half cycle pairs method

8/10/2019 Half Cycle Pairs Method

1/16

Half Cycle Pairs Method for

Harmonic Analysis ofCycloconverter Voltage Waveform

Naveed Ashraf, Athar Hanif, Umar

Farooq, Muhammad Usman Asad,

Faiqa Rafiq


2/16

Abstract

A new scheme to determine the harmonic

components of a single-phase cyclo-conveter Computes the Fourier coefficients of the resultant

positive and negative half cycle pairs of the outputvoltage waveform and adds them as one by theprinciple of superposition to determine the Fouriercoefficients of the complete output voltagewaveform.

This broad scheme can be easily extended to theother types of the single-phase and three-phase ac-

ac controllers including the on-off control andphase angle control.

The presented method is theoretically proved usingMATLAB and PSPICE soft wares.


3/16

Cycloconverter


4/16

Proposed Scheme

0 0

1

( ) cos( ) sin( )2 2

n n

n

n t n t v t a a b

=

= + +

1

0

0

o

n

a

a

=

=

/2

1

0

4sin( ).sin( ) ( )

2 2

T

n m

n tb V t d t

T

=

1 2

4 sin( )2

(4 )

m

n

nV

bn

=


5/16

Proposed Scheme (Contd.)

2

/ 2

4sin( ).sin( ) ( )

2 2

T

n m

T

n tb V t d t

T

= 2 2

4 sin( )2

(4 )

m

n

nV

bn

=

1 2n n nb b b= +

2

8 sin( )2

(4 )

m

n

nV

bn

=


6/16


0 0

1

( ) cos( ) sin( )

2 2

n n

n

n t n t v t a a b

=

= + +

0 21,3,5

8 sin( )2( ) sin( )

(4 ) 2

m

n

nV

n tv t

n

=

=

0

if

mf

=0 2 2

1,3,5

8 sin( )2( ) sin( )

( ) 2

m

n

nV

n tv t

m n

=

=

01 2

8 sin( )2( ) sin( )

( 1) 2

mV

tv t

m

=


7/16


1n =

0 2 21,5,73

24 sin( )

3( ) sin( ) sin( )3 ( ) 3

m

m

nn

nV

V n tv t tm n

=

= +

01 224 sin( )

3( ) sin( )( 1) 3

mV

tv tm

=

0 2 21,3,5

32 sin( )[1 cos( )]

4 4( ) sin( )( ) 4

m

n

n nV

n tv t m n

=

+

=

01 2

32 sin( )[1 cos( )]4 4

( ) sin( )( 1) 4

mV t

v t m

+

=

1n =

0 ( ) sin( )

5

mVv t t = +

2 21,3,75

40 sin( )[1 2 cos( )]5 5 sin( )( ) 5

m

nn

n nV

n t

m n

=

+

01 2

40 sin( )[1 2 cos( )]5 5( ) sin( )( 1) 5

m

Vtv t

m

+

=


8/16

Simulation Results

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

m = 2

Normalize

dAmplitude

Harmonic Order


9/16

Simulation Results (Contd.)

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

m = 3

NormalizedAmplitude

Harmonic Order


10/16


0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

m = 4

Normalized

Amplitude

Harmonic Order


11/16


0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

m = 5

Normalized

Amplitude

Harmonic Order


12/16



13/16


14/16

Conclusions This paper illustrates an easy and simple

approach to find the harmonic componentsof a single phase cycloconverter. Thepresented method for harmonics analysisdescribes that the output voltage wave-form

is formed by summation of half cycle pairs.The harmonic coefficients of the outputvoltage are computed by computing theharmonic coefficients of each individual half

cycle pair. The harmonic coefficients of theoutput voltage are computed with the helpof superposition.


15/16

References M. H. Rashid, Power Electronics: Devices, Circuits, and Applications, 2nd ed., Prentice Hall, 2004.

G. Hunter, V. Ramsden, A Mill-motor Including Drive Using a Three Pulse Cycloconverter with DoubleIntegral Phase Control, Proc. International Conference on Power Electronic Drives and EnergySystems for Industrial Growth, pp. 447-451, 1998,

J. Pontt, J. Rodriguez, E. Caceres, I. Illanes, J. Rebolledo, Cycloconverter Behavior for a Grinding MillDrive Under Firing Pulses Fault Conditions, Proc. Industry Applications Conference, pp. 645-649,2005.

D. R. Nayanasiri, D. M. Vilathgamuwa, D. L. Maskell, Half Wave Cycloconverter Based PhotovoltaicMicroinverter Topology with Phase Shift Power Modulation, IEEE Trans. On Power Electronics, vol.28, no.6, pp. 27002710, 2013.

Shashi B. Dewan, M. D. Kankam, A Method for Harmonic Analysis of Cycloconverters, IEEE Trans.On Industry and general Applications, vol. IGA-6, no.5, pp. 455462, Sep. 1970.

A. W. Leedy, W. C. Dillard, and R. M. Nelms, Harmonic Analysis of Two-Level Sinusoidal PWMInverter Using the Method of Pulse Pairs, IEEE Trans. On Industry and general Applications, vol. 5,pp. 1683-1688, Jul. 2005.

Michail A. Slonim, P. P. Biringer, Harmonics of Cycloconverter Voltage Waveform (New Method ofAnalysis), IEEE Trans. On Industrial Electronics and Control Instrumentation, vol. IECI-27, no.2, pp.5356, May 1980.

Kenneth Scot Smith and Li Ran, Input Current Harmonic Analysis of Pseudo 12-Pulse 3-Phase to 6-Phase Cycloconverters, IEEE Trans. On Power Electronics, vol. 11, no.4, pp. 629640, July 1996.

Shashi B. Dewan, M. D. Kankam, Modeling and Simulation of a Cycloconverter Drive System for

Harmonic Studies, IEEE Trans. On Industrial Electronics, vol. 47, no.3, pp. 533541, June 2000.


16/16

Questions?

half cycle pairs method

Documents