DTC-SVM control for three phase induction motors

By principle, Direct Torque Control (DTC) is used to adjust stator flux and electromagnetic torque. Simple structure and very good dynamic behavior are main features of DTC. However classical DTC has some disadvantages, the most important of them is the high ripple torque. In this paper we propose some variety of DTC combined with FOC structures. Hysteresis controllers and switching table are replaced by PI controllers and space vector modulator. Three algorithms work in fixed switching frequency are developed, can overcome the aforementioned drawback. The proposed schemes are described clearly. Simulation results prove the effectiveness, reliability and correctness of the proposed methods.


I. INTRODUCTION
A various algorithms of control are implemented and marketed in the industry for induction motor. The most recognized are: Scalar Control (V/f), Field Oriented Control (FOC) and Direct Torque Control (DTC). DTC control was proposed in the middle of 80s by I. Takahashi as alternative for the Field Oriented Control. The DTC strategy proposed to replace motor decoupling and linearization via coordinate transformation, like in FOC, by hysteresis controllers.
The objective of the DTC is to maintain the motor torque and stator flux within a defined band of tolerance by selecting the most convenient voltage vector. The control action is obtained by using hysteresis controllers and switching table [1].
Since it was introduced, a large number of papers appear in the literature to improve the performance of DTC of induction machines [2,3,7]. General problems associated with DTC drive are large ripple torque in the steady state and low sampling time that makes his implementation difficult on a digital processor [4].
Many researchers are oriented to combine the principles of DTC and FOC control in the same structure [3, 4, 5, and 6]. The present paper deals this principle. Hysteresis controllers and switching table are replaced by PI controllers and space vector modulator. In this sense, three algorithms are developed. Fundamental theoretical and limits of such approach are presented, discussed and compared with each other. The entire control schemes are simulated with Matlab/Simulink. Some concluding remarks are outlined.
In section 2, mathematical model of induction motor (IM) and three phase inverter with its commands are described. An overview of classical DTC is presented in section 3. The improvements made to conventional DTC are mentioned and detailed in section 4. Section 5, provides digital simulation results and comments. This paper achieved by general conclusion in section 6.

A. Induction motor model
In Park reference frame (d-q), stator and rotor voltage-flux equations are given as: Where p ω and r ω are respectively Park and rotor pulsations.
The magnetic state of the induction motor is governed by stator and rotor currents and fluxes as given by equation (2).
The electromagnetic torque generated by the induction machine can be expressed by various equivalent relations. The most popular torque relation is given by (3): U.S. Government work not protected by U.S. copyright The equation of the dynamic rotor rotation can be expressed as: Where: Te electromagnetic torque, L T load torque, In further consideration the friction factor will be negated ( f K = 0).

B. Three phases inverter model
We consider that the machine is feed by a conventional voltage inverter. This converter has only eight possible voltage vectors. Two of them have zero values and the six others are given by (5) The SVM technique approximates a reference instantaneous voltage sref v by a combination of the switching states corresponding to the basic space vectors. This means that it is required for the average of inverter voltage output to be equal to the reference voltage sref v for any period s T .
While referring to fig.1 the average value of the voltage applied to the inverter in a switching period is equal to: τ k and τ k+1 are the durations for which switching states Separating the real part of the imaginary part in the relationship (8), we find: The angle ξ is the angle of v ref with respect to the considered sector. The coefficient v ρ corresponding to the ratio voltage is defined by: Such that the sum  Takahashi Table to deliver an appropriate voltage vector to the inverter.
Equation (1) implies that stator flux vector trajectory in a stationary reference frame verifies: Voltages vectors of inverter are constant during a sampling period Ts. In addition, the stator resistance can be assumed constant for a long running time. The equation (12)

A. DTC-SVM with Closed -Loop Flux Control (DFC)
The DTC-SVM Scheme with Closed -Loop Flux Control is a new method of control for asynchronous machine [3]. This command differs from the conventional DTC by using a vector modulation which ensures constant switching frequency. Switching commands of the inverter are generally derived by SVM modulation which from information flux trends determines the most appropriate switching. In the fixed reference, the stator flux is obtained from the following equation (17): In the control structure of Fig. 2, the rotor flux is assumed as a reference. The reference stator flux components defined in the rotor flux coordinates can be calculated from the following equations: It is necessary that the stator flux vector in the fixed reference reaches its reference: In this structure, the idea is to control the two important variables of the asynchronous machine: the flux and torque. Their settings are made by control voltages that are generated by proportional integral controllers (PI). These controllers must minimize the error between the mean values of variables and references by imposing a new reference voltage vector at each switching period [19]. SVM command is used to obtain the switching states of the inverter keys. The synoptic DTC-SVM is given in fig.4. Hysteresis controllers and switching table have been eliminated, which eliminates the problems associated with them.

2) Torque and Flux Control in Stator Flux Coordinates
The transfer function of PI controllers is given as follows: ( )   fig.4, SVM Model is replaced by DVC (Direct Voltage Control) structure [8,9]. DVC approach is designed to be applied in various applications for AC drives fed with a three-phase voltage source inverter working with a constant switching time interval as in the direct torque control-space vector modulation (DTC-SVM) scheme. The approach DVC is to choose the voltage vector suitable for the minimization integral criterion between the reference voltage vector v sref and the voltage vector selected by the inverter switching at any period Ts. Thus the SVM may be replaced by the selection at any time one of the voltage vectors of the inverter which minimizes the integral of the error.
The chosen vector is designated by the integer n(t) corresponding to the number of the voltage vector to be selected. This integer between 1 and 7 will be selected according to the criteria mentioned by the relation (27): To minimize the integral of the error, we must find the minimum of the two components of this error: 2 2 ( ) min ( ( )) min( ( ( )) ( ( )) ) These figures below prove that the proposed approaches give a good response on the torque and stator flux. The torque ripple of the electromagnetic torque in classic DTC which is resulted by the cyclic sector changes of stator flux vector and produces sharp edges is now eliminated ( fig.10, 11, 12). Despite electromagnetic torque is regulated by all structures, it is better in the last method. It can also be seen the improvement in motor acceleration and the change in motor's torque using DFC, DTC-SVM and DTC-DVC control.
In fig.10 and fig.11, DTC with PI controller shows an overshoot of the electromagnetic torque. By referring to Figure 12, we can draw the following table.  V. CONCLUSION This paper has presented a modified Direct Torque Control methods for PWM-Inverter fed asynchronous motor drive using constant switching frequency. Constant-switchingfrequency is achieved by using space vector modulation (SVM). Direct voltage control (DVC) which has the same meanings as SVM allows reducing ripple torque and minimizing the number of commutation keys SVM. Based DTC-SVM and DTC-DVC system is compared to the classic DTC scheme for torque control. Simulation results obtained for the DTC-SVM and DTC-DVC illustrate a considerable reduction in torque compared to the existing classical DTC system and a good dynamic and static performance.