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Direct torque control

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SIMULATION AND ANALYSIS OF DIRECT TORQUE CONTROLLED INDUCTION MOTOR

SIMULATION AND ANALYSIS OF DIRECT TORQUE CONTROLLED INDUCTION MOTOR

Chapter 1INTRODUCTION OF DIRECT TORQUE CONTROL INDUCTION MOTOR DRIVE1.1 Introduction

The control and estimation of induction motor drives constitute a vast subject, and the technology has further advanced in recent years. Induction motor drives with cage-type machines have been the workhorses in industry for variable speed applications in a wide power range that covers fractional horsepower to multi-megawatts. These application include pumps and fans, paper and textile mills, subway and locomotive propulsions, electric and hybrid vehicles, machine tools and robotics, home appliances, heat pumps and air conditioners, rolling mills, wind generation systems, etc. In addition to process control, the energy saving aspect of variable-frequency drives is getting a lot of attention nowadays.The control and estimation of ac drives in general are considerably more complex than those of dc drives, and this complexity are the need of variable-frequency, harmonically optimum power supplies, the complex dynamics of ac machines, machine parameter variations, and the difficulties of processing feedback signals in the presence of harmonics.There are two ways to control ac drives (1) Scalar control (2) Vector controlScalar control techniques of voltage fed and current fed inverter drives are somewhat simple to implement but the inherent coupling effect gives sluggish response and the system is easily prone to instability because of higher order system effect. For example, If the torque is increased by incrementing the slip, flux tends to decrease. This flux variation is always sluggish. So, this flux decrease is then compensated by the sluggish flux control loop feeding in additional voltage. This dipping of flux reduces the torque sensitivity with slip and lengthens the response time. This explanation is also valid for current-fed inverter drives.The above mentioned problem can be solved by Vector control. The invention of vector control in the beginning of 1990s, and the demonstration that an induction motor can be controlled like separately excited dc motor. Because of dc machine like performance, vector control is known as decoupling, orthogonal or transvector control.In mid-1980s, an advanced scalar control technique, known as direct torque control, was introduced for voltage fed inverter drives. This technique was claimed to have nearly comparable performance with vector controlled drives without introducing more complexity as vector control. More details about direct torque is given briefly in this chapter.

1.2 Classifications of Different Control Methods Figure 1.1 General Classification of Induction Motor Control MethodsTable 1.1 Drive and Control VariablesDrive Control Variables

DC DrivesArmature current, IaMagnetizing current,Im

AC Drives(PWM)Output VoltageOutput Frequency, F

Direct Torque ControlMotor Torque & Motor Magnetizing Flux

In above Table 1.1, various drives and its control variables are shown. Here given variables are controlled in respective drive systems. And in Table no 1.2, comparison of various drives is given.

Table 1.2 Comparison of Various DrivesControl TypeTorque ControlFlux ControlResponseAdvantages

Disadvantages

DC DriveDirectDirectHighHigh AccuracyGood torque responseSimpleMotor maintenanceMotor costEncoder required for high accuracy

Scalar Frequency ControlNoneNoneLowNo encoderSimpleLow accuracyPoor torque response

FluxvectorcontrolIndirectDirectHighHigh accuracyGood torque responseEncoder always required

DirectTorque controlDirectDirectHighNo encoderModerate accuracyExcellent torque responseEncoder required for high accuracy

1.3 DC Drive Analogy In order to understand direct torque control scheme, one should have knowledge about vector control and its control principle as explained in this topic. As we know that vector control technique has dc like performance; dc drive analogy for separately excited dc motor is explained here.

The equation of electromagnetic torque is given by,

or (1.1)

Where, = Armature current (Torque component)

= Field current (Flux component)

= Field flux

= = constants

Ia IM Inverter

If Ia M

If

Figure 1.2 Separately Excited DC Motor

Ia Vector control

Figure 1.3 Vector Controlled Induction Motor

Torque FieldComponent Component

Torque FieldComponent Component The construction of dc machine is such that the field flux f produced by the current if is perpendicular to the armature flux a which is produced by armature current ia. These quantities are stationary in space and orthogonal or decoupled in nature. This means that when torque is controlled by controlling the current ia, the flux f is not affected and we get fast transient response and high torque/ampere ratio with rated f. Similarly, when the field current is controlled, it affects the field flux (f) only, but not the flux a. This is because of decoupling. Because of the inherent coupling problem, an induction motor cannot generally give such fast response.1.4 Vector Control of Induction MotorDC machine-like performance can be extended to an induction motor if machine control is considered in a synchronously rotating reference frame (de qe), where the sinusoidal variables appear as dc quantities in steady state. In Figure 1.2(b), the induction motor with the inverter and vector control in the front end is shown with control current inputs, ids* and iqs*.These currents are the direct axis component and quadrature axis components of the stator current respectively, in a synchronously rotating reference frame. With vector control, ids is analogous to field current if and iqs is analogous to armature current Ia of a dc machine. Therefore the torque can be expressed as

Or (1.2)

Where, = Torque component of current

= Flux component of current

= Peak value of sinusoidal flux

= = constantsThis dc machine like performance is only possible if ids is oriented (or aligned) in the direction of flux r and iqs is established perpendicular to it, as shown by the space vector diagram on the right of Figure. This means that when iqs* is controlled, it affects the actual iqs current only. But does not affect the flux r .Similarly, when ids* is controlled, it controls the flux only and does not affect the iqs component of current. This vector or field orientation of currents is essential under all operating conditions in a vector controlled drive. Note that when compared to dc machine space vectors, induction machine space vectors rotate synchronously at frequency e , as indicated in the figure .In summary, vector control should assure the correct orientation and equality of command and actual currents.But vector control has disadvantages like the huge computational capability required and the compulsory good identification of motor parameters. Other disadvantages are Coordinate transformations are required, current controllers are required, PWM signals generator. The performance of this method is very sensitive to change in the values of various quantities Thus, to overcome from more computational steps are required to estimate various quantities, complexity and to retain the performance obtained in vector control technique, new technique called Direct Torque Control is proposed by I. Takahashi and T. Nogouchi. 1.5 Direct Torque Control of Induction MotorSince, DTC (direct torque control) introduced in 1985, the DTC was widely used for Induction Motor Drives with fast dynamics. Despite its simplicity, DTC is able to produce very fast torque and flux control, if the torque and the flux are correctly estimated, is robust with respect to motor parameters and perturbations .Unlike FOC (field oriented control), DTC does not require any current regulator, coordinate transformation and PWM signals generator. In spite of its simplicity, DTC allows a good torque control in steady-state and transient operating conditions to be obtained. Main Features of DTC are as follows:

(1) Direct control of flux and torque.(2) Indirect control of stator currents and voltages.(3) Approximately sinusoidal stator fluxes and stator currents.(4) High dynamic performance even at standstill

Main Advantages of DTC are as follows:

(1) Absence of co-ordinate transforms.(2) Absence of voltage modulator block, as well as other controllers such as PID for motor flux and torque.(3) Minimal torque response time, even better than the vector controllers.(4) Absence of voltage modulator as well as other controllers.(5) Decoupled control of torque and stator flux(6) Excellent torque dynamics with minimal response time.(7) Inherent motion-sensor less control method since the motor speed is not required to Achieve the torque control.

However, Some Disadvantages are also present such as:

(1) Possible problems during starting. It was suggested by that by compensating the statorResistance.(2) voltage drop so that stator flux can be constructed quickly, which makes DTC be applicable for low speed region.(3) Inherent torque and stator flux ripple, which was overcome by when suggesting a unified torque and flux control method using DTC-based induction motor drive

Chapter 2MATHEMATICAL MODEL OF PROPOSED DIRECT TORQUE CONTROL FED INDUCTION MOTOR

2.1 Proposed Block Diagram of DTC fed Induction Motor

ref error - Vdc +Vector Selection Table

Flux Controller

+ Sa - Sb Torque Controller

Tref n(r) Sc + Terror Sector Detection

- ds qs Flux&Torque Estimator

Testimated IA3 phase to 2 phase Transformation of Voltages&Currents

IB estimated 3 Phase IM

Figure 2.1 Block Scheme of Direct Torque Control Method

2.2 Principle of Direct Torque ControlDirect Torque Control (DTC) has become an alternative to field oriented control or vector control of induction machine. It was introduced in Japan by Takahashi (1984) and Depenbrock (1985).DTC of induction machine has increasingly become the best alternative to Field-Oriented Control methods. The block diagram of DTC system for an induction motor is as shown in Figure 2.1 the DTC scheme comprises torque and flux estimator, hysteresis comparators for flux and torque and a switching table. The configuration is much simpler than the vector control system due to the absence of coordinate transforms between stationary frame and synchronous frame and PI regulators. It also doesnt need a PWM and position encoder, which introduces delay and requires mechanical transducers respectively. DTC based drives are controlled in the manner of a closed loop system without using the current regulation loop. DTC scheme uses a stationary d-q reference frame (fixed to the stator) having its d-axis aligned with the stator q-axis. Torque and flux are controlled by the stator voltage space vector defined in this reference frame. The basic concept of DTC is to control directly the stator flux linkage (or rotor flux linkage or magnetising flux linkage) and electromagnetic torque of machine simultaneously by the selection of optimum inverter switching modes. The use of a switching table for voltage vector selection provides fast response, low inverter switching frequency and low harmonic losses without the complex field orientation by restricting the flux and torque errors within respective flux and torque hysteresis bands with the optimum selection being made. The DTC controller comprises hysteresis controllers for flux and torque to select the switching voltage vector in order to maintain flux and torque between upper and lower limit.

2.3 Induction Motor ModellingThe main objective of DTC is to control the induction motor. The per-phase equivalent circuit of an induction motor is valid only in steady-state condition. In an adjustable speed drive like the DTC drive, the machine normally constitutes an element within a feedback loop and hence its transient behaviour has to be taken into consideration.The induction motor can be considered to be a transformer with short circuited and movingSecondary. The coupling coefficients between the stator and rotor phases change continuously in the course of rotation of rotor. Hence the machine model can be described by differential equations with time-varying mutual inductances.For simplicity of analysis, a three phase machine which is supplied with three-phase balanced supply can be represented by an equivalent two-phase machine as shown in Figure 2.2.The time-varying inductances are to be eliminated so as to obtain the dynamic model of the induction motor . The time-varying inductance that occur due to an electric circuits in relative motion and electric circuits with varying magnetic fields can be eliminated by transforming the rotor variables associated with fictitious stator windings. For transient studies of adjustable speed drives, the machine as well as its converter is modelled on a stationary reference frame.2.4 Three Phase to Two Phase Conversion

bs

as

cs

Figure 2.2 Stationary Frame as-bs-cs to ds-qs Axes TransformationAssume that the ds-qs axes are oriented at angle, as shown in Figure 2.2.The voltages vdss and vqss can be resolved into as-bs-cs components and can be represented in the matrix form is given by following transformation matrix,

(2.1)And its Inverse transformation matrix is given as below,

(2.2)

Where, is zero sequence component and it is used here to make complete homogeneous transformation matrix 3*3. It is convenient to set = 00 in equation 2.2.so we get new matrix as below,

(2.3) is angle between 3 phase stationary frame and 2 phase stationary frame. But for reducing the complexity we take =0.It means both frames are align. So this matrix is converted into the following form. By using equation 2.3, we can easily convert three phase quantities in to two phase quantities. Here we have taken voltage but quantities like flux and current are also transformed into two phase ds-qs frame using equation 2.3.2.5 Torque and Flux EstimatorUsing equation 2.3, the motor flux and torque are calculated from the machine terminal voltages and currents. The ds qs voltages and currents in stationary reference are given as below.

Ids and Iqs are given as below,

(2.4)

(2.5)

And Vds and Vqs are given as below,

(2.6)

(2.7)

If Vs is supply voltage and Rs is stator resistance per phase then voltage equation is given by,

(2.8) So, from equation 2.8,

(2.9)

As we know from above equation that, flux is the function of voltage. so, by integrating voltage with respect to time we get flux.

Thus, from equations 2.4 and 2.6, flux is given by,

(2.10)

And from equations 2.5 and 2.7, flux is given by,

(2.11)The magnitude of the stator flux can be estimated by

(2.12)

Now, By using the flux components, current components and IM number of poles, the electromagnetic torque can be calculated by

(2.13)

This estimated flux and estimated torque are compared with reference flux and reference torque respectively.

2.6 Flux Comparator

Two level hysteresis comparator is used for Flux comparator to compare reference flux and estimated flux. The error in flux is then given by 1 or 0.This two level comparator has band of 2H. flux error = 1 = Increase in flux ; if estimated flux < reference flux - H (2.14a) flux error = 0 = Decrease in flux ; if estimated flux > reference flux + H (2.14b) 2.7 Torque ComparatorThree level hysteresis comparator is used for Torque comparator to compare reference torque and estimated torque. The error in torque is then given by 1,0,-1.This three level comparator has band of 2HT.

Torque error = 1 = Increase in torque; if estimated Torque < reference Torque HT (2.15a) Torque error = 0 ; if estimated Torque = reference Torque (2.15b)Torque error = -1 = Decrease in torque; if estimated Torque > reference Torque + HT (2.15c)2.8 Inverter and SwitchingThree legs inverter is used to supply three phase induction motor. Inverter diagram is shown as below:

Figure 2.3 IGBT based 3 Legs InverterThere are two switches per leg of inverter. As we know that, both of them are complimentary to each other. Means if for particular leg, if upper switches is on or 1 then lower one set to off or 0. So, only upper three switches of three legs are taken as a reference because remaining three lower switches are complementary for respective legs.Since there are three legs, no of possible combinations are given by 23 = 8.These possible combinations are realised by switching the inverter with respective switching.The 8 possible states of inverter with output phase voltages and Vds and Vqs is given in below table 2.1.StatesSaSbScVas

VbsVcsVqsVds

0 (V0)0000

0000

1(V1)100

0

2(V2)110

3(V3)010

4(V4)011

0

5(V5)001

6(V6)101

7(V7)1110

0000

Table 2.1 Different States of Inverter

From table 2.1,it is clear that there are two zero vectors((V0), (V7)) and six non zero vectors((V1), (V2), (V3), (V4), (V5), (V6)).Using above table2.1, Voltage Vds and Vqs are represented in ds qs reference frame.As shown in Figure 2.4, whole frame is divided in to 6 sectors having 600 angular spams.Phasor V0 and V7 are located at origin.

Boundary of various sectors is given by angle as follows, -30