29

CHAPTER 3

A LOW FREQUENCY PULSE WIDTH MODULATION

STRATEGY FOR CYCLOCONVERTERS

3.1 INTRODUCTION

Power quality problems are of increasing concern in contemporary

industry particularly with progress in the application of ac-ac conversion

systems involving power electronic converters (Lander 1987). It augurs the

need of proper harmonic management methods to acquire a complete

understanding of harmonic source behaviors and necessitate the need to

explore the interactions between the converter and other system components

(Syam et al 2004 a, Wang et al 2000, Syam et al 2004 b). The ac-ac

conversion systems and their control strategies are thus under intense research

to meet the requirements of the utilities.

A control strategy refers to a set of firing signals that trigger the

devices in a cycloconverter to achieve a specific target output voltage and

frequency (Miyazawa et al 1989, Ishiguro et al 1991). The use of a particular

control strategy may help to improve the shape of the input current and/or

output voltage (Basirifar et al 2011). However the available approaches do not

appear to offer the desired performance. It is in this prelude that modifications

in the existing PWM techniques are contemplated to contribute in this

perspective.

There is a growing interest in the use of cycloconverters for bulk

power transfer in a good number of applications (Das et al 1997).

30

Cycloconverters inherit the ability to provide simultaneous voltage and

frequency transformation without the help of intermediate stage reactive

component by synthesizing a low frequency waveform from appropriate

sections of a higher frequency source (Pelly 1971, Lander 1987, Chu et al

1989, Shicheng Zheng et al 2009). However it assuages the dent of harmonics

and consequent effects of increased losses, deliberate de-rating and lower

efficiency. It therefore continues to urge the development of new measures to

build methodologies in order to refine the shape of the specified output

voltage (Agrawal et al 1992, Jeevananthan et al 2007 a).

3.2 PROBLEM FORMULATION

The main aim is to design a low frequency, programmed PWM

(PPWM) strategy in order to minimize the distortion in the output voltage of

single phase cycloconverters. The proposed EAC (Grahame Holmes et al

2003) attempts to reduce the lower order harmonic content especially in the

low output voltage range. The performance of this scheme is evaluated

through MATLAB based simulation and validated using a prototype. The

approach involves deriving mathematical relations for a host of techniques

and ventures to highlight the merits of this methodology.

3.3 EXISTING TECHNIQUES

The cycloconverter, being a primordial converter imbibes a facility

to work with a family of control schemes. A number of firing schemes appear

to revolve around to suit specific applications. Jeevananthan et al (2007 a)

proposed a host of most commonly used methods (a) constant firing angle

method (CFAM), (b) cosine wave crossing method (CWCM),

(c) HWSVFAM and (d) QWSVFAM. The standard single phase 230V, 50 Hz

AC waveform seen in Figure 3.1 (a) is considered as the input and a

frequency transformation (Kf) ratio of three is chosen to explain the schemes.

31

3.3.1 Constant Firing Angle Method

Figure 3.1(b) shows the output voltage waveform for CFAM, where

the delay angle is allowed to vary according to the voltage requirements of

the load. This is a simple straightforward method, which gives a crude output

waveform with considerable harmonic content resulting in its poor THD.

3.3.2 Cosine Wave Crossing Method

Figure 3.1(c) shows the output voltage waveform for CWCM in

which the comparison of a sinusoidal reference of output frequency with two

cosine carriers of input frequency (cosine and inverted cosine) generates the

gating pulses.

3.3.3 Half Wave Symmetry Variable Firing Angle Method

The HWSVFAM is a closer approximation to a sine wave that is

synthesized by phase delaying the firing of the switches as shown in

Figure 3.1(d). It is a modified version of CFAM and operates with a different

firing angle for different input half cycles. However, the firing angle of the

first and Kfth

(third for this case) pulses are same, and hence the name half

wave symmetry. The load receives a full input half cycle at its peak period

th

fK 1

2 and progressively reduces its conduction for other sections owing

to fact that the output fundamental component requires controlled phase area

proportional to its instantaneous values.

3.3.4 Quarter Wave Symmetry Variable Firing Angle Method

The QWSVFAM is basically a modified phase controlled

cycloconversion, which makes use of hybrid commutation (both natural and

forced commutation) for enabling quarter wave symmetry in the output. Each

32

input half cycle is phase controlled in such a way that the position of each

output pulse (phase controlled half cycle) is as close as possible to the desired

sinusoidal output voltage in addition to their proportionality average value as

seen in the output voltage waveform in Figure 3.1(e). It is similar to

HWSVFAM in the first quarter of any output half cycle while the second

quarter differs, which is the exact mirror image of the first quarter. In this

method, the delay angles of segments vary in such a way that in addition to

average value of each segment, the pulse orientations also lie as closely as

possible to the variations of desired sinusoidal output voltage and renders

reduced the harmonics.

Though the symmetric firing schemes viz., HWSVFAM and

QWSVFAM support a marginal improvement, still there is a definite need to

introduce refinements in the available strategies to harness a much lower

distortion in the output voltage.

Figure 3.1 Input/ output voltage waveforms (a) input (b) output-CFAM

(c) output-CWCM (d) output-HWSVFAM and

(e) output-QWSVFAM

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3.4 MATHEMATICAL EXTRACTION OF THE PROPOSED

EAC STRATEGY

The existing cycloconversion strategies introduce lower order

harmonics and increase the THD. The mission is to develop a low frequency,

PPWM strategy that provides an improved performance in terms of minimal

lower order harmonics and reduced THD. The EAC is a refined PWM

strategy suitable for single-phase to single-phase cycloconverter. The width of

the PWM pulses in this approach is determined by making the area of the

PWM signal equal to that under the sampled target waveform, irrespective of

the number of samples. It orients to compute the pulse widths for a wide

range of input and output conditions. The basic principle of the EAC method

is illustrated in Figure 3.2.

Figure 3.2 EAC for cycloconverter

34

The area enfolded by the target output waveform in the kth

sampling

period is represented by,

i

i

k

m

kT 0

k 1

m

A M sin t dt

k T0 f f

k 1M kA cos cos

mK mK (3.1)

The pulse width at each sampling period is calculated by equating

the area under the target in every sampling period with the area of the actual

output. The area enfolded by the actual output waveform in the corresponding

kth

sampling duration is given by

i

i

k 1

m 2m 2

k O f 0

k 1

m 2m 2

A sin K tdt

kOf 0

2A sin k 0.5 sin

K m 2 (3.2)

where, m is the number of samples per half cycle of the input waveform,

2M is the modulation depth, o is the output frequency, o

fi

K is the

frequency transformation ratio and i is the input frequency.

The pulse width, ‘ ’ for kth

sampling period is calculated by

equating the area under the target waveform represented by Equation (3.1) to

the area under the actual output waveform given by Equation (3.2).

35

0 f f f 0

k 1M k 2cos cos sin k 0.5 sin

mK mK K m 2

1 X2 sin

Y (3.3)

where

ff f

k 1 kX K M cos cos

mK mK

j 1Y 2 1 sin k 0.5

m

The Fourier constants and harmonic analysis of output voltage are

determined as follows.

0n n

n 1

a nx nxf (x) a cos b sin

2 3 3 (3.4)

T

2

n

0

4 nxa f (x) cos dx

T 3

3

mn

0

2V nxa sin x cos dx

3 3

k 1

m 2m 2m

n

k 1

m 2m 2

2V nxa sin x cos dx

3 3

36

k 1

m 2m 2m

n

k 1

m 2m 2

V n na sin( 1)x sin( 1)x dx

3 3 3

j 1 mn

k 1 k 11 n ncos 1 cos 1

n 3 3 m 2m 2 3 m 2m 2V

a ( 1)

k 1 k 11 n ncos 1 cos 1

n 3 3 m 2m 2 3 m 2m 2

(3.5)

3

mn

0

2V nxb sin xsin dx

3 3

k 1

m 2m 2m

n

k 1

m 2m 2

V n nb cos 1 x cos 1 x dx

3 3 3

j 1 mn

k 1 k 11 n nsin 1 sin 1

n 3 3 m 2m 2 3 m 2m 2V

b ( 1)

k 1 k 11 n nsin 1 sin 1

n 3 3 m 2m 2 3 m 2m 2

(3.6)

where j=1 for odd chopping and j=2 for even chopping for a particular value

of Kf.

The third order Fourier constants and harmonic analysis of output

voltage are determined as follows.

3

m3

0

2Vb sin x sin xdx

3

37

k 1

m 2m 2m

3

k 1

m 2m 2

Vb 1 cos 2x dx

3

j 1 m3

2k 1Vb 1 cos sin

3 m (3.7)

k 1

m 2m 2m

3

k 1

m 2m 2

2Va sin x cos xdx

3

j 1 m3

2k 1Va 1 sin sin

3 m (3.8)

The advent of PWM appears to revelutionise the performance of

switched converters in the sense they inherit the facility to be programmed

and suit precise design requirements. The firing pulse generated using some

form of PWM based approaches hold merit and influence the operation of the

circuit in a satisfactory manner. It is precisely the fact as to why a pulse width

modulation technique is contemplated as a prerogative in the perspective of

triggering a power device.

3.5 MULTIPLE PULSE MODULATION METHOD

The multiple pulse modulation (MPM) where several equidistant

pulses per half cycle are generated at the points of intersection of the carrier

and reference signal waves is explored as a firing mechanism suitable for

cycloconverters. A triangular carrier and a square reference wave are chosen

and the pulse width is allowed to change in accordance with the requirements

38

by varying the amplitude of the square wave. The Figure 3.3 shows the output

voltage waveform for MPM.

Figure 3.3 Output voltage waveform

The value of the actual output voltage (rms) in the cycloconverter

is given by,

2 32 2 2 2 2 2 2

0 m m m

2

1V V sin td t V sin td t V sin td t

3

0 m

sin 2

2V V2

(3.9)

The Fourier constants and harmonic analysis of output voltage are

determined as follows.

0n n

n 1

a nx nxf (x) a cos b sin

2 3 3 (3.10)

T

2

n

0

4 nxa f (x)cos dx

T 3

39

3

mn

0

4V nxa sin x cos dx

6 3

c

c

(2 V )(k 1)

m 2mm

n

V(k 1)

m 2m

V n na sin( 1)x sin( 1)x dx

3 3 3

c c

j 1 mn

c c

(2 V ) V )1 n (k 1) n (k 1)cos 1 cos 1

n 3 3 m 2m 3 m 2mVa ( 1)

(2 V ) V )1 n (k 1) n (k 1)cos 1 cos 1

n 3 3 m 2m 3 m 2m

(3.11)

3

mn

0

2V nxb sin x sin dx

3 3

c

c

(2 V )(k 1)

m 2mm

n

V(k 1)

m 2m

V n nb cos( 1)x cos( 1)x dx

3 3 3

c c

j 1 mn

c c

(2 V ) V )1 n (k 1) n (k 1)sin 1 sin 1

n 3 3 m 2m 3 m 2mVb ( 1)

(2 V ) V )1 n (k 1) n (k 1)sin 1 sin 1

n 3 3 m 2m 3 m 2m

(3.12)

40

The third order Fourier constants and harmonic analysis of output

voltage are determined as follows.

3

m3

0

2Vb sin x sin xdx

3

c

c

(2 V )(k 1)

m 2mm

3

V(k 1)

m 2m

Vb 1 cos 2x dx

3

j 1 c cm3

(1 V ) (V 1)V 2(k 1)b ( 1) cos sin

3 m m m m(3.13)

3

m3

0

2Va sin x cos xdx

3

c

c

(2 V )(k 1)

m 2mm

3

V(k 1)

m 2m

Va sin 2xdx

3

j 1 cm3

(V 1)V 2(k 1)a ( 1) sin sin

3 m m m (3.14)

3.6 SIMULATION

The power circuit of a cycloconverter for a single-phase output

with a single-phase input is shown in Figure 3.4. Basically it consists of two

back-to-back connected full converters (P-converter and N-converter).

A series of positive (rectified) input half cycles appears across the resistive

load when the P-converter is gated, while series of negative input half cycles

result when the N-converter is operated in an open blanking mode of

approach. The configuration sets the load frequency to be a fraction of the

input frequency.

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Figure 3.4 Power circuit of single phase cycloconverter

The single-phase cycloconverter with different control strategies is

simulated using MATLAB. The circuit specifications are intuitively chosen to

acquire a target output voltage of close to 100V (rms) fundamental at one

third the input frequency across a 110 resistive load.

An intuitive investigation reveals that the viable number of samples

(m) lies in the range of eight and two for a modulation depth (M) that varies

from 0.1 and 0.636. The suitable value for m in the low output voltage range

is eight where the M varies from 0.1 to 0.18 while the same is two in the

higher output voltage range for which M is between 0.54 and 0.636.

Therefore, the study echoes the appropriate choice of the modulation depth

and the number of samples to land at the desired output voltage. The trail and

error procedure yields a modulation depth of 0.46 and 3 samples to yield the

specified target voltage in all the schemes. The output voltage obtained for

M=0.46 and m=3and their respective harmonic spectra are depicted in

Figures 3.5 to 3.10. It is to be noted that the performance of EAC is obtained

for the same number of samples as observed from Figures 3.9 and 3.10.

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Figure 3.5 Output voltage and spectrum – CFAM

Figure 3.6 Output voltage and spectrum – CWCM

Figure 3.7 Output voltage and spectrum –HWSVFAM

Figure 3.8 Output voltage and spectrum –QWSVFAM

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Figure 3.9 Output voltage and spectrum – MPM

Figure 3.10 Output voltage and spectrum – EAC

The entries in Table 3.1 contain the amplitudes of the target

fundamental and harmonic components 3, 5 and 7 in terms of percentage of

fundamental component for the same modulation depth and number of

samples to illustrate the lower value of THD for EAC. It is interesting to note

from Table 3.2 that EAC offers an exhilarating performance even when

compared with MPM scheme on a similar platform. The results re-incarnate

the creation of the new firing strategy so as to accomplish an improved

performance for cycloconverters.

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Table 3.1 Comparison of lower order harmonics and THD using

existing phase angle controlled and proposed EAC methods

StrategyVo1

(V)V3 V5 V7

THD

(%)

CFAM 104.2 46.56 80.37 64.24 124.29

CWCM 104.3 46.6 80.39 64.33 124.16

HWSVFAM 104.5 45.48 71.45 50.18 119.71

QWSVFAM 104.4 6.01 8.58 77.74 99.49

EAC 104.2 1.45 12.18 17.25 75.38

Table 3.2 Comparison of lower order harmonics and THD using MPM

and proposed EAC methods

StrategyVo1

(V)V3 V5 V7

THD

(%)

MPM 105.0 39.11 44.96 14.88 114.58

EAC 104.2 1.45 12.18 17.25 75.38

The variation of amplitudes of harmonic orders over a specific

output voltage range for a modulation depth ranging from 0.44 to 0.52 with

three samples for the different control schemes seen in Figure 3.11 go to

highlight the supremacy of EAC.

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Figure 3.11 Variation of harmonic order with THD (%) for m=3

46

Similarly the variation of harmonic orders with respect to THD

obtained by varying M from 0.1 to 0.18, with eight samples for the different

control schemes in the defined output voltage range is shown in Figure 3.12.

Figure 3.12 Variation of harmonic order with THD (%) for m=8

3.7 HARDWARE IMPLEMEMTATION

The scheme seen in Figure 3.4 is implemented through a suitable

prototype constructed with the specific purpose to operate in the same

horizon. A real time windows target using MATLAB is used to generate

switching pulses to the constructed prototype converter based on MOSFET

(IRF840) switches. The switching angles are calculated in off-line for

different operating points of the converters. The virtual reality toolbox

seamlessly integrates with real-time workshop targets. It supports simulations

that use code generated by real-time workshop and a third-party compiler on

the desktop computer. The virtual reality toolbox also supports code executed

in real time on external target computers. The schematic pulse generation

using the real time target of MATLAB is shown in Figure 3.13.

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Figure 3.13 Schematic of real time workshop based pulse generation scheme

The systematic digital generation of EAC pulses corresponding to

the target output voltage of close to 100V(rms) along with the output voltage

waveform is shown in Figure 3.14.

Figure 3.14 Pulse pattern and output voltage

The fabricated hardware with the work bench is illustrated as a

photograph in Figure 3.15. It is tested in the same operating states and the

output voltage waveforms along with their harmonic spectra are drawn in

Figures 3.16 to 3.21 for the different control schemes. It is noteworthy to

observe that the experimental arrangement annotates more or less similar

performance thus bringing out the efficacy of the developed control

algorithm. The tabulated readings in Table 3.3 authenticate the findings and

served to validate the simulated response.

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Figure 3.15 Cycloconverter prototype

Figure 3.16 Output voltage and harmonic spectrum –CFAM

Figure 3.17 Output voltage and harmonic spectrum -CWCM

49

Figure 3.18 Output voltage and harmonic spectrum – HWSVFAM

Figure 3.19 Output voltage and harmonic spectrum - QWSVFAM

Figure 3.20 Output voltage and harmonic spectrum – MPM

Figure 3.21 Output voltage and harmonic spectrum - EAC

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Table 3.3 Comparison of existing and proposed control strategies

Simulated values Experimental values

Strategies Vo1

(v)V3 V5 V7

THD

(%)

Vo1

(v)V3 V5 V7

THD

(%)

CFAM 104.2 46.56 80.37 64.24 124.29 107.8 50.7 86.1 72.0 122.7

CWCM 104.3 46.60 80.39 64.33 124.16 108.0 50 87 67.9 122.4

HWSVFAM 104.5 45.48 71.45 50.18 119.71 107.7 51.5 76 53.3 119.5

QWSVFAM 104.4 6.01 8.58 77.74 99.49 103.4 7.8 8.5 79.5 102.4

MPM 105.0 39.11 44.96 14.88 114.58 103.6 39.7 46.1 15 115.7

EAC 104.2 1.45 12.18 17.25 75.38 106.2 2.3 14.1 18.9 75.5

The constructed prototype hardware is also tested with the firing

pulses generated in the same way shown in Figure 3.15 for an R-L load with

R=110 and L= 5mH. The output voltage and output current waveforms

shown in Figure 3.22 prove that proposed EAC also works with R-L load.

(a) (b)

Figure 3.22 (a) Output voltage and (b) output current waveforms for

RL load

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3.8 SUMMARY

The concept of EAC has been implemented for a single phase

cycloconverter to drive home the benefits of extracting an entire range of

output voltage. It has been found to yield appreciable lowering of the THD

values almost through the entire operating range of output voltage. A

significant contribution has been to illustrate the superiority of the proposed

technique even over a PWM based methodology typically in the lower ranges

of the output voltage. The performance of the existing firing schemes has

been elucidated to highlight the attractive features of the developed algorithm

and portray its capability in drive applications where low speed operation is

required.