VLA, Monica ENACHE, Ion CAUTIL University of Craiova, acampeanu@emucvro Abstract In the esign stage of synchronous machine an especially of those require by high performance rive systems (for example inustrial robots), often is necessary the preetermination of ynamic characteristics, using moelling an simulation The simulation results an their correlation with reality, essentially epen on the way the synchronous machine is moelle The general mathematical moel [3] is particularize for reluctance synchronous machine On this basis quantitative ata of interest for estimating transient phenomena are obtaine Keywors synchronous machines, ynamic regime 1INTROUCTION In many practical applications the position an the spee must be precisely controlle, regarless the existing perturbations (variations of voltage, of resistant torque, etc) All these requirements can be achieve using external feeback loops which correct the errors of the system [7], [] Another simpler possibility is to utilize the internal feeback loops, part of the operation principle of the riving motor, which allow to get the esire spee or rotor position, without external loops [1], [5] Such motor is the synchronous motor It allows in a simple way to get a spee epening only on the frequency of supply voltage The motors with electromagnetic excitation are utilize at large power, while the reluctance motors an motors with permanent magnets are the best technical an economical solution for small an meium power The reluctance motor presents well known avantages More, utilization of static converters mae possible the spee control with goo performances This is the main reason which allowe the utilization of reluctance motors in inustrial applications The present paper offer the possibility of preetermination of ynamic performance of reluctance motors, essential in precision rive systems BASICS OF THE MATHEMATICAL MOEL Our starting point is given, as usually, by the Park equations of the synchronous machine which are consiere together with the equations connecting flux linkage an currents [] u = [ R][] i + [ [ ] ]; [ ] T = t [ q ] σ + σ + σ + σ + = Ls i m m = Lm im q = Ls iq mq mq = Lmqimq = L i m i m i + i = L i mq i mq = iq + i = (1) The rotor quantities are reporte to stator The mathematical moel of the synchronous machine is consiere to have the form: X q [] u = A + BX q ;[] u = [ u uq ] T () t X q correspons to iverse combinations of state variables an A, B are matrices whose form is etermine by the choice of the state variables (currents only, flux linkages only or some mixture of currents an flux linkages) In the following we consier as state variables the currents of the machine winings In this case, to the state vector the matrices [3] = A Lm q q T X = i i i i correspon to Lmq Lm Lσ L mq Lσ 39

2 Annals of the University of Craiova, Electrical Engineering series, No 33, 9; ISSN Rs ω( ) B = ω( ) Rs ωlm R At equation () we a the movement equation ωlmq R J ω J β m M r = =, p t p (3) t 3 m = p[ ( Lm Lmq ) i iq iiq Lmqi i ] In the referential system, q we consier u = U cos( ω1t β ), uq = U sin( ω1t β ) β = ωt + β The spee of the main magnetic fiel m uring the ynamic processes will be ϕ ω = + ω, (4) t ϕ 1 mq m mq = cos sin ϕ ϕ t sinϕ = m t t m m, cos ϕ =, m = m + mq m The fluxes are simply obtaine, epening on the consiere state variables, see (1) The above notations are those of [3] an use by some authors 3 SIMULATION RESULTS In the sequel we stuy the ynamic performances of a reluctance synchronous machine with star wining an rate voltage U n =V We take into account the particular case of starting an synchronization The effects of leakage inuctance of stator wining, of resistances of, amping winings an also of mechanical inertia J, are especially analyse The propose moel is use The simulations were performe in Matlab using a fifth-orer Runge-Kutta with variable step metho The motor parameters are: R s =5Ω, L sσ =1H, L σ =8H, L σ =6H, L =71H, L q =6H, R = 1,5Ω, R = 3Ω, p=, J=4kgm The curves ω ( t), ω ( t), ( ω) m mq were simulate consiering the rate torque M n =95Nm an various L sσ, R, R, J, which significantly m, ( ) affect the ynamic an stationary performances Figs 1 presents the characteristics consiering the rate parameters The ynamic electromagnetic torque is important in the first moments of starting (Fig 1b) an, consequently, the starting an synchronization process is short (Fig 1a) In Fig1a one can observe too the clear connection between the mechanical an electromagnetic transient processes, in fact one electromechanical process As we can see from Fig 1b, the synchronization process is goo, the steay state point of synchronism being reache practically in the absence of torque oscillations Like the electromagnetic torque the characteristic ( ) m mq in the case of a firm synchronization finalizes in a well efine synchronous operation point (see Fig 1c) The simulations presente suggest that the consiere motor has goo ynamic an stationary performances Figs -6 present the characteristics for ifferent values of R, R, L sσ, J Figs a an b correspon to R = 3Ω One can observe that an increase in R affects, the motor performances The starting process is longer, the electromechanical oscillations are larger an the synchronous operation is reache after relatively important oscillations of the electromagnetic torque Figs 3, 4 consier R = 5Ω an R = 1 5Ω respectively Compare to Fig 1b as a reference, one can see firmly ampe oscillations of electromagnetic torque aroun the synchronous spee (Fig 3) an a prolonge process of ampe oscillations (Figs 4) of the electromagnetic torque in the neighborhoo of the synchronous spee which can affect the motor performances Fig 4b etails these oscillations Figs 5 consiers L s σ = 15H All characteristics show an asynchronous operation In the Fig 5b (an etails in Fig 5c) the close limit cycle inicates the limits in which m(t) an ω () t oscillate permanently at asynchronous operation Like the electromagnetic remain close torque, the characteristics ( ) m mq in a limit cycle (Fig 5) Fig 6 consiers J=1 kgm Compare with the reference characteristics of Fig 1, one can see an increase of uration of ynamical regime (Fig 6a), an as consequence of the number of electromechanical oscillations The ynamical process finalizes as above, with a synchronous operation but with a number of oscillations of larger amplitue, aroun the 4

3 Annals of the University of Craiova, Electrical Engineering series, No 33, 9; ISSN synchronous operation (Fig 6b) The etaile Fig 6c, confirms the absence of a limit cycle, an a final synchronous operation The same conclusion results also from the Fig 6, in which the limit cycle is not present Figure b: Characteristic ( ) ω m, R = 3Ω Figure 1a: Characteristic ω () t, () t ω Figure 1b: Characteristic m ( ω) Figure 3: Characteristic ( ) ω m, R = 5Ω Figure 1c: Characteristic m ( mq ) Figure 4a: Characteristic ( ) ω m, R = 1 5Ω Figure a: Characteristic ω () t, () t ω, R = 3Ω Figure 4b: Characteristic ( ) ω m, R = 1 5Ω, etail 41

4 Annals of the University of Craiova, Electrical Engineering series, No 33, 9; ISSN Figure 5: Characteristic m ( mq ), L s σ = 15H Figure 5a Characteristic ω () t, ω t, L s = 15H () σ Figure 6a: Characteristic ω () t, () t ω, J=1 kgm Figure 5b: Characteristic ( ) ω m, L s = 15H σ Figure 6b: Characteristic m ( ω), J=1 kgm An increase of mechanical inertia of the machine, compare with the reference one in Fig 1, oes not improve the ynamical characteristics Changing the stator resistance R s oes not moify significantly the ynamical characteristics compare with those of Fig 1; the simulation results are not presente 4 CONCLUSIONS Figure5c:Characteristic ( ) ω m, L s = 15H, etail σ The paper presents the particular ynamic moel of the reluctance synchronous machine, consiering the wining currents as state variables Figure 6c Characteristic m ( ω), J=1 kgm, etail 4

5 Annals of the University of Craiova, Electrical Engineering series, No 33, 9; ISSN allows valuable preeterminations, absolutely necessary, for convenient esign of synchronous reluctance motors intene to operate in a require ynamical regime REFERENCES Figure 6 Characteristic m ( mq ), J=1 kgm Many simulations allow the following general conclusion: a variation even in tight limits of the consiere parameters, can unergo structural moifications in the ynamic characteristics The equation (4) contains valuable information about the velocity ω () t of the main rotating magnetic fiel uring the transient processes A close connection between ω () t an ω ( t) is observe in all simulations shown above The consiere moel [1] N Balbo, R anrea, L Malesani, P Tomasin: Synchronous reluctance motors for low-cost, meium perfomance rives, EPE 93, Brighton, vol 6 rives II, 1993, p [] A Campeanu: A New Approach of the Torque Control for the Synchronous Motor with Permanent Magnets, Proceeings of the 7 th International Power Electrics & Motion Control Conference, PEMC'96, Buapest, 1996, p 8-34 [3] A Campeanu, I Cautil: On the Transient Behavior of Saturate Synchronous Machines, Rev Roum Sci Techn Electrotechn et Energ 53, 4, Bucarest, 8, p [4] MA Enache, A Campeanu, C Nica: Aspects Regaring Asynchronous Starting of Reluctance Synchronous Motors, Proceeings of CNAE 8, Timisoara, Romania, 8, p [5] A Fratta, A Vagati: Synchronous Reluctance vs Inuction Motor: a comparison, PCIM 9, Nurnberg, Germany, 199, p [6] VB Honsinger: Steay-State Performance of Reluctance Machines, IEEE Trans on Power Apparatus an Systems, no 1,1991,p