OPTIMAL FLUX LOSS MODEL BASED OF SPEED SENSORLESS VECTOR CONTROL INDUCTION MOTOR Emad Hussein, Peter Mutschler Technische Universität Darmstadt, Darmstadt, Germany Email:
[email protected]
Abstract The paper presents a cheap and accurate loss model based controller to improve the efficiency and the power factor of the speed sensorless controlled induction motor. The proposed controller calculates the optimal air gap flux verifying high efficiency especially at light load, improving the power factor, and stable operation for a high load step disturbance. The proposed model is cheap where no additional hardware is required. The accuracy and the fast response of the proposed controller in comparison with an online search control method are proved by the experiment results. The efficiency, and the power factor improvements for speed sensorless induction motor by using the optimal flux compared with the rated flux are examined experimentally.
1 Introduction An improved efficiency of the three-phase induction motor is considered to be a major subject for energy saving, as most of the electrical power consumed in industry is used in induction motors. In an effort to improve the motor efficiency, there have been improvements in the design techniques [13, 15] (not available for motor already working). In many applications, an additional substantial energy saving is possible by changing from constant speed drives to variable speed (i.e. converter fed) drives and implementing new methods to calculate the optimal air gap flux. The strategies to improve motor efficiency are: 1) search control method (SC) and 2) loss model based controller (LMC). In a search controller the motor input power is measured, and one physical quantity such as air gab flux or stator current or DC current is varied till the minimum input power is detected for a given load torque and speed [3, 4, 6, 9]. The drawbacks of the search controller are: 1) slow convergence and torque variations 2) extra hardware is required. But in the loss model-based control [2,5-8,10,12,14] the optimal efficiency value is calculated depending on the calculation of the total motor losses, and selects a flux level that minimizes the losses. The LMC overcomes the drawbacks of a SC method, where it is fast, does not produce torque variation, and can used for a speed sensorless controlled induction motor as in this paper.
The accuracy of the LMC depends on the correct modeling of the motor losses. In [8] the optimal flux at steady state is calculated, as function in the stator current, but it does not include the saturation effect. By neglecting the stray and mechanical losses a simple LMC is proposed in [5,7,12]. In [6] the optimal efficiency point is found by equalizing the losses related to the torque producing current with the losses related with the field producing current by help of a PIcontroller. A hybrid method is proposed in [2] using a LMC and SC where the first estimate is from the LMC and the subsequent adjustment of the flux is through the SC. But the LMC is sensitive to the loss model inaccuracies, and parameters variation. So in this paper, the new expression for the optimal flux is calculated from an accurate LMC, where motor losses consists of the copper loss, iron loss, friction, windage, stray, and harmonic losses, are represent as function of the air gap flux, including the non-linearity of the magnetizing inductance and the effect of the temperature on the motor parameters (stator and rotor resistances). This is described in section 2, 3, and section 4. The proposed LMC that is used in improving the efficiency for a speed sensorless controlled induction motor is described in section 5 and 6. Experiments results showing the benefits of the proposed controller compared with SC are included in section 7. Conclusions are given in section 8.
2 Induction Motor Variables The single-phase equivalent circuit of the induction motor at steady state is shown in Fig.1. The following symbols are used in this paper. Rs: stator resistance Rr: rotor resistance (referred to stator side) Rstr: Strays resistance Rfe: magnetic loss resistance Xs: stator leakage reactance Xr: rotor leakage reactance (referred to stator side) Xm: magnetizing leakage reactance S1, S2, S3: magnetizing curve coefficients Cfw: friction and windage coefficient Ke,Kh : eddy, hystresis coefficients V: supply voltage E: air gap voltage T: electromagnetic torque P: pole pairs I : Air gap flux
1) Copper losses: The electric losses in the stator and rotor winding. Temperature and influence of skin effect of the winding would be necessary for a correct copper losses calculation. To circumvent this, the rotor resistance is estimated on-line by using a model reference adaptive control (MRAC) [16] as shown in fig. 2. The rotor resistance is the output of a PI controller. The input of the PI controller is the stator resistance voltage drop ( i ds R s ) minus the decoupled voltage
I opt : Optimal air gap flux n: rotor speed fs: supply frequency Ȧs: angular supply frequency =2ʌfs Ȧ: angular motor speed= 2ʌ n Ȧe: electrical angular rotor speed = Ȧ*P s: slip Is: stator current Ir: rotor current Im: magnetizing current R
R
s tr
I
s
S
V
X
(V
E
s
X
I R
m
m
).
For a step change in the rotor resistance from 2.1 ohm to 4.2 ohm, the MRAC method can track a step change in the rotor resistance in less than one second as shown in fig. 3.
Xr
Im
d_d
r
R r/ s
cu rren t con tro l via de cou plin g syn . fram e vo ltage
syn. frame IM elec. model
V d_d
From the equivalent circuit Fig. 1, the following expressions are deduced. (1) E ZsI , Im ZsI / X m As the magnetizing reactance is highly nonlinear, the magnetizing curve is expressed as follows: (2) I m S 1I S 2I3 S 3I5 From equations (1) and (2) the magnetizing reactance is. X m Z s I / I m Z s I /(S 1 I S 2 I 3 S 3 I 5 ) (3) X m Z s /(S 1 S 2 I 2 S 3 I 4 ) Ir
E
2
§ Rr · 2 ¨ ¸ X r © s ¹
ZsI
Ir2
Rr §1 s · ¨ ¸ Z © s ¹
Rr §1 s · ¨ ¸ Ze © s ¹
P Ir2
(Z s Z e ) Z s PI
2
(8)
For simplicity neglecting the effect of the rotor leakage reluctance X r , the stator current is. (9) I s2 # I r2 I m2 Combining (1) and (5) into (9), the stator current relation becomes. 2
2
§ Zs · § sZ s · 2 2 I s2 # ¨ ¸ I ¸ I ¨ © Rr ¹ © Xm ¹
i qs
Rr
4 .5 4 3 .5 3 2 .5 2
0 .5
1
1 .5
Fig.3 Rotor resistance estimation
(7)
sZ s R r
PI
1 /(R S V L s U )
(6)
From equation (5), (6), (7) we obtain T
Vq
T im e ( s e c )
And the slip is.
s
V d_d
VZ s L S
Fig.2 MRAC for rotor resistance estimation
(4)
The electromagnetic torque relation is. T
PI
i ds
i qs
i ds
(5)
r
RS
r
Ir # sZ sI R
V Z sL S
The induction motor operates with a small slip, so 2 § Rr · 2 holds and the rotor current is approximated as ¨ ¸ ²² X © s ¹
1 /(R S V L s U ) ZsLS
i qs
Rotor Resistance (ohm)
2
Vd
ZsL S
And the rotor current expression is. § Rr · 2 ¨ ¸ X r © s ¹
i ds
Fig.1 Induction Motor equivalent circuit
P I
(10)
The stator resistance is assumed constant, based on assuming a constant winding temperature of 80 0C. Where 80 0C represents half the Class F allowable temperature rise at 40 0C ambient [16]. So the stator and rotor copper losses are: Pcu , s I s2 R s , Pcu , r I 2r R r 2) Iron losses: Losses due to eddy currents and hystresis.
P
K 1 s Z 2
fe
e
2 s
K h 1 s Z s . I
2
The terms, which contain the slip (s), are related to the rotor iron losses. When the motor operates under normal condition (s
