AUTOMATIC FOOT DUST CLEANING

MACHINE

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CONTENTS

CHAPTER NO DESCRIPTION PAGE NO

1 ABSTRACT 3

2 INTRODUCTION 4

3 WORKING PRINCIPLE 4

4 INDUCTION MOTOR 5

5 DYNAMIC MODELLING OF THE INDUCTION MOTOR 19

6 PRINCIPLES OF VECTOR CONTROL 27

7 INDOOR BLOWER PSC MOTOR 28

8 ADVANTAGES 30

9 APPLICATIONS 31

10 CONCLUSION 32

11 REFERENCES 32

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1. ABSTRACT:

This project deals with the fabrication of Automatic Foot Dust cleaning

machine. The aim of this project work is to develop and modernized process for

cleaning the foot dust automatically on/off the machine.

It is very useful for cleaning the foot dust. It can be widely used in houses,

hospitals, auditorium, shops, computer centers, etc. In modern days interior

decorations are becoming an important role in our life. Cleaning of foot dust is a

very important one for our health and reduces the man power requirement.

Every day children are playing games in the ground and their dress, foot,

body having dust. They are clean all the dust containing before entering into the

room or home. In our project foot dust are cleaned automatically by putting the

step in the machine. Hence our project is very useful in our day to day life.

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2. INTRODUCTION

Automatic Foot Dust Cleaning Machine is very much useful in

hospitals, houses, auditorium, shops, computer centers etc; it is very simple in

construction and easy to operate. Anybody can operate this machine easily. It

consists of large number of brush and this brush is used to clean the foot dust.

Hence it is very useful in hospitals, houses, etc. The time taken for cleaning is

very less and the cost is also very less. Maintenance cost is less. There are several

numbers of foot dust cleaning machine and are working under different principles

and the cost is also very high.

In our project is very simple drive mechanism and easy to operate any

persons and children. The size of the machine is also portable, so we can transfer

from one place to other place very easily. In our Automatic foot dust cleaning

machine is simple, all house holding device; even children can also operate it

easily with safety. It is very important one for each and every houses and

hospitals etc.

3. WORKING PRINCIPLE

The automatic foot dust cleaning machine is shown bellow figure. The foot

is kept on the pushing rod; the push button is activated automatically. The main

supply 230V A.C is given to the single phase induction motor. The motor is

running its normal speed. The motor pulley is already connected to the main shaft

pulley with the help of belt drive. The main shaft is rotating according to the speed

of the motor and pulley dimension.

The several numbers of brushes are mounted on the main shaft. The brushes

are rotated due to the rotation of the main shaft. This brushes cleaning the dust in

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the foot or shoes. After cleaning the dust in the foot, the foot was removed from

the machine. The pushing rod is back to its original position due to the spring

action. The bush button is off, so that cut off the main supply to the single phase

induction motor. The motor is off, so that the main shaft is off.

4. INDUCTION MOTOR

I. OBJECTIVES

A.

To experimentally evaluate the circuit model elements for a 3-phase induction motor.

B.

1. To start and test the performance of an induction motor under full load when it is powered from the three-phase line by a FVNR (full voltage, non-reversing) combination starter.

2. To compare the actual performance of a three-phase induction motor with that predicted by the circuit model.

3. To start an induction motor, examine variable speed operation, and perform a full-load test when it is powered by the AC Test Drive.

4. To obtain the data for the torque vs. speed and current vs. speed characteristics of the induction motor using a lab computer program.

II. THEORY AND BACKGROUND

A. CONSTRUCTION

The induction machine has two parts - stator and rotor. The stator carries a distributed 3-phase winding. The stator winding is the input/output winding and is the armature of the machine. The lab machine has a squirrel cage rotor. A squirrel cage rotor has solid bars in the slots and they are shorted together at the ends.

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B. OPERATION

When a balanced 3-phase voltage is supplied to the armature, a rotating magnetic field is produced (just as in a synchronous machine). The speed of rotation is the synchronous speed given by

s 4f1

p rad / s

or

ns 120 f1

p rpm,

where p is the number of poles of the armature winding and f1 is the line frequency.

However, the rotor rotates at a speed less than the synchronous speed. We will designate the angular speed of the rotor in rad/s by   and the speed in rev/min (rpm) by n. The slip speed is speed of the rotor relative to the field, i.e.,

Slip speed = s – (rad/s) = ns – n rpm

The per-unit slip, or, simply slip, is defined as

s s

s

ns nns

The magnitude and frequency of the rotor induced voltage depends on the speed of the relative motion (between rotor and field), which is

slip speed = s – = s s.

The rotor frequency is, thus,

f2 = sf1

The voltage induced (and thereby the current) in the squirrel cage rotor is balanced three-phase with the same number of poles as in the armature. The balanced 3-phase current at the frequency of f2 causes a rotating magnetic field that rotates at the slip speed (s – ) with respect to the rotor, which means at synchronous speed with respect to the stator. The two rotating fields (stator field and rotor field) rotate at the same (synchronous) speed and maintain a certain angular relationship with each other in steady state.

C. EQUIVALENT CIRCUIT

The equivalent circuit given in Figure 1 serves as an approximate circuit model for one phase of the induction motor.

6

+

–

I1 I2 x2 x1

xm

r1

r2

r2 1 s

s r2s

V1

Figure 1. Per phase Equivalent Circuit of Induction Motor

The symbols used in Figure 1 are defined below:V1 = line-to-neutral terminal voltage. The phase windings are considered to be

in a Y configuration.r1 = stator resistance per phasex1 = stator leakage reactance per phaser2 = rotor resistance referred to the stator, per phasex2 = rotor leakage reactance referred to the stator, per phasexm = a shunt reactance supplied to provide a path for the magnetizing

component of the current flowing in the stator. It is this current which produces the revolving field in the motor.

Note that core losses and rotational losses are not accounted for in the equivalent circuit. Omitting core losses causes small but negligible errors. The mechanical power and torque calculated using the equivalent circuit are the generated values. Rotational losses may be subtracted to obtain actual output values. Another approximation is that r2 is constant. In most general purpose motors, r2 varies with the frequency of the rotor currents (and also temperature). It is necessary to use the correct value of r2.

D. LABORATORY EVALUATION OF THE EQUIVALENT CIRCUIT IMPEDANCES.

Three tests are required to evaluate the impedances of the equivalent circuit of a polyphase induction motor:

1. Stator DC resistance measurement.2. No-load test.3. Blocked-rotor test.

Since an "equivalent" circuit is being developed, and only the three line terminals of the stator winding are brought out, one is free to assume either that the winding is connected in a Y configuration, or that it is connected in a configuration. It is easier to deal with a Y circuit, so that is the usual assumption. Thus, for example, the DC

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resistance between any two terminals of the winding is taken to be twice the resistance of one stator phase.

1. DC resistance test.

Two terminals of the induction motor are connected to a DC supply through a circuit breaker, ammeter and a load box. The load box is used to limit the current through the motor. Its resistance is adjusted to bring the current to roughly the rated value, and the voltage across the two terminals of the motor is measured.

Then r1 12

VDCIDC

.

Since V1 (Figure 1) is DC, x1 = xm = 0, and the rotor impedance is not coupled to the stator.

2. Blocked-rotor test.

For this test, the motor shaft is clamped so that it cannot turn. The motor terminals are connected to a 3-phase supply. The rotor becomes the secondary of a transformer operating at the supply frequency. However, in normal operation the frequency of the rotor currents is s*60 or 60s, which is about 2 Hz. Since these machines have deep bars, a 60 Hz blocked-rotor test would yield a value of r2 which is too high. Reduced frequency is recommended by many authors, and by the IEEE standards. We will use a supply frequency of 15 Hz to obtain a value of r2 more nearly correct for full load calculations. This supply frequency produces a rotor current distribution similar to full-load conditions, and still permits the AC transducers to output stable readings. Transducers are provided to measure line voltage, the three line currents, and power (two wattmeter method). Current will be limited to the rated value. The measured quantities will be designated Vbr, Ibr, Pbr. These measurements permit the calculation of the blocked-rotor impedance, Zbr.

Approximation: Under the assumption, s = 1, the current thru xm is quite small, compared to I2, and will be neglected. Thus it is assumed that:

I1br = I2br ,and as a result,

V1brI1br

Zbr Rbr jxbr .

It must be realized that we are attempting to construct a 60 Hz equivalent circuit, while the blocked rotor test is performed at another frequency (say, fbr). The sum of actual reactances (for the 60 Hz circuit) x1 + x2 will be obtained by

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x1 x2xbr

60fbr

where xbr is the reactance calculated by the test. To split x1 and x2 from the sum, note that the lab machine is a general purpose machine of NEMA Design B so that

x1 = 0.4 (x1 + x2)and

x2 = 0.6 (x1 + x2).

3. No-load test

The motor is operated free of any shaft load for this test. The motor is connected to a 3-phase AC line with instrumentation provided to measure line voltage, line currents, and power. An AC source of rated voltage and rated frequency is used and the terminal line voltage (Vnl), average line current (Inl), input power (Pnl), and no-load impedance Znl) are determined.

Since the slip is nearly zero, r2/s is very large and thus the outer branch of the equivalent circuit can be considered open circuited. This assumption can be employed for calculations. We have, then,

Znl = r1 + j x1 + j xm

E. PREDICTING INDUCTION MOTOR PERFORMANCE FROM THE EQUIVALENT CIRCUIT

It is assumed that the equivalent circuit elements have been determined, and the synchronous speed (ns) is known. The problem: Given the applied voltage and the slip, s, find the output speed, horsepower, torque, input current, power, and power factor. Also find the rotor and stator copper losses, and the efficiency.

From AC circuit theory, it is clear that if the equivalent circuit parameters, line voltage, and slip (or equivalently, speed) are known, two mesh equations may be solved to obtain phasor currents I1 and I2. (Use V1 as the reference phasor.) Applying the per phase model results to the three phase motor yields the following predictions.

Speed = ns (1 - s); where ns = 120 f/p, rev./min., and p is the number of poles.

Pg = Rotor Power Input = 3 I22 r2

s Watts

Developed Mechanical Power (DMP) = 1 s Pg or 3 I22

r21 s

s Watts

Horsepower = Pout746

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SCL = Stator Copper Loss =3 I12

r1 Watts

PF = Power Factor = cos I1

Pin = Power Input = 3|V1| |I1| (PF) (Watts)

Efficiency = PoutPin

III. THE LABORATORY MACHINE

The induction machine of the laboratory has the following name plate data:

H.P. 5; Phase 3; Hz 60; Design B;RPM 1750; Amps (for 230V) 12.5; Amps (for 460V) 6.25

The stator has two 3-phase windings. The corresponding phases may be connected in series or in parallel. For a series connection, the rating of 460 V, 6.25 A applies and for a parallel connection 230 V, 12.5 A. The latter applies for our case. Thus before starting lab work, you must remember to connect the two 3-phase windings in parallel

IV. INSTRUCTOR LABORATORY PREPARATION

The blocked rotor test in Day 1 will need a special supply, namely, 3-phase AC of 15 Hz. This section assists the instructors to generate this supply. A separate work station with a synchronous machine is to be used and the supply will reach other stations through the station tie line.

The circuit connections and procedure will be somewhat similar to Day 3 of Synchronous Machine experiment, except that no synchronization will have to be performed. Connect the field windings of the synchronous machine to the outlets of the Field Exciter. Connect the three terminals of the armature of the machine to the 1M contactor through the three-phase transducer package. Use voltmeters to measure line-to-line voltages. The output sides of the 1M contactors go to the tie lines. See Figure 2 for the circuit diagram.

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Field Exciter

Synchronous Machine

3-phase Meter

Package

F

F

1

2

Tie Line

1MFigure 2. Circuit for Generating the Special Supply

Turn the dyno and AC Test Drive circuit breakers ON and put the contactor panel in the HAND mode. 2M may be OFF as it is not used. To protect the field exciter, make sure that the field connection is made and the exciter is off. Now make the following settings on the dyno:

SPEED mode; FULL field; Current Limit = 50%.

The mode (MANUAL/COMPUTER) is your choice. Turn the dyno on with the speed setting at zero. Increase the speed to 450 rpm (±2 rpm). (450 rpm will generate a frequency of 15 Hz). Now turn the exciter on and increase If watching the generated voltage. Increase If (0.6 - 0.7 A) such that the line-to-line generated (open circuit) voltage is 60 (±1) volts. When the current will be drawn, the voltage will drop down to about 15 V.

This supply will be used in the Blocked Rotor Test. At one time the supply should be made available to only one station and other stations must have no connections made to the tie line. Upon making the connection, the line current should be approximately 12.5 A. If there is a sizable difference, adjust If, which changes the voltage.

When all are done, first reduce If to zero and turn the exciter off. Thereafter, reduce the dyno speed to zero and turn it off.

V. LABORATORY PROCEDURE - DAY 1

In the first day's work, experiments will be performed for determining impedances of the equivalent circuit. The MONITOR computer program will act as your "multimeter" for these experiments.

A. DC RESISTANCE TEST

The schematic for this test is given in Figure 3. Connect the two leads from the DC circuit to any two stator terminals of the induction motor. There should be no other connection to the motor. Make sure all of the load box switches are in the off (center) position. Using proper procedures, connect the input to the 125 V DC laboratory supply. Have your wiring checked by your instructor. Close the circuit breaker and line contactor

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1M. By proper manipulation of the load-box switches (connecting resistive elements successively in parallel), bring the DC current through the two stator phase windings up to approximately the rated AC value (12.5A). Read and record Vdc and Idc. Open the line contactor, turn off the power at the main power panel, and disconnect the circuit.

If the 250 V DC supply is used instead of 125 V, a slightly different configuration is to be adopted for the load box. If the resistors (which are 39 ohms each) are connected in parallel then the current through each would be about 6.4 amps, which would be well over the rated current of the element. Thus, groups of two resistors (in series) should be connected in parallel in this case.

125 V dc

1M

Load Box

I

Vexternal dcvoltmeter

Induction Motor

Figure 3. Schematic for DC Stator Resistance Test

B. NO-LOAD TEST

The schematic for this test is given in Figure 4. Be sure that the motor is uncoupled from the dynamometer. Connect the motor terminals to the output of the transducer package which encompasses power measurement by the 2-wattmeter method. Then make connections to the Combination Starter output, using proper safety procedures. Your wiring should be checked by your instructor before proceeding. Close the circuit breaker and press START on the Combination Starter panel. The no-load speed should be about 1799 rpm. Read and record the line currents, line voltage, and wattmeter readings (you may prefer to just print the monitor and highlight the channels of interest, as usual). STOP the induction motor from the Combination Starter.

Note: Actually, the induction motor is self-starting, but the Combination Starter is used to make the starting smoother.

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I

Induction Motor

I

I

A

C

B

P

P

P

A

C

B

V

V

Combination Starter

230 V3

60 Hz

Figure 4. Schematic for No-Load and Full-Load Motor Tests.

C. BLOCKED ROTOR TEST

With the power turned off, connect the motor to the transducer package and 3-phase contactor 1M to the Station Tie-Line, as shown in Figure 5. Your instructor should verify your wiring. The transducer package is to include power measurement by the two-wattmeter method. Now clamp the shaft of your motor as explained by your instructor. One member of the group should hold the clamp (so that the shaft doesn't bang to a stop). IMPORTANT: Only one group (station) at a time may connect to the tie-line. On a signal from your instructor, close 1M. Allow the readings to stabilize (5 seconds or so), then capture the data on the computer screen. Turn OFF the 1M 3-phase contactor and remove the wires from the station tie-line. Highlight line currents, voltages, and power readings on your print-out. The average of Ia, Ib, and Ic will be Ibr.

I

Induction Motor

I

I

A

C

B

P

P

P

A

C

B

StationTie-Line

(energized at15 V, 15 Hz)

V1M

low voltageoutput

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Figure 5. Schematic for Blocked-Rotor Test

VI. LABORATORY PROCEDURE - DAY 2

For this period, the objectives are full load operation of the induction motor with line supply and AC Test Drive supply, and obtaining data for induction motor characteristics by a computerized test.

A. FULL LOAD TEST WITH LINE OPERATION

The motor must be coupled to the dyno with the chain guard in place. Unpin and zero the torque table with the computer. The circuit for this test is the same as that used for the no-load test (Figure 4). After your instructor has checked your wiring, START the induction motor. If the direction of rotation is not positive (as per our convention), STOP the motor, interchange two terminals at the motor connection, re-zero the torque table, and again START.

The speed should be slightly less than the no-load speed. Capture the data on the computer display for later reference. Place the dyno control in the CURRENT mode, FULL field. Set the current to 0 with the Current Limit at 30%. START the dynamometer. There should be no change in the speed of the machine. Now increase the Current Control slowly in the sense opposite to the direction of rotation. One member of the lab group should observe the computer read-out to determine when full-load speed (1750 ±2 rpm) is reached. (Note: It may be necessary to increase the Current Limit slightly to achieve full-load speed) Read and record line voltage, line currents, wattmeter readings, torque, and speed or just get a print-out of the data on the computer screen. STOP the dynamometer, then STOP the induction motor, and turn OFF the combination starter.

B. AC TEST DRIVE SUPPLY

A detailed description of AC Test Drive is in the Synchronous Machine Experiment 6 (Section III: Laboratory Equipment). Here, the induction machine is operated with this kind of supply.

The circuit diagram is the same as in Figure 4, except for two differences:

(a) The AC input is from the 3-phase output terminals of the AC Test Drive (rather than the combination starter).

and (b) Connect one of the line voltages to an isolation package.

Alter/make the connections and have them checked by your instructor. Re-zero the torque table. Turn ON the circuit breaker for the AC Test Drive.

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With the frequency (voltage) control set to zero, start the drive by frequency control. If the direction of rotation is "wrong," reduce the frequency control to zero, STOP the AC Test Drive, alter the FORWARD/REVERSE switch setting and again START. Smoothly increase the frequency control. (This is known as "soft-starting"). Watch how variable speed operation is possible (in full range) and note that speed above 1800 rpm is possible. (How does it compare with line operation?)

Connect the output of the isolation package to an oscilloscope to examine the waveform of the line-to-line voltage. Use "Line Triggering" on the scope and vary the frequency control of the AC Test Drive so that the picture on the scope becomes stationary. In this condition, the AC input to the motor is at 60 Hz. Roughly copy the waveform onto your notebook noting down the associated scales. (Optional: take a picture using a Polaroid camera.)

Get a print-out of the data on the computer display for the existing condition. Why are current, speed etc. different from the line operation case?

Set the dynamometer and apply a load just as in Part A (line operation) and record the data on the computer display. CAUTION: Be certain that you are loading the motor; i.e. increasing dyno current (torque) in the direction opposing rotation. The AC Test Drive is not regenerative, and a "run-away" condition may occur if you drive the machine as a generator. (However, regeneration is possible in line operation.)

Reduce the dyno current setting to zero and turn if off. Reduce the frequency/voltage knob of the AC Test Drive and turn it off.

C. COMPUTERIZED TEST FOR CHARACTERISTICS

In this part of the experiment, the dyno will force the induction motor through speeds zero (blocked rotor) through 1800 rpm (synchronous speed). The computer will run the test in accordance with your specifications and record the data.

The circuit for this test is given in Figure 6. Note that here 230 V, 60 Hz is used (instead of the combination starter or the AC Test Drive). The data to be obtained is for Torque vs. Speed and Current vs. Speed graphs. Hence, measurements of voltages and powers are not required. The ammeters of the transducer package are designed for a maximum current of 25 A, but current magnitudes in the experiment will be well over that value. Therefore, the current will be measured through a current transformer (CT). The CT ratio of 50:5 is selected based on

(a) the actual maximum magnitude of the current and (b) avoidance of saturation (for the sake of accuracy).

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Induction Motor

CT 50:5

IA

230 V 60 Hz Output

Terminals

1M Contactor

Figure 6. Circuit Diagram for Computerized Characteristics Test

The wiring diagram is given in Figure 7 (so that you can verify your connections). With the circuit wired and checked by the instructor, unpin and zero the torque table reading from the computer.

Manually start the induction motor to check the direction of rotation. If it is opposite to the "+" direction marked, STOP the motor, and reverse the phase sequence. Once the direction of rotation has been verified, STOP the motor.

Exit the MONITOR program and enter the INDUCTION MACHINE program from the Power Experiments menu. Be sure that all needed circuit breakers and switches are turned ON. Also, the thermocouple must be connected, otherwise a false temperature measurement may not let the test proceed (due to the thermal protection feature in the program).

For the numerical values (test parameters) requested by the program, enter the following:

Initial Speed (RPM): 1860Final Speed (RPM): 0Ramp Time (seconds) 10 (sec.)Dyno Current Limit : 100 %

When all values have been entered, select "Continue with above values" and press <Enter>. When the computer displays, "Press any key when all switches have been set", do the following:

Put the dyno control into COMPUTER mode, Select FULL field on the dyno panel, Put the 1M contactor in the AUTO position.

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FURNAS

125 V DC 250 V DC

DYNAM- DRIVE

DC TEST DRIVE

230 V ACAC TEST

DRIVE

ICL

STARTERAC COMB

IAL

IBR

ID

ICR

IBL

IAR

230 V AC AC STARTER

TIE LINE

AC TEST DC TEST

125 V DC 250 V DC

A F

Furnas Motor Control Center

CIRCUIT BREAKERSCONTROL POWER

110 V AC

THERMOCOUPLE

2-STEP STARTER

TACH

BLOWER

2A

IE

2BInduction Motor

CT

sec

pri

Figure 7. Wiring Diagram for Figure 6.

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Once you press a key to start the test, the dyno will be turned on first and then the 1M contactor will be turned on. Note that the dyno is set to SPEED mode by the program. The speed setting will be ramped according to the test parameters entered and the data stored. When the program exits, save the data file.

When the test is over, place all controls in MANUAL or HAND position to avoid accidental starting. You should obtain a printed copy of the data and check to see if it is reasonable.

Notes:(i) The experiment for gathering data for the required characteristics cannot

be conducted in a manual way ("Manual" Method). The large currents required for the test would destroy the motor. In the computerized method, the large currents are of short duration and so tolerable.

(ii) The dyno is placed in the SPEED mode by the program. If the dyno is placed in the CURRENT mode, it would be a complicated procedure to obtain data for the complete characteristics.

VII. CALCULATIONS AND GRAPHS

1. Determine the impedances (resistances and inductances) of the equivalent circuit model using the DC test, Blocked Rotor test, and No-Load test data.

2. Use this model to predict motor performance at the same voltage and speed as in the full load line operation.

3. Calculate the average line current, power, power factor, horsepower, and efficiency from:

(a) full load line operation data, and (b) full load AC Test Drive Supply data.

4. From the computer controlled experiment data, plot Torque vs. Speed and (Average) Current vs. Speed from 0 to 1800 rpm. Discard points (if any) above 1800 rpm.

VIII. ANALYSIS

1. Prepare a table comparing predicted and measured performance of the induction motor operated from the 230 V line. Mention some sources of the discrepancies.

2. Compare efficiencies from line and inverter (AC Test Drive) operation and comment on the difference.

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3. In terms of the equivalent circuit, explain the relationship of increasing current and decreasing power factor as the motor is slowed below synchronous speed.

4. Examine the graphs in the neighborhood of ns. In terms of the equivalent circuit, what are the speed, torque, power, and stator current at ns?

5. Dynamic modelling of the induction motor

Vector control purpose

Mechanical motion

Linear motion

For linear motion, the forces acting on a body may usually be simplified to a driving force, Fe, acting on the mass, and an opposing force (or load), Fl, as shown on Figure 1.

Figure 1: A body acted on by two forces.

For translational motion the following may be written:

In any speed and position control of linear motion, force is the fundamental variable which needs to be controlled.

Rotary motion

If the motion is rotary about an axis instead of translational, a situation as shown in Figure 2 arises.

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Figure 2: A body acted on by two torques.

For rotary motion the following may be written:

In any speed and position control of rotary motion, torque is the fundamental variable which needs to be controlled.

Torque in an electric drive

Electromagnetic torque produced by a motor is opposed by load torque. The difference, , will accelerate the system.

Figure 3: A load acted on by a motor

For motor-load motion the following may be written:

Torque is the fundamental variable which needs to be controlled. Note that under steady state conditions angular speed is constant and .

DC-motor drive performance

One of the most essential qualities of a motor is the ability to generate torque. The total torque may be described by

where Ia is the current flowing in the armature and ka becomes a factor describing the physical shape of the winding. DC machine equivalent circuit is shown in Figure 4.

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Figure 4: DC machine equivalent circuit

To change as a step, the armature current ia is changed as a step by the power-processing unit as shown in Figure 5.

Figure 5: DC-motor drive performance

Emulation of DC-motor drive performance

In vector control of induction-motor drives, the stator phase currents , and

are controlled in such a manner that delivers the desired electromagnetic

torque while maintains the peak rotor-flux density at its rated value. The

references values and are generated by the torque, speed, and position control loops. The total torque may be described by

Simulation of induction machine using Matlab and Simulink21

Traditionally in analysis and design of 3-phase induction motors, the “per-phase equivalent circuit” is shown in Figure 6 has been widely used. In the circuit, Rs (Rr) is the stator (rotor) resistance and Lm is called the magnetizing inductance of the motor. Note that stator (rotor) inductance Ls (Lr) is defined by

Ls = Lls + Lm, Lr = Llr + Lm (1.1)

where Lls (Lrs) is the stator (rotor) leakage inductance. Also note that in this equivalent circuit, all rotor parameters and variables are not actual quantities but are quantities referred to the stator.

Figure 6: Conventional Per-phase Equivalent Circuit

It is also known that induction motors do not rotate synchronously to the excitation frequency. At rated load, the speed of induction motors are slightly (about 2 - 7% slip in many cases) less than the synchronous speed. If the excitation frequency injected into the stator is wsyn and the actual speed converted into electrical frequency unit is wm, slip s is defined by

s = (wsyn - wm ) / wsyn = wslip / wsyn, (1.2)

and wslip is called the slip frequency which is the frequency of the actual rotor current.

Although the per-phase equivalent circuit is useful in analyzing and predicting steady-state performance, it is not appropriate to explain dynamic performance of the induction motor.

Dynamic model in space vector form

In an induction motor, the 3-phase stator windings are designed to produce sinusoidally distributed mmf in space along the airgap periphery. Assuming uniform airgap and neglecting the effects of slot harmonics, distribution of magnetic flux will also be sinusoidal. It is also assumed that the neutral connection of the machine is open so that phase voltages, currents and flux linkages are always balanced and there are no zero phase sequence component in the system.

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For such machines, the notation in terms of the space vector is very useful. For a sinusoidal 3-phase quantity of constant rms value, the space vector of the stator voltage, current and flux linkage are constant-magnitude vectors rotating at the frequency of the sinusoid with respect to the fixed (stationary) reference frame. With space vector notation, voltage equations on the stator and rotor circuits of induction motors are,

where the voltages v and currents i are vectors, and where the resistance R and inductance L are matrices. Eq. 34 describes the electromagnetic system by a set of 6x6 matrices of differential equations. The coupling between stator and rotor is dependent on the rotor-position.

Phase transformation

In many cases, analysis of induction motors with space vector model is complicated due to the the fact that we have to deal with variables of complex numbers. When induction motors are controlled by a vector drive, control computation is often done in the synchronous frame. Since actual stator variables either to be generated or to be measured are all in stationary a-b-c frame, frame transform should be executed in the control. The most popular transform is between stationary a-b-c frame quantities to synchronously rotating d-q quantities.

If the goal is to create a rotating space vector describing a circle, three phases with sinusoidal currents are not necessary. From analytic geometry it is known that the circle may be described by two coordinates in space (x and y). This may be used in this case, by placing two coils at 90º and by supplying them with sinusoidal current displaced by 90º (or π/2). These two coils are usually named the d-coil and the q-coil. In the rotating frame of reference the frame of reference in regard to the phase A is named the d-axis (for direct axis) and the other axis is named the q-axis (for quadrature axis).

This method reduces the three-phase system to a two-phase system.

Doing this, it is possible to model the cross-couplings between the individual coils. A further advantage is that in steady-state, the currents flowing in the coils are a DC current. Using the rotating frame of reference, the differentials of any state value (d/dt) are zero in steady-state and when the differentials are different from zero, they give the change from steady-state only. The rotating frame of reference also has the advantage that the rotor-angle is known (it is a state).

Transformation of currents, voltages, flux-linkage, etc.

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What remains is to define a method for performing the phase transformations to the rotating frame of reference. The transformation is done by defining a transformation-matrix for the systems as

where f denote currents, voltages, flux-linkage, etc. For current case, this is shown in Figure 7.

Figure 7. Transformation of phase quantities into dq winding quantities (current case).

The electromagnetic torque

Properly the most important task for the induction motor is to produce a torque on the shaft. The developed torque may be written on the flowing form,

d-q equivalent circuit

The result from the above is a set of equations describing the electromagnetic system in the rotating frame of reference. The equations describing the system may be interpreted as equivalent circuits, which may help in understanding the dynamics of the system.

Using this set of equations, it is possible to construct an equivalent-diagram of the d-, and q-axis individually. For the rotating frame of reference the resulting equivalent diagram for each of the axis is shown in Figure 105 .

a) d-axis

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b) q-axisFigure 8. dq-winding equivalent circuits.

Solving the system: Voltages as Inputs

What remains is to find a strategy for solving the differential equations given in Eq. 5555. One possibility exist: solving for the flux linkages and then calculating the currents. The flux linkage associated with the d-, q-axis are calculated as

Computer simulation

In order to carry out computer simulations, it is necessary to calculate intial values of the state variables, that is, of the flux linkages of the dq windings. These can be calculated in terms of the initial values of the dq windings currents. These currents allow us to compute the electromagnetic torque in steady state, thus the initial loading of the induction machine. Initial conditions are computed in Example 3-1 and in the matlab file EXE_1.m (or EXE_2.m).

Finally, the Simulink model is shown in Figure 9.

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Eq. 3-48

Figure 3-13 Simulation of Example 3-3; File Name EX3_3_1.mdl

Entradatrifasica

ELECRODINAMICS

DQ-WINDING REPRESENTATION

-K-

rad/s --> RPM

1s

Va

Vb

Vc

Wmech

i_dq

abc --> dq

Vc

Vb

Va

f(u)

Torque Eq. 3-47

Info

Load Torque

1/Jeq

Inertia

Start

Double Click toload parameters and initial conditions

Plot

After Simulation, Double Click toplot results using MATLAB

Wmech

Tem

Tem RPMi_dq

Electromagnetic Torque on the Rotor d-Axis

weber-vueltas

La figura 2.11 muestra las relaciones de causalidad entre i, H, B, Φ, y λ.

El flujo enlazado por el devanado q del rotor es

El devanado q tiene una inductancia constante . Por tanto, la fuerza magnetomotriz que genera este flujo enlazado es

El campo magnetico H (aplicando )

La densidad de campo en el entrehierro debida a es

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Del mismo modo la densidad de campo en el entrehierro debida a es

Por lo tanto:

Analisis dinamico en terminos de los devanados dq

The concept of vector control has opened up a new possibility that induction motors can be controlled to achieve dynamic performance as good as that of DC or brushless DC motors. In order to understand and analyze vector control, the dynamic model of the induction motor is necessary. It has been found that the dynamic model equations developed on a rotating reference frame is easier to describes the characteristics of induction motors.

It is the objective of the article to derive and explain induction motor model in relatively simple terms by using the concept of space vectors and d-q variables. It will be shown that when we choose a synchronous reference frame in which rotor flux lies on the d-axis, dynamic equations of the induction motor is simplified and analogous to a DC motor.

representacion en los devanados dqrelaciones matematicas de los devanados dqtorque electromagnetico

6. PRINCIPLES OF VECTOR CONTROL

So far, we have not paid attention to the alignment of the rotating reference frame with respect to the physical coordinate. Noting in Eq. 3.28 that torque is directly proportional to Iqs if λqr = 0, one can choose the rotating d-axis to be the angle of the rotor flux linkage. In fact, this choice offers a lot of advantages of simplifying control and analysis of the motor. Other choices frequently used in direct vector control are stator flux linkage

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frame (d-axis is aligned to the stator flux linkage) and airgap flux linkage frame, which will be discussed briefly at the end of the section.

7. INDOOR BLOWER PSC MOTOR

PURPOSE;

The indoor blower fan assembly (fig.1) is responsible for moving air through the heat exchanger, through the duct work and into the living space. Typically, the assembly consists of a direct drive motor, a centrifugal blower wheel with forward curved blades and a double inlet blower wheel housing. The assembly must overcome the resistance of the furnace air passageways, filter, and ductwork to provide adequate supply air to the living space. Most furnaces use a simple PSC motor with a capacitor to drive the indoor blower assembly.

THE INDOOR BLOWER MOTOR CIRCUIT

When a call for heat is received by the IFC, the pre-purge (induced draft furnace) and the ignition sequence begin. Once the main burners are firing and sufficient flame current is being detected, the furnace begins a timed on indoor blower delay warm up period. (Usually around 45 seconds) Once the delay period has elapsed, the IFC energizes the indoor blower motor assembly through the heat terminal. (fig.2) If the indoor motor fails to start or quits running during the heat cycle, the high limit control will trip and shut down the burners.

When the thermostat is satisfied, the gas valve is de-energized, the induced draft motor begins a 5 second post purge cycle, and the IFC begins a timed off

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fig. 1

fig. 2

indoor blower delay period. At the completion of the blower delay off period, the indoor blower motor is de-energized and the cycle is finished.

INDOOR BLOWER FAN PSC MOTOR CHECK

The blower motor features an internal thermal overload to protect the motor winding from overheating. If the motor is hot, allow it to cool down before checking the motor.

TOOLS NEEDED;MULTIMETER

PROCEDURE; SINGLE SPEED PSC MOTOR WITH INTERNAL OVERLOAD

1. Disconnect power to the furnace.

2. Using an ohmmeter, check the indoor blower motor capacitor. (Remember, always discharge the capacitor with an insulated screwdriver BEFORE attempting to test it.) This is to prevent shock and the possible destruction of your meter. Place one ohmmeter lead on each of the capacitor terminals. If the capacitor is working properly, the ohmmeter should ramp up and then ramp down. If the capacitor fails to respond, it is bad and must be replaced. If it is good, go to the next step. (If the capacitor is swollen or damaged, the above step is unnecessary)

3. Using an ohmmeter, check for resistance between the common and run windings, and between common and start windings of the indoor blower motor. You should measure resistance between each winding (fig.3) If you measure infinite resistance from both common to run and common to start windings, the internal overload is open and the motor must be replaced. (The motor should be cool to the touch when testing.) If you measure infinite resistance from common to only one winding, the winding is open and the motor must be replaced.

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fig. 3

fig. 4

4. Check the resistance from the motor winding leads to the motor case (fig. 4) You should measure infinite resistance. If you measure any amount of resistance, the motor is shorted to ground. Replace the motor. If all of the motor windings check out OK, proceed to the next step.

5. Restore power to the furnace and initiate a call for heat. When burner flame is established, use a voltmeter to measure the voltage at terminals HEAT and CIR N on the IFC board, (fig. 5) The IFC should send out 120 volts through these terminals to the indoor blower motor after the blower delay ON period has expired. If no voltage is present after the blower delay ON is completed, replace the IFC board.

8. Advantages:

Manual effort is reduced.

Operating time is less.

Cleaning and polishing can be done at same time.

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fig. 5

Power consumption is less.

Operating Cost is less.

Design is very simple.

Easy fabrication.

It occupies less floor area.

Initial cost is less.

Net weight is less.

Maintenance cost less.

It can be used in various places

Smoother operation.

9. Disadvantages

They are easily damaged if the voltage exceeds the rated valueThe power measured value is approximate value only.

10. Applications

Domestic purpose.

Hospitals.

Computer centers.

Auditoriums.

Cultural centers.

Schools.

Colleges.

Large scale industries.

Medium scale industries.

Theatres.

Educational institutions.

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11. Conclusion:This report has detailed the development, testing and results of an automated cleaning system prototype in its opening stages of research. A set of requirements that the system was intended to perform was supplied along with a number of restrictions applied. The restrictions included the required inclusion of the cleaning system into the existing IWARD robot platform as well as the issues regarding the installation of certain technologies due to the operating environment. A prototype was shown to be successful within the given parameters, but further development is required in order to improve upon the progress which was achieved. The conclusions summaries’ the successful aspects of the system, the areas in need of attention should further research be conducted, and the flaws discovered throughout the duration of the research period.

12. References

[1] http://www.iward.eu/cms/index.php[2] http://www.iward.eu/cms/index.php?option=com_joomgallery&func=viewcategory&catid=3&Itemid=67[3] http://www.medicaljobsireland.ie/tag/hospital-hygiene-audit-results/[4] http://www.hmi.ie/Documents/february_2009/cover_story_hygiene_report%20hm_Feb_09_p12.pdf[5] http://www.mrsainfection.org/mrsa-in-ireland.php[6] http://www.wsh.nhs.uk/InfectionControl/MRSA.htm[7] Chen & Schelin: Design of Distance Monitoring Algorithm for RoboticApplications. The University of Iowa, Spring 2009[8] Design and Implementation of Cricket-based Location Tracking System.International Journal of Electronics, Circuits and Systems Volume 2 Number 1[9] Marklund: Building a mobile robot with optical tracking and basic SLAM.Luleå University of Technology, January 2009

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