Scalar control structure of an asyncronous motor at maximum torque.

Chioncel, Cristian ; Chioncel, Petru ; Gillich, Nicoleta 等

1. INTRODUCTION

The speed control at asynchronous and synchronous machine is realised in presents through the modification of the frequency of the voltage supply, based on the fundamental principle:

[n.sub.1] = [f.sub.1] / [p.sub.1] (1)

where [n.sub.1]--speed of the stator rotating magnetic field, [f.sub.1] frequency of stator voltage, [p.sub.1]--number of pair pools.

The number of pair pools can be changed, but difficult, through construction rates, but not enough precisely, so that the only solution is to change the frequency of the voltage supply.

The control of the asynchronous machine is studied in many papers and different publications (Garlasu et al., 2007), where complex control methods are proposed, with difficult practical implementation. The proposed method, with variable rotor pulsation during the speed up acceleration, [[omega].sub.r], is simpler and presents a high efficiency, as the obtained results are showing.

In further research, the proposed method will be studied in the case of constant rotor pulsation [[omega].sub.r] during the speed up acceleration.

2. CONTROL SCHEME FOR MAXIMUM ELECTROMAGNETIC TORQUE

The control algorithm for ASM realize the speed [rpm] control by: constant stator flux [[psi].sub.s], constant useful flux [[psi].sub.h] and constant rotor flux [[psi].sub.r]. By constant stator flux, we obtain the highest values for the electromagnetic torque, by constant useful flux with 20% luster, and the lowest values are obtained by constant rotoric flux, case where the dynamic characteristics are linear and ideal for rapid controls.

The lowest currents at the same rotation speed are by rotoric constant flux and the highest, by stator constant flux (Biriescu , 1997).

Next we propose a control scheme by maximum electromagnetic torque, maxim through the entire control period. The maximum torque value is given by the value of the rotor flux [[psi].sub.r] and maximum allowed rotor pulsation [[omega].sub.r], taking in account the limitations dictated to the stator current, so that the maximum current protection should not act.

The maximum torque is achieved at the maximum values of the rotoric current and flux (Babescu et al, 2005):

[M.sub.max] = 3 [p.sub.1] [[psi]sub.rmax] [I.sub.rmax] (2)

where [[psi].sub.rmax] = [[psi].sub.rN] (nominal rotoric flux) and [I.sub.rmax]--maximal allowed value for the rotor current.

The maxim rotor current (Babescu et al, 2005) is limited by the maxim allowed value for the statoric current, based on the relation (Biriescu, 1997)

[I.sub.rmax] = [[omega].sub.r] M / [square root of [R.sup.2.sub.2] + [([[omega].sub.r] [L.sub.2]).sup.2]] [I.sub.sadmx] (3)

where M--electromagnetic torque, [R.sub.2]--rotor resistance and [L.sub.2]--rotor inductance.

The allowed stator current, [I.sub.sadm] is known from the catalogue data and can vary between the nominal value [I.sub.sN] and k times higher as the nominal value, depending on the machines load (given by the number and length of control cycles during on hour).

From the value of the current [I.sub.sadm], using the relation (Quang et all, 2005)

[I.sub.sadmx] = + [psi] rN / [MR.sub.2] [square root of [R.sup.2.sub.2] + ([[omega].sub.r] [L.sub.2]).sup.2]] (4)

the computing rotor pulsation [[omega].sup.*.sub.r] will be calculated (for [DELTA] [[omega].sub.mec] > 0.5, the case NO in figure 1):

[[omega].sup.*.sub.r] = 1 / [L.sub.2] [square root of [([MR.sub.2] [I.sub.sadm] / [psi] rN).sup.2] - [R.sup.2.sub.2]] (5)

In this way the computing statoric pulsation [[omega].sup.*] can be work out with the relation:

[[omega].sup.*] = [[omega].sub.mec] + [[omega].sub.r.sup.*] (6)

With [[omega].sup.*] and [[omega].sub.r.sup.*] determinate, the stator voltage, that changes also, will be computed:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

The described steps, included in a structural scheme for speed controlling (Chioncel, 2008), for maximum allowed acceleration, on reasons of maxim allowed rotor flux and maxim allowed stator current, is presented in figure 1.

[FIGURE 1 OMITTED]

During the acceleration period, the maximum torque value is reached and assured through maximal values of the voltage and frequency. When the prescribed value of the rotor speed [[omega].sub.mec] is achieved, voltage and frequency returns to values regarded by the stationary regime, adequate to the prescribed value.

The electromagnetic torque, in stationary regime and for [[omega].sub.mec] = [[omega].sup.*.sub.mec] has the same value with those of the resistant torque [M.sub.rez] His value is computed from the movement equation:

[M.sub.rez] = [M.sub.elmg] - J d [[omega].sub.mec] / dt (8)

From this value of the resistant torque, by nominal rotor flux, the rotor pulsation will be computed:

[[omega].sub.r] = [R.sub.2] [M.sub.elmg] / 3 [p.sub.1] [[psi].sup.2.sub.rN] (9)

3. COMPUTING AND SIMULATION RESULTS OF THE PROPOSED ALGORITHM FOR AN ASM

The simulation results are obtained for an ASM, with the following nominal parameters (Chioncel et all, 2007): L1 = L'2=0.1[H]; [R.sub.1] = [R'.sub.2] = 5[[OMEGA]]; [L.sub.1[sigma]] = [L'.sub.2[sigma]] = 0.02[H]; [sigma] = 0.36, [L.sub.U] = M=0.08H, [U.sub.N] = 380V, [p.sub.1] = 1, [[psi].sub.sN] = 1.2[Wb]

The initial conditions are: stator flux [[psi].sub.s] = 1.2[Wb], [[omega].sub.mec] (0) = 280[rad/s]. To get the maximum acceleration, we need following computing vales

--For [I.sub.Sadm] = 30 [A], the rotor pulsation [[omega].sup.*.sub.r] is:

[[omega].sup.*.sub.r] = 1 / [L.sub.2] [square root of [([MR.sub.2] [I.sub.sadm] / [psi] rN).sup.2] - [R.sup.2.sub.2] = 115 [rad / s] (10)

--Computing stator pulsation: [[omega].sup.*] = [[omega].sub.mec] + [[omega].sup.*.sub.r] = 280 + 115 = 395 [rad/s]

--Stator voltage (7) Us = 696[V].

The accelerations subsist until the prescribed speed is reached, whereupon voltage and frequency get back to the prescribed values of torque and speed: [M.sub.elmg] = 16.66[Nm], n = 2961 [rpm]. For the simulation, in the case where the inertial moment is J = 0,01[kg[m.sup.2]], we get the following results, figure 2:

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

It can be observed that the response time during the speed reaches the prescribed value, is 0.01[s], much lower (ten times) than the control method when the maximum torque is not chose during the control period (Chioncel, 2008).

The initial value of the stator current [I.sub.Sadm] = 30[A] is with 76% exceeded and from that reason, the maximum current protection has to be adjusted by [I.sub.max] = 53[A], figure 3. Taking in consideration the very short time of the transient process, the thermal protection does not act.

During the transient control period, when the electromagnetic torque is maxim, his value is almost double comparing to the case when this value is not maximised (Chioncel, 2008).

4. CONCLUSIONS

The presented computing method for ASM speed control by maximising the electromagnetic torque, represents a modern solution for the automatic control for many electric drive systems meet in practice, where a very quick answer to the appeared perturbations is necessary.

The prescribed speed is achieved in an asymptotic way. As well, the same trend in time has the other values too: stator current, electromagnetic torque, rotor flux.

Until the prescribed speed is reached, the rotor flux exceeds the nominal value, that makes that the motor functions in saturation regime.

The presented control algorithm repeats after a period, so that each change that appears during the control process, are always corrected.

6. REFERENCES

Babescu, M & Paunescu, D. (2005) Analiza matematica a dinamicii masinilor electrice (Mathematical analyze of the dynamic behavior of electric machines), Ed. Politehnica, Timisoara

Biriescu M., Masini electrice rotative. Parametrii, caracteristici, incercari (Rotating electric machines. Parameters, test, characteristics), Ed de Vest Timisoara, 1997

Cristian P. Chioncel, Marius Babescu, Petru Chioncel, Nicoleta & Gilbert-Rainer Gillich, (2007) Speed control method for asynchronous motor Annals of DAAAM 2007 & Proceedings of the 18th International DAAAM Symposium, Zadar 2007, pp. 137-138

Cristian P. Chioncel (2008), Contributii privind controlul turatiei la masina asincrona (Contribution regarding the speed control of asynchronous machine), Seria 1, Nr.9, Ed Politehnica, Timisoara

Garlasu St., Ruja I, Breaban F., (2005) Controlul miscarii (Movement control), Ed Orizonturi Universitare, Timisoara

Quang, Ph. & Schoenfeld, R. (2005) Dynamische Stromregelung zur Drehmomenteinpregung in Drehstromantrieben mit Pulswechselrichter (Dynamic current control for pulsation in alternative machines with pulse inverter), Journal Electrical Engineering, Springer, Berlin, page numbers 317-323