FACULTY OF

ENGINEERING, SCIENCE AND BUILT ENVIRONMENT

DEPARTMENT OFELECTRICAL POWER ENGINEERING

ELECTRICAL MACHINES IV

REPORT TITTLE:

INDUCTION MACHINES DYNAMICS

5/3/2013

Lecturer Name:

Student Name: Mr. M.C. Leoaneka

i

Abstract

This experiment is proposed the dynamic simulation of a three phase induction motor

based on the theoretical calculation and the computer simulation.

The dynamic simulation plays a vital role in the validation of the design process of the

motor drive system and it is needed for eliminating inadvertent design mistakes and

resulting error in the prototype construction and testing. This report gives the simulation

of a dynamic performance of induction motor performed by the aid of the PSIM, a

computerized software package version 9.2.1.

ii

Acknowledgement

First and foremost I would like to thanks the “Almighty God”. Without his help and

blessing I would not have been able to finish this report.

I would like to express my most sincere gratitude to All Durban University of Technology

Lecturers who have provided me with information. All my colleagues and friends who

direct or indirectly have contributed for the completion of this report.

I would also like to thanks my family, specially my dear mother Isabel Jose for her

unlimited support and love and my girl friend Halala Zulu that have been so patient and

helpful.

iii

ContentsAbstract...................................................................................................................................................... ii

Acknowledgement.................................................................................................................................... iii

List of Symbols.........................................................................................................................................vi

1- Introduction...........................................................................................................................................1

1.1- Objectives......................................................................................................................................1

2.0- The theory..........................................................................................................................................2

2.1- Methods of Monitoring Mynamic Condition in an Induction Motor..........................................2

2.1.1- Thermal Monitoring................................................................................................................2

2.1.2- Torque Monitoring..................................................................................................................2

2.1.3- Noise Monitoring....................................................................................................................3

2.1.4- Vibration Monitoring...............................................................................................................3

2.2.0- Behviour of an Induction Motor under Dynamic Condition...................................................3

2.2.1- Inrush Current........................................................................................................................3

2.2.2- Voltage Dip.............................................................................................................................4

2.2.3- Frequency Dip........................................................................................................................4

2.2.3- Acceleration Time..................................................................................................................4

2.2.4- Torque.....................................................................................................................................5

2.2.5- Reactive Power and Starting Power Factor.......................................................................5

2.3.1- Mitigate the Problem of Dynamic Condition.......................................................................5

3.0- The Methodology..............................................................................................................................6

3.1- The theoretical Calculations........................................................................................................6

3.1.1- Starting Current Calculations...............................................................................................7

3.1.2- Zth & Vth Calculation.............................................................................................................7

3.2.0- Thevenin Equivalent Circuit......................................................................................................7

3.2.1- Rotor Current Calculations...................................................................................................8

3.2.2- Starting Torque Calculations................................................................................................8

3.2.3- Slip at Maximum Torque...........................................................................................................8

3.2.4- Maximum Torque......................................................................................................................8

4.0- Induction Motor Modelling................................................................................................................9

4.2- Discussion of the results............................................................................................................13

4.2.1- Moto Current (Ia)..................................................................................................................13

4.2.2- Motor Speed.........................................................................................................................13

4.2.3- Motor Torque........................................................................................................................13

4.2.4- Torque * Speed (Motor Power)..........................................................................................13

iv

4.3-Motor with load (0-100Nm) simulation results..........................................................................14

4.3- Discussion of the results............................................................................................................16

4.3.1- Moto Current (Ia)..................................................................................................................16

4.3.2- Motor Speed.........................................................................................................................16

4.3.3- Motor Torque........................................................................................................................16

4.3.4- Torque * Speed (Motor Power)..........................................................................................16

5- Conclusion..........................................................................................................................................17

7- Recommendations.............................................................................................................................17

9- Reference............................................................................................................................................18

10- Appendix...........................................................................................................................................19

10.1- Appendix (a)..............................................................................................................................19

10.2-Appendix (b)...................................................................................................................................20

10.3- Appendix (c).....................................................................................................................................21

v

List of Symbols

Vl Line Voltage

Vph Phase Voltage

f Supply frequency

Ls Stator inductance

Rs Stator resistance

Lr Rotor inductance

Rr Rotor resistance

Lm Magnetizing Inductance

Xls Stator inductative Reactance

Xlr Rotor Inductive Reactance

Xlm Magnetizing Rectance

Ns Synchronous Speed

S Slip

SmT Slip at Maximum Torque

Tst Starting Torque

Ist Starting Current

Z1 Total Impedance

Tem Maximum Torque

Vth Thevenin Voltage

Zth Thevenin Impedance

J Moment of Inertia

vi

1- Introduction

An induction motor is simply an electric transformer whose magnetic circuit is separated

by an air gap into two relatively movable portions, one carrying the primary and the

other the secondary winding. Alternating current supplied to the primary winding from an

electrical power supply induces an opposing current in the secondary winding, when the

latter is short-circuited or closed through external impedance. Relative motion between

the primary and secondary structure is produced by the electromagnetic forces

corresponding to the power thus transferred across the air gap by induction.

The essential features which distinguish the induction machine from other type of

electric motors is that the secondary currents are created solely by induction, as in a

transformer instead of being supplied by a dc exciter or other external power sources,

as in synchronous and dc machines.

1.1- Objectives

The purpose of this experiment is to study and analyse the behaviour of and induction

motor under the dynamic condition, when the motor is initially unloaded and later is

loaded and the load is increased from one value of inertia to the other. Then comparing

the results obtained from theoretical calculation and those obtained from the practical

simulation.

1

2.0- The theory

2.1- Methods of Monitoring Mynamic Condition in an Induction Motor

Condition monitoring is defined as the continuous evaluation of the health of the plant

and equipment throughout its service life. It is of vital importance to be able to detect

faults while they are still developing.

The followings are one of the condition monitoring method applicable to induction motor:

2.1.1- Thermal Monitoring

The thermal monitoring of electrical machines is accomplished either by measuring the

local or bulk temperature of the motor,or by parameter estimation. A stator current fault

generates excessive heat in the shorted turns and heat promulgates the severity of the

fault until it reaches a destructive stage.

2.1.2- Torque Monitoring

All types of motor faults produce the sidebands at special frequencies in the air gap

torque. However it is not possible to measure the air gap torque directly. The difference

between the estimated torques from the model gives an indication of the ecxisteVnce of

broken bars. From the input terminals, the instantaneous power includes the charging

and discharging energy in the windings. Therefore, the instantaneous power cannot

represent the instantaneous torque. From the output terminals, the rotor, shaft, and

mechanical load of a rotating machine constitute a torsional spring sytem that has its

own natural frequency.

2

2.1.3- Noise Monitoring

Noise monitoring is done by measuring and analyzing the acoustic noise spectrum,

acoustic noise from air gap eccentricity in induction motors can be used for fault

detection. However, the application of noise measurements in a plant is not practical

because of the noisy background from the other machines operating in the vacinity.

2.1.4- Vibration Monitoring

All electric machines generate noise and vibration, and the analysis of the produced

noise and vibration can be used to give information on the condition of the machies.

Even very small amplitude of vibration of machine frame can produce high noise.

2.2.0- Behviour of an Induction Motor under Dynamic Condition

2.2.1- Inrush Current

This is the initial current seen by the motor during the starting operations. The inrush

current directly relates to mechanical stress of the bearings and

belts on the motor load (Cohen, 1995). The resistive or copper losses are proportional

to the square of current, I2R, and therefore affect the efficiency. The power lost is

dissipated as heat, causing thermal stress to the machine and affecting its upkeep cost

and overall lifetime.

3

2.2.2- Voltage Dip

The allowable amount of voltage dip is usually dependent on the size of

the network and the load torque characteristics. The latter is due to the fact that the

torque is approximately proportional to the square of the voltage. According to (IEEE

Std 399- 1997, 1998), the allowable voltage dip range can vary between 80% and 95%

of the rated value.

The minimum voltage dip for NEMA type B motors is approximately 80%, given a static

prime mover torque, so as to achieve the 150% of rated torque required to accelerate

the rotor during starting (NEMA, 2009).Tables describing general use and the locked-

rotor starting kVA are given Appendix C. In power systems a common voltage dip limit

is 94% of rated voltage. Shunt capacitors and other reactive power compensators are

often used to improve voltage response.

2.2.3- Frequency Dip

To maintain system stability it is important to retain as close to the fundamental

frequency of the system as possible. The frequency dip is usually not considered as

important as the voltage dip.

2.2.3- Acceleration Time

The time it takes to approximately reach the rated speed of the

motor. It is often indicative of other parameters such as torque and current. Faster

acceleration time is desired, but often means that high-rated current and other

undesirable affects occur. However, a longer acceleration can mean that the applied

torque is too low and that a still significant current is applied over a longer span of time

resulting in a still too high amount of thermal stress to the motor.

4

2.2.4- Torque

The speed-torque curve is used to represent the required torques of the motor for

different speeds. During start-up the initial locked rotor starting torque must be met to

overcome the potential energy at standstill, and the accelerating torque must be

exceeded to maintain acceleration or the motor will stall (IEEE Std 399-1997, 1998),

(Larabee, Pellegrino, & Flick, 2005), and (Kay, Paes, Seggewiss, & Ellis, 1999)

2.2.5- Reactive Power and Starting Power Factor

It is important to take into account the high reactive power consumed by the motor. In

such a case, the rating of the upstream equipment may need to be rated higher than the

steady-state condition (Kay, Paes, Seggewiss, & Ellis, 1999). The reactive power during

start-up is closely related to the voltage dip. Typical values of the power factor are about

0.20 for motors under 1000 HP (IEEE Std 399-1997, 1998). The locked rotor kVA per

HP is defined for each NEMA code letter, see Appendix C, which can help determine

the expected starting reactive power corresponding with the starting power factor

(Chapman, 2005).

2.3.1- Mitigate the Problem of Dynamic Condition

In order to mitigate these problems several methods are being used such as:

Full voltage, reduced voltage, incremental voltage, soft-starter, and variable frequency

drives.

Another starting technique is to control the applied torque of the attached prime mover,

such as the fluid coupling method. Other methods not discussed below include single-

phase starting of a three-phase motor that can be found in work by (Badr, Alolah, &

Abdel-Halim, 1995). The reader is also referred to (Ansari & Deshpande, 2009) for a

review the problems associated with unbalanced voltage starting.

5

3.0- The Methodology

3.1- The theoretical Calculations

Induction Motor

data

Formulae & Quantity calculations

VL= 380V

f = 50Hz

4 poles (p=2)

Rs= 0.54Ω

Ls= 0.29mH

Rr= 0.056Ω

Lr= 0.54mH

Lxm= 31mH

J= 0.001kgm2

XLs= 2π*f*Ls = 2π*50*0.29*10−3= 0.091Ω

XLr= 2π*f*Ls = 2π*50*0.54*10−3= 0.169Ω

XLm= 2π*f*Ls = 2π*50*31*10−3= 9.74Ω

ns = fp

= 502

= 25rad/sec, Ns= 60*25 =

1500r.p.m

Vph = VL√3

= 380√3

= 219.4V

At starting S=1, hence Rr (1−S )

S = 0

Table 1: Calculations

0.194ohm 0.056ohm0.091ohm 0.1696ohm

9.74ohm r2(1-s)/sVph= 219.4V

Rs Xs

Xm

Rr Xr

Figure 1: Circuit Diagram

6

3.1.1- Starting Current Calculations

Z1= (Rs+jXs) +(Rr+ jXr )×( jXm)Rr+ jXr+ jXm

= (0.194 + j0.091) +(0.056+ j0.169 )∗( j 9.74)0.056+ j 0.169+ j 9.74

= 0.357

∟46 ˚Ω

Istarting = VphZ 1

= 219.40.357

= 614.56 A

3.1.2- Zth & Vth Calculation

Zth = (Rs+ jXs )×( jXm)Rs+ jXs+ jXm

= (0.194+ j0.091 )×( j 9.74)0.194+ j 0.091+ j 9.74

= 0.212∟26.26˚ = (0.190 + j 0.0938) Ω

Vth = Vth Xj Xm

Rs+ jXs+ j Xm = (219.34) X j 9.74

0.194+ j0.091+ j 9.74 = 217.28V

3.2.0- Thevenin Equivalent Circuit

0.19ohm 0.056ohm0.0938ohm 0.1696ohm

Vth= 217.28V

Rth Xth Rr Xr

Figure 2: Thevenin Equivalent Circuit

7

3.2.1- Rotor Current Calculations

Ir = Vt hZt

= 217.28

0.19+ j 0.0938+0.056+ j 0.1696 = 602.86A

3.2.2- Starting Torque Calculations

Tst = 3∗Vt h2∗Rr

2πns∗[(Rt h+Rr)2+¿ = 3׿¿ = 389.62Nm

3.2.3- Slip at Maximum Torque

SmT = Rr

√(Rt h)2+(Xr+Xr)2 =

0.056

√(0.19)2+(0.1696+0.0938)2 = 0.1724

3.2.4- Maximum Torque

Tem = 3×Vt h2

4 π ×ns ׿¿ = 3×217.28

2

4 π ×25׿¿ = 875.67 Nm

8

4.0- Induction Motor Modelling

To simulate the circuit under dynamic condition the schematic diagram in the figure (3)

below has been drawn. Then, relevant data are being inserted into the programs.

For simulating the first experiment the figures below gives the detailed of the data

inserted: Figure (4) gives all the parameters of the motor, figure (5) gives parameters

required in the simulation control. Figure (6) gives the data for the external load

connected to the motor; figure (7) gives the parameter for the voltage steps. And figure

(8) gives the data for the supply power.

Figure 3: Induction Motor Schematic Diagram (100-250Nm load)

9

Figure 4: Induction Motor Input Data Figure 5: Simulation Control Input Data

Figure 6: Step (2-Level) Input Data Figure 7: Mechanical Load Input Data

10

Figure 8: Supply Power Input Data

11

Figure 9: Current, Speed, Torque and Torque*Speed wave forms

0K

-0.5K

-1K

0.5K

1K

I_a

Motor Current

0

-500

500

1000

1500

2000

Speed

Motor Speed

0

-200

200

400

600

800

1000

Torque

Motor Torque

0 2 4 6 8 10

Time (s)

0K

-200K

200K

400K

600K

800K

1000K

1200K

Torque*Speed

Torque * Speed

12

4.2- Discussion of the results

When simulating the motor under these conditions we observe in the waves forms that:

4.2.1- Moto Current (Ia)

The motor reaches a maximum current values of 914.8A at 8msec, after 8msec the

currents starts decreasing and reaches a value of 52.68A at 7.3sec, then after 8 secs at

nearly 8.2secs the motor reaches a steady value of 63.1A which continues with up until

the load changes again.

4.2.2- Motor Speed

The motor starts accelerating from standstill and reaches the synchronous speed of

1493RPM at 8 secs, and continues with it until there is any a load change or

disturbances in the supply Voltage.

4.2.3- Motor Torque

The motor reaches a maximum torque value of 833.37Nm at 94msec and then starts

decreasing and nearly 3.2sec it reaches 4995Nm. Then, the torque starts increasing

again and after 6 sec it reaches its maximum value again. At 6.24secs starts decreasing

and at 8.7sec it reaches a steady value of 241.6Nm.

4.2.4- Torque * Speed (Motor Power)

The motor reaches its maximum power of 1.06MW at 6.2sec, and after that the power

starts decreasing, and at 8, 8 sec the power goes to a steady value of 361.96KW.

13

4.3-Motor with load (0-100Nm) simulation results

In this part of experiment we simulate the motor when the load changes from 0-100Nm, all other motor data remains the same just on the voltage step see figure 7 that we change the values.

A

I_aIM

V

Speed

V

Torque

Motor_Load

380V

Vs50Hz

Torque_Step

1000

Simulator control

Figure 10: Induction Motor Schematic Diagram with load (0-100Nm)

14

Figure 11: Current, Speed, Torque & Torque * Speed wave forms

0K

-0.5K

-1K

0.5K

1K

I_a

Motor Current

0

500

1000

1500

2000

Speed

Motor Speed

0

-200

200

400

600

800

1000

Torque

Motor Torque

0 2 4 6 8 10

Time (s)

0K

-200K

200K

400K

600K

800K

1000K

1200K

Torque*Speed

Torque * Speed

15

4.3- Discussion of the results

When simulating the motor under these conditions we observe in the waves forms the

following:

4.3.1- Moto Current (Ia)

The motor reaches a maximum current values of 914.8A at 8msec, after 8msec the

currents starts decreasing and reaches a value of 36.9A at 6sec, then after 6 secs starts

decreasing a bit more and from 8.54sec and so on it gets a steady value of 43.3A,

assume without load.

4.3.2- Motor Speed

The motor starts accelerating from standstill and reaches the maximum speed o of

1500RPM at 6 sec, then continuous with this speed until there is any a load change or

disturbances in the supply Voltage.

4.3.3- Motor Torque

The motor reaches a torque of 499.6 Nm at 2.52sec, and then at 4.89sec it reaches its

maximum torque of 825.95Nm. After 4.98secs the torque starts decreasing and at

6.89sec it reaches a minimum torque of 0.603Nm.Then it starts increasing again and

reaches a steady torque value of 97.2Nm at 8.74sec.

4.3.4- Torque * Speed (Motor Power)

The motor reaches its maximum power of 1.06MW at 6.2sec, and after that the power

starts decreasing, and at 8, 8 sec the power goes to a steady value of 361.96KW.

16

5- Conclusion

It has been seen that after these experiments that the load plays a vital role in the

acceleration time of the motor, so the bigger the load the longer is the time for the motor

to reach its normal speed. That’s why induction motors suffers a lot when the load

suddenly changes.

7- Recommendations

It is recommended that in order to mitigate the problems with dynamics several methods

are being used such as:

Full voltage, reduced voltage, incremental voltage, soft-starter, and variable frequency

drives.

17

9- Reference

Books:

1- MEHTA, V. K. & MEHTA, R. 2002. Principles of electrical machines: for degree, A.M.I.E., diploma and other engineering examinations, New Delhi, S. Chand.

2- BIMBHRA, P. S. 1995. Generalized theory of electrical machines, New Delhi U6 - ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info:sid/summon.serialssolutions.com&rft_val_fmt=info:ofi/fmt:kev:mtx:book&rft.genre=book&rft.title=Generalized+theory+of+electrical+machines&rft.au=Bimbhra%2C+P.+S&rft.date=1995-01-01&rft.pub=Khanna&rft.externalDocID=12284 U7 - Book U8 - FETCH-dut_catalog_122841, Khanna.

3- MEHTA, V. K. & MEHTA, R. 2002. Principles of electrical machines: for degree, A.M.I.E., diploma and other engineering examinations, New Delhi, S. Chand.

Internet research

4- http://www.drivetechinc.com/articles/IM98VC1.pdf

5- http://www.montefiore.ulg.ac.be/~vct/elec047/dyn_of_ind_mac.pdf

6- http://www.jatit.org/volumes/research-papers/Vol5No6/16Vol5No6.pdf

18

10- Appendix

10.1- Appendix (a)

VARIABLE SPEED DRIVE

19

10.2-Appendix (b)

20

10.3- Appendix (c)

Motor Soft Starter

21