VHDL Simulation of direct torque controlled induction motor drive.

Pandian, G. ; Reddy, S. Rama

Introduction

DC motors have been used during the last century in industries for variable speed control applications, because its flux and torque can be controlled easily by means of changing the field and armature currents respectively. Furthermore, operation in the four quadrants of the torque speed plane including temporary standstill was achieved. Almost a century, induction motor has been the work-horse of industry due to its. robustness, low cost and less maintenance. The induction motors were mainly used for essentially constant speed applications because of the unavailability of the variable-frequency voltage supply. The advancement of power electronics has made it possible to vary the frequency of the voltage supplies relatively easy, thus has extended the use of induction motor in variable speed drive applications [1]. But due to the inherent coupling of flux and torque components in induction motor, it could not provide the torque performance as good as the DC motor.

Field oriented control (FOC) of induction motor was introduced that has open a new horizon to the induction motor applications. The method, which uses frame, transformed the performance of induction motor similar to that of the DC motor. The implementation of this system however is complicated and furthermore FOC, in particularly indirect method which is widely used, is well known to be highly sensitive to parameter variations due to the feed-forward structure of its control system. Another induction motor control technique known as direct torque control (DTC), which was introduced about a decade ago, has a relatively simple control structure yet performs at least as good as the FOC technique [2].

Until quite recently, micro-controllers have been used extensively in vector control of induction motors. However, to obtain a high bandwidth control system and improve the performance of induction motor drives, particularly in servo applications, the use of a fast processor is inevitable. In a DTC drive, flux linkage and electromagnetic torque are controlled directly and independently by the selection of optimum inverter switching modes. The required optimal switching voltage vectors can be selected by using a so called optimum switching voltage vector look up table. The simulation waveforms of DTC are not presented in the literature [1-14]. In the present work an attempt is made to simulate DTC system.

DTC Principles

Figure 1 shows the schematic of one simple form of the DTC induction motor drive, employing a voltage source inverter (VSI). In this scheme the stator flux is the controlled flux, thus it will be referred to as a stator flux based DTC induction motor drive. The voltage source six pulse inverter fed stator flux based DTC induction motor drive is shown [3]. Direct torque control involves the separate control of the stator flux and the torque through the selection of optimum inverter switching modes the optimum switching table had been shown in Table 1. The reference value of the stator flux linkage space vector modules is compared with the actual modulus of the stator flux linkage space vector and the resulting error is fed into the two level starter flux hysteresis comparator. Similarly, the reference value of the electromagnetic torque is compared with the actual value and the electromagnetic torque error signed is into the three level torque hysterics comparator. The outputs of the flux and torque comparators are used in the inverter optimal switching table which also uses the information on the position of the stator flux linkage space vectors [5]. The flux linkage and electromagnetic torque error are restricted within their respective hystersis bands. The DTC scheme requires flux linkage and electromagnetic torque estimators. However, it is not necessary to monitor the stator voltage since they can be reconstructed by using the inverter switching modes and the monitored d.c links voltage. The electromagnetic torque can be estimated by using closed loop speed control can be obtained by using a speed controller whose output gives the torque reference, and the input to the speed controller is the difference between the reference speed and the actual speed.

The DTC drive consists of DTC controller, torque and flux calculator, and a voltage source inverter. The configuration is much simpler than the FOC system due to the absence of frame transformer, pulse width modulator and position encoder, which introduce delays and requires mechanical transducer. The implementation of DTC is simple in structure and requires a fast processor to perform on-line calculations of electromagnetic torque and stator flux based on sampled terminal variables [7]. If a three phase VSI is connected to an induction motor, there can be eight possible configurations of six switching devices within the inverter. As a result, there are eight possible input voltage vectors to the induction motor.

DTC utilizes the eight possible stator voltage vectors, two of which are zero vectors, to control the stator flux and torque to follow the reference value within the hysteresis bands. The voltage space vector of a three-phase system is given by:

[[bar.V].sub.s] (t) = 2/3([v.sub.sA](t) + [av.sub.sB](t) + [a.sup.2][v.sub.s] C(t)), (1)

where a = [e.sup.j2/3[pi]]

[V.sub.sA], [V.sub.sB], and [V.sub.sC] are the instantaneous phase voltages. For the switching VSI, it can be shown that for a DC link voltage of [V.sub.d], the voltage space vector is given by:

[[bar.V].sub.s](t) = 2/3 [V.sub.d] ([S.sub.a](t) + [S.sub.b] (t)a + [S.sub.c](t)[a.sup.2]), (2)

[S.sub.a](t), [S.sub.b](t) and [S.sub.c] (t) are the switching functions of each leg of the VSI, such that,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]

Direct Flux Control

The induction motor stator voltage equation is given by:

[[bar.v].sub.s] = [R.sub.s][[bar.i].sub.s] + d [[bar.[PSI]].sub.s]/dt (3)

Where [[bar.v].sub.s], [[bar.i].sub.s] and [[bar.[PSI]].sub.s] are the stator voltage, current and stator flux space vectors respectively. According to equation (3), if the stator resistance is small and can be neglected, the change in stator flux, [DELTA][[bar.[PSI]].sub.s], will follow the stator voltage, i.e.,

[DELTA][[bar.[PSI]].sub.s] = [[bar.v].sub.s][DELTA]t (4)

This simply means that the tip of the stator flux will follow that of the stator voltage space vector multiplied by the small change in time. Hence if the stator flux space vector is known, its locus can be controlled by selecting appropriate stator voltage vectors. In DTC the stator flux space vector is obtained by calculation utilizing the motor terminal variables. The stator flux is forced to follow the reference value within a hysteresis band by selecting the appropriate stator voltage vector using the hysteresis comparator and selection table.

Direct Torque Control

As shown by Takashashi and Noguchi [8], under a condition of a constant mechanical frequency and stator flux magnitude, when a step increase in the stator angular frequency is applied at t=0, the rate of change of torque at time t=0 is proportional to the slip frequency of the stator flux with respect to the rotor mechanical speed. Thus,

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

[FIGURE 1 OMITTED]

where [[omega].sub.sl] is the angular slip frequency of the stator flux with respect to the rotor mechanical frequency. This means that the rate of change of torque can be made positive or negative regardless of whether the stator flux is increasing or decreasing. If the torque and stator flux is kept within their hysteresis bands by selecting appropriate voltage vectors, an independent control over the torque and stator flux is accomplished. If the stator flux space vector plane is divided into six sectors or segments as shown in Figure 3, a set of table of which voltage vector should be chosen in a particular sector (either to increase stator flux or to reduce stator flux and either to increase torque or to reduce torque) can be constructed.

DTC Algorithm

The figure 2 presents the methodology of a DTC drive:

Induction motor is a system to be voltage controlled. The inverter applies threephase voltage signals determined by changes on the switching keys, which are calculated by the algorithm.

Switching table calculates the switching keys according to a strategy as a function of the torque and flux comparators and the spatial sector in which the stator flux is lying at calculation time.

Motor model is a mathematical model used to calculate flux, currents and voltages referred to the stator in [alpha][beta] stationary coordinates and electrical torque. It is the most complex part of the algorithm, involving multiplications and a square root evaluation. These operations are computed serially in order to reduce hardware area in the prototyping step. DC link voltage [V.sub.d] and stator currents ([i.sub.1] and [i.sub.2]) are determined by three serial A/D converters, which correspond to the slower part of the algorithm, taking 25[micro]s to perform the operation. The conversions are executed simultaneously.

Torque and flux comparators are two and three-level relays with hysteresis--they are used to compare torque and flux references with their actual values.

Sector evaluation is a function that calculates the position of stator flux vector in [alpha][beta] coordinates in a plane. In this case, the plane is divided into 6 sectors corresponding to the voltage vectors that can be applied by their inverter.

The motor model is composed by the equations and [V.sub.[alpha]], [V.sub.[beta]], [i.sub.[alpha]], [i.sub.[beta]], [[lambda].sub.[alpha]], [[lambda].sub.[beta]] are coordinate components of stator voltage, current and flux calculated in the pervious instant.

[V.sub.d] is the DC link voltage, [i.sub.1] and [i.sub.2] are stator current values of two of the three phase lines to which the motor is linked. Cha, Chb and Chc previous instant. Rs is stator resistance estimate evaluated off-line. Ta is the A/D converter sampling time. Equations 1 and 2 transform current and voltage components measured in a 16-bit value by the A/D into [alpha][beta] components which are adequate to DTC algorithm [10]. Voltage components needs switching commands applied in the previous instant to be calculated. Equation.3, corresponds to an integration using forward equal methods. Sampling time (Ts) precision is critical to DTC implementation since it affects flux estimation. Equation 4 estimates electrical torque, which is directly controlled as a main proposition of DTC technique. Equation 5 calculates flux magnitude, which is used in the flux control loop.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

Equations for Modeling the Motor are as follows:

1. Stator Voltages in [alpha][beta] coordinates

[V.sub.[alpha]] = [V.sub.d]/3* (2*Cha-Chb-Chc);

[V.sub.[beta]] = sqrt (3 /3* [V.sub.d]* (Chb-Chc);

2. Stator Currents in [alpha][beta] coordinates

[I.sub.[alpha]] = [i.sub.1].

[I.sub.[beta]] = sqrt (3)/3* ([i.sub.1] +2* [i.sub.2]);

3. Stator Flux Estimation

[[lambda].sub.[alpha]]= [[lambda].sub.[alpha]OLD] + Ts*([V.sub.[alpha]] -Rs* i[alpha]);

[[lambda].sub.[beta]]= [[lambda].sub.[beta]OLD] + Ts*([V.sub.[beta]] -Rs* i[beta]);

4. Torque Estimation

torque = 3/4 *p* ([I.sub.[beta]]*[[lambda].sub.[alpha]]*[[lambda].sub.[beta]] );

5. Stator Flux magnitude determination

[lambda]mod= sqrt ([[lambda].sub.[alpha]]^2+[[lambda].sub.[beta]]^2);

DTC Architecture

DTC algorithm is implemented in an architecture composed by five main blocks: motor model. flux comparator, sector evaluation, torque comparator and switching table. The available processing time is dictated by the A/D converters, corresponding to 25[micro]s. This time interval is partitioned into five time slots, allowing for the processing of input samples. The motor model module uses time slots 1 to 3. In the first time slot (id1) 16-bit samples are read from the A/D converters. Modules flux comparator, sector evaluation and torque comparator are processed in parallel in the fourth time slot, while last time slot is used to compute the switching table (Cha, Chb, Chc). Motor model module has three 16-bit inputs supplied by A/D converters: [i.sub.1], [i.sub.2] and [V.sub.d] and produces four outputs: torque, [[lambda].sub.[alpha]], [[lambda].sub.[beta]] and [lambda]mod. The motor modeling equations are implemented according to the architecture. As can be observed, complex mathematical operations are performed such as multiplications and a square root. Sector evaluation is a module that receives stator flux components as inputs and determinates the position of the flux vector in a plane divided into six sectors denominated sectors 1 to 6. To determinate the position of stator flux, magnitude is compared with projection components in the axes [alpha] and [beta]. In the algorithm implementation, many digital properties have to be considered. Characteristics such as quantization sampling, and adopted binary format are key performance factor in the control process.

Simulation Results

The DTC architecture is simulated using Xilinx Package. The results of flux comparator are shown in figure4. The results of torque comparator and sector evaluator are shown in figure 5 & 6. The switching table wave forms are shown in figure 7. The simulated wave forms of control signals are shown in figure 8. The results of DTC blocks are shown in figure.9. The actual torque is compared with set torque and the actual flux is compared set flux. The pulse width of the driving pulse is selected such that actual torque is equal to set torque. From the simulation results it is observed that the motor develops a torque equal to the set torque.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

[FIGURE 7 OMITTED]

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

Conclusion

The architecture proposed is written in synthesizable VHDL. The actual torque is compared with set torque and the actual flux is compared set flux. The pulse width of the driving pulse is selected such that actual torque is equal to set torque. From the simulation results it is observed that the motor develops a torque equal to the set torque.

References

[1] Buja, G., Casade, D., "Tutorial 2: The Direct Torque Control of Induction Motor Drives", ISIE, 1997.

[2] H. Tamia and Y. Hori, Speed Sensor less Field--Orientation Control of induction machine, IEEE Trans. Indus. Appln. Vol. 29, pp.175-180, Jan / Feb 1993.

[3] Peter Vas: Sensor less Vector and Direct Torque Control, Oxford University Press, London, 1998.

[4] Jun-Koo Kang, Seung-Ki Sul: "New Direct Torque Control of Induction Motor for Minimum Torque Ripple and Constant Switching Frequency", IEEE Transactions on Industry Applications, Vol.35, No.5, Sept/Oct. 1999.

[5] D. Casadei, G. Serra, A. Tani: "Analytical Investigation of Torque and Flux Ripple in DTC Schemes for Induction Motors", IEEE-IAS Annual Meeting 2002.

[6] G.Buja,D. Casadei, G. Serra: "DTC-Based Strategies for Induction Motor Drives, IEEE-IAS Annual Meeting 2002, pp.1506-1516.

[7] T.Noguchi, M.Yamamoto, S.Kondo, I.Takahashi: "Enlarging Switching Frequency in Direct Torque-Controlled Inverter by Means of Dithering, IEEE Transactions on Industry applications, Vol.35, No.6, Nov/Dec. 1999.

[8] Takahashi Isao, Noguchi Toshihiko : "A New Quick-Response and High-Efficiency Control Strategy of an Induction Motor" IEEE Transactions on Industry Applications, Vol. IA-22, No.5, Sept/Oct. 1986.

[9] Thomas G. Habetler, Deepakaraj M. Divan: "Control Strategies for Direct Torque Control Using Discrete Pulse Modulation", IEEE Transactions on Industry Applications, Vol.27, No.5, Sept/Oct. 1991.

[10] Aubepart, F., Poure, P., Girerd, C., Chapuis, Y.A., Braun, F., "Design and Simulation of ASIC-Based System Control: Application ", to Direct Torque Control of Induction Machine", ISIE'99-Bled, Slovenia, 1999, pp. 1250-1255.

[11] Giovani Griva, Thomas G. Habetler. "Performance Evaluation of a Direct Torque Controlled Drive in the Continuous PWM-Square Wave Transition Region", IEEE Transactions on Power Electronics, Vol.10, No.4, July 1995.

[12] Barbara H. Kenny, Robert D. Lorenz, "Stator and Rotor Flux Based Deadbeat Direct Torque Control of Induction Machines", IEEE Transactions on Industrial Electronics, Vol.30, No.4, 2001.

[13] Thomas G. Habetler, Francesco Profumo, Michel Pastorelli: "Direct Torque Control of Induction Machines Over a Wide Speed Range", IEEE-IAS Annual Meeting, Conf. Rec. 1992,pp.600-606.

[14] Kevin D. Hurst, Thomas G. Habetler. "A Simple, Tacho-Less, I. M. Drive with Direct Torque Control Down to Zero Speed", IEEE Transactions on Industry Applications, 1995, Vol.5, No.5,pp. 563-569.

G. Pandian

Research Scholar, Sathyabama University, Chennai.

pandian1960@yahoo.co.in

S. Rama Reddy

Electrical and Electronics Engineering,

Jerusalem College of Engineering, Chennai.

srr_victoy@yahoo.com

Table 1 : Switching Table

Counter Clockwise          Sec   Sec   Sec   Sec   Sec   Sec
                           I     II    III   IV    V     VI

Inc Flux (0)   Inc T(01)   100   110   010   011   001   101
               Dec T(00)   000   111   000   111   000   111
Dec Flux (1)   Inc T(01)   110   010   011   001   101   100
               Dec T(00)   111   000   111   000   111   000

Counter Clockwise          Sec   Sec   Sec   Sec   Sec   Sec
                           I     II    III   IV    V     VI

Inc Flux (0)   Inc T(10)   001   101   100   110   010   011
               Dec T(00)   000   111   000   111   000   111
Dec Flux (1)   Inc T(10)   011   001   101   100   110   010
               Dec T(00)   111   000   111   000   111   000