SPEEDAM 2008 International Symposium on Power Electronics, Electrical Drives, Automation and Motion
Adaptive stator flux estimator for the induction machine Direct Torque Control T. Kasmieh*
[email protected] * Higher Institute for Applied Sciences and Technology, P.O.Box 60318 Damascus, (Syria) Abstract--The paper presents a new stator flux estimator for the induction machine Direct Torque Control (DTC). The study aims to develop an estimator which gives good stator flux feedback values even when the stator resistor varies with the machine temperature. In DTC algorithm, stator electric equation is usually used to calculate the stator flux error. The value of this error is used with the torque error to determine the optimal voltage space vector that gives a simultaneous changing of the torque and the flux in the desired direction. The accuracy of the DTC depends on the proper calculation of the stator flux. The main objective is to build a stator flux estimator depending on the rotor electric equation. Since the time response of the rotor flux is bigger than the time response of the stator flux, this new estimator is less sensitive to the variation of the rotor resistor. The behaviour of the developed estimator is enhanced in an adaptive way to take into account the variation of the saturation level in the air gap of the induction machine.
II. STATOR FLUX ESTIMATOR BASED ON ROTOR ELECTRIC EQUATION
The classical stator flux estimator uses the stator electric equation written in a fixed two-phase reference: Ψ=0, Fig. 1. Vs = Rs I s +
d Φs dt
Fig. 1. Two-phase model of an induction motor
Index Terms--Induction machine saturated model, Direct Torque Control, Stator flux estimation.
Fig. 2 shows simulation results of a 45(KW) induction machine controlled by the DTC with the previous estimator considering that there is a difference of 15% between the motor stator resistor and its value implemented in the control estimator.
I. INTRODUCTION Thirteen years after developing Space Vector Control (SVC) by F. Blaschke in 1971 [1], I. Takahashi and M. Depenbrock presented a new technique for the induction machine torque control called Direct Torque Control [2] [3]. DTC is based on applying the good voltage space vector in order to achieve the desired flux and torque variations. DTC permits to have very fast dynamics without any intermediate current control loops. The main problem with DTC is in the calculation accuracy of the stator flux at each sampling period. Usually, this calculation is easily done by using the stator electric equation. The performance of this flux estimator is highly dependent on the value of the stator winding resistor, which varies with the motor temperature. The paper proposes a new estimator technique that uses the rotor electric equation. It shows that this estimator is less sensitive to the variation of the rotor resistor, but more sensitive to the variation of the saturation level. To overcome this problem, an adaptive estimator is proposed, based on a previous saturation phenomenon study [4]. In order to show the accuracy of the presented flux estimator, simulation results are presented using A_MOS program [5].
Fig. 2. Stator electric equation estimator results with 15% increase for the stator resistor
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III. NEW STATOR ESTIMATOR SENSITIVITY TO THE VARIATION OF THE SATURATION LEVEL.
We see that this difference may cause oscillations to the motor speed, and this problem is more important for low speed. To develop the new estimator we write the stator fluxes as function of the stator currents and the rotor fluxes. From the flux currents relationships:
It is clear that the new estimator will be more sensitive to the variation of saturation level. Fig. 4 shows simulation results using A_MOS program. This program takes into account the variation of saturation level in the motor model, so the cyclic inductances vary with the modulus of the magnetizing current vector [4]. For this simulation a flux weakening phase is done, and a load toque of 110(Nm) is applied. We notice that there is a big difference between the desired stator flux and the real one. This influences the dynamic behaviour of the motor speed.
Φ sd = Ls I sd + MI rd Φ sq = Ls I sq + MI rq Φrd = Lr I rd + MI sd Φrq = Lr I rq + MI sq
we have M .Φ Lr rd M M2 Φ sq = σ Ls .I sq + .Φrq , σ = 1 − Lr Lr Ls Φ sd = σ Ls .I sd +
At each sampling period we measure the stator currents and calculate the rotor fluxes using the rotor electric equations: dΦ rd d ( pθ) = − Rr I rd − Φ rq dt dt dΦ rq d ( p θ) = − Rr I rq + Φ rd dt dt
Where p is the number of pole pairs and θ is the rotor angle. The new estimator does not use the stator resistor, so any change in its value will not influence the behaviour of the estimator. Contrarily, the estimator uses the value of the rotor resistor which determines the time constant of the rotor flux. Fig. 3 shows that for an increase of 15% in the rotor resistor value, the DTC with the new estimator gives better results than those presented in Fig. 2.
Fig. 4. New estimator sensitivity to the variation of saturation level
To overcome this problem we propose to tune the new estimator parameters at each sampling period according to the estimator magnetizing current modulus. The schematic of the DTC using this estimator is presented in Fig. 5.
Fig. 3. New estimator results with 15% increase for the rotor resistor
We note here that the new estimator needs the motor speed at each sampling period.
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This algorithm, proposed in [6], needs to adapt all currents and flux controllers’ parameters. It is important to mention that we can build an estimator that combines the classical estimator and the new one according to the functioning conditions [7]. The classical estimator can be used at high speed, but at low speed, it is better to use the new stator flux estimator. REFERENCES [1] Blaschke, F.: A new method for the structural decoupling of A.C. induction machine. IFAC Duesseldorf (Germany), October 1971. [2] Noguchi, T.; Takahashi, I.: Quick torque response control of an induction motor based on a new concept. IEEE Tech, vol. RM84-76, September 1984, pp. 61-70,. [3] Depenbrock, M.; Steimel A.: High power traction drives and convertors. Proc. of Elect. Drives Symp.’90 - Capri, 1990, pp. I 1–9, [4] Kasmieh, T.; Lefèvre, Y.; Roboam, X.; Faucher, J: Establishment of two-phase non-linear simulation model of the dynamic operation of the induction machine. EPJ European Physical Journal, 1998, pp. 57-66. [5] Kasmieh, T: Presentation of a powerful opened simulator for the saturated induction motor traction system. Proc. of SPEEDAM ’02 - Ravello (Italy), June 2002, pp. A1 24-A1 37. [6] Kasmieh, T.; Roboam, X.; Faucher, J: Vector control law for variable saturation level of an induction motor. ELECTROMOTION, vol. 10, 2003, pp. 93101,. [7] Vas, P: Sensorless vector and direct torque control. Oxford science publication, 2003.
Fig. 5. Adaptive flux DTC estimator
Fig. 6 shows the improvement of the new adaptive estimator.
Fig. 6. 45(KW) motor behavior with the adaptive stator flux estimator
IV. CONCLUSION This paper presents in details a new flux estimator for DTC technique of an induction motor. The estimator uses the rotor electric equation. The estimator is less sensitive to the variation of the motor temperature, but it is more sensitive to the variation of the saturation level. An adaptive solution was proposed to tune the estimator parameters according to the saturation level of the motor. Nevertheless the adaptive part added to the DTC algorithm, its computation time remains very small comparing to the Space Vector Control algorithm that takes into account the variation of the saturation level.
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