This paper presents a comparison between vector control and direct torque control techniques for induction motor. The main characteristics of vector control and direct torque control are studied by simulation. Both have their own advantages and disadvantages. The performances of the two control techniques are evaluated in terms of torque and current ripples. The transient responses are also studied for load toque variation and implementation complexity. The simulation results show that the vector control schemes gives better performance for variable load but require complex transformations in their basic configuration. However the choice for the DTC appears advantageous as it do not require complex transformations, and presents a low cost solution for applications where low torque ripple is not a major issue.
Keywords - Control of Drive, Induction motor, Direct torque control, Vector control.
I. INTRODUCTION
The Induction machine is an important class of electric machines which finds wide applicability as a motor in industry. More than 85% of industrial motors in use today are in fact induction motors. It is substantially a constant speed-motor with a shunt characteristics; a few percent drop from no load to full load. It is singly excited (stator fed) machine. The torque developed in this machine has its origin in current induction in the rotor which is only possible at non-synchronous speed; hence the name asynchronous machine. On the other hand torque in a synchronous machine is developed only at synchronous speed when the "locking" of the two fields takes place. Therefore the induction motor is plagued by the stability problem inherent in the synchronous motor. Since it is a singly fed machine, it draws its excitation current from the mains to set up the rotating field in the air-gap which is essential for its operation. As a consequence it inherently has a power factor less than unity which usually must be corrected by means of shunt capacitors at motor terminals [1].
After having a brief introduction, the question may arise that why only induction motor, then the answer lies in advantages offered by the machine, which can be listed as low maintenance, low cost, low weight, good efficiency, good overloading capacity, low inertia, solid robustness.
But all these advantages come along with a serious disadvantage and that is unavailability of inherent flexible speed control. With the gift of development in power electronics, we are able to control the speed of induction motor quite efficiently. There are several strategies to control the induction motor as scalar control, vector control (Field-Oriented Control, FOC), direct torque control (DTC), fuzzy based control [2].
It is now recognized that the two high performance control strategies for induction motor drives are field-oriented control (FOC) and Direct Torque Control (DTC). They have been invented respectively in the 70's and 80's [3], [4].
These control strategies are different on the operation principle, but their objectives are the same. They aim both to control effectively the motor torque and flux in order to force the motor accurately track the command trajectory regardless of the machine and load parameter variation or any extraneous disturbances. Both control strategies have been successfully implemented in industrial products [6], [7]. The supporters of field-oriented control and direct torque control claim the superiority of their strategy versus the other [9]. Up to now, the question has not been clearly answered.
The purpose of this paper is to present a comparative study on these two control strategies in order to clarify the "myth". The comparison is based on various criteria including basic control strategies, static and dynamic performance, and parameter sensitivity and implementation complexity. The study is done along with individual simulation of each strategy. Initially the theory of induction machine model is given. The understanding of this model is mandatory to understand both the control strategies (i.e. FOC and DTC). For this the induction machine model and its simulation are discussed in detail [9].
II. VECTOR CONTROL OF INDUCTION MOTOR
The idealized three-phase induction machine is assumed to have symmetrical air gap. The dq0 reference frames are usually selected on the basis of convenience or compatibility with the representations of the network components. The two common reference frames used in the analysis of induction machine are the stationary and synchronously rotating reference frames.
Induction machine equations in stationary reference frame are written as,
Stator and rotor voltage equations:
Flux linkage equations:
Often times machine equations are expressed in terms of the flux linkages per second, ψ's, and reactance x's, instead of λ's and L's. These are related simply by the base or rated value of angular frequency, ωb, that is
Torque equations:
The equation of the motion of the rotor is obtained by equating the inertia torque to the accelerating torque, that is:
The field oriented control scheme consists of controlling the stator currents represented by a vector. This control is based on projections which transform a three phase time and speed dependent system into a two coordinate (d and q coordinates) time invariant system.. These projections lead to a structure similar to that of a DC machine control. Field oriented machines need two constants as input references, the torque component (aligned with the q coordinates) and the flux component (aligned with the d coordinates).
For a synchronously rotating dq0 frame whose d-axis is aligned with the rotor field, the q-component of the rotor field,, in the chosen reference frame would be zero, that is
With zero, the torque equation reduces to
which shows that if the rotor flux linkage, , is not disturbed, the torque can be independently controlled by adjusting the stator q-component current, .
Fig 1. A field oriented control scheme for torque control.
III. DTC OF INDUCTION MOTOR
The block diagram of direct torque and flux control is shown in Fig 2 and Fig 3 explains the control strategy. The speed control loop and the flux program as a function of speed are shown.
Fig 2 Direct torque and flux control block diagram
The command stator fluxand torque magnitudes are compared with the respective estimated values, and the errors are processed through hysteresis-band controllers. The flux loop controller has two levels of digital output according to the following relations:
Where, = total hysteresis-band width controller.
Fig 3(a) Trajectory of stator flux vector in DTC control
The circular trajectory of the command flux vector with the hysteresis band rotates in an anti-clockwise direction. The stator flux is constrained within the hysteresis band and tracks the command flux in a zigzag path. The torque control loop has three levels of digital output, which have the following relations:
3(b)Inverter voltage vectors and corresponding stator flux variation in time Δt
The feedback flux and torque are calculated from the machine terminal voltages and currents. The signal computation block also calculates the sector number S(k) in which the flux vector lies. There are six sectors (each /3 angle wide), as in Fig 3(a). The voltage vector table block in Fig 2 receives the input signals and S(k)and generates the appropriate control voltage vector (switching states) for the inverter by lookup table, which is shown in table 1(the vector sign is deleted). The inverter voltage vector (six active and two zero states) and a typical are shown in Fig 3(b). Neglecting the stator resistance of the machine, we can write
Which means that can be changed incrementally by applying stator voltage for time increment Δt. The flux increment vector corresponding to each of six inverter voltage vectors is shown in Fig 3(b). The flux in machine is initially established to at zero frequency (dc) along the trajectory OA shown in Fig 3(a). With the rated flux, the command torque is applied and the vector starts rotating.
Table I applies the selected voltage vector, which essentially affects both the torque and flux simultaneously.
Table I.
SWITCHING TABLE of INVERTER VOLTAGE VECTORS for DTC
Hψ
HTe
S(1)
S(2)
S(3)
S(4)
S(5)
S(6)
1
1
V2
V3
V4
V5
V6
V1
0
V0
V7
V0
V7
V0
V7
-1
V6
V1
V2
V3
V4
V5
-1
1
V3
V4
V5
V6
V1
V2
0
V7
V0
V7
V0
V7
V0
-1
V5
V6
V1
V2
V3
V4
The flux trajectory segments AB, BC, CD and DE by the respective voltage vectors are shown in Fig 3(a). The total Tr, Since is more filtered, it moves uniformly at frequency ωe , whereas movement is jerky. The average speed of both, however, remains same in the steady-state condition. Table II summarizes the flux and torque change (magnitude and direction) incremental torque due to . Note that stator flux vector changes quickly by , but the change is very sluggish due to large time constant for applying the voltage vectors for the location of shown in Fig 3(b). The flux can be increased by the vectors (vector sign is deleted), whereas it can be decreased by the vectors. Similarly, torque is increased by the vectors, but decreased by the vectors. The zero vector (V0 or V7) short-circuits the machine terminals and keeps the flux and torque unaltered. Due to finite resistance (rs) drop, the torque and flux will slightly decrease during the short-circuit condition.
Table II.
FLUX and TORQUE VARIATIONS DUE to APPLIED VOLTAGE VECTOR.
Voltage
Vector
V1
V2
V3
V4
V5
V6
V7
OR V0
ΨS
↑
↑
↓
↓
↓
↑
0
Te
↓
↑
↑
↑
↓
↓
↓
VI. SIMULATION RESULTS
A. Steady-State Performance
The comparison between the VC and DTC control schemes reveals that the input current amplitude is much higher in the case of the DTC and the torque ripple is more significant in DTC scheme. The torque and the stator current waveform obtained with DTC and VC schemes are shown in Fig. 4. (a) - (d), respectively. Table III summarizes the torque ripple for two operating speeds.
(a)
(b)
(c)
(d)
Fig 4. (a) Torque (DTC), (b) Torque (VC), (c) Stator Current (DTC) (c) Stator Current (VC)
Table III
TORQUE RIPPLE in percent
Speed rad/s
350
500
VC
16
16
DTC
18
22
B. Transient Performance
These results show that using the DTC scheme a better
speed response can be achieved in terms of settling time.
The settling times for the two cases are summarized in
Table IV.
Table IV
SETTLING TIME in second.
Speed rad/s
VC
DTC
350
0.430
0.395
500
0.606
0.577
(a)
(b)
Fig 5. (a)Speed response(VC), 500rad/s, (b) Speed response(DTC),500rad/s
V. CONCLUSIONS
In this paper, main characteristics of field-oriented and direct torque control schemes for induction motor drives are studied and simulated with a view of highlighting the advantages and disadvantages of each approach. Initially, the model of an induction machine is analyzed. Vector controlled drives gives better performance than any other scalar method like V/f control etc. But the DTC drive is found to be comparable in all aspects to that of Vector controlled drive. It is difficult to state clearly on the superiority of DTC versus FOC because of the balance of the merits of the two schemes.
With the additional computation required to improve the basic FOC schemes, as compared to DTC scheme, they will attain comparable performance and complexity. Then the choice of once or other scheme will depend mainly on specific requirement of the application.
