Harmonics In A SVPWM Scheme For V/F Control Of An ... Scheme For V/F Control Of An Induction Motor traditional pattern, the dwell a time are stored in tables, as for a V/f control,

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Available online through - http://ijifr.com/searchjournal.aspx Published On: December 31, 2015

Copyright©IJIFR 2015

International Journal of Informative & Futuristic Research ISSN: 2347-1697

Volume 3 Issue 4 December 2015 Research Paper

Abstract

In this paper a V/f control using a simple space vector modulation scheme is suggested. Basically a rotating space vector is required. This is achieved by generating space vectors in each sector of the space vector hexagon one after another after a switching time interval. Intuition tells us that more the number of space vectors in each sector, lesser the harmonics generated and smoother the output waveform. This paper examines the harmonics resulting from a simple SVPWM algorithm used to do V/f control of an induction motor and implemented using the TMS320F28335 DSP.

1. Introduction

Speed control of an induction motor can be achieved today by using V/f control for coarse control

or accurate control using vector control or DTC (Direct torque control)[1-2]. In this paper an

inexpensive V/f control algorithm is put forward which uses voltage space vectors to generate a

three phase voltage supply to run an induction motor [3]. The harmonics present in the phase

voltages are measured, and help analyse the efficacy of the system [4]. A number of voltage space

vectors are generated in each sector of the space vector hexagon, the resulting phase voltages are

observed and their Fourier analysis done. In our approach the induction motor speed taken in

electrical Hertz is divided into four ranges. The number of vectors per sector to be generated

depends on the speed range. Lower the speed; more are the space vectors to be generated [5-6].

One simple strategy tried was to use one space vector per sector when the motor speed is 45 to 50

Hz. Two space vectors per sector when the speed is between 30-45 Hz, three space vectors per

sector when the speed is between 15-30Hz and four below 15Hz. The harmonic analysis was done

for this in order to formulate a better strategy if required. The space vectors are generated in a

Harmonics In A SVPWM Scheme For

V/F Control Of An Induction Motor Paper ID IJIFR/ V3/ E4/ 078 Page No. 1454-1464 Research Area Power Electronics

Keywords Harmonics, Induction Motor, Space Vectors, SVPWM.

1st A.N. Maheswarappa

Professor

Department Of Electrical & Electronics Engineering

Global Academy of Technology, Bangalore

2nd

Dr. Sanjay

Lakshminarayanan

Associate Professor

Department Of Electrical & Electronics Engineering

M.S.Ramaiah Institute of Technology, Bangalore

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ISSN: 2347-1697 International Journal of Informative & Futuristic Research (IJIFR)

Volume - 3, Issue -4, December 2015 Continuous 28th Edition, Page No.:1454-1464

A.N. Maheswarappa, Dr. Sanjay Lakshm inarayanan:: Harm onics In A SVPWM Schem e For V/F Control Of An Induction Motor

traditional pattern, the dwell a time are stored in tables, as for a V/f control, the dwell times for a

speed range are constant and only the dead time to, and varies with the frequency.

Figure 1: Space Vector in a sector

Ts= sampling time, To= zero vector time duration, T1 and T2 are time durations of two adjacent

vectors. At 50 Hz, the phase voltage applied on the motor needs to be the rated voltage of

amplitude 325V per phase. Hence V1 needs to be (3/2)(325)=487.5V. Vdc*Cos(30)=487.5V

orVdc=562.9 Volts.

Hence the DC link voltage of the voltage source inverter is maintained at 563V constant. Thus at

50Hz operation, TS= (1/6)(1/50)=3.33ms, T1 = 3.33ms, T2 = 0, T0=0.( Using the above three

equations (1),(2),and(3)).

Table -1: Dwell times around 50Hz

45 Hz<f<=50 Hz, =0

TS 1/(6*f)

T1 3.33ms

T2 0

To TS- T1- T2

Now consider the frequency range from 30 to 45 Hz, where two space vectors are produced per

sector. The angles are =0 and =30. Ts, To, T1 and T2 are calculated while maintaining constant

V/f.

60

Vdc

V1

)1()60(

)60(..1

1

Sin

SinT

V

VT S

dc

)2()60(

)(..1

2 Sin

SinT

V

VT S

dc

)3(210 TTTT S

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Table-2: Two vectors per sector

30 Hz<f<=45Hz

=0 =30

TS 1/(12*f) 1/(12*f)

T1 1.443ms 0.833ms

T2 0 0.833ms

To TS- T1- T2 TS- T1- T2

Similar calculations are done for the frequency range from 15 to 30 Hz but with three space vectors

in each sector which are tabulated as below:

Table-3: Three vectors per sector

15 Hz<f<=30 Hz

=0 =20 =40

TS 1/(18*f) 1/(18*f) 1/(18*f)

T1 0.954ms 0.708ms 0.376ms

T2 0 0.376ms 0.708ms

To TS- T1- T2 TS- T1- T2 TS- T1- T2

It may be seen that in table-3, the dwell times at =20 and for =40 get swapped, which is explained by the symmetry of the two vectors. Finally for frequency below 15Hz, four vectors per sector are used. The table below gives the dwell times for the vectors.

Table-4: Four vectors per sector

0 Hz<f<=15 Hz

=0 =15 =30 =45

TS 1/(24*f) 1/(24*f) 1/(24*f) 1/(24*f)

T1 0.715ms 0.584ms 0.413ms 0.214ms

T2 0 0.214ms 0.413ms 0.584ms

To TS- T1- T2 TS- T1- T2 TS- T1- T2 TS- T1- T2

The PWM pattern can be synthesized easily using these tables alone and the code is simplified. The code can be written to include a gradual speed variation from the present speed to the required motor speed. Space vector V1 in a sector is shown in fig (1).it is time averaged of two adjacent vectors in a sector.

2. Implementation Of SVPWM In a sampling interval of TS the durations of T1 and T2 have to be defined. The dead time To is split

into two halves, first a delay of To/2 is given after which T1 and T2 are constructed followed by the

remaining To/2. This is done by the “compare” mode in a timer of the DSP. The DSP has an up-

counting counter with a time period of TS. The up-counting timer may be represented as a triangular

saw tooth waveform. The timer‟s output is high initially while the value in the compare register is

being compared to the up counting timer register. When there is a match the output goes low. The

value of To/2 is compared first. Simultaneously the value of To/2+ T1 is compared and so also

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To/2+ T1+ T2. By subtraction of the levels of the signals as shown in the figure. 5, we can obtain the

durations T1 and T2.

In fig. 2, are shown the three “compare” outputs P, Q and R which are the PWM outputs of the

DSP. “Q-P” gives the T1 duration and “R-Q” gives the T2 duration. Digitally they may be obtained

by “EX-ORing” instead of subtraction.

The sector in which the vector lies is given by the sector number “SECTOR” which consists of

three bits, like 001 for the first sector or 010 for the second etc. The SECTOR determines whether

the switch gate pulse is produced in the T1 interval or the T2 period so that the overall space vector

is averaged.

Table-5: Switch selection table

Sl.No. SECTOR Sa

1

Sa

2

Sb

1

Sb

2

Sc

1

Sc

2

1 001 1 1 0 1 0 0

2 010 1 0 1 1 0 0

3 011 0 0 1 1 0 1

4 100 0 0 1 0 1 1

5 101 0 1 0 0 1 1

6 110 1 1 0 0 1 0

7 Others 0 0 0 0 0 0

The table is formed by an inspection of the six vectors forming the radii of the space vector hexagon. The gate pulses Sa, Sb and Sc to the upper three switches of the three phases are found as below, the bottom switches are complements of the top with dead time added.

Sa= T1 .Sa1+ T2. Sa2

Sb= T1 .Sb1+ T2. Sb2

Sc= T1 .Sc1+ T2. Sc2

Figure 2: Synthesis of pulses

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3. Simulation Of SVPWM

The input to the simulation program is the frequency of operation. This determines the number of

vectors to be constructed per sector and a triangular carrier of the required frequency is generated.

Next an appropriate look up table is used to find the levels To/2, To/2+T1 and To/2+T1+T2 which

are compared with the triangular carrier to produce P, Q and R as in Fig. 2. From this the pulses of

duration T1 and T2 result. From the knowledge of the sector number, the gate pulses to the

MOSFETs or IGBTs can be generated based on the switch selection table.

The simulation program was run and a harmonic analysis was done to see the relative harmonic

levels in the line to line voltages at different frequencies of operation. The V/f ratio was also

checked.

Figure 3: Line to line voltage at 50 Hz.

Figure 4: Harmonic content in line to line voltage at 50 Hz

Figure 5: Line to line voltage at 45 Hz

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

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Figure 6: Harmonics in line to line voltage at 45 Hz

4. Observations

Line voltages and harmonics at different frequencies are shown in figure(1) to figure(10). At 50 Hz,

the 6n±1 harmonics are seen and they decay rapidly from a value of 20% to a negligible value by

41st to 43rd order.

At 45Hz, the 13th harmonic is 30% and the harmonics alternate in value while reducing to less than

5% by the 59th and 61st orders. At 30 Hz, the 17th and 19th components are prominent with

magnitudes of 40% and 70% respectively. However by the 61st order the magnitudes die down to

10%. In the case of operation at 15 Hz, the magnitude of the 23rd harmonic is about 70% and the

25th harmonic is 101%. The 47th and 49th values are again dominant but other harmonics are

small. The 25th harmonic corresponds to a frequency of 25x15=375 Hz which will see a higher

inductive reactance which attenuates the current of this frequency.


0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6

x 105

-500

-400

-300

-200

-100

0

100

200

300

400

500

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Figure 8: Harmonics at 30 Hz


Figure 10: Harmonic content at 15 Hz.

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

0.6 0.8 1 1.2 1.4 1.6 1.8

x 105

-500

-400

-300

-200

-100

0

100

200

300

400

500

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

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5. Motor Current

An induction motor model with following parameters was used to observe the output of the

inverter.

M=0.272 H

Rs=2.08

Rr=1.19

Lr=0.28 H

Ls=0.28 H

p=2 Pole pairs

B=0.1

J=0.25

(All in SI units)

The motor currents and harmonics at different frequencies are shown in figure (11) to figure (16).

At 50Hz it has prominent 5th and 7th harmonics and a bit of 11th and 13th harmonics. At 30 Hz,

the motor current has the harmonics at 17th and 19th predominate as 3 space vectors are generated

in each sector; hence the 6n±1 harmonics are active. The third harmonic is absent in all the cases.

At 15 Hz, the current has 23rd and 25th harmonics of amplitude 45% and 55% respectively.

Figure 11: Motor phase current` at 50Hz

Figure 12: Harmonics in the current at 50Hz.

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

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The motor speed seems to be close to 120f/P rpm with a slight amount of slip of about 5%.

Figure 13: Motor current at 30 Hz

Figure14: Harmonics in current at 30Hz

Figure 15: Motor current waveform at 15 Hz

2.09 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17

x 105

-20

-10

0

10

20

30

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

1.7 1.8 1.9 2 2.1 2.2

x 105

-30

-20

-10

0

10

20

30

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Figure 16: Current harmonics at 15 Hz

6. Conclusion

This method of SVPWM seems to work well with tolerable values of voltage and current harmonics

and the motor speed responds to the excitation frequency quite well. This is achieved with simple

code using DSP.

7. References [1] M S Aspalli, Asha R , P V Hunagund, “Three Phase Induction Motor Drive Using Igbts and

Constant V/F Method,” International journal of advanced research in electrical, electronics and

instrumentation engineering, Vol. 1, Issue 5, November 2012.

[2] Sujeet Kumar Soni, Anil Gupta, “Analysis of SVPWM Based Speed Control of Induction Motor

Drive with using V/F Control Based 3 Level Inverter,” International journal of scientific

engineering and technology, (ISSN : 2277-1581) Volume No.2, Issue No.9, pp : 932-938, 1 Sept.

2013.

[3] Shilpa V. Kailaswar and R.A.Keswani ,“Speed Control of Three Phase Induction Motor by V/f

Method for Batching Motion System” International Journal of Engineering Research and

Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 3, Issue 2, March -April 2013,

pp.1732-1736.

[4] El-Nobi A. Ibrahim1 Mohamed Elbesealy, “V/F control of Three Phase Induction Motor Drive with

Different PWM Techniques”, Innovative Systems Design and Engineering ,ISSN 2222-1727 (Paper)

ISSN 2222-2871 (Online), March 2013 Vol.4, No.14.pp131-144.

[5] Cuckoo Joy, Jyothi. K. G, “V/f Control of Induction Motor Using Space Vector Modulation,” ISSN:

2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovat ive

Technology (IJEIT) Volume 3, Issue 10, April 2014 42

[6] Gaber El-Saady, El-Nobi A. Ibrahim, Mohamed Elbesealy, “V/F control of Three Phase Induction

Motor Drive with Different PWM Techniques,” Innovative Systems Design and Engineering, Vol. 4,

Issue 14, 2013, pp 131-44.

[7] Alfredo,Thomas A. Lipo and Donald W. Novotny, “A New Induction Motor V/f Control Method

Capable of High-Performance Regulation at Low Speeds” IEEE Trans. Industry Applications, Vol.

34, No. 4 July/ August 1998.

[8] B. Hariram and N.S. Marimuthu, “Space vector switching patterns for different applications – a

comparative analysis”, in Proc. IEEE International Conference of Industrial Technology, Hong

Kong, 2005, pp. 1444-1449.

[9] I. Boldea, „„Control issues in adjustable speed drives, ‟‟ IEEE Industrial Electronics Magazine, Vol.

2, No. 3, Sept. 2008, pp. 32 - 50.

[10] C. S. Sharma & TaliNagwani “Simulation and Analysis of PWM Inverter Fed Induction Motor

Drive” International Journal of Science, Engineering and Technology Research (IJSETR) Volume 2,

Issue 2, February 2013, pp 359 - 366.

0 10 20 30 40 50 600

0.2

0.4

0.6

0.8

1

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Author’s Biographies

Mr. A. N. Maheswarappa received BE degree in Electrical and Electronics Engineering from Mysore University, Karnataka, India in the year 1987 and M.Tech. Degree from NITK Surathkal, Karnataka, India in 1994. He is currently working at Global Academy of Technology in E&E Dept., Bangalore, India. He is having 27 years of teaching experience. At present he is pursuing towards his doctoral degree from VTU, Karnataka, India.

Dr Sanjay Lakshminarayanan received the B.Tech. degree from the Indian

Institute of Technology (IIT), Kharagpur, India, in 1990 and the M.Sc.

(Engg.) degree in Electrical Engineering from the Indian Institute of Science

(IISc) Bangalore, India, in 1995 and Ph.D. degree in 2007 from the Indian

Institute of Science (IISc), Bangalore, India. He has been in the industry for

about ten years. He was with Grentel Technologies, Cochin, Hical Magnetics

Pvt. Ltd, Bangalore, and GE Medical Systems, Bangalore and has a teaching

experience of about Nine years. His research interests are in the area of power

converters, PWM strategies, and motor drives.

Documents

Harmonics In A SVPWM Scheme For V/F Control Of An ... Scheme For V/F Control Of An Induction Motor traditional pattern, the dwell a time are stored in tables, as for a V/f control,