Electrical Machinery Lab-i_manual_jan-may 2019.pdf

MANIPAL INSTITUTE OF TECHNOLOGY Manipal - 576104

DEPARTMENT OF ELECTRICAL & ELECTRONICS ENGINEERING

Laboratory Manual for ELECTRICAL MACHINERY LABORATORY – I [ELE 2211]

4th semester B.Tech. (E&E) JAN – MAY 2019

CONTENTS Lab class

Title of experiment

Page

1.

Introduction to Electrical Machinery Lab-I

1

2.

A. OC & SC tests on Single Phase Transformer B. Sumpner’s test

5 13

3.

A. Connection of Single Phase Transformers as Three Phase bank B. Scott connection of Transformers

19 24

4.

Polarity test and Parallel operation of Single Phase Transformers

27

5.

No load and Blocked rotor tests on Three Phase Induction Motor

34

6.

A. Load Test on Three phase Squirrel Cage Induction Motor B. Load Test on Three phase Slip Ring Induction Motor

45 51

7.

Load Test on Induction Generator

57

8.

A. Load Test on Single phase Induction Motor B. OCC of DC Generator

64 69

9.

A. Load Test on DC Shunt Generator B. Load Test on Cumulative Compound DC Generator

75 81

10.

Dynamic modelling of Three Phase Induction Motor

85

Note: Experiment no. 2 to 9 will be conducted cyclically by the student batches.

Course learning outcomes: At the end of the laboratory course, students will be able to:  Identify the parts of electrical machines covered.  Perform tests to find the circuit parameters of Transformer and Induction Machines.  Estimate the performance parameters of Transformer and Induction Machines from their circuit models.  Interconnect given single phase transformers as a three phase bank.  Conduct experiments to observe the steady state operating characteristics of Induction Machines & DC Generators.  Observe dynamic characteristics of the Induction motor using the model given.

Laboratory Examination Evaluation Pattern: A. Continuous Evaluation 

Preparation



Conduction



Documentation



Regularity

B. Semester End Evaluation

: 60 %

: 40 %



Procedure

: 10



Conduction

: 10



Calculations

: 10



Oral viva

: 10

Instructions to the students  General instructions:

 Be regular, attentive and actively participate.  Before coming to the laboratory, prepare well for the experiments to be conducted.  At the beginning of each lab session, students should note down the name plate details of the machines from the designated bed, where the experiment is conducted and prepare the list of meters required.  Have clarity on the observations made & conclusions drawn.  Complete the calculations & graphs and submit them for scrutiny.  If you miss one or more experiments, due to some reason, discuss it with the faculty in-charge and find ways of completing the same.  If you miss a practical class because of medical or other genuine reason, report it to the faculty in charge with documental support and see how those experiments can be completed.  It is mandatory to complete ALL the experiments.  Cost will be recovered from the respective student batch for the damage of equipment due to careless handling.  Safety instructions:  Wearing a pair of shoes is compulsory.  You will work with rotating machinery. Do NOT wear loose fitting clothes.  Do not leave your hair loose.  Get the wiring checked by the instructor before starting the experiment.  Report accident/ damage of equipment to the lab staff/faculty on duty.

Experiment No. 1

Date:

INTRODUCTION TO ELECTRICAL MACHINERY LAB - I Aim of the Experiment: Familiarisation of parts of transformer, single phase induction motor, three phase induction motor, DC generator and their accessories. 1. Three Phase Transformer(Distribution Transformer):

1

2. Three Phase Squirrel Cage Induction Motor:

3. Three Phase Slip Ring (or Wound Rotor) Induction Motor:

2

4. Single Phase Induction Motor: Fan End Shield Fan

Capacitor Stator Bearing

Centrifugal Switch

Terminal Box

Rotor

Shield end Flange

5. DC Machine:

Field Winding Pole Shoe Armature

Frame

Commutator Carbon Brush

3

6. Three Point Starter:

Resistor Studs* Starter Arm

Overload Release

Holding Coil

(*Resistors are placed behind and connections are made to the resistor studs)

4

Experiment No. 2A Expt. Bed No. B7

Date:

OC & SC TESTS ON SINGLE PHASE TRANSFORMER Aim of the Experiment: To conduct the open circuit (OC) and short circuit (SC) tests on the given single phase transformer and to predetermine (i) equivalent circuit parameters (ii) voltage regulation and (iii) efficiency. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: kVA rating

:

Primary voltage

:

Secondary voltage

:

Frequency

:

Apparatus Required: Apparatus

Rating

1. Single phase auto Transformer 2. AC Voltmeter 3. AC Ammeter 4. LPF Wattmeter 5. UPF Wattmeter

5

Nos. required

OC Test:

Procedure for OC Test: 1. Make the connections as shown in above circuit diagram. 2. Keeping the autotransformer at its zero output position, switch ON the AC supply. 3. Adjust the autotransformer output so that the voltmeter reads the rated voltage across the LV winding of transformer. 4. Note down all the meter readings. 5. Bring the autotransformer to zero output position and switch OFF the supply. OC Test Data: Multiplication Factor for LPF wattmeter =

V

= Applied Voltage V0 (V)

No Load Current I0 (A)

6

×I × pf of wattmeter Full scale deflection

×

×

=

Wattmeter Reading × Multiplication factor = P0 (W)

SC Test:

Procedure for SC Test: 1. Make the connections as shown in above circuit diagram. 2. Keeping the autotransformer at its zero output position, switch ON the AC supply. 3. Gradually increase the output voltage of autotransformer till the ammeter reads the rated full load current of the HV side. 4. Note down all the meter readings. 5. Bring the autotransformer to zero output position and switch OFF the supply. SC Test Data: Multiplication Factor for UPF wattmeter =

V

= Applied Voltage VSC (V)

Short Circuit Current ISC (A)

7

×I × pf of wattmeter Full scale deflection

×

×

=

Wattmeter Reading × Multiplication factor= PSC (W)

Determination of Equivalent Circuit Parameters: From OC Test Data:

No load power factor = cos !" =

#" = $" %"

Iron loss component of no load current = %& = %" cos !" =

Magnetising component of no load current = %( = %" sin !" = Core loss resistance *referred to LV side+ = ,&-. =

$" = %&

Magnetising reactance *referred to LV side+ = /(-. =

From SC Test Data:

$" = %(

Equivalent resistance referred to HV side = ,45. = ,64 = Equivalent impedance referred to HV side = 845. =

$7& = %7&

#7& 6 = %7&

6 6 Equivalent reactance referred to HV side = /45. = /64 = 9845. − ,45. =

Equivalent resistance referred to LV side = ,4-. = ,45. × ; Equivalent reactance referred to LV side = /4-.

$-. 6 < = $5.

$-. 6 = /45. × ; < = $5.

*Where V?@ and VA@ are voltages of high voltage and low voltage sides respectively+

Approximate equivalent circuit referred to LV side:

8

Voltage Regulation Curve: Percentage voltage regulation at different load power factors is given by: % Regulation =

%6 *,64 cos ! ± /64 sin !+ × 100 H6

(where, I2 is the magnitude of secondary current, R2e and X2e are the equivalent resistance and reactances referred to the secondary, E2 is the secondary side voltage on No load, +ve sign for lagging power factor load and –ve sign for leading power factor load). Secondary current, I6 =

K = H6

Load pf Cos 

% voltage regulation at full load Lagging pf Leading pf

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 UPF

Load power factor corresponding to zero voltage regulation = cos MtanNO P =

QRS

TRS

Load power factor corresponding to max. voltage regulation = cos MtanNO P =

9

UV

TRS QRS

leading

UV

lagging

Efficiency versus Fraction of full load:

Core loss of the transformer = Reading of wattmeter during OC test = #& = #" = Full load current of the transformer = %6Z- =

K = H6

(where ‘S’ is the VA rating of the transformer)

Full load copper loss of the transformer = #&[Z-

%7& 6 =; < × #7& = %6Z-

(where Isc and Psc are the readings of Ammeter and Wattmeter respectively during SC test)

Where,

% Efficiency at given load =

\ = ^_`abcde df fghh hd`i =

\ × K × cos ! × 100 *\ × K × cos !+ + #& + *\ 6 × #&[Z- + %6

%6Z-

`ei cos ∅ = hd`i kf= (Assume pf =0.8 lagging for this calculation) Fraction of full load l

Copper loss lm × nopqr

% Efficiency pf= Unity

pf=0.8

0.25 (1/4 load) 0.5 (1/2 load) 0.75 (3/4 load) 1.0 (Full load) 1.25 (5/4 load)

Maximum Efficiency:

#& Fraction of full load at which efficiency is maximum = \( = s = #&[Z% Maximum Efficiency = =

\( × K × cos ∅ × 100 *\( × K × cos ∅+ + 2 × #&

10

Nature of Graphs: a. Voltage Regulation Curve

b. Efficiency versus Fraction of full load

11

Note: Draw the graphs on graph sheet, label them completely & enclose here. Conclusions:

12

Experiment No. 2B Expt. Bed No. B7

Date:

SUMPNER’S TEST Aim of the Experiment: To conduct back to back test on the given two identical single phase transformers and to predetermine (i) equivalent circuit parameters (ii) voltage regulation and (iii) efficiency. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: kVA rating

:

Primary voltage

:

Secondary voltage

:

Frequency

:

Apparatus Required: Apparatus

Rating

1. Single Phase Auto Transformer 2. AC Voltmeter 3. AC Ammeter 4. LPF Wattmeter 5. UPF Wattmeter

13

Nos. required

Circuit Diagram:

14

Procedure: 1. Make the connections as shown in circuit diagram. 2. Keeping the autotransformers at their zero output position, switch ON the AC supply. 3. Adjust the autotransformer-1 such that the voltmeter ‘V1’ reads the rated voltage of the LV windings. 4. Observe the voltage indicated by the voltmeter across the SPST switch. a) If it reads zero, the e.m.f’s induced in the HV windings are in phase opposition and the windings are properly connected. b) If it reads twice the rated voltage of HV winding, then HV windings are not properly connected. Hence, decrease the output voltage of autotransformer1 to zero and switch off the AC supply. Interchange the HV terminals of any one transformer and repeat the steps 2 to 4. 5. Close the SPST knife switch. 6. Gradually increase the output voltage of autotransformer-2 till the ammeter ‘I2’ reads the rated current of the HV winding. 7. Keep this setup ON for 30 minutes and then note down all the meter readings. 8. Bring the autotransformers to their zero output positions and switch off the AC supply. LV Side Test Data: Multiplication Factor for LPF wattmeter =

V

×

=

Applied Voltage V1 (V)

×I × pf of wattmeter Full scale deflection

LV Side Current I1 (A)

15

×

=

Wattmeter Reading × Multiplication factor= P1 (W)

HV Side Test Data: Multiplication Factor for UPF wattmeter =

V

× pf of wattmeter

Full scale deflection

×

= Applied Voltage V2 (V)

×I

×

Wattmeter Reading × Multiplication factor= P2 (W)

HV Side Current I2 (A)

Determination of Equivalent Circuit Parameters: From LV Side Test Data:

Iron loss of each transformer = #& =

#O = 2

No load current drawn by each transformer = %" = No load power factor = cos !" =

#& = $O %"

%O = 2

Iron loss component of no load current = %& = %" cos !" =

Magnetising component of no load current = %( = %" sin !" = Core loss resistance *referred to LV side+ = ,&-. =

$O = %&

Magnetising reactance *referred to LV side+ = /(-. =

16

=

$O = %(

From HV Side Test Data:

Copper loss of each transformer = #&[ =

#6 = 2

Voltage applied across each transformer = $7& =

$6 = 2

Equivalent resistance referred to HV side = ,45. = ,64 = Equivalent impedance referred to HV side = 845. =

$7& = %6

#&[ = %66

6 6 = Equivalent reactance referred to HV side = /45. = /64 = 9845. − ,45.

Equivalent resistance referred to LV side = ,4-.

$-. 6 = ,45. × ; < = $5.

Equivalent reactance referred to LV side = /4-. = /45. × ;

$-. 6 < = $5.

*Where $5. and $-. are voltages of high voltage and low voltage sides respectively+

Equivalent circuit referred to LV side:

Note: From the above equivalent circuit parameters, the regulation curve and the plot of efficiency & losses at various loads can be drawn. 17

Conclusions:

18

Experiment No. 3A Expt. Bed No. B8

Date:

CONNECTION OF SINGLE PHASE TRANSFORMERS AS THREE PHASE BANK Aim of the Experiment: To connect the given three, single-phase transformers as three phase bank in (i) Star-Delta and (ii) Delta- Star configurations. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: kVA rating

Primary voltage (V)

Secondary voltage (V)

Frequency (Hz)

Transformer A: Transformer B: Transformer C:

Apparatus Required: Apparatus

Rating

1. Three Phase Auto Transformer 2. AC Voltmeter 3. AC Ammeter 4. SPST Switch 19

Nos. required

1. STAR-DELTA Configuration:

20

2. DELTA-STAR Configuration:

21

TYPE

LOAD

NEUTRAL

VL1

VL2

IL1R

IL1Y

IL1B

IL2R

IL2Y

IL2B

IN

WITH BALANCED WITHOUT

STARDELTA

WITH UNBALANC ED

22

WITHOUT

DELTA -STAR

BALANCED

------

----

UNBALANC ED

------

----

TRANSF. RATIO

Procedure: 1. Make the connections as in circuit diagram. 2. Keep the auto transformer at zero output position and the SPST open (for STAR-DELTA configuration only). 3. Switch ON the 3 phase AC supply and increase the autotransformer output such that the voltmeter VL1 reads 200 V. 4. Switch on the balanced resistive load such that the three ammeters connected on the secondary side read equal values. 5. Note down the meter readings. 6. Repeat the above steps by making the load unbalanced and note down the meter readings. 7. Close the SPST switch and repeat steps 4 to 6. 8. Switch off the load and decrease the autotransformer to zero output position. 9. Switch OFF the AC supply.

Note: The connection for STAR-DELTA and DELTA-STAR are shown in the experiment. The other configurations, namely STARSTAR and DELTA-DELTA can be checked by suitably connecting the primary and the secondary sides.

Conclusions:

23

Experiment No. 3B Expt. Bed No. B6

Date:

SCOTT CONNECTION OF TRANSFORMERS

Aim of the Experiment: To connect the given two, single-phase transformers in Scott connection and show that the secondary voltages are at right angles to each other. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: kVA rating

Primary voltage (V)

Secondary voltage (V)

Frequency (Hz)

Main Transformer: Teaser Transformer:

Apparatus Required: Apparatus

Rating

1. Single phase auto transformer 2. AC Voltmeter 3. AC Ammeter 4. DPST Switch

24

Nos. required

Secondary Voltages at Right Angles

Procedure: 1. Make the connections as shown in the above circuit diagram with the primary of the teaser transformer connected to 86.6 % tapping. 2. Switch ON the 3 phase AC supply. 3. Increase the autotransformer output so that the voltmeter V1 reads 100 V. 4. Note down the meter readings. 5. Repeat steps 3 and 4 for a voltmeter reading of 200V. 6. Decrease the autotransformer output voltage to zero and switch OFF the AC supply.

25

Test Data:

Tapping

86.6%

V1 (V)

V2M (V)

V2T (V)

100 200

100%

100 200

Conclusions:

26

V (V)

m m 9vmw + vmx

Experiment No. 4 Expt. Bed No. B4

Date:

POLARITY TEST & PARALLEL OPERATION OF TRANSFORMERS Aim of the Experiment: To conduct the polarity test on the given transformer and to operate two single-phase transformers in parallel to share a common load. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details:

kVA rating

Primary voltage (V)

Secondary voltage (V)

Frequency (Hz)

Transformer A: Transformer B: Apparatus Required: Apparatus

Rating

1. Single phase autotransformer 2. AC Voltmeter 3. AC Ammeter 4. UPF Wattmeter 5. SPST Switch 6. DPST Switch

27

Nos. required

1. Polarity Test:

Procedure for Polarity Test: 1. Make the connections as in above circuit diagram. 2. Switch ON the AC supply. 3. Increase the autotransformer output so that the voltmeter Vs reads a small voltage say 30 V. 4. Observe the reading of the voltmeter. If the voltmeter V1 reads less than the applied voltage, the terminals connected to the voltmeter are of similar polarities. (P1 and S1). If voltmeter reads higher than the applied voltage, they are of opposite polarities. 5. Reduce the autotransformer output to zero and switch OFF the supply. Test Data: Applied Voltage Vs (V) Transformer-A

Transformer-B

28

Voltmeter Reading V1 (V)

2. SC Test (to be conducted separately for each transformer):

Procedure for S.C Test: 1. Make the connections as shown in the above circuit diagram. 2. Keeping the autotransformer at its zero output position, switch ON the AC supply. 3. Gradually increase the output voltage of autotransformer till the ammeter reads the rated current of the HV side. 4. Note down all the meter readings. 5. Bring the autotransformer to zero output position and switch OFF the supply. S.C Test Data: Multiplication Factor of wattmeter =

V

Applied Voltage Vsc (V)

×I × pf of wattmeter = Full scale deflection Short Circuit Current Isc (A)

Transformer-A Transformer-B

29

Wattmeter Reading × Multiplication Factor= Psc (W)

3. Parallel Operation:

30

Procedure for Parallel Operation: 1. Make the connections as in the above circuit diagram. 2. Switch ON the AC supply. 3. Observe the reading of voltmeter across SPST switch. If it shows zero, close the SPST switch. Else, switch OFF the supply, interchange S1 & S2 of any one transformer. 4. Close the DPST load switch. Switch ON the load in steps and for each step, note down the meter readings. 5. Reduce the load to zero. Open DPST switch and switch OFF the supply. Test Data of Parallel Operation: Trial

VL

(V)

IL

(A)

IA

(A)

{| = v| × }|

IB

(A)

{~ = v| × }~

(VA)

(VA)

Theoretical Calculations: From SC Test Data of Transformer-A: Equivalent resistance reffered to HV side = ,45. = ,64 =

Equivalent impedance reffered to HV side = 845. =

$7& = %7&

#7& 6 = %7&

6 6 Equivalent reactance reffered to HV side = /45. = /64 = 9845. − ,45. =

Equivalent resistance reffered to LV side = ,4-.

$-. 6 = ,45. × ; < = $5.

Equivalent reactance reffered to LV side = /4-. = /45. × ;

31

$-. 6 < = $5.

{• = v| × }•

(VA)

*Where V?@ and VA@ are voltages of high voltage and low voltage sides respectively+ Equivalent Impedance of Transformer A = 8• = ,4-. + ‚/4-. =

From SC Test Data of Transformer-B:

Equivalent resistance reffered to HV side = ,45. = ,64 = Equivalent impedance reffered to HV side = 845. =

$7& = %7&

#7& 6 = %7&

6 6 Equivalent reactance reffered to HV side = /45. = /64 = 9845. − ,45. =

Equivalent resistance reffered to LV side = ,4-.

$-. 6 = ,45. × ; < = $5.

Equivalent reactance reffered to LV side = /4-. = /45. × ;

$-. 6 < = $5.

*Where V?@ and VA@ are voltages of high voltage and low voltage sides respectively+ Equivalent Impedance of Transformer A = 8ƒ = ,4-. + ‚/4-. =

Power Delivered by each Transformer: Secondary Current of Transformer A = %• = %- ×

Secondary Current of Transformer B = %ƒ = %- ×

8ƒ = 8• + 8ƒ

8• = 8• + 8ƒ

(Since the load is mostly resistive, the angle of IL is considered equal to zero) Active power from Transformer A = #• = $- × %• × cos !• =

Active power from Transformer B = #ƒ = $- × %ƒ × cos !ƒ =

(Where !• and !ƒ are the angle between $- & %• and $- & %ƒ respectively). 32

Conclusions:

33

Experiment No. 5 Expt. Bed No. A5

Date:

NO LOAD & BLOCKED ROTOR TESTS ON 3 PH. INDUCTION MOTOR Aim of the Experiment: To conduct No-load test and Blocked-rotor test on a 3 phase Induction Motor and to predetermine its performance characteristics by (i) Equivalent circuit analysis (ii) Circle diagram Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: Rated output power: Supply voltage : Full load current : Rated speed : Apparatus Required: Apparatus

Rating

1. Three phase autotransformer 2. AC Voltmeter 3. AC Ammeter 4. LPF Wattmeter 5. UPF Wattmeter 6. D.C Voltmeter 7. D.C Ammeter 34

Nos. required

1. No Load Test:

Procedure: 1. Make the connections as in above circuit diagram. 2. Keeping the autotransformer at zero output voltage position and no mechanical load on the motor, switch ON the 3 phase AC supply. 3. Increase the autotransformer output voltage till the voltmeter reads the rated voltage of the motor. 4. If one of the wattmeter shows a negative reading, interchange its pressure coil terminals, C and V and the reading is to read as a negative value. 5. Note down all the meter readings. 6. Reduce the autotransformer output voltage to zero and switch OFF the AC supply. No Load Test Data: Multiplication factor of wattmeter =

V

Multiplication factor of wattmeter W1 =

×I × pf of wattmeter Full scale deflection

Multiplication factor of wattmeter W2 =

35

Applied Voltage, VNL (V)

No Load Current, INL (A)

Wattmeter Reading × Wattmeter Multiplication Factor W1

W2

Power I/P PNL=W1+W2 (W)

2. Blocked Rotor Test:

Procedure: 1. 2. 3. 4. 5.

Make the connections as shown in the circuit diagram above. Keep the autotransformer at its zero output voltage position. By suitable means, block the rotor of the motor from free running. Switch ON the 3 phase AC supply. Gradually increase the output voltage of the autotransformer such that the ammeter reads the rated current of the motor. 6. Note down the meter readings. 7. Reduce the autotransformer output voltage to zero and switch OFF the AC supply.

36

Blocked Rotor Test Data: Multiplication factor of wattmeter =

V

Multiplication factor of wattmeter W1 =

×I × pf of wattmeter Full scale deflection

Multiplication factor of wattmeter W2 = Applied Voltage, VBR (V)

SC Current, IBR (A)

Wattmeter Reading × Wattmeter Multiplication Factor W1

W2

Power I/P PBR=W1+W2 (W)

3. Measurement of DC Resistance:

Procedure: 1. Make the connections as shown in the circuit diagram above. 2. Keeping all the switches of the lamp load in OFF position, switch ON the DC supply. 3. Switch ON the required number of lamps and note down all the meter readings. 4. Repeat step 3 until the ammeter reads the rated per phase current of the motor. 5. Reduce the current to zero by switching OFF all the lamps and switch OFF the DC supply.

37

DC Resistance Test Data: Applied Voltage, VDC (V)

DC Resistance R …† = V…† ⁄I…† (Ω)

Current Drawn, IDC (A)

Average DC Resistance = R

ˆ

=

Resistance of the stator winding *per phase+ = ,O = 1.25 × R

ˆ

=

A. Performance Analysis by Equivalent Circuit Parameters: From No Load Test Data: The stator of the motor is delta Connected. No load voltage per phase = $" = $Š- = No load current per phase = %" =

%Š-

√3

=

No load power drawn per phase = #" =

No load power factor = cos !" =

#Š= 3

#" = $" × %"

Iron loss component of no load current = %& = %" cos !" =

Magnetising component of no load current = %( = %" sin !" = Core loss resistance per phase *referred to stator+ = ,& =

$" = %&

Magnetising reactance per phase *referred to stator+ = /( =

38

$" = %(

From Blocked Rotor Test Data: Short Circuit voltage per phase = $•Ž = $ƒQ =

Short circuit current per phase = %•Ž =

%ƒQ

√3

=

Power drawn per phase during Blocked Rotor Test = #•Ž = Equivalent resistance referred to stator = ,4O =

#•Ž 6 = %•Ž

Equivalent impedance referred to stator = 84O =

$•Ž = %•Ž

#ƒQ = 3

6 6 = Equivalent reactance referred to stator = /4O = 984O − ,4O

Resistance of Rotor referred to stator = ,6• = ,4O − ,O =

Equivalent circuit referred to Stator:

39

1 Equivalent resistance of mechanical load reffered to stator = ,-• = ,6• ; − 1< ‘ “““ $ " %’6• = Rotor current referred to stator = *,4O + ,-• + + ‚/4O

Performance Calculations:

%’" = No Load current drawn = %& − ‚%(

%’O = Stator current = %’6• + %’"

cos ! = Power factor of motor = cos *Angle between $O `ei %O + #”• = Power input to the motor = 3 × $" × %O × cos ! #– = Power developed by the motor = 3 × %6• × ,-• = Efficiency of the motor =

#– #”•

6

—7 = Synchronous speed of the the motor = N = Speed of the the motor = —7 *1 − ‘+

T– = Torque developed by the motor = Slip

,-•

0.001

0.005

0.01

120 × f = #

#– × 60 2™ × N 0.02

%6• %O

cos ! #”• #– N

T–

40

0.03

0.04

0.05

0.1

Drawing the Circle Diagram: 1. Draw the co-ordinate axes. Let the Y axis represent the phase voltage VPH1. 2. Choose a suitable current scale. (say 1 cm = A) 3. Draw the no-load current phasor OA such that Length š~ =

| I" |

Current Scale

and OA makes an angle ϥ with the Y-Axis.

No load pf angle = !" = tanNO ž

=

√3 × *WO − W6 + Ÿ= WO + W6

(Where W1 and W2 are the wattmeter readings obtained during the No Load test)

4. At A draw a line parallel to X-Axis. 5. Draw the short circuit current phasor OB such that V

Isc × ;V 0 < |ISC rated | SC Length š• = = = Current Scale Current Scale

and OB makes an angle œ

¡

with the Y-Axis.

Short circut pf angle = !•Ž = tanNO ž

√3 × *WO − W6 + Ÿ= WO + W6

(Where W1 and W2 are the wattmeter readings obtained during the Blocked Rotor test)

6. Join AB. This represents the equivalent rotor current during blocked rotor when rated / normal voltage is applied. 7. Draw perpendicular bisector of AB to cut the horizontal line through A at C. 8. With C as center and CA as radius, draw the semi-circle. 9. Draw BD perpendicular to AD meeting the X-Axis at G. 10. The length of BG represents the short circuit power with normal voltage applied. 11. Neglecting the small length DG, BD  BG. Divide BD such that BE R•6 = = ED R O

Then the power scale is: Power scale = 1cm = §ℎ©_© ª•Š

%•Ž ¬-®4¯ 6 « ° = = ª•Ž × %•Ž

41

£¤¥ ¦…

=

§`bb‘

Circle Diagram:

42

Performance Calculations: 1.

Fix the operating point P on the circle diagram corresponding to either the input current per phase or the output power.

2.

Draw PT perpendicular to OG such that it touches the output line at Q, the Torque line at R and the line AD at S.

3.

Join OP.

4.

Operating power factor =

5. 6. 7. 8.

Input current per phase = IO = Length OP × Current scale = PT = OP

Input power = PT × Power scale =

Rotor copper loss = QR × Power scale =

Stator copper loss = RS × Power Scale = No load loss = DG × Power scale =

9.

Rotor input = PR × Power scale =

10.

Slip =

11.

Torque =

12.

Power output = PQ × Power scale =

13.

Efficiency =

QR = PR

Rotor input × 60 = 2π × N•

PQ = PT

43

To find maximum quantities from Circle Diagram: 1. Maximum Power Output: Draw a tangent to the circle parallel to the output line AB and find the point of contact P1. Drop a perpendicular from this point to X-Axis. The output corresponding to this point is the maximum output power. 2. Maximum Torque: Draw a tangent to the circle parallel to the torque line AE and find the point of contact P2. Drop a perpendicular from this point to X-Axis. The torque corresponding to this point is the maximum torque. 3. Maximum Power Factor: Draw a tangent to the circle from O and determine the point of contact. The power factor corresponding to this point is the maximum power factor. 4. The Starting torque: Since BE represents the copper loss at short circuit condition and BE lies on the circle, BE represents the starting torque.

Note: Draw the circle diagram on a graph sheet, label it completely & enclose it here. Conclusions:

44

Experiment No. 6A Expt. Bed No. B5

Date:

LOAD TEST ON 3 PHASE SQUIRREL CAGE INDUCTION MOTOR Aim of the Experiment: To conduct load test on the given three phase Squirrel Cage Induction Motor and to obtain its performance characteristics. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: Rated output power: Supply voltage

:

Full load current

:

Rated speed

:

Apparatus Required: Apparatus

Rating

1. UPF Wattmeter 2. AC Voltmeter 3. AC Ammeter 4. Tachometer

45

Nos. required

Circuit Diagram:

46

Procedure: 1. 2. 3. 4. 5. 6.

7. 8. 9.

Make the connections as shown in the circuit diagram. Note down the initial readings on the spring balance. Switch ON the 3 phase AC supply. Start the motor by pressing START (green) button on the STAR-DELTA starter. Pour some water into the brake drum. Increase the tension of the belt around the brake drum, in steps (until the ammeter reads the rated current). At each step, note down the meter and spring balance readings and speed. Decrease the mechanical load by loosening the belt. Stop the motor by pressing STOP (red) button on the STAR-DELTA starter. Switch OFF the AC Supply.

Performance Calculations: Multiplication factor of wattmeter =

V

×I × pf of wattmeter Full scale deflection

Multiplication factor of wattmeter W1 = Multiplication factor of wattmeter W2 = —7 = Synchronous speed of the motor = , = Radius of the brake drum =

120 × f = #

´

Pµ = Input power to the motor = ªO + ª6 ¶ = O/P Torque = *KO ~K6 + × 9.81 × ,

% ‘ = Percentage slip = ;

—7 − — < × 100 —7

pf = Power factor = cos »tan−1 «√3 × ;

ªO − ª6 <°¼ ªO + ª6

2™ × — × ¶ P½¾¿ = Output power of the motor = 60 P½¾¿ % = Percentage efficiency = × 100 Pµ

47

Nature of Graphs:

48

Trial

VL (V)

IL (A)

Wattmeter reading × Multiplication factor W1

W2

N

Spring balance readings S1

S2

Pin

T

% Slip

pf

Pout

%

49

Note: Draw the performance characteristics on a graph sheet, label them completely and enclose here. Conclusions:

50

Experiment No. 6B Expt. Bed No. A5

Date:

LOAD TEST ON 3 PHASE SLIP RING INDUCTION MOTOR Aim of the Experiment: To conduct load test on the given three phase Slip Ring Induction Motor and to obtain its performance characteristics. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: Rated output power: Supply voltage

:

Full load current

:

Rated speed

:

Apparatus Required: Apparatus

Rating

1. UPF Wattmeter 2. AC Voltmeter 3. AC Ammeter 4. Tachometer

51

Nos. required

Circuit Diagram:

52

Procedure: 1. Make the connections as shown in the circuit diagram. 2. Note down the initial readings on spring balance. 3. Keeping external resistance at its maximum position (Pos. 1), switch ON the 3 phase AC supply. 4. Start the motor by pressing the START (Green) button on the DOL starter. 5. Bring the external resistance to minimum position (Pos. 4). 6. Note down the meter readings, spring balance readings and speed. 7. Pour some water into the brake drum. 8. Increase the tension of the belt around the brake drum, in steps (until the ammeter reads the rated current). At each step, note down the meter and spring balance readings and speed. 9. Decrease the mechanical load by loosening the belt. 10. Stop the motor by pressing the STOP (Red) button on the DOL Starter. 11. Switch OFF the AC supply.

53

Performance Calculations:

Multiplication factor of wattmeter =

V

×I

Full scale deflection

Multiplication factor of wattmeter W1 = Multiplication factor of wattmeter W2 = —7 = Synchronous speed of the motor = , = Radius of the brake drum =

120 × f #

´

Pµ = Input power to the motor = ªO + ª6 ¶=

O torque = *KO ~K6 + × 9.81 × , P

% ‘ = Percentage slip = ;

—7 − — < × 100 —7

pf = Power factor = cos »tan−1 «√3 × ;

× pf of wattmeter

ªO − ª6 <°¼ ªO + ª6

2™ × — × ¶ P½¾¿ = Output power of the motor = 60 P½¾¿ % = Percentage efficiency = × 100 Pµ

54

Trial

VL (V)

IL (A)

Wattmeter reading × Multiplication factor W1

W2

N

Spring balance readings S1

S2

Pin

T

% slip

pf

Pout

%

55

Nature of Graphs:

Note: Draw the performance characteristics on a graph sheet, label them completely and enclose here. Conclusions:

56

Experiment No. 7 Expt. Bed No. A12

Date:

LOAD TEST ON INDUCTION GENERATOR Aim of the Experiment: To observe the transition of Induction Machine from motoring to generating mode of operation and to obtain the characteristic curves of Induction Generator. Background Theory: Students are required to refer to reference books & write this section independently. Name Plate Details: Rated output power: Supply voltage

:

Full load current

:

Rated speed

:

Apparatus Required: Apparatus

Rating

1. UPF Wattmeter 2. AC Voltmeter 3. AC Ammeter 4. DC Voltmeter 5. DC Ammeter 6. SPST Switch 7. Rheostat 8. Tachometer

57

Nos. required

Circuit Diagram:

58

Procedure: 1. Make the connections as shown in the circuit diagram. 2. Keeping DC supply switch open and shunt field rheostat of DC machine at maximum position, start the Induction Motor using DOL starter. 3. Reduce the shunt field rheostat and observe the reading of DC voltmeter across the SPST switch. 4. If the reading of this voltmeter increases, switch OFF the DC supply, STOP the induction motor using DOL starter, Switch OFF the AC Supply and interchange the terminals of the DC supply or DC generator). Repeat from step 2. 5. Adjust the shunt field rheostat such that voltage VS across the SPST switch is zero. Close the SPST switch thereby connecting the DC Generator in parallel with the DC supply. 6. Adjust the shunt field rheostat to bring the speed of the Motor-Generator set to nearly synchronous speed such that the sum of the two wattmeter readings is zero. Under this condition, the induction machine is neither taking power from the supply nor giving power to the supply. This condition is called the floating condition. (If one of the wattmeter shows the negative reading, interchange its pressure coil terminals C and V and the reading is to read as a negative value). 7. Note down the meter readings and also the speed which is the actual synchronous speed. 8. Increase the speed approximately by 2 %. The DC machine is operating as a DC motor and driving the induction machine as an induction generator. 9. Note down all the meter readings and the speed at every step. 10. Increase the speed in steps, up to 15 % greater than the synchronous speed and at each step note down the meter readings & the speed. 11. Reduce the speed to synchronous speed, switch OFF the DC supply and the AC supply.

59

Performance Calculations: Multiplication factor of wattmeter =

V

×I × pf of wattmeter Full scale deflection

Multiplication factor of wattmeter W1 =

Multiplication factor of wattmeter W2 = Input power to DC motor = $ÀŽ × %ÀŽ =

Á‘‘g´ce 80 % ©ffcac©eaà fd_ bℎ© ÄÅ ´`aℎce©,

ÀŽ

= 0.8

Output power of DC motor = ÀŽ × $ÀŽ × %ÀŽ = = %ekgb bd ceigabcde ©e©_`bd_ #ÆÇÈ = Output power of Induction Generator = ªO + ª6

Efficiency of Induction Generator, % Power factor = cos ! =

#ÆÇÈ

ÉÊ

=

˾¿Ì¾¿ ½Í µ ξϿµ½ É Î¾Ï¿µ½

√3 × $- × %-

IÑ = In phase component of load current = %- × cos !

IÒ = Quadrature component of load current = %- × sin !

60

Ð ¿½Ð

Ð ¿½Ð µ ̾¿

× 100 =

Nature of Graphs:

61

Trial

VL (V)

IL (A)

Wattmeter reading × Multiplication factor W1

W2

VDC

IDC

(V)

(A)

N (rpm)

Pout (IG)

%

IG

pf

IP

IQ

62

Note: Draw the performance characteristics on a graph sheet, label them completely and enclose here. Conclusions:

63

Experiment No. 8A Expt. Bed No. A13

Date:

LOAD TEST ON SINGLE PHASE INDUCTION MOTOR Aim of the Experiment: To conduct load test on the given single phase Induction Motor and to obtain its performance characteristics. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: Rated output power: Supply voltage

:

Full load current

:

Rated speed

:

Apparatus Required: Apparatus

Rating

1. Single phase autotransformer 2. UPF Wattmeter 3. AC Voltmeter 4. AC Ammeter 5. Tachometer

64

Nos. required

Circuit Diagram:

65

Procedure: 1. Make the connections as shown in the circuit diagram. 2. Note down the initial readings on the spring balance. 3. With no mechanical load on the brake drum, switch ON the AC supply. 4. Gradually increase the autotransformer output such that the voltmeter reads 230 V. 5. Note down all the meter readings and also the speed. 6. Pour some water into the brake drum. 7. Increase the tension of the belt around the brake drum, in steps (until the ammeter reads the rated current). 8. At each step, note down the meter and spring balance readings and speed. 9. Decrease the mechanical load by loosening the belt. 10. Decrease the autotransformer output to zero and switch OFF the AC supply. Performance Calculations: Multiplication factor of wattmeter =

V

×I × pf of wattmeter = Full scale deflection

—7 = Synchronous speed of the Motor =

, = Radius of the brake drum =

Pµ = Input power to the motor = ªO

120 × f = #

´

¶ = output torque = *KO ~K6 + × 9.81 × , % ‘ = Percentage slip = ;

Power factor =

#”• $- × %-

—7 − — < × 100 —7

P½¾¿ = Output power of the motor = %

= Percentage efficiency =

2™ × — × ¶ 60

P½¾¿ × 100 Pµ

66

Trial

VL (V)

IL (A)

Wattmeter reading × Multiplication factor W1 = Pin W1

N

Spring balance readings S1

S2

T

% slip

pf

Pout

%

67

Nature of Graphs:

Note: Draw the performance characteristics on a graph sheet, label them completely and enclose here. Conclusions:

68

Experiment No. 8B Expt. Bed No. A10

Date:

OCC OF DC GENERATOR Aim of the Experiment: To obtain the open circuit characteristics (OCC) of a separately excited DC generator at rated speed and to determine, a) Critical field resistance at rated speed. b) Critical speed, voltage built up by the generator at rated speed. c) To plot the OCC at different speeds. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: Rated output power: Supply voltage

:

Full load current

:

Rated speed

:

Apparatus Required: Apparatus

Rating

1. DC Voltmeter 2. DC Ammeter 3. Rheostat, Rh1 4. Rheostat, Rh2 5. SPST Switch 6. Tachometer 69

Nos. required

Circuit Diagram to obtain Open Circuit Characteristics:

Procedure: 1. Make the connections as shown in the above circuit diagram and switch ON the DC supply. 2. Slowly reduce the motor armature rheostat Rh2. 3. Check the speed of the motor. If it is less than rated speed, increase the motor field rheostat Rh1 till the motor runs at rated speed. 4. With SPST open, note down the reading on the voltmeter connected across the DC generator. 5. Close the SPST switch. 6. Vary the generator field current by varying the potential divider Rh3 in steps. At each step, maintain the speed of the motor using Rh1 and note down the generated voltage. 7. Repeat this until the generated voltage is slightly more than the rated voltage of generator. 8. Decrease the field current of the generator in similar steps and note down the generated voltage until the field current becomes zero. 9. Bring the motor rheostats back to their original positions and switch OFF the DC supply. 10. 70

Test Data: Speed N1 = Field Current (A)

Increasing Gen Voltage (V)

rpm Decreasing Gen Voltage (V)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

71

Speed N2 = 690 rpm Increasing Gen Voltage (V)

Decreasing Gen Voltage (V)

Measurement of Shunt Field Winding Resistance:

Procedure: 1. Make the connections as shown in the above circuit diagram. 2. Keeping the rheostat in maximum position, switch ON the DC supply. 3. Vary the rheostat in steps and note down the readings of voltmeter and ammeter. 4. Switch OFF the DC supply. Test Data: Voltmeter reading (V)

Ammeter reading (A)

Shunt Field Resistance, R ÓÔ =

Average Ø ÙÚ =

72

@½Õ¿Ö ¿ Ð Ð ×ÖÖ ¿ Ð Ð

ε

ε

Ω

(Ω)

Nature of Graph (OCC at Rated Speed, N=690 rpm):

Critical Speed & Critical Field Resistance:

Critical Field Resistance = R Ï = Slope of the tangent drawn to the linear portion of the =

OCC that passes through the origin. Ω

Voltage builtup = H–( = voltage corresponding to the point at which R ÓÔ line and OCC

Critical speed = NÏ =

NÏ =

=

at rated speed meet.

R ÓÔ ×N RÏ

volts

¿ Î

*§ℎ©_© N

73

¿ Î

c‘ bℎ© _`b©i ‘k©©i df bℎ© ÄŠ©e. +

Note: Draw the OCC on a graph sheet, label it completely and enclose here. Conclusions:

74

Experiment No. 9A Expt. Bed No. A1

Date:

LOAD TEST ON DC SHUNT GENERATOR Aim of the Experiment: To conduct the load test on the given DC shunt generator and plot its internal and external characteristics. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: DC generator

DC motor

Rated output power: Supply voltage: Full load current: Rated speed: Apparatus Required: Apparatus

Rating

1. DC Voltmeter 2. DC Ammeter 3. Rheostat, Rh1 4. Rheostat, Rh2 5. SPST Switch 6. Tachometer

75

Nos. required

Circuit Diagram for Load Test:

76

Procedure for Load Test: 1. Make the connections as shown in the circuit diagram. 2. With the load DPST switch kept open, switch ON the DC supply. 3. Move the arm on the 3 point starter slowly till ON position is reached. 4. Run the motor at rated speed by increasing the motor field rheostat ‘Rh1’. 5. By decreasing the generator field rheostat ‘Rh2’, build up the generator voltage such that the voltmeter ‘VL’ reads the rated voltage. 6. Note down the no load readings. 7. Close the DPST switch. 8. Increase the generator current ‘IL’ in steps using the lamp load. 9. For each step, keep the motor speed constant at the rated speed of the DC generator, by using ‘Rh1’ and note down the meter readings. 10. Repeat steps 8 and 9 until the DC ammeter reads the full load current of generator. 11. Decrease the load current to zero and open the DPST switch. 12. Bring the rheostats to their original positions. 13. Switch OFF the DC supply. The arm on the three point starter will automatically return to its original position in few seconds. Test Data: Trial No.

Load Voltage VL

Load Current IL

Field Current ISH

Armature Current

(V)

(A)

(A)

(A)

77

}Ü

Armature Generated Voltage Voltage ÝÞ Drop (V)

(V)

Measurement of Armature Resistance:

Procedure: 1. Make the connections as shown in the above circuit diagram. 2. Keeping the switches of the lamp load in OFF position, switch ON the DC supply. 3. Switch ON the lamps in steps and note down the readings of DC voltmeter and DC ammeter. 4. Switch OFF all the lamps and switch OFF the DC supply. Test Data: Voltmeter reading (V)

Ammeter reading (A)

Armature Resistance, R =

Average Ø Ü =

78

@½Õ¿Ö ¿ Ð Ð ×ÖÖ ¿ Ð Ð

ε

ε

(Ω)

Ω

Calculations:

I = Armature current = IA + Iß?

Armature voltage drop = I × R

E = Generated voltage = $- + *I × R +

Nature of Graphs:

79

Note: Draw the internal and external characteristics on a graph sheet, label them completely and enclose here. Conclusions:

80

Experiment No. 9B Expt. Bed No. A6

Date:

LOAD TEST ON CUMULATIVE COMPOUND DC GENERATOR Aim of the Experiment: To conduct the load test on the given Cumulative compound generator and to plot its external characteristics. Background Theory: Students are required to refer to reference books & write this section independently.

Name Plate Details: DC generator

DC motor

Rated output power: Supply voltage: Full load current: Rated speed: Apparatus Required: Apparatus

Rating

1. DC Voltmeter 2. DC Ammeter 3. Rheostat, Rh1 4. Rheostat, Rh2 5. SPST Switch 6. Tachometer

81

Nos. required

Circuit Diagram for Load Test:

82

Procedure: 1. Make the connections as shown in the circuit diagram. 2. With the load DPST switch kept open, switch ON the DC supply. 3. Move the arm on the 3 point starter slowly till ON position is reached. 4. Run the motor at rated speed by increasing the motor field rheostat ‘Rh1’. 5. By decreasing the generator field rheostat ‘Rh2’, build up the generator voltage such that the voltmeter ‘VL’ reads the rated voltage. 6. Note down the no-load readings. 7. Close the DPST switch. 8. Increase the generator current ‘IL’ in steps using lamp load. 9. For each step, keep the motor speed constant at the rated speed of the DC generator, using ‘Rh1’ and note down the meter readings. 10. Repeat steps 8 and 9 until the ammeter reads the full load current of generator or motor. 11. Decrease the load current to zero and open the DPST switch. 12. Bring the rheostats to their original positions. 13. Switch OFF the DC supply. The arm on the three point starter will automatically return to its original position in few seconds. Test Data: Trial No.

Load Voltage VL

Load Current IL

Field Current ISH

Armature Current

(V)

(A)

(A)

(A)

83

}Ü

Nature of Graph:

Note: The internal characteristics of the DC compound generator can be drawn by first measuring the resistance of the Armature (A-AA) and series winding (Y-YY) separately and determining the Internal voltage Eg suitably.

Note: Draw the external characteristics on a graph sheet, label it completely and enclose here. Conclusions:

84

Experiment No. 10

Date:

DYNAMIC MODELLING OF THREE PHASE INDUCTION MOTOR Aim of the Experiment: To simulate a standard mathematical model of Induction Machine and observe the transients in line currents, voltages , torque and speed in the machine during starting and loading. Background information: In the steady state model of induction machine, all electrical transients are neglected during starting, braking and load changes. The dynamic model considers the instantaneous effects of varying voltages/currents, stator frequency and torque disturbance. The dynamic model of the induction motor is derived using a two phase motor in direct and quadrature axes. The equivalence between the three phase and two phase machine models is derived from simple observation, and this approach is suitable for extending it to model an n-phase machine by means of a two phase machine. Principle and Outline: The dynamic model of a two phase machine

Vqs   Rs  Ls p V    ds     c  Ls Vqr   Lm p    Vdr  ( c   r )  Lm

 c  Ls

Lm p

Rs  Ls p ( c   r )  Lm

 c  Lm Rr  L r p

Lm p

(c   r )  Lr

 c  Lm

  I qs   I  Lm p    ds  ( c   r )  Lr   I qr     Rr  Lr p   I dr  ------ (1)

3  P  Lm  I qs  I dr  I ds  I qr  ----------------------------------------------------- (2) 4 d Te  J  r  B  r  TL ----------------------------------------------------------------- (3) dt Te 

85

The transformation from two phase to three phase   Vqs  Vds   2     3  Vos   

cos( c ) sin( c ) 1 2

2  2  ) cos( c  ) 3 3  Vas  2  2     sin( c  ) sin( c  )   Vbs --------------- (4) 3 3    1 1  Vcs   2 2

cos( c 

 cos( c ) sin( c )  Ias    Ibs   cos(  2   ) sin(  2   ) c c    3 3  Ics   2 2  cos( c  ) sin( c  )  3 3

1 1 1

  I    qs     I ds  -------------------- (5)      I os  

Where, Vas , Vbs and Vcs are the three phase stator voltages of the Induction machine. Ias , Ibs and Ics are the three line currents in the stator of Induction machine. Iar , Ibr and Icr are the three line currents in the rotor of Induction machine. Rs is the resistance of stator winding. Ls is the stator inductance. Lr is the rotor inductance. Rr is the resistance of rotor winding. Lm is the mutual inductance between stator and rotor. ωr is the electrical angular rotor speed. ωc is the speed of the reference frame. θc is the angular position of the reference frame with respect to stator. Vqs , Vds are the quadrature and direct axis stator voltages respectively. Vqr , Vdr are the quadrature and direct axis rotor voltages respectively. Iqs , Ids are the quadrature and direct axis stator currents respectively. Iqr , Idr are the quadrature and direct axis rotor currents respectively. Te is the electromagnetic torque developed in the machine. Tl is the applied load torque. J is the moment of inertia of the machine and B is the constant of friction.

86

Procedure: 1. Induction machine model (equations 1 to 5) are implemented in the MATLAB/Simulink software package. 2. The input to the model are the three phase stator and rotor voltages and the mechanical load torque. The outputs are: Three phase stator and rotor currents, electromagnetic torque developed and rotor speed.

Fig 1. Top level view of the model

87

88 Fig 2. Subsystem level view

3. MATLAB script file is created to enter the machine parameters.

Fig 3. Screenshot of the Matlab Script file containing the machine parameters.

4. The Simulink model is configured to simulate using Runge-Kutta method at a fixed time step of 0.1ms. 5. The MATLAB script is run followed by the Simulink model; Waveforms are observed in scopes connected.

89

Results: The simulation results of a 200V, 60Hz, 4 pole, 5HP squirrel cage induction machine is shown. The machine is started at no load and a load of 30Nm is applied after 0.7s. 1. Stator Voltages: 200

150

100

50

0

-50

-100

-150

-200 0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

2. Stator Currents: 200

150

100

50

0

-50

-100

-150 0

0.5

1

90

1.5

3. Electromagnetic Torque: 80

60

40

20

0

-20

-40

-60 0

0.5

1

1.5

4. Rotor Speed: 2000

1800

1600

1400

1200

1000

800

600

400

200

0 0

0.5

1

91

1.5

5. Torque Vs Speed: 80

60

40

20

0

-20

-40

-60 0

200

400

600

800

1000

92

1200

1400

1600

1800

2000