Modelling of Speed Observer System for Sensorless Control of Three Phase Induction Motor

Presented By ABHIK DAS, ROLL NO: 14201612001

ARINDAM DATTA, ROLL NO: 14201612013ATANU MAJI, ROLL NO: 14201612014AYAN MAITI, ROLL NO: 14201612015

SARTYAKI MANNA, ROLL NO: 14201612043SAYANTAN PAUL, ROLL NO: 14201612045

SNEHASIS BANERJEE, ROLL NO: 14201612048

Guided by Mrs. SAYANTI MAULIK

Speed Sensor System

Speed Sensor is an analog/digital device which is used to measure speed.

In controlling AC Machine Drives Speed Transducers such as Tacho-Generators, Resolvers or Digital Encoders are commonly used to obtain speed information.

DISADVANTAGE OF COMMONLY USED SENSORS

Speed Sensors has some disadvantages-

•They are usually expensive

•The speed sensor and the corresponding wires will take up space

•The Efficiency of these Speed Sensors decreases

•Frequently maintenance required

•In defective and aggressive environments, the speed sensor might be the weakest part of the system

What is Sensorless Control?

Usually Sensorless control is defined as a control scheme where no mechanical parameters like, speed and torque, are measured.

Traditional vector control systems use the method of flux and slip Estimations based on measurements of the phase currents and DC link voltage of the inverter but this has a large error in speed estimation particularly in the low-speed range.

The model reference adaptive system (MRAS) techniques are also used to estimate the speed of an induction motor. These also have a speed error in low-speed range and settle to an incorrect steady-state value.

In recent years, non-linear observers are used to estimate induction motor parameters and states.

• Closed-loop speed and position control : It is an essential feature for high-precision drives employed for servos, machine tools and robots.

• The field-oriented control(FOC) :

The recent trend in field-oriented control is towards the use of sensorless techniques that avoid the use of speed sensor and flux sensor.

In our Project, We have used The Speed Observer System for Estimation of Speed.

Methods for Flux and Speed Estimation

What is Obsever?

All states are not available for feedback in many cases and one needs to estimate unavailable state variables.

Estimation of unmeasurable state variables is commonly called observation. A device (or a computer program) that estimates or observes the states is called a state-observer or simply an observer. If the state-observer observes all state variables of the system, regardless of whether some state variables are available for direct measurement, it is called a full-order state-observer.

An observer that estimates fewer than the dimension of the state-vector is called reduced-order state-observer or simply a reduced-order observer.

If the order of the reduced-order state observer is the minimum possible, the observer is called minimum-order state observer.

Speed Observer System

Estimation of the rotor speed of an induction motor without the use of speed sensors is the main focus.

Estimation of rotor speed is done by using the two-phase vector model of the induction motor in d-q and - reference frames.

The rotor speed estimated by the speed observer system is used to estimate the parameters of the induction motor.

The whole work of Speed Observer System is done by MATLAB 7.12

Basic Block Diagram of Speed Observer System

Where will be the Block put in Sensorless Control?

Space Vector and System Modelling

Space Vectors The space vector approach is commonly used to model the dynamic behavior of AC

machines. The space vector is a complex variable, whose amplitude and angle can vary arbitrarily with time.

Space Vector of Three-Phase Current System

For the analysis of the three-phase ac machine, certain assumptions are made for the three-phase stator. The assumptions are as follows: 

In the stator-winding system of a three-phase ac machine, each phase windings represents a specially formed solenoid.

 The distribution of the field and of the MMF respectively, along the air gap are sine waves and that the individual phase windings are symmetrically distributed along the circumference of the stator iron.

Space Vector and System Modelling

• In this figure, a current of instantaneous value ia flows in the armature coil aa (fig) then the related current vector is collinear with the magnetic axis of the phase winding aa.

•The same conditions are valid for the armature coils bb and cc, which is excited by currents of instantaneous, values ib and ic respectively.

•The resultant current to be

Spatial Currents in a Three-phase Stator

a cbi i i i

Space Vector and System Modelling

In a development of this idea, it may be stated that since this space vector is confined to a plane, we can use the method of complex numbers to describe and define it. Consider, a Gaussian plane with its real axis along the magnetic axis of the phase winding aa.  

Fig shows the position of real and imaginary axes in

this plane. Now we are able to define mathematically the three phase vectors and also the sum vector. As seen in fig the vector of ia is always collinear with the real axis; hence,Representation of

Spatial Currents in a 3-Phase Stator in the Complex plane

a ai i

Space Vector and System Modelling

That is, it is a variable real quantity. From fig. the vector ib is

The space vector ic is given by,where,

The symbols a and a2 are used solely to define the spatial directions of the vectors ia, ib and ic. These vectors

always remain in the same fixed position with respect to the stator of the machine while their magnitudes change with time. Thus, the sum vector can be written in complex form as:

Thus, the space vector of the three-phase current system is given by,

120jb b bi i e ai

240 2jc c ci i e a i

120 1 32 2

ja e j 2402 1 32 2

ja e j

2a cbi i ai a i

223s a cbi i ai a i

Flux and Voltage Vectors

In the same way as we have derived a stator current vector for a three-phase machine, we may also establish flux and voltage vectors. Denoting the instantaneous values of the total flux linked with the individual phase as a, b and c, the space vector of the linked fluxes becomes

and for the voltage vector we similarly obtain,

where, ua, ub and uc denote the instantaneous values of the phase-to-neutral voltages of the stator coils.

223s a cba a

223s a cbu u au a u

Voltage Equations

Making use of space vectors, we can write the voltage equations of a three-phase machine. The voltage equations of the individual phase coils are:

………(1) ………..(2) …..(3) Here, we have assumed symmetrically wound three-phase stator with equal resistance Rs in each phase

winding. Thus, on multiplying equation (1) by 2/3, equation (2) by 23a and equation (3) by 2/3a2, and subsequently adding together the left and right-hand sides of these equations, we obtain

So the stator voltage equations of a three-phase motor can be condensed into single vectorial equation

This equation is a very simple expression of stator quantities in a three-phase machine; it describes the variations of voltages, currents and linked fluxes simultaneously in the three-stator phases. It reduces the number of equations from three to one, without affecting the universal validity of the basic voltage equations.

aa a s

du i R dt b

sb bdu i R dt

cc c s

du i R dt

2 2 22 2 23 3 3a a c s a cb b b b

du au a u i ai a i R a adt

ss s s

du i R dt

Rotor Quantities

We may also write vector equations for the rotor. We assume at first that the wound rotor of the machine is also equipped with a three-phase winding system. In this case, it is easy to write the equations, since the rotor current becomes,

where, ira, irb and irc designate the instantaneous values of the rotor currents in the

rotor coils a, b and c. The equations relating to the rotors flux linkages and voltages are as follows:

and the rotor voltage equation becomes,

223r ra rcrbi i ai a i

223r ra rc rca a

223r ra rcrbu u au a u

rr r r

du i R dt

Coordinate Transformation

This Fig shows two reference frames : The first frame, at rest, is fixed to the

stator. The current vector is is defined by the instantaneous magnitude is and phase angle .

The real axis of the rotating reference frame includes an angle ‘x’ with the real axis of the coordinate system at rest.

Clarke Transformation

The Clarke transformation is basically employed to transform three-phase to two-phase quantities. The two-phase variables in stationary reference frame are sometimes denoted as and . As shown in fig.6 the -axis coincides with the phase a-axis and the -axis leads the -axis by 90.

0 0 abcf T f

0

1 11 2 22 3 303 2 2

1 1 12 2 2

T

Transformation Matrix = [T0] Relationship Between the and abc Quantities

Park Transformation

The Park’s transformation is a well-known transformation that converts the three-phase quantities to two-phase synchronously rotating frame. The transformation is in the form of:

0dq dqo d abcf T f

0

2 2cos cos cos3 3

2 2 2sin sin sin3 3 31 1 12 2 2

d d d

dq d d d dT

d is the transformation angle

cos sinsin cos

dq

iii i

Axes , with Space Phasors F, F Axes d, q with Space Phasors Fd, Fq

Simulation Block Diagram of Speed Observer System

Coordinate Transformation Block

In this particular block the currents and voltages are transformed in the d-q reference frame. The stator input voltages are taken as usd and usq. The three phase transient currents ia, ib irrespectively are used as input currents to the stator. The three phase currents are transformed to the d-q reference axes by using the Park’s Transformation according to the following equations:

Coordinate Transformation Block

Flux Simulator Block

In this particular block the rotor flux linkages in the d-q reference axes i.e. and are estimated by using the voltage model of the induction motor. The inputs used for this block are the voltages usd and usq and the currents id and iq. The equations used in this block are as follows:

1ˆ ˆ ˆ ˆˆ ˆ r

comsds sqsd sd rd rd

d u R i Kdt

1ˆ ˆ ˆ ˆˆ ˆ rsq com

sq s sq rq rqsdd u R i Kdt

ˆˆ ˆ s rrrd sd sdm m

L LL iL L

ˆˆ ˆ s rrrq sq sq

m m

L LL iL L

Flux Simulator Block

Steady State Speed Calculation

The rotor speed estimation is good only at steady state, but during the transients there is an error, which increases with a decrease in speed response. This block shows how to calculate the rotor speed from the steady state relationships. The inputs used for this block are the estimated flux components ,voltages ud and uq, the currents id and iq and also the estimated value of .

The equations used in this block are as follows:2

3 12 4

3 22

sirm

a x i a qa x

s ss sq u i u i

12 r sm s rx i i

22 r sm r sx i i

2 221 rm rx

1212

21

m mrm r

r m

L xR L x Output Block is

Steady State Speed Calculation

Steady State Speed Calculation This is used as an input for the PI controller and thus we obtain the steady

state rotor flux linkage speed as,

When the rotor speed is estimated by using the steady state value of the rotor flux linkage speed, the error will be 2% under this condition as compared to when the rotor speed is estimated without the steady state considerations. The graph of rotor speed with steady state considerations is as shown in last of the slides.

12

21

1 1ˆˆ 1 1rm m

rq rm rr m

L xK RT s L xTs

PI Controller Block

The input for this block is the estimated quantity of flux component i.e. . The equations used in this block are as below:

where, K and T are the constants known as PI parameters. Thus the output for for this block is the estimated rotor flux linkage speed .

1ˆ 1r K T s

1 ˆ1 rqK T s

Rotor Speed Calculation Block

In this particular block the rotor speed is finally estimated by using the rotor flux linkages speed, as estimated in the above-mentioned block. The inputs for this block are the currents id and iq and the rotor flux linkages speed, . The equation used in this block for estimation of rotor speed is:

where. Rr is the rotor resistance and Lr is the rotor inductance. The values of these parameters are also taken as stated in the data-sheet. Thus the output of this block is the estimated rotor speed.

ˆˆ ˆ ˆr

r sqr

r sd

R iL i

Output of Simulation of Speed Observer System

CONCLUSION

Using the voltage model of the induction motors simulates the speed observer system.

The simulation work is carried out using both steady state and transient conditions.

Used this system in fixed point digital signal processor &field programming gate arrays.

Research is going on this system for past 10 years.

We present this work to drive an applicable method for sensorless control of IM.

Thank You