4 Direct Torque Control Of Induction Motor Using Simulink

Proceedings of the 10th Mediterranean Conference on Control and Automation - MED2002 Lisbon, Portugal, July 9-12, 2002.

TORQUE AND SPEED MODES SIMULATION OF A DTCCONTROLLED INDUCTION MOTOR Nuno M. Silva1, António P. Martins2, Adriano S. Carvalho2 1

MSc student, Faculdade de Engenharia da Universidade do Porto, Rua Dr Roberto Frias, 4200-465, Porto, Portugal, - e-mail: [email protected] 2

Faculdade de Engenharia da Universidade do Porto, Instituto de Sistemas e Robótica, Rua Dr Roberto Frias, 4200-465, Porto, Portugal, - fax: +351 22 5081443, e-mail: [email protected]

Keywords: Converter control, Induction motor, an optimal switching vector, making possible fast torque response, low inverter switching frequency Direct Torque Control, Simulation and low harmonic losses.

Abstract By the huge advantages associated, induction motors drives are still justifying research and development. This paper presents the work developed in Direct Torque Control (DTC) based drives. With a growing importance in several applications, this method was object of a deep study, either in simulation environment and hardware implementation. The reached results confirm some weaknesses and several strengths, pointing out his worth in strength control, particularly in robotics.

1 Introduction

Figure 1 shows the usual block diagram of a DTC controller. Motor ~

~ AC input

Gate signals 1, 2, 3

Switching logic

φ θ τ Φref Tref

+ Φs 2 x +y2 y

x

α, β

Isα Isβ Vsα Vsβ

+

T -

Rs R s

*

+

p

* Φsα Φsβ

-

+ - +

In the past, AC drives were only used in small demanding applications, regardless the advantages Figure 1. Block diagram of a DTC control system. of AC motors opposite to DC motors, since the high switching frequency inverters cost was rather With DTC it is possible to obtain direct flux and competitive. electromagnetic torque control, indirect voltage With the developments in the power electronics and current control, sinusoidal current and flux, area, the vector control methods, which use fast low torque ripple, superior torque dynamics and microprocessors and DSP’s, made possible the use hysteresis band dependent inverter switching of induction motors in typically DC motors frequency [5], [2]. dominated areas, since the current components producing torque and flux are decoupled, achieving the system separately excited DC motor similar features.

Among its main advantages are the absence of: coordinate transformation (which are usually necessary in most vector control drives), modulation specific block, and the absolute The Direct Torque Control (DTC) method, position determination. developed by German and Japanese researchers However, there are some problems during start up [8], [3], allows direct and independent and at low speed values, like the difficulty in start electromagnetic torque and flux control, selecting up current control and high influence of the motor

parameters, as well as variable switching frequency The operation may be described by the following manner: and the need of flux and speed estimators. With the inclusion of a speed estimator in the system, it is possible to obtain gains in hardware complexity reduction and bigger mechanical endurance, making possible the operation in a hostile environment and decreasing the maintenance needs. Simultaneously the noise and motor-load inertia immunity are increased. However it is necessary to use speed estimation techniques, like: open loop estimators, model reference adaptive systems (MRAS), [6]; Luenberger observers, [7]; Kalman filters, [4]; fuzzy logic estimators, [9] or neural networks, [1].

Sk=1 Æ top switch closed, bottom switch opened. Sk=0 Æ top switch opened, bottom switch closed. Assuming that the n point is a virtual neutral, the line-neutral voltage may be evaluated; Vkn, Equation (2):

1  V1n = 3 (2S1 − S 2 − S 3 ) ⋅ Vdc  1  V2n = (2 S 2 − S1 − S 3 ) ⋅ Vdc 3  1  V3n = 3 (2S 3 − S1 − S 2 ) ⋅ Vdc 

(2)

In this paper, it is introduced the work developed in simulation and experimentation associated to the The application of the Clarke transformation implementation of a DTC based, DSP controlled allows the attainment of a generic vector drive, of an asynchronous machine, in torque and expression, Equation (3): speed modes. 2 2 V = Vα + jVβ = (V1n + aV2n + a V3n ) (3) 3 2 The control process implemented In a voltage source two level three phase inverter, represented in figure 2, and neglecting the switching interval effect (dead-time, snubbers), feeding a three phase, balanced, wye connected load, the voltage measured between the output of each branch and the 0 point can have two values, Vdc or 0 V, given by Equation (1):

where a = e

j

2π 3 .

Using the measured inverter output currents and voltages, the motor flux is estimated, and then the electromagnetic torque is estimated.

In this set of operations it becomes specially important the stator flux estimation. In this Vk 0 = S k × Vdc (1) application, it has been implemented an open loop estimator, with the flux calculated by stator voltage being Sk the control signal of k branch, and Vdc the integration, and considering the stator losses, voltage in the DC bus. Equation (4).

(

)

Φ s = ∫ U s − Rs I s dt Vdc

1

V2n

2 3

n V3n

V10 V20 V30

0

V1n

(4)

Being p the number of pole pairs, the electromagnetic torque is determined by the following expression, Equation (5):

(

Tem = p ⋅ Im Φ s ⋅ I s *

)

(5)

2.1 Electromagnetic torque control mode

The electromagnetic value resulting from the previous stage is then compared with the electromagnetic torque reference, using the three Figure 2. Schematic of a voltage source two level level hysteresis comparator, represented in figure 3. In this manner, the result may be increase, three phase inverter. S1

S2

S3

decrease or maintain the torque, depending on the comparator output.

Tref

90o 150o

+

210o

-

θ5

τ

0

30o

θ2

θ4

1

T

θ3

θ1 θ6

330o

270o

-1

Figure 3. Three level hysteresis comparator: τ=1⇒ increase torque; τ=0⇒ maintain torque; τ=-1⇒ decrease torque. In a similar way, the flux value will be compared with a flux reference, but using a two level hysteresis comparator, shown in figure 4. The result will be used to increase or decrease the flux.

Figure 5. (α, β) plane division in six angular sectors. τ

φ

θ1

θ2

θ3

θ4

θ5

θ6

+1

1

V2

V3

V4

V5

V6

V1

0

1

V7

V0

V7

V0

V7

V0

-1

1

V6

V1

V2

V3

V4

V5

+1

0

V3

V4

V5

V6

V1

V2

0

0

V0

V7

V0

V7

V0

V7

-1

0

V5

V6

V1

V2

V3

V4

1

Table 1: Optimal switching selection table.

Φref +

In figure 6 it is represented the relative positions of Φ the stator and rotor fluxes and the stator current vectors. From figure 6, and as can be seen in figure Figure 4. Two level hysteresis comparator: φ= 1 ⇒ 7, the next applied voltage vector, will cause a displacement in the stator flux vector in order to increase flux; φ= 0 ⇒ decrease flux. reach the results determined by the comparators. An important factor in these operations is the hysteresis band of the two comparators. A narrow y window will give a better current flux waveforms ω but will also increase the inverter switching frequency. -

φ

0

For the switching vector selection it is necessary to know the angular sector in which the actual flux is located. The actual position can be determined by Equation (6), from the orthogonal flux components:  Φ sβ θ = arctg   Φ sα

   

(6)

Is

Φs γ

Φr

x

Figure 6. Stator and rotor fluxes and stator current vectors.

The θ angle returned by Equation (6) determines According to the stator flux vector position, it is the sector where the flux is, (figure 5). applied the voltage vector that satisfies the table The combination of the comparators outputs and entries requirements. the sector is then applied to an optimal switching table (Table 1) which will give the voltage vector Considering the situation presented in figure 6, if it is wanted a torque increase and flux maintenance it to be applied to the inverter.

should be applied voltage vector V3, as it will be Afterwards, with the measured stator currents, it is the one that will cause the bigger displacement of obtained the electrical motor frequency. At last, the the stator flux vector in the direct direction. electrical speed is calculated by the following expression, Equation (9): V3

β θ3

90º

150º

V1

V4

θ2

Φs

V5

30º

V6

θ1

θ4

α

210º

330º

θ5

270º

 T ω r = p ω e − R r e  Φr2 

V2

θ6

Figure 7. Possible voltage vectors to be applied to a stator flux vector.

   

(9)

This method has some error sources, since beyond using motor parameters that may have errors, there are still the flux and electrical angular speed calculations as the more complex quantities. In the speed mode operation, the estimated speed is compared with the speed reference. The error is applied to speed controller, which supplies an electromagnetic torque reference.

3 Simulation

Instead, vector V6 would cause a bigger 3.1 Simulation platform displacement in the inverse direction. Every time the torque is out of the hysteresis bounds a null Using the per phase equivalent circuit of a three phase induction motor, with the parameters vector is applied (V0 or V7). presented in Table 2 (obtained with a set of essays 2.2 Speed control mode according to the IEEE 112 Standard) it was It is also possible to implement a speed controller implemented a control algorithm in the simulation in closed loop using the DTC method. For that, it software package “SABER”. becomes essential to know the rotor mechanical speed. To meet this requirement it has been developed a rotor speed estimation algorithm. Between several options, as referred earlier in this paper, there are open loop estimators, neural network and fuzzy logic based models and observers. However, due to methods complexity and to the implementation available means, an open loop estimator have been chosen.

U

220/380 V

Xm

22,92 Ω

I

18.5/11.5 A

Xs

1,7 Ω

P

4 kW

Xr

1,7 Ω

Cos ϕ

0.78

Rs

1,48 Ω

Poles

4

Rr

1,05 Ω

Table 2: Motor parameters. In the presented application, the rotor flux is The implementation was made considering the calculated from Equation (7): subsequent experimental validation in a hardware Lr (7) platform composed of diode rectifier and a Φr = Φ s − σLs I s = Φ rx + jΦ ry MOSFET three phase inverter, being the control Lm algorithm accomplished with a TMS320F240 where, Lm is the magnetizing inductance, Lr the digital signal processor. rotor inductance, Ls the stator inductance and σ the leakage factor, calculated according to Equation The control algorithm has been implemented using a C function, which simulates the microcontroller, (8): and the remainder components with the simulator Lm σ= (8) blocks. In this way, the migration to the hardware system is made easier. ( L s + Lm )( Lr + Lm )

(

)

twice the nominal speed), having the motor no load After the algorithm implementation it were made coupled to the shaft. several essays in order to evaluate the controller behavior, either in torque control mode, either in speed control mode. 3.2 Simulation results

3.2.1 Torque control mode

In the essay presented in figure 8, in a first instant the electromagnetic torque and the flux references have been kept constant, being the load torque varied later. Afterwards, an electromagnetic torque reference step is applied, being the torque and flux kept constant. Figure 9. Electromagnetic torque step response. In this case, it is possible to verify an error of approximately 15 rad/s between real and measured speeds (figure 10). This error is due to the used speed estimation method.

Figure 8. Electromagnetic torque behavior, with load torque applied.

and

flux

As can be seen in figure 8, the system behavior is good, even in extreme conditions like the overload regime, in which the system has been submitted between instants t=0.25 s and t=0.375 s, tracking, even so, the supplied electromagnetic torque reference. The observed ripple in both electromagnetic torque and flux is due to the use of hysteresis controllers.

Figure 10. Estimated and measured speed. In figure 11 it is possible to observe both the controller generated electromagnetic torque and flux references, as well as the field weakening action.

In figure 9, it can be seen an excellent response to an electromagnetic torque step, being fast (tr=500 4 Conclusions µs) and without overshoot. Is this paper it has been presented an implementation of the DTC control method 3.2.2 Speed control mode associated with a three phase induction motor. Two The speed controller essay was made supplying a control modes have been implemented, the speed reference of ω=300 rad/s (approximately electromagnetic torque mode and the speed control mode.

[2] P. C. Costa. “Controlo directo do binário do motor de indução trifásico. Análise em frequência”, MSc Thesis (in portuguese), Faculdade de Engenharia da Universidade do Porto, (1997). [3] M. Depenbrock. “Direct self-control (DSC) of inverter-fed induction machine”, IEEE Transactions on Power Electronics, vol. 3, nº4, pp. 420-429, (1988). [4] Y.-R. Kim, S.-K. Sul, M.-H. Park. “Speed sensorless vector control of induction motor using extended Kalman filter”, IEEE Transactions on Industry Applications, vol. 30, nº 5, pp. 1225-1233, (1994). Figure 11. Field weakening mode operation.

[5] C. A. Martins. “Contrôle direct du couple d’une machine asynchrone alimentée par convertisseur multiniveaux à fréquence imposée“, PhD Thesis (in french), Institut National Polytechnique de Toulouse / Faculdade de Engenharia da Universidade do Porto, (2000).

Although the existence of a not so interesting behavior in the speed control mode, the results as torque controller were excellent. In fact, due to the speed estimator inferior performance, the speed controller mode has a less interesting behavior, inserting a significant error, implying a new speed estimation system implementation with higher [6] F.-Z. Peng, T. Fukao. “Robust speed identification for sensorless vector control of precision. induction machines”, IEEE Transactions on However, the torque controller simulation results Industry Applications, vol. 30, nº5, pp.1234were very good verifying, as expected, an excellent 1249, (1994). torque control response, either in steady-state or transient regime. The good results continued [7] J. Song, K.-B. Lee, J.-H. Song, I. Choy, K.Ba. Kim. “Sensorless vector control of steadily even when the system was submitted to the induction motor using a novel reduced-order most demanding essays, like overload operation. extended Luenberger observer”, in Proceedings of the 2000 IEEE Industry 5 Acknowledgement Applications Society Conference, vol. 3, pp. 1828-1834, (2000). The work presented in this paper was partially funded by FCT (Fundação para a Ciência e a [8] I. Takahashi, T. Noguchi. “A new quickTecnologia), under POSI (Programa Operacional response and high-efficiency control strategy Sociedade de Informação) of QCA III (Quadro for an induction motor”, IEEE Transactions Comunitário de Apoio). on Industry Applications, vol. 22, nº 5, pp.

6 References [1] L. Ben-Brahim. “Motor speed identification via neural networks”, IEEE Industry Applications Magazine, Jan/Feb, pp.28-32, (1995).

820-827, (1986). [9] P. Vas, A.F. Stronach, M. Neuroth. “A fuzzycontrolled speed-sensorless induction motor drive with flux estimators”, in Proceedings of the 7th International Conference on Electrical Machines and Drives, pp. 315-319, (1995).