Speed Control - Induction Motors

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Speed Control of Induction Motorusing V/f Technique

(Phase I)

A thesis submitted in partial fulfillment of the requirements for the degree of

Bachelor of Technology

Submitted by

Jeetesh Kumar (08010815)

Kamakhya Prasad Basumatary (08010817)

Supervisor

Professor A. K. Gogoi

(Professor, Department of Electronics and Electrical Engineering, IIT Guwahati )


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Certificate

This is to certify that the work contained in this thesis entitled Speed Control of Induction Motor usingV/f technique , is a bonafide work of Jeetesh Kumar (08010815) and Kamakhya Prasad Basumatary(08010817) , carried out in the Department of Electronics and Electrical Engineering, IIT Guwahati undermy supervision and it has not been submitted elsewhere.

Date:

Place:

(Supervisor s Signature)

A.K.Gogoi

Proffesor,

Department of Electronics and Electrical Engineering

IIT Guwahati


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Contents:

1. Introduction 12. Operation of induction motors2

2.1 Equivalent circuit and control of speed of induction motor.22.2 Pulse Width Modulated Inverter..52.3 Three phase harmonic filter ..6

3. Basic features of the project73.1 Determining the parameters of induction motor..73.2 Modeling of 3- phase voltage source inverter in MATLAB Simulink113.3 Harmonic Distortion in the motor...12

4. Potential Applications...135. Future work/ Plan for overall thesis..14


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1 Introduction:

It is very important to control the speed of induction motors in industrial and engineeringapplications. Efficient control strategies are used for reducing operation cost too. Speed controltechniques of induction motors can be broadly classified into two types scalar control and vector

control. Scalar control involves controlling the magnitude of voltage or frequency of the induction motor.

Figure1. Torque-Speed characteristic of induction Motor

Having known the Torque-speed characteristic of the motor, its speed can be controlled in three ways:

i) Changing the number of polesii) Varying the input voltage at fixed frequencyiii) Varying both the input voltage and frequency accordingly

To maintain torque capability of the motor close to the rated torque at any frequency , the air gap flux, ag is maintained constant. Any reduction in the supply frequency without changing the supple voltage willincrease the air gap flux and the motor may go to saturation. This will increase the magnetizing current,distort the line current and voltage, increase the core loss and copper loss, and it makes the system noisy.

The air gap voltage is related to ag and the frequency f as,

Eag =k 1 ag f (1)

Input voltage, V sk 1 ag f (2)

or, ag = constant Vsf

(3)

where k 1 is a constant.


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We shall be concentrating on the third method throughout the project, beginning with analyzing theparameters of the induction motor and the harmonic contents.

2 Operation of induction motors:

When a balanced set of three-phase sinusoidal voltages is applied to the stator of an inductionmotor, a constant amplitude flux is produced in the air-gap which rotates with a constant speed called thesynchronous speed. For a p pole machine, the synchronous speed is given as

Ns =120f

p (revolutions per minute) (5)

where, f is the frequency of the applied voltages and currents. Due to the rotating air-gap flux, a counter-emf, called the air-gap voltage is induced in each of the stator phases at frequency f. The torque in aninduction motor is produced by the interaction of the air-gap flux and the rotor currents. If the rotorrotates at synchronous speed, there is no relative motion between the air-gap flux and the rotor, and hencethere is no induced voltages, currents and torque in the rotor. At any other speed r of the rotor in thesame direction of the air-gap flux rotation the motor moves with respect to the air-gap flux at a relativespeed called the slip speed sl ,where

sl = s - r (6)

The slip speed normalized by the synchronous speed gives the slip :

=

= srs (7) 2.1 The equivalent circuit and control of speed of induction motor:

To study the behavior of the induction motor at various operating conditions, it is convenient toderive an equivalent circuit of the motor under sinusoidal steady state operating conditions. For abalanced 3 phase system, equivalent circuit for any one phase will suffice.

Figure 2. Equivalent circuit of the induction motor

From the per-phase equivalent circuit of the induction motor, the current drawn by the circuit is,


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Is =Vs

R s+R r +j(X ls+X lr ) (8)The air-gap power is given as,

Pag = 3 | I s | 2Rrs

(9)

=3V s2

Rs+R r 2+j Xls+X lr 2 .R rs

(10)

Mechanical output power is given as,

Pm = (1-s)P ag (11)

Hence, the mechanical torque is given as,

Te =Pm

m (12)

=1s P ag(1s)s (13)

=3 Is 2Rr '

ss (14)=

3

s .V2s

R s+R r

s2+ Xls+X lr 2 .

R rs

(15)

Plotting the torque against slip or speed gives us the torque-speed characteristic of the motor.

Figure 3. Torque-speed curve for normal operation Figure 4. Torque-speed curve for variable voltage


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Maximum torque,

TE/f =2

8 2 lr (20)Equation (20) shows that the maximum torque is independent of frequency and hence remains the same

for each E/f and the maximum torque occurs at a speed lower than the synchronous speed for eachcombination of E and f . However, we get a slightly different set of curves for constant V/f, so for fixedV, E changes with operating slip and the maximum torque is reduced, as shown in figure 6.

2.2 Pulse-Width-Modulated inverter:

For obtaining variable speed/ voltage control of induction motors, various DC-ACconverters (inverters) are used to drive the motors. The function of the inverter is to change a DCinput voltage to a symmetric AC output of desired magnitude and frequency. A typical three-

phase inverter is shown in the figure below. A balanced set of sinusoidal voltages are fed as inputto the inverter to obtain a constant rectified DC voltage, which is again smoothed through the DClink capacitor(s). The semiconductor switches are eventually driven by the smoothed DCvoltage.

The output voltage may be fixed or variable at a fixed or variable frequency. Variablevoltage can be obtained by varying the gain of the inverter, which is usually done by using PulseWidth Modulation (PWM) control within the inverter.

Figure 7. A variable frequency 3-phase motor drive ( inverter)

In PWM inverters the gating signals for the 6 switches are generated by comparing asinusoidal reference signal with a triangular wave. The frequency of the reference signaldetermines the inverter output frequency and its peak amplitude controls the modulation index,which in turn controls the rms output voltage. Figure 8 shows the typical process of generating asinusoidal PWM signal. V control_A , V control_B, V control_C are the reference signals equally shiftedaway from one another (120) and these are compared with the instantaneous points of the carrier


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3 Basic features of the project:

We start off with finding the parameter variations of the induction motor during its operation,particularly the variations in rotor resistance and reactance due to the variations in frequency of the motor.We also look into the harmonic contents of the electrical quantities (voltages and currents) at different

stages of the drive set-up and make proper adjustments to minimize the effects of harmonics to get abetter control of the motor.

3.1 Determining the parameters of the induction motor:

The most widely used tests for determining the motor parameters are:

i) DC test: To find the stator resistance.ii) No-Load test: To find the magnetizing branch inductance and core loss resistance.iii) Locked- rotor test: To find the rotor resistance and reactance.

DC test:

A DC voltage is applied to the stator. In this case the equivalent circuit will consist only of thestator resistance. For motors with star connected stator terminals (as used in the simulations) the circuitfor DC test is given as:

Figure 10. Equivalent circuit for DC test.

The stator voltage can be found out as,

Rs =Vdc2I dc

(21)

No-Load test:

Figure 10.is the equivalent circuit for the No-Load test.


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Figure 11. Equivalent circuit for No-Load test Figure 12. Equivalent circuit for locked-rotor test

Here the rotor circuit is kept open and the slip is zero. The magnetizing branch impedance is largecompared to the stator impedance. Hence the voltage drop across the stator impedance is neglected andthe total power drawn is assumed to be entirely consumed as core loss.

The no-load power factor is given by

cos 0 = P 1Vs I0 (22)where, P 1 is the input power per phase.

Magnetizing current is calculated as,

Im = I 0 sin 0 (23)

and the core-loss current is given by,

Ic = I 0 cos 0 (24)The magnetizing inductance is found as,

Lm =Vs

2 f s Im (25)

The core-loss resistance is given by,

Rc =VsIc

(26)

Locked-Rotor test:

The rotor is blocked and kept at standstill. For this test the slip is unity and the equivalentcircuit looks like a secondary-shorted transformer. The magnetizing branch impedance is highercompared to the rotor impedance and so the magnetizing branch is neglected in the equivalentcircuit.


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The short-circuit power factor obtained from the equivalent circuit is given by,

cos sc= PscVsc Isc (27)where , V sc snd I sc are the short-circuit voltage and current respectively.

The short-circuit impedance is given by,

Zsc =VscIsc

(28)

The rotor resistance is given as,

Rr = Z sc cos sc R s (29)

The total leakage reactance is given as,

Xeq = Z sc sin sc (30)Xeq is the sum of the stator and referred-rotor leakage reactance

Xeq = X ls+ X lr (31)

Usually the value of stator reactance is taken same as that of the referred rotor leakage reactance. Foraccurate results, the following pattern can be followed for various motors:

Motor Stator inductance (% of X eq) Rotor inductance (% of X eq)Squirrel Cage Class A 50 50Squirrel Cage Class B 40 60Squirrel Cage Class C 30 70Squirrel Cage Class D 50 50

Wound Rotor 50 50Table 1. Standard stator and rotor inductances for induction motors

For the simulations we have used a squirrel-cage induction motor with the following parameters:

Nominal Power= 5 hp ; Nominal Line-line Voltage = 460 V ; Frequency= 60 Hz

We run the simulation for different values of input frequency and observe the induction motorparameters:

Frequency(Hz) L m R c R r Xeq R s

60 0.208 582.692 1.017 4.45 1.11550 0.207 728.86 1.018 3.726 1.11540 0.209 906.4 1.020 2.982 1.11530 0.211 898.73 1.018 2.257 1.11520 0.210 549.48 0.411 2.132 1.115

Table 2. Motor parameters at different frequencies.

The variation of parameters with frequency is due to the skin effect and other non-linear imperfectionssuch as heating and main flux path saturation. This analysis of parameters is important for vector control


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schemes. The changes in the magnetizing parameters are critical for obtaining self-excitation in self-excited induction machines. Measuring data at zero and synchronous speed is very difficult. At zero speedthe machine is switched on with full voltage, due to which a transient current is produced , the peak valueof which may be substantially higher than the steady-state current. This problem can be solved by rotatingthe motor in reverse direction, reversing the phase sequence and start sampling as soon as the speedreaches zero. At synchronous speed, the induction motor will not normally run at synchronous speed.This can be solved by coupling the induction motor with a synchronous motor with the same number ofpoles, such that the measured data is taken at exact synchronous speed[14].

The control scheme used in the project is an open loop control (manual control) in whichcontrolling parameters are fixed or set by a user and the system finds its own equilibrium state. In the caseof a motor the desired operating equilibrium may be the motor speed or its angular position. Thecontrolling parameters such as the supply voltage or the load on the motor may or may not be under thecontrol of the user. If any of the parameters such as the load or the supply voltage are changed then themotor will find a new equilibrium state, in this case it will settle at a different speed. The actualequilibrium state can be changed by forcing a change in the parameters over which the user has control.

Frequency(Hz) Speed(rpm) Torque(Nm)

20 594 21.0625 731 20.8730 871 18.0435 1045 25.8640 1165 20.4245 1298 20.3650 1443 21.3455 1578 20.1660 1708 21.8

Table3. Motor speed and torque at different frequencies, at load 19.78 pu [speed up test]

The double tuned harmonic filter used to filter harmonic distortion ( Figure 9) consists of a seriesLC circuit and a parallel RLC circuit. If f 1 and f 2 are the tuning frequencies, the filter is tunedapproximately the geometric mean frequency f m=f 1f 2.

Tuned harmonic order,

n =f mf 1

= XCXL (32)The quality factor of the double tuned filter is defined as the quality factor of the parallel L, R elements atthe mean frequency f m, and is given by,

Q =R

L2 f m (33)


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3.2 Modeling a 3-Phase voltage source inverter in MATLAB Simulink:

A 3-phase voltage source inverter is designed in Simulink using MOSFETs as switchingdevices.

Figure 13. 3-phase sinusoidal PWM inverter

Figure 14a. Line current without filter at no-load; THD= .7366

Figure 14b. Line current without filter at load 19.78 pu; THD= 0.4009

Figure 14c. Line current with filter at no-load; THD= 0.2612


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Figure 14d. Line current with filter at load 19.78 pu; THD= 0.0818

From the simulation results (Figures 14a 15d, 15, 16) we observe,

i) THD of line current in the system with filter is lower than the system withoutfilter.

ii) THD of line current in the system is lower if system is loaded than the systemwithout load.

iii) Similar results are obtained in case of line voltages, rotor and stator currents, andthe fluxes.

iv) The steady state fluctuation in torque and speed is also reduced after applicationof filter and mechanical load.

3.3 Harmonic distortion in the induction motor:

The induction motor has been assumed to be driven by ideal 3 phase, balanced, and sinusoidal setof voltages. But practically the supply phases are not perfectly sinusoidal and these contain higherfrequency components that are harmonics of the fundamental frequency [3]. Harmonics also appear due

to the non-linear load connected to the supply in the form of inverters and motors. Generally theharmonics generated by 3-phase PWM 6-pulse inverters, like the one used here, are the odd harmonicsexcluding the multiples of 3 rd harmonic ( 5,7,11, 13, etc.) [3]. The most prominent among theseharmonics are the 5 th, 7 th, 11 th and 13 th . As the order of harmonic gets higher, their magnitude becomesnegligible and these are easier to eliminate using filters.

The harmonic distortion present in any signal is measured by the Total Harmonic Distortion(THD) and is given by,

THD =

AnA1

=2

2 (34)

where, A n are the rms values of the non-fundamental harmonic components and A 1 is the rms value of thefundamental component.

The drive model is first simulated without using any filter and we get the following responsesfrom the motor:


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Figure 15. Simulation graphs of motor parameters without harmonic filter

The drive model is simulated again, for the same time period and with the same specifications,with a 3-phase harmonic filter at the inverter output. Following are the results:

Figure 16. Simulation graphs of motor parameters with harmonic filter


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References:

[1] Muhammad H. Rashid, Power Electronics- Circuits , Devices and Applications , Third Edition,Pearson 2004

[2] Bimal K. Bose, Modern Power Electronics and AC Drives , Pearson 2002

[3] Ned Mohan, Tore M. Undeland, and William P. Robbins, Power Electronics- Converters,Applications and Design , Wiley India Edition 2010

[4] R. Krishnan, Electric Motor Drives, Modeling, Analysis, and Control, Pearson 2001

[5] Thida Win, Nang Sabai, and Hnin Nandar Maung , Analysis of Variable Frequency Three PhaseInduction Motor Drive, World Academy of science, Engineering and Technology 42 (2008) pp. 647-651.

[6] Mehmet Akbaba, Motor Input Voltage and Rectifier Firing Angle Variation With Load Torque inConstant Current Operated Induction Motors, Mathematical a

nd Computational Applications, Vol. 14,no.1, pp. 73-84, 2009.

[7]

[8] K. L. Shi, T. F. Chan, Y. K. Wong, and S. L. Ho, Modelling and Simulation of the Three PhaseInduction Motor Using Simulink, International Journal of Electrical Engineering Education, Vol. 36, pp.163-172, Manchester U.P., 1999.

[9] A. A. Ansari and D. M. Deshpande, Mathematical Model of Asynchronous Machine in MatlabSimulink, International Journal of Engineering Science and Technology, Vol.2(5), pp. 1260-1267, 2010.

[10] P. Pillay and V. Levin, Mathematical Models for Induction Machines, pp. 606-616, IEEE, 1995.[11] Technical Guide- Induction Motors fed by PWM frequency inverters, http://www.weg.net

[12] M.A.A. Younis, N.A. Rahim and S. Mekhilef, Harmonic Reduction inThree- Phase ParallelConnected Inverter, World, Academy of Science, Engineering and Technology, 50, pp. 944-949 (2009).

[13] C. Grantham and D.McKinnon, Rapid parameter Determination of Induction Motor analysis andControl,

[14] D.J. McKinnon,D. Seyoum, and C. Grantham, INVESTIGATION OF PARAMETERCHARACTERISTICS FOR INDUCTION MACHINE ANALYSIS AND CONTROL , The Institutionof Electrical Engineers, IEE, Michael Faraday House, Six Hills Way, Stevenage, SG1 2AY, pp. 320-325,2004
http://www.weg.net/http://www.weg.net/http://www.weg.net/http://www.weg.net/

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Speed Control - Induction Motors