Implementation Of FOC Technique And DTC Technique For The Torque Control Of Induction Motor And Their Comparison

Implementation Of FOC Technique And DTC Technique For The Torque Control Of Induction Motor And Their Comparison

Mr. Kiran B. Sonkhedkar

AbstractField-oriented control and direct torque control are becoming the industrial standards for induction motors torque control. This paper is aimed to give a contribution for a detailed comparison between the two control techniques, emphasizing advantages and disadvantages. The performance of the two control schemes is evaluated in terms of torque and current ripple, and transient response to step variations of the torque command. The analysis has been carried out on the basis of theresults obtained by numerical simulations, where secondary effects introduced by hardware implementation are not present.

Index TermsDirect field oriented control, direct torque control, discrete space vector modulation, field oriented control, pulse-width modulation.

I. INTRODUCTION

ALMOST 30 years ago, in 197 F.Blaschke [1] presented the first paper on field oriented control (FOC) for induction motors. Since that time, the technique was completely developed and today is mature from the industrial point of view. Today field oriented controlled drives are an industrial reality and are available on the market by several producers and with different solutions and performance [2] [19]. Thirteen years later, a new technique for the torque control of induction motors was developed and presented by Takahashi as direct torque control (DTC) [20][22], and by M. Depenbrock as direct self control (DSC) [23][25]. Since the beginning, the new technique was characterized by simplicity, good

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performance and robustness [20][31]. Using DTC or DSC it is possible to obtain a good dynamic control of the torque without any mechanical transducers on the machine shaft. Thus, DTC and DSC can be considered as sensorless type control techniques. The basic scheme of DSC is preferable in the high power range applications, where a lower inverter switching frequency can justify higher current distortion. In this paper, the attention will be mainly focused on the basic DTC scheme, which is more suitable in the small and medium power range applications.

Several papers have been published on FOC and DTC in the last 30 years, but only few of them was aimed to emphasize differences, advantages and disadvantages.

The name direct torque control is derived by the fact that, on the basis of the errors between the reference and the estimated

values of torque and flux, it is possible to directly control the inverter states in order to reduce the torque and flux errors within the prefixed band limits.

Unlike FOC,DTC does not require any current regulator, coordinate transformation and PWM signals generator (as a consequence timers are not required). In spite of its simplicity, DTC allows a good torque control in steady-state and transient operating conditions to be obtained. The problem is to quantify how good the torque control is with respect to FOC. In addition, this controller is very little sensible to the parameters detuning in comparison with FOC.

On the other hand, it is well known that DTC presents some disadvantages that can be summarized in the following points:

1. difficulty to control torque and flux at very low speed;

2. high current and torque ripple;

3. variable switching frequency behaviour;

4. high noise level at low speed;

5. lack of direct current control.

   Thus, on the basis of the experience of the authors, the aim of this paper is to give a fair comparison between the two techniques (FOC and DTC) in both steady- state and transient operating conditions. The comparison is useful to indicate to the users which one of the two schemes can be efficiently employed in the various applications that today require torque control.

   II PRINCIPLE OF FOC.

   The principle of the field oriented control (FOC) the induction motor is based

   q d

   Fig.1 Phesor diagram describing the FOC scheme

   From Fig.1 it can be established that

   on an analogy to the separately excited DC motor. In this motor flux and torque

   = 0 =

   can be controlled independently. The algorithm can be implemented using simple regulator, e.g. PI-regulator.

   And =

   Hence the flux equation gets reduced to

   Considering the d-q model of the induction machine in the reference frame

   rotating at synchronous speed The

   =

   1+

   ( )

   field-oriented control implies that the

   And torque can be expressed as:

   component of the stator current would be

   = 3

   (

   )

   aligned with the rotor field and the component would be perpendicular to

   2

   This can be accomplished by choosing as sped of the rotor flux and locking the phase of the reference frame system such that the rotor flux is aligned precisely with the d axis, as illustrated in Figure 1 below.

   Following which the expression for can be reduced to

   2

   2

   = 3 p ( )

   = 3 p

   2

   = 3 p 2

   * The FOC Algorithm *

   2

   1. Measure the stator phase current

      , and

   2. Transform these set of three phase

      Torque component Flux component of current

      current

      Hence the analogy with the DC machine performance is clearly established, while keeping the flux constant. The electric torque is proportional to the

      component of the current and flux

      is proportional to the component of the current.

      he block diagram of the direct field oriented control (DFOC) is shown in fig.2 in which the estimator or observer calculates the rotor flux angle . Inputs to the estimator or observer are stator voltages and currents.

      Fig.2 Basic block diagram of DFOC

      current on to two axis system. This conversion will provide the values if ,and from the measured values of , and where ,and are the time –

      varying quadrature current values as viewed from the stators perspective.

   3. Calculate the rotor flux and its orientation

   4. Rotate the two -axis coordinate system such that it is an alignment with the rotor flux, using the transformation angle calculated at the last iteration of the control loop. This conversion provides the

      , values from ,and

   5. Flux error signal formed using flux reference and estimated flux value. A PI controller is used then to calculate the * using the error signal. * is generated

      using the reference torque value and the estimated flux value.

   6. * and * are converted to set of three phase currents to produce , and

7. , , and , ,

are compared using hysteresis to generate the gate signal

1. PRINCIPLE OF DTC.

   The machine equations in the stator reference frame in terms of space vectors

   q- axis

   are

   2

   2

   = 3 p ( )

   = +

   = + ( )

   = +

   –

   2

   1. xis

      =(

      – 2)

      +

      Fig.3 vector diagram of stator and rotor flux

      = (1- 2

      )

      +

      = 6

      +

      From the Fig.3 vector diagram following equations are written.

      Where the 6 is rotor leakage factor

      = cos

      2

      6 = (1- )

      =

      sin

      = 1 (

      6

      –

      )

      = cos

      = sin

      6

      6

      = 1

      ( –

      )

      = 3 p

      [ sin

      The torque equation for the induction motor is

      2 6

      cos – cos sin ]

      = 3 ( )

      = 3 p

      2 2 6

      2

      2

      = 3

      6

      [

      sin( )

      )

      = k sin

      Where k is constant

      p

      p

      .

      .

      3

      k = 2 6

      the basic block diagram for the DTC of induction motor is shown in Fig.4.

      Fig.6 Torque hysteresis comparator.

      Whereas the error between the stator flux magnitude and reference flux magnitude is the input of the two level hysteresis comparator. Fig. 5 & 6 illustrates the flux and torque comparator respectively.

      The selection of appropriate voltage vector is based on is based on switching table given in table-1. The input quantities are the stator flux sector and the output of two hysteresis comparator. Assuming the flux stator flux vector laying in sector 1 of the d-q plane. The vectors used by the DTC technique is given in the Fig.7.

      3 2

      Fig.4 basic block diagram of DTC

      The error between the estimated torque T and reference torque T* is output of the three level hysteresis comparator

      Fig.5 Flux hysteresis comparator.

      0

      4

      1

      8 Sector -1

      5 6

      Fig.7 voltage vectors utilised in basic DTC scheme when the stator flux is in sector 1.

      TABLE-1

      Basic switching table

      Sector status		1	2	3	4	5	6
      = 1	dm= 1	2	3	4	5	6	7
      	dm= 0	7	0	7	0	7	0
      	dm= -1	6	1	2	3	4	5
      = 0	dm = 1	3	4	5	6	1	2
      		0	7	0	7	6	7
      	dm = 0
      		5	6	1	2	3	4
      	dm= -1

      This simple approach allow a quick torque response to be achieved, but the steady state performance is characterised by undesired ripple in current, flux & torque. This behaviour is mainly due to the absence of information about the torque and the rotor speed values in voltage vector selection algorithm.

      The DTC algorithm

      1. Measure the values of stator currents i.e. , , and

         , ,

      2. Transform these set of three phase current on to two axis system. This conversion will provide the values if ,and from the measured values of , and where ,and are the time –

         varying quadrature current values as viewed from the stators perspective. Similarly calculate the voltages

      3. Rotate the two -axis coordinate system such that it is an alignment with the rotor flux, using the

         transformation angle calculated at the last iteration of the control loop. This conversion provides the

         , values from ,and and values , from the & .

      4. Using these values calculate the values of torque, flux & angle i.e.

      5. Calculate the reference values of the torque* and flux* from the actual speed of the rotor.

      6. Give actual values and reference values of torque and flux to the hysteresis controller. And the angle is given as input to the sector selector. Which finds the sector in which the flux is laying.

      7. The hysteresis controller is generates the appropriate gate signals as per the switching table shown in table no.1

2. SIMULATION RESULTS AND ANALYSIS.

Fig.8 & Fig.9 shows the simulink model of the FOC scheme and the DTC respectively. The torque response , speed response and the stator currents of the induction motor are shown in Fig.9 & 10 for the FOC and DTC respectively. In both the cases the load torque is initially 10 Nm. & 30 Nm. At 1 sec is applied. And reference speed is set to 500rpm, &1000rpm at 0sec & 1sec respectively.

Fig.8 Matlab/Simulation of FOC

scheme

In the DTC scheme direct control of the stator current is not present and this may determine over currents when step variation of torque and flux are applied to the input command. With reference to the torque an indirect torque current control can be obtained introducing a limit to the maximum torque value. With reference to the stator flux it can be noted command causes large variation of

Fig. 9 Matlab/Simulation of DTC scheme.

Fig8. stator currents (Iabc), rotor speed, and electromagnetic torque response of vector control scheme.

the stator current. It is well known that the basic DTC scheme is affected by undesirable

Fig.10 stator flux trajectory of DTC scheme

Fig.11 stator flux trajectory of FOC scheme.

phenomena at low speed. In these operating conditions the control system selects many times zero votage vectors, determining a reduction of flux level

owing to the effects of stator resistance voltage drop. Fig.10 &11 shows the stator flux trajectory for DTC scheme & FOC scheme respectively

V Conclusion And future prospects.

The aim of the paper was, implementation of DTC & FOC schemes of control for the induction motor and their fair comparison by analysing the outputs of both the techniques, to allow the user to indentify the more suitable solution for any application that requires torque control

From the analysis can be concluded that the DTC scheme has the upper hand as compare to the FOC except that it has the more toque ripples, and the large variable switching frequency causes the more switching losses and the ripple which can be reduced by using the space vector pulse width modulation direct torque control (SVPWMDTC) many researches are going on the field to implement the DTC with minimum ripples in the torque. Also by designing the sliding mode

Stator resistance 1.115

Stator inductance 0.005974H

Rotor resistance 1.083

Rotor inductance 0.005974H

Mutual inductance 0.2037H

Pole pair 2

Inertia 0.002

REFERENCES

1.) A. Nabae, K. Otsuka, H. Uchino, and R. Kurosawa, An approach to flux control of induction motors operated with variable-frequency powesupply, IEEE Trans. Indust. Applicat. Syst., vol. IAS 16, pp. 342 349, May/Jun 1980

Fig.9 stator currents (Iabc), rotor speed, and electromagnetic torque response of DTC technique scheme.

controller we can further reduce the ripples from the output hence the output torque variation will be more perfect and smooth.

Appendix

The test macine used in the MATLAB/simulation is 3phase, 50HZ induction machine having the following parameter

Power output 5HP

Rated Voltage 350V

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