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Vector Control Simulation of Induction Machine

Using Simulink Environment

ADRIAN ŞCHIOP, NISTOR DANIEL TRIP, NICOLAE DRĂGHICIU,

SIMONA CASTRASE, CORNELIA GORDAN, ROMULUS REIZ

Department of Electronics

University of Oradea

5, Armatei Române str., Oradea, 410087, Bihor

ROMANIA

Abstract: - In this paper, a Simulink implementation of an induction machine model is described. With the modular system, each block solves one of the model equations; therefore, unlike black box models, all of the machine parameters are accessible for control and verification purposes. After the implementation, one example is given with the model used in drive applications, such as indirect vector control.

Key-Words: - Vector control, Induction machine, AC drives, Simulink model

1 Introduction

Usually, when an electrical machine is simulated in circuit simulators, its steady state model is used, but for electrical drive studies, the transient behaviour is also important. One advantage of Simulink over circuit simulators is the ease in modelling the transients of electrical machines and drives and to include drive controls in the simulation.

As long as the equations are known, any drive or control algorithm can be modeled in Simulink. However, the equations by themselves are not always enough; some experience with differential equation solving is required.

Simulink induction machine models are available in the literature [1], [2] but they appear to be black boxes with no internal details. Some of them recommend using S-functions, which are software source codes for Simulink blocks. This technique does not fully utilise the power and ease of Simulink because S-function programming knowledge is required to access the model variables. S-functions run faster than discrete Simulink blocks, but Simulink models can be made to run faster using “accelerator”. Both of these require additional expense and can be avoided if the simulation speed is not that critical. Another approach is using the Simulink Power System Blockset [3]. This blockset also makes use of S-functions and is not as easy to work with as the rest of the Simulink blocks. In this paper, a modular, easy to understand Simulink induction motor model is described. With the modular system, each block solves one of the model equations; therefore, unlike black box models, all of the machine parameters are accessible for control and verification purposes.

2 Induction motor model

The induction machine d-q or dynamic equivalent circuit is shown in Fig.1.

[pic]

Fig.1 Dynamic or d-q equivalent circuit of an

induction machine.

[pic] (1)

The flux linkage expressions in terms of the currents can be written from Fig.1 as follows:

λs=Lsis+Lmir Ls=Lls+Lm (2)

λr=Lrir+Lmis Lr=Llr+Lm

Torque expression is:

[pic] (3)

Oftentimes, machine equations are expressed in terms of the flux linkages per second, F's, and reactances, x's, instead λ's and L's. These are related by the base or rated value of angular frequency ωb, that is:

F=ωbλ; x=ωbL (4)

We can write:

[pic] (5) [pic]

The modelling equations of a squirrel cage induction motor in state space is:

[pic] (6)

where

d: direct axis,

q: quadrature axis,

s: stator variable

r: rotor variable,

Fij is the flux linkage (i=d or q ;j=s or r),

rr: rotor resistance,

rs: stator resistance,

xls: stator leakage reactance,

xlr: rotor leakage reactance,

P: numbers of poles,

Tem: electrical output torque,

Tmech: load torque,

ωe: stator angular electrical frequency,

ωb: motor angular electrical base frequency,

ωr: rotor angular electrical speed.

3 Simulink implementation

The inputs of a squirrel cage induction machine are the three-phase voltages, their fundamental frequency, and the load torque. The outputs, on the other hand, are the three phase currents, the electrical torque, and the rotor speed.

The d-q model requires that all the three-phase variables have to be transformed to the two-phase arbitrary rotating frame. Consequently, the induction machine model will have blocks transforming the three-phase voltages to the d-q frame and the d-q currents back to three-phase. The induction machine model implemented in this paper is shown in Fig. 2.

[pic]

Fig.2 The complete induction machine Simulink model.

Fig. 3 shows the inside of d-q model block where each equation from the induction machine model is implemented in a different block. First, consider the flux linkage state equations because flux linkages are required to calculate all the other variables.

[pic]

Fig.3. Induction machine dynamic model implementation in Simulink

These equations could be implemented using Simulink “State-space” block, but to have access to each point of the model, implementation using discrete blocks is preferred. Fig. 4 shows what is inside of the block Fqs. All the other blocks in column 1 are similar to this block.

[pic]

Fig.4 Fqs block

Once the flux linkages are calculated, the rest of the equations can be implemented without any difficulty.

The resulting model is modular and easy to follow. The blocks in the first two columns calculate the flux linkages, which can be used in vector control systems in a flux loop. The blocks in column 3 calculate all the current variables, which can be used in the current loops of any current control system and to calculate the three-phase currents. The two blocks of column 4, on the other hand, calculate the torque and the speed of the induction machine, which again can be used in torque control or speed control loops. These two variables can also be used to calculate the output power of the machine. Fig. 5 shows torque and speed of the machine with step change in load torque and plugging.

[pic]Fig.5 Speed and torque variation with step change

in load torque and plugging

4 Vector control operation

The results of the vector control simulation are shown in Fig.6 where the speed command and load torque profiles are presented. As seen in this Fig. 6, the speed tracking and response to the torque disturbance are very good. The simulation model that was used and which models the vector controlled induction motor drive is shown in Fig.7 with the two reference currents indicated by "*" as inputs. The d winding reference current ids^e* controls the rotor flux linkage, whereas the q winding current iqs^e* controls the electromagnetic torque Tem developed by the motor. The reference dq winding currents, outputs of the speed regulator, are converted into the reference phase currents ias*, ibs* and ics*. Speed regulator was designed in [4]. A current-regulated switch-mode converter can deliver the desired currents to the induction motor, using a tolerance-band control described in [5].

[pic]

Fig.6 Simulation results

Conclusion

In this paper, implementation of a modular Simulink model for induction machine simulation has been presented. Unlike most other induction machine model implementations, with this model, the user has access to all the internal variables for getting an insight into the machine operation.

Any machine control algorithm can be simulated in the Simulink environment with this model without actually using estimators. The ease of implementing controls with this model is also demonstrated with one example.

[pic]

Fig. 7 Model of vector controlled induction motor

References:

[1] V.Năvrapescu, M. Covrig, P.Todos, Comanda numerică a vitezei maşinii asincrone, Editura ICPE, Bucureşti , 1998;

[2] A. Dumitrescu, I.Ştefan, Comanda numerică a acţionărilor electrice de tip sensorless, Editura ICPE, Bucureşti, 2000;

[3] G. Sybille, P. Brunelle, "Power Systems Blockset", The Math Works, Inc.2000;

[4] A. Şchiop, "Analysis and design of speed controllers for vector controlled induction motor drives", EMES'03, May 2003, Oradea.

[5] A.Şchiop, "PSPICE Simulation of the current regulated inverter fed induction machine", RSEE 2002, June 2002, Oradea.

[6] K.Lavanya, B.Umamaheswari, S.K.Patnaik A Novel Loss Estimation Technique for Power Converters, WSEAS SOSM 2004

[7] Fayez F. M. El-Sousy, M. M. Salem, High Performance Simple Position Neuro-Controller for Field-Oriented Induction Motor Servo Drives, WSEAS NNA 2004

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