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Application of neural network structure in voltage vector selection of direct torque control induction motor.

Introduction

The induction motor is very popular in variable speed drives due to its well known advantages of simple construction, ruggedness, and inexpensive and available at all power ratings. Progress in the field of power electronics and microelectronics enables the application of induction motors for high-performance drives where traditionally only DC motors were applied. Thanks to sophisticate control methods, induction motor drives offer the same control capabilities as high performance four quadrant DC drives. A major revolution in the area of induction motor control was invention of field-oriented control (FOC) or vector control by Blaschke [1] and Hasse [2].

In vector control methods, it is necessary to determine correctly the orientation of the rotor flux vector, lack of which leads to poor response of the drive. The main drawback of FOC scheme is the complexity. The new technique was developed to find out different solutions for the induction motor torque control, reducing the complexity of FOC schemes known as Direct Torque control (DTC).

Direct Torque control (DTC) for induction motor was introduced about twenty years ago by Japanese and German researchers Takahashi and Noguchi [3]-[4]. DTC was considered as an alternative to the field oriented control scheme to overcome the weakness of scheme. In DTC, the torque and flux are directly controlled by using the selection of optimum voltage vectors. The switching logic control facilitate the generation of the stator voltage space vector, with a suitable choice of the switching pattern of the inverter, on the basis of the knowledge of the sector (supplied by the stator flux model block) in which the stator flux lies, and of the amplitudes of the stator flux and the torque. The sector identification depends on the accurate estimation of stator flux position. Novel artificial intelligence- based stator flux estimator for induction motor has been proposed by [5].

The ANNs are capable of learning the desired mapping between the inputs and outputs signals of the system without knowing the exact mathematical model of the system. Since the ANNs do not use the mathematical model of the system, the same. The ANNs are excellent estimators in non linear systems [6]-[7].

In this paper, a small neural network switching vector selection scheme, to control the torque and flux is proposed.

The organization of this paper goes on in the following order. In Section 2, it will be presented the mathematical model and basic concept of DTC for induction motor drive. In Section 3, it will be described the basis of artificial neural networks and implementation of ANN to the DTC scheme. The results of simulation will be presented in Section 4 for the proposed scheme validation. In Section 5, it will be presented the conclusions of this work.

Mathematical Model of Induction Motor and Basic Concept Of DTC

The dynamic model of the induction motor is derived by transforming the three phase quantities into two phase direct and quadrature axes quantities. The mathematical model in compact form can be given in the stationary reference frame as follows [8].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

[[PSI].sub.ds] = [L.sub.s] [i.sub.ds] + [L.sub.r] [i.sub.dr], [[PSI].sub.qs] = [L.sub.s] [i.sub.qs] + [L.sub.r] [i.sub.qr] (2)

[[PSI].sub.dr] = [L.sub.r] [i.sub.dr] + [L.sub.s] [i.sub.ds], [[PSI].sub.qr] = [L.sub.r] [i.sub.qr] + [L.sub.s] [i.sub.qs] (3)

Where vds, vqs, ids, iqs Rs, Ls, Rr, Lr, Lm, [empty set]ds, [empty set]qs, [empty set]dr, [empty set]qr and .r are the d-q axes voltages and currents, stator resistance, stator inductance, rotor resistance, rotor inductance, mutual inductance between the stator and rotor windings, stator flux linkages, rotor flux linkages and the rotor position respectively.

The electromagnetic torque obtained from machine flux linkages and currents is as:

[T.sub.e] = 3/2 P/2 [L.sub.m] ([i.sub.qs] [[psi].sub.dr] - [i.sub.ds] [[psi].sub.qr]) (4)

Where [T.sub.e], P, [[psi].sub.dr], [[psi].sub.qr] are the electromagnetic torque, number of poles, rotor d-q axes fluxes respectively.

The electromagnetic torque equation can also be obtained in stationary reference frame as

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (5)

Where [[theta].sub.e] is the angle between the stator and rotor flux linkage space vectors, as shown in Fig.1.

[FIGURE 1 OMITTED]

where [sigma] = Leakage coefficient 1 - [[L.sup.2.sub.m]/[L.sub.s][L.sub.r]]

The stator flux linkage, voltage and torque equations in d-q axis stationary reference frame can be obtained as follows

[v.sub.ds] = [R.sub.s] [i.sub.ds] + p[[psi].sub.ds] (6)

[v.sub.qs] = [R.sub.s] [i.sub.qs] + p[[psi].sub.qs] (7)

[[psi].sub.qs] = [integral]([v.sub.ds] - [R.sub.s] [i.sub.ds]) dt (8)

[[psi].sub.qs] = [integral] ([v.sub.qs] - [R.sub.s] [i.sub.qs]) dt (9)

[[psi].sub.s] = [square root of ([[psi].sup.2.sub.ds] + [[psi].sup.2.sub.qs] (10)

[[theta].sub.e] = [tan.sup.-1] ([[psi].sub.qs]/[[psi].sub.ds]) (11)

From equation (5) it is clear that the motor torque can be varied by changing the rotor or stator flux vectors. The rotor time constant of a standard squirrel-cage induction machine is very large, thus the rotor flux linkage changes slowly compared to the stator flux linkage. However, during a short transient, the rotor flux is almost unchanged. Thus rapid changes of the electromagnetic torque can be produced by rotating the stator flux in the required direction, which is determined by the torque command. On the other hand the stator flux can instantaneously be accelerated or decelerated by applying proper stator voltage phasors. Depending on the position of the stator flux, it is possible to switch on the suitable voltage vectors to control both flux and torque. The proposed ANN based DTC scheme is shown in fig.2

[FIGURE 2 OMITTED]

DTC Twelve Sector Table (12_DTC)

In Conventional DTC there are two states per sector that present a torque ambiguity. Therefore, they are never used. In a similar way, in the modified DTC there are two states per sector that introduce flux ambiguity, so they are never used either. It seems a good idea that if the stator flux locus is divided into twelve sectors instead of just six, all six active states will be used per sector. Consequently, it is arisen the idea of the twelve sector modified DTC (12_DTC). This novel stator flux locus is introduced in Fig.3

[FIGURE 3 OMITTED]

FD/FI: Flux Decrease/Increase. TD/TI: Torque Decrease/Increase.

TsD/TsI: Torque small Decrease/Increase.

Notice how all six voltage vectors can be used in all twelve sectors, disappearing all ambiguities.

It is necessary to define small and large variations. It is obvious that V1 will produce a large increase in flux and a small increase in torque in sector [S.sub.12]. On the contrary, [V.sub.2] will increase the torque in large proportion and the flux in a small one. It is reasonable to deduce that the torque error should be divided in the number of intervals that later on will be measured. Therefore, the hysteresis block should have four hysteresis levels at is suggested in Tab. 2.

Artificial Neural Network Based Voltage Vector Selection

ANN has a very significant role in the field of artificial intelligence. The artificial neurons learn from the data fed to them and keep on decreasing the error during training time and once trained properly, their results are very much same to the results required from them, thus referred to as universal approximators [9]. The most popular neural network used by researchers are the multilayer feed forward neural network trained by the back propagation algorithm [10]. There are different kinds of neural networks classified according to operations they perform or the way of interconnection of neurons. Some approaches use neural networks for parameters estimation of electrical machines in feedback control of their speeds [11, 12]. Here we have used a feed forward neural network to select the voltage vector. For this purpose different configurations of networks were used and the best configured network is proposed and depicted in the Fig. 2.

The neural network for the selection of voltage vector is given in Fig.4, which is based on four inputs, d-axis stator flux, q-axis stator flux, hysteresis flux and hysteresis torque.

The Network is a 4-5-1 feed forward network with first layer of hyperbolic tangent sigmoid transfer function, second layer of log sigmoid transfer function and third layer of linear transfer function. Training method used was Gradient Descent with momentum back-propagation. The neural network was trained to performance 0.00001 msec. The back-propagation algorithm is used to train the neural network[13][14]. As soon as the training procedure is over, the neural network gives almost the same output pattern for the same or nearby values of input. This tendency of the neural networks which approximates the output for new input data is the reason for which they are used as intelligent systems.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Simulation Results

The results of simulation obtained in this paper are for the induction motor of 200 HP and parameters are given in appendix I. The machine model is implemented for 12 sector DTC scheme and proposed ANN based 12_DTC scheme using Matlab/Simulink.

The Simulation results for Twelve sector DTC (12_DTC) and ANN based Twelve sector DTC are shown in figures 6 and 7. From Figure 6 and 7 the following effects can be observed

(i) In the time interval 0.02s to 0.25s, the fan speed increases due to the 600 Nm acceleration torque produced by the induction motor.

(ii) At t = 0.25s, the electromagnetic torque jumps down to 0 Nm and the speed decreases because of the load torque opposed by the fan.

(iii) At t = 0.5s, the motor torque develops a -600 Nm torque and allows braking of fan. During braking mode, power is fed back to the DC bus and the bus voltage increases. Due to saturation, the braking chopper limits the DC bus voltage to 700V.

The flux stays around 0.8Wb throughout the simulation. The flux and torque oscillation amplitudes are observed to be slightly higher than 0.02 Wb and 10 Nm respectively. This is due to the combined effects of the 15 [mu]s DTC controller sampling time, the hysteresis control and the switching frequency limitation.

From the simulation results it can be observed that, the results with and without neural networks are almost similar. However, the stability of the system, an inherent phenomena of neural networks gets improved in case Neural network based DTC.

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

Conclusions

In this paper, the ANN based switching voltage vector selection has been proposed for DTC of induction motor drive. The proposed scheme performance is compared with the Twelve sector DTC scheme. From the simulation results, it can be observed that the performance of the Twelve sector DTC and ANN based Twelve sector DTC schemes are almost similar. But, owing to the stability and learning capability of neural networks, the proposed method can be considered as better technique.

Appendix I

The parameters of the three-phase induction motor employed for simulation purpose in SI units are

Rs = 14.85e-3, Rr = 9.295e-3, Ls = 0.3027e-3 H, Lr = 0.3027e-3 H, Lm = 10.46e-3 H

P = 2, J =10 Kg/m2

Load torque (Nm) = 0.08

Torque reference value (Nm) = 600

Flux reference value(Weber) = 0.8

Torque hysteresis value (Nm) = 10

Flux hysteresis value (Weber) = 0.02

Sampling time, Ts(Sec) = 20e-6

References

[1] F. Blaschke, "The principle of field orientation as applied to the new transvector closed-loop control system for rotating-field machines," Siemens Rev., 1972.

[2] K. Hasse, "Zum Dynamischen Verhalten der Asynchron-machine bei Betriek Mit Variabler Standerfrequenz und Standerspannung," ETZA, Bd. 9, p. 77, 1968.

[3] I. Takahashi and T. Noguchi, "A new quickresponse and high efficiency control strategy of an induction machine," IEEE Trans. Ind. Applicat., vol. 22, pp. 820-827, Sep./Oct. 1986.

[4] I. Takahashi and Y. Ohmori, "High performance direct torque control of an induction motor," IEEE Trans. Ind. Application., vol. 25, pp. 257- 264, Mar./Apr. 1989

[5] L. M. Gnesiak, B. Ufnalski "Neural Stator Flux Estimator with Dynamical Signal Preprocessing" IEEE conf. (AFRICON 2004), pp. 1137-1142.

[6] K.Funashi, "On the Approximation of degree in Control and Automation at Continuos Mappings by Neural Networks" Neural Networks, vol.2 pp 183192, 1989.

[7] B. Kosco, "Neural Networks and Fuzzy Systems: A Dynamic Systems Approach to Machine Intelligence". Englewood Cliffs, NY Prentice Hall 1992.

[8] C. M. Ong, Dynamic Simulation of Electric Machinery Using Matlab/Simulink, Prentice Hall, 1997.

[9] Lippmann, "And Introduction to Computing student at the same institute with Neural Networks Nets," IEEE ASSP pp 4 -21, Mar., Apr. 1987.

[10] LiMin Fu, "Neural Networks in Computer Intelligence", McGraw-Hill Inc., pp. 153-264, 1994.

[11] F. J. Lin, J. C. Yu and M. S. Tzeng, "Sensorless Induction Spindle Motor Drive Using Fuzzy Neural Network Speed Controller", Electric Power Systems Research, vol. 58, pp. 187-196, 2001.

[12] D. Kukolj, F. Kulic and E. Levi, Design of Speed Controller for Sensorless Electric Drives Based on AI Techniques: a Comparative Study, Artificial Intelligence in Engineering, vol. 14, pp. 165-174, 2000.

[13] S. Haykin, "Neural Networks--A Comprehensive Foundation", Prentice Hall, 1999.

[14] M. T. Hagan and M. B. Menhaj, Training Feed forward Networks with the Marquardt Algorithm, IEEE Trans. on Neural Networks, vol. 5, No. 6, pp. 989-993,1994.

A. Sivasubramanian (1) and B. Jayanand (2)

(1) Ph.D Research Scholar, Dr. M.G.R. University, Chennai, Tamil Nadu, India E-mail: sivapollachi2002@yahoo.co.in

(2) Assistant Professor, Department of Electrical and Electronics Engineering, Government Engineering College, Thrissur, Kerala, India E-mail: jayanandb@gmail.com
Table 1: Table for sectors 12 and 1 in the 12_DTC. Notice how all
six voltage vectors can be used in all sectors
disappearing all ambiguities.

[S.sub.12]               INCREASE

Stator Flux   [V.sub.1],[V.sub.2],[V.sub.6]
Torque        [V.sub.1],[V.sub.2],[V.sub.3]
[S.sub.1]                INCREASE
Stator Flux   [V.sub.1],[V.sub.2],[V.sub.6]
Torque        [V.sub.2],[V.sub.3],[V.sub.4]

[S.sub.12]               DECREASE

Stator Flux   [V.sub.3],[V.sub.4],[V.sub.5]
Torque        [V.sub.4],[V.sub.5],[V.sub.6]
[S.sub.1]                DECREASE
Stator Flux   [V.sub.3],[V.sub.4],[V.sub.5]
Torque        [V.sub.5],[V.sub.6],[V.sub.1]

Table 2: Switching table for the 12 DTC.

[phi]                               F1

[tau]           TI           TsI           TsD          TD

[S.sub.1]    [V.sub.2]   * [V.sub.2]     [V.sub.1]   [V.sub.6]
[S.sub.2]    [V.sub.3]     [V.sub.2]   * [V.sub.1]   [V.sub.1]
[S.sub.3]    [V.sub.3]   * [V.sub.3]     [V.sub.2]   [V.sub.1]
[S.sub.4]    [V.sub.4]     [V.sub.3]   * [V.sub.2]   [V.sub.2]
[S.sub.5]    [V.sub.4]   * [V.sub.4]     [V.sub.3]   [V.sub.2]
[S.sub.6]    [V.sub.5]     [V.sub.4]   * [V.sub.3]   [V.sub.3]
[S.sub.7]    [V.sub.5]   * [V.sub.5]     [V.sub.4]   [V.sub.3]
[S.sub.8]    [V.sub.6]     [V.sub.5]   * [V.sub.4]   [V.sub.4]
[S.sub.9]    [V.sub.6]   * [V.sub.6]     [V.sub.5]   [V.sub.4]
[S.sub.10]   [V.sub.1]     [V.sub.6]   * [V.sub.5]   [V.sub.5]
[S.sub.11]   [V.sub.1]   * [V.sub.1]     [V.sub.6]   [V.sub.5]
[S.sub.12]   [V.sub.2]     [V.sub.1]   * [V.sub.6]   [V.sub.6]

[phi]                               FD

[tau]           TI           TsI          TsD         TD

[S.sub.1]    [V.sub.3]     [V.sub.4]   [V.sub.7]   [V.sub.5]
[S.sub.2]    [V.sub.4]   * [V.sub.4]   [V.sub.5]   [V.sub.6]
[S.sub.3]    [V.sub.4]     [V.sub.5]   [V.sub.0]   [V.sub.6]
[S.sub.4]    [V.sub.5]   * [V.sub.5]   [V.sub.6]   [V.sub.1]
[S.sub.5]    [V.sub.5]     [V.sub.6]   [V.sub.7]   [V.sub.1]
[S.sub.6]    [V.sub.6]   * [V.sub.6]   [V.sub.1]   [V.sub.2]
[S.sub.7]    [V.sub.6]     [V.sub.1]   [V.sub.0]   [V.sub.2]
[S.sub.8]    [V.sub.1]   * [V.sub.1]   [V.sub.2]   [V.sub.3]
[S.sub.9]    [V.sub.1]     [V.sub.2]   [V.sub.7]   [V.sub.3]
[S.sub.10]   [V.sub.2]   * [V.sub.2]   [V.sub.3]   [V.sub.4]
[S.sub.11]   [V.sub.2]     [V.sub.3]   [V.sub.0]   [V.sub.4]
[S.sub.12]   [V.sub.3]   * [V.sub.3]   [V.sub.4]   [V.sub.5]

SFD/FI: Flux Decrease/Increase.

TD/=/I: Torque Decrease/Equal/Increase.

(* best possible approximate state).
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Author:Sivasubramanian, A.; Jayanand, B.
Publication:International Journal of Applied Engineering Research
Article Type:Report
Geographic Code:1USA
Date:Jun 1, 2009
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