Power Factor Improvement of an AC-DC Converter via Appropriate sPWM Technique

K. Georgakas, A. Safacas University of Patras, Department of Electrical and Computer Engineering, Laboratory of Electromechanical Energy

Conversion, 26500 Rion-Patras, GREECE

Abstract— The power control of a DC load can be achieved via an AC-DC converter consisting of a rectifier bridge and a switching element operating by sPWM technique. The use of such a converter causes a lot of high harmonics at the AC side, which reduce the power factor and distort the grid voltage. Using passive filter in the converter input to avoid the high harmonics consequences the power factor decrease. To improve the power factor an appropriate sPWM operation of the switching element is proposed in this paper. The system behavior is studied through simulation and experimental investigation. The power factor correction is verified.

I. INTRODUCTION It is well known that the power control of a DC load

feeding by the grid is achieved by the use of an AC-DC converter structure operating through a sPWM technique. In figure 1 one can see such a converter structure consisting of a MOSFET single phase rectifier bridge in series connected with a switching MOSFET5. In the case of an ohmic – inductive load a parallel freewheeling diode is necessary. The rectification becomes by the parasitic bridge MOSFET diodes, while the MOSFETs 1-4 enable the power inversion, if an active load is considered.

AC VoltageSource

Lf

Cf

ElectricalLoad

MOSFET1

MOSFET2

MOSFET4

MOSFET3

Do

MOSFET 5

A

B

.

.

PassiveFilter

R

L

Figure 1. An AC-DC converter structure for supplying a DC load.

The sPWM operation can be succeeded by comparison of a sinusoidal voltage waveform (Uc)in phase to the grid voltage (Ug) with a high frequency triangular waveform in order to obtain a switching pulse waveform. The pulse duration inside of a half sinusoidal period is not constant and the pulse of the maximum duration is located exact at the middle of the half period, while the pulse of the minimum duration appears at the beginning of that, as it appears in figure 2a. Figure 3 shows the waveforms of the grid voltage (50Hz) and the corresponding current pulse

waveforms (switching frequency 5 kHz). In case of an ohmic DC load the basic harmonic of the grid current pulse waveform (fig.3a) is in phase with the grid sinusoidal voltage waveform. If the DC load is ohmic-inductive one, then the basic current harmonic is shifted in relation to the voltage waveform U g (fig.3b). In the case that a sinusoidal waveform Uc is leading upon the grid voltage Ug by an angle ‘a’ via comparison to the triangular waveform (fig.2b), a grid current pulse waveform is obtained of which the basic harmonic is shifted to the grid voltage. In this way the grid current basic harmonic can becomes in phase with the grid sinusoidal voltage, if we have an ohmic-inductive DC load. It means that the power factor can be corrected. In this paper an extensive investigation of the influence of the leading or lagging angle ‘a’ to the power factor via simulation as well as experimentally has been carried out.

2a

2b

Figure 2. Pulse waveforms obtained by sPWM when ‘a’=0o (2a) and ‘a’≠0o (2b).

3a

3b

Figure 3. Grid voltage and current in the case of ohmic load (3a) and ohmic-inductive load (3b).

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II. POWER FACTOR INVESTIGATION USING SIMULINK/MATLAB SIMULATION

The power factor calculation is achieved by Simulink/Matlab simulation using the appropriate models for the system which is shown in figure 1. First, the simulation has been carried out without input passive filter for two different loads: a) ohmic load and b) ohmic inductive load (several values), by a switching frequency fsw=5 kHz. The power factor as a function of the angle ‘a’ mentioned above is depicted in the figures 4, 5 for an effective load power of P=1200W. Figure 14 shows the power factor in the case that a DC motor is used as a load. In figure 15 is PF=f(‘a’) by fsw=10 kHz. In figures 11 and 12 the waveforms of the ac input voltage and current are shown. The figures 6, 7, 8, 9 and 10 show the spectrum of the input current for characteristic values of the angle ‘a’. In the case of ohmic load (R=20Ω) the power factor gets its maximum value (PFmax=0,6548) by ‘a’=0°, which is relatively a low value because of the great current high harmonic content. If the load has ohmic-inductive character, the maximum PF value is obtained by a negative value of angle ‘a’. This happens because the control voltage Uc mentioned above is leading by the angle ‘a’ upon the grid voltage Ug in order to achieve that the basic current harmonic is in phase with the grid voltage. In this point it must be remarked that the sPWM procedure, controlled by the signal Uc, leads to the correction of the power factor through the moving of the current waveform to the left in the figure 12, what can be easy shown if the figures 11 and 12. So, the waveforms of uin(t) and iin(t) get more similar to the waveform of figures 13. But, by moving of the waveform iin(t) increase the high harmonic content, as it can be shown in the figures 6, 7, 8, 9 and 10, which are getting through FFT analysis of the input current waveform iin(t) using the Origin software. It is obviously that the high harmonic content of iin(t), for example, by ‘a’=0° is lower than that by ‘a’=-45o (fig.7 and 10). Beginning from ‘a’=0° and gradually going on to ‘a’=-45° the harmonics of the 5th, 7th, 9th and 11th order increase.

- 2 0 - 1 5 - 1 0 - 5 0 5 1 0

6 5 , 4 7 0

6 5 , 4 7 2

6 5 , 4 7 4

6 5 , 4 7 6

6 5 , 4 7 8

6 5 , 4 8 0

PF [%

]

' a ' [ o ]

R = 2 0 Ω

Figure 4. Power factor (PF) as a function of the angle ‘a’ by ohmic

load and switching frequency 5 kHz without input filter (simulation results).

-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 2578,0

78,5

79,0

79,5

80,0

80,5

81,0

81,5

82,0

82,5

83,0

83,5

84,0

84,5

85,0

PF [%

]

'a' [o]

L=10mH, R=20Ω

L=30mH, R=20Ω

L=50mH, R=20Ω

L=100mH, R=20Ω

L=200mH, R=20Ω

Figure 5. Power factor (PF) as a function of the angle ‘a’ by ohmic-

inductive load as a parameter and switching frequency 5 kHz without input filter (simulation results).

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 00

1

2

3

F re q u e n c y (H z )

I [A

]

Figure 6. Grid current harmonic content for angle ‘a’=18ο and ohmic-inductive load without input filter (R=20Ω, L=30mH)

(simulation results).

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 00

1

2

3

F re q u e n c y (H z )

I [A

]

Figure 7. Grid current harmonic content for angle ‘a’=0ο and ohmic-inductive load without input filter (R=20Ω, L=30mH)

(simulation results).

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 00

1

2

F re q u e n c y (H z )

I [A

]

Figure 8. Grid current harmonic content for angle ‘a’=-9ο and ohmic-inductive load without input filter (R=20Ω, L=30mH)

(simulation results).

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 00

1

2

3

F re q u e n c y (H z )

I [A

]

Figure 9. Grid current harmonic content for angle ‘a’=-36ο and ohmic-inductive load without input filter (R=20Ω, L=30mH)

(simulation results).

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 4 0 0 0 0 5 0 0 0 00

1

2

3

F re q u e n c y (H z )

I [A

]

Figure 10. Grid current harmonic content for angle ‘a’=-45ο and ohmic-inductive load without input filter (R=20Ω,

L=30mH) (simulation results).

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0.20 0.21 0.22

-200

0

200

iin

uin

u(t)

[V],

i(t

)*10

[A]

t [s]

Figure 11. Grid voltage and current waveforms for ‘a’=0o and ohmic-

inductive load (R=20Ω, L=30mH) without input filter (simulation results).

0.06 0.07 0.08

-400

-300

-200

-100

0

100

200

300

400

iin

uin

u(t)

[V],

i(t

)*10

[A]

t [s]

Figure 12. Grid voltage and current waveforms for ‘a’=-45o and ohmic-

inductive load (R=20Ω, L=30mH) without input filter (simulation results).

0.20 0.22

-200

0

200 Iin

Uin

u(t)

[V],

i(t

)*10

[A]

t [s]

Figure 13. Grid voltage and current waveforms for ‘a’=0o and ohmic

load (R=20Ω) without input filter (simulation results).

-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20

72

73

74

75

76

77

PF [%

]

a [o]

5 kHz 10 kHz

Figure 14. Power factor (PF) as a function of the angle ‘a’ by DC

motor load and switching frequency 5 kHz and 10 kHz without input filter (simulation results).

As mentioned above, the phase angle of the basic current harmonic φ1 can be defined through the angle ‘a’. Using the values of the calculated power factor and of the spectrum analysis the value of φ1 can be calculated as follow:

As the power factor of the basic harmonic is 2k2

11

Icos =PF 1+THD THD=

I,withϕ ⋅ ∑

(1)

where I1 = rms value of the basic current harmonic and

2 2 2 2k 3 5 7

2500I = ....I I I I+ + +∑

(2)

the rms value of the high harmonics, using the known values of PF, I1 and Ik, the values of cosφ1 and also φ1 can be calculated. The results of such a calculation are shown in table I.

For example, for ‘a’=18°, ohmic-inductive load (R=20Ω, L=30mH), fsw=5 kHz, Ug=220 V, fg=50 Hz and P=1200W, the following values have been obtain:

I1=3,56 A, I3=0,8918 A, I5=0,16 A, …… I100=1,112 A, I200=0,534 A, I300=0,3 A, I400=0,2 A, I500=0,4 A, PF=78,27 %,

2 2 2k 3 5

2

2500

1

I = .... 1,622531121 A,

THD=0,455767168, cos 7827 1 0,455767 =0,857168 40,

I I I

ϕ

+ + =

⋅ +=

∑

TABLE I. CALCULATION OF THE COSΦ1 USING THE SIMULATION RESULTS

(WITHOUT INPUT FILTER)

Angle ‘a’ PF cosφ1 φ1 [ο] ‘18ο’ (lag) 0,7827 0,8574 30,9 ‘9ο’ (lag) 0,7928 0,8792 28,45 ‘0ο’ 0,8009 0,8928 26,77 ‘-90’ (lead) 0,8069 0,8929 26,76 ‘-180’ (lead) 0,8108 0,8986 26,02 ‘-360’ (lead) 0,8128 0,9019 25,59 ‘-450’ (lead) 0,8113 0,9025 25,51 ‘-540’ (lead) 0,8085 0,9141 23,92 ‘-630’ (lead) 0,8042 0,8986 26,02 In the table I one can see that using the proposed

operation mode of the sPWM method, an improvement of the power factor can be achieved. We remark that by ‘a’=0° is PF=0,8009, while by ‘a’=-36° is PF=0,8128, it means that an improvement of 1,48% has been succeeded. Figure 15 shows the function PF=f(‘a’) by switching frequency fsw=10 kHz and P1,2=1000W, 1600W. In the case of this switching frequency value the results are very similar to the case of fsw=5 kHz.

If a passive filter with appropriate L-C values (L=100mH, C=1μF) at the converter input is used, the simulation results of the system are those which are depicted in the figures 16, 17, 18, 19, 20, 21 and 22. The PF values are increased in all cases, so that an improvement of about 10% is achieved (in comparison to PFmax in the two cases: with and without filter). The spectrum analysis show that the high order harmonics (fk>800 Hz) doesn’t appear (fig.18,19 and 20). The current waveforms are different compared to those in case that no filter is used, as the figures 21 and 22 show.

Table II is obtained in similar way as table I. One can remark that by leading angle ‘a’=-54° the current basic harmonic is in phase with the grid voltage. The maximum

Proceedings of the 15th Mediterranean Conference onControl & Automation, July 27 - 29, 2007, Athens - Greece

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value of PF is at ‘a’=-36°, by fsw=5 kHz and P=1200W. Comparing the PF values for ‘a’=0° and ‘a’=-36° one can see that an improvement of 4,47% has been succeeded.

-50 -40 -30 -20 -10 080

81

88

89

90

1000 [W]

1500 [W]

PF [%

]

degrees [0]

Figure 15. Power Factor (PF) as a function of the angle ‘a’ for

switching frequency 10 kHz without input filter by the output power as a parameter (simulation results).

-60 -50 -40 -30 -20 -10 0

90

91

92

93

94

95

96

97

98

PF [%

]

'a' [o]

L=10mH , R=20Ω L=30mH , R=20Ω L=0mH , R=20Ω L=100mH, R=20Ω L=200mH, R=20Ω

Figure 16. Power factor (PF) as a function of the angle ‘a’ by five values of ohmic-inductive load with input

filter and switching frequency 5 kHz (simulation results).

-9 0 -8 0 -7 0 -6 0 -5 0 -4 0 -3 0 -2 0 -1 09 1

9 2

9 3

9 4

9 5

9 6

PF [%

]

'a ' [o]

1 2 0 0 W 5 0 0 W

Figure 17. Power Factor (PF) as a function of the angle ‘a’=0o for

switching frequency 10 kHz with input filter by output power as a parameter (simulation results).

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 4 8 0 0 5 0 0 0 5 2 0 00

1

2

3

F re q u e n c y (H z )

I [A

]

Figure 18. Grid current harmonic content for angle ‘a’=0ο with input filter

and ohmic-inductive load (R=20Ω, L=10mH) (simulation results).

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 5 0 0 00

1

2

3

4

F re q u e n c y (H z )

I [A

]

Figure 19. Grid current harmonic content for angle ‘a’=-27ο with input

filter and ohmic-inductive load (R=20Ω, L=10mH) (simulation results).

0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 4 8 0 0 5 0 0 0 5 2 0 00

1

2

3

F r e q u e n c y (H z )

I [A

]

Figure 20. Grid current harmonic content for angle ‘a’=-40,5ο with input

filter and ohmic-inductive load (R=20Ω, L=10mH (simulation results).

1 . 2 0 1 . 2 1 1 . 2 2

- 2 0 0

0

2 0 0

i i n

u i nu(

t) [V

],

i(t)*

10 [A

]

t [ s ]

Figure 21. Grid voltage and current waveforms for ‘a’=0o and ohmic-

inductive load (R=20Ω, L=30mH) with input filter (simulation results).

0 . 1 0 0 . 1 1 0 . 1 2

- 2 0 0

0

2 0 0

i in

uin

u(t)

[V],

i(t

)*10

[A]

t [ s ]

Figure 22. Grid voltage and current waveforms for ‘a’= -36o and ohmic-

inductive load (R=20Ω, L=30mH) with input filter (simulation results).

TABLE II. CALCULATION OF THE COSΦ1 USING THE SIMULATION RESULTS

(WITH INPUT FILTER)

Angle ‘a’ PF cosφ1 φ1 [o] ‘0ο’ 0,8986 0,9334 21 ‘-27o’ (lead) 0,934 0,985 9,93 ‘-31,5o’ (lead) 0,9381 0,9866 9,39 ‘-36o’ (lead) 0,9388 0,9871 9,21 ‘-45o’ (lead) 0,9349 0,9973 4,21 ‘-54o’ (lead) 0,9179 ≈ 1 ≈ 0

III. EXPERIMENTAL RESULTS A MOSFET converter has been designed and

constructed in the laboratory and its operation was

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controlled by a microprocessor 80C196MC. This system including an input filter (L≈3mH, C≈3μF) has been used for the experimental investigation. The experimental results are depicted in the figures 23, 24, 25, 26, 27, 28 and 29.

-100 -80 -60 -40 -20 0 20 40 60

0,70

0,75

0,80

0,85

0,90

0,95

PF [%

]

'a' [o]

Figure 23. Power factor (PF) as a function of the angle ‘a’ for ohmic-inductive load (R=180Ω, L=30mH) by swi-

tching frequency 5 kHz with input filter (experimental results).

-60 -40 -20 0 20 40 60

0,65

0,70

0,75

0,80

0,85

PF

[%]

'a ' [o]

Figure 24. Power factor (PF) as a function of the angle ‘a’ for ohmic-inductive load (R=180Ω, L=30mH) and switching frequency 2,5 kHz with input filter (experimental results).

-60 -40 -20 0 20 40 60

0,70

0,75

0,80

0,85

0,90

0,95

1,00

PF [%

]

'a' [o]

Figure 25. Power factor (PF) as a function of the angle ‘a’ for ohmic-inductive load (R=180Ω, L=100mH) by swi-tching frequency 5 kHz with input filter (experimental results).

-60 -40 -20 0 20 40 60

0,75

0,80

0,85

0,90

0,95

1,00

PF [%

]

'a ' [o] Figure 26. Power factor (PF) as a function of the angle ‘a’ for

ohmic-inductive load (R=180Ω, L=100mH) by swi-tching frequency 10 kHz with input filter (experimental results).

-40 -30 -20 -10 0 10 20

0 ,94

0 ,95

0 ,96

0 ,97

0 ,98

0 ,99

1 ,00

1 ,01

PF

[%]

'a ' [o]

10 kH z 5 kH z

Figure 27. Power factor (PF) as a function of the angle ‘a’ for

ohmic load R=30Ω and by switching frequency 5 kHz with input filter (experimental results).

Figure 28. Grid voltage and current waveforms for ‘a’=0o, ohmic

load (R=180Ω) and switching frequency 10 kHz (experimental results).

Figure 29. Grid current waveform for ‘a’=0o, ohmic-inductive

load (R=180Ω, L=30mH) and switching freque-ncy 2,5 kHz (experimental results).

In general, the differences between simulation and

experimental results are small. In all cases the power factor has high values (0,85…0,99) depended on the switching frequency, the load R-L values, the output power and the L-C values of the input filter.

IV. CONCLUSIONS The simulation and experimental results show that there

is a leading angle ‘a’ by which the power factor becomes maximum. The value of this angle depends on the nature of the load, the output power, the input filter and the switching frequency. A sinusoidal signal (voltage Uc) created by microprocessor and leading upon the sinusoidal grid voltage determines the sPWM converter operation and so the appropriate value ‘a’ can be achieved. The target is to shift the grid current waveform relatively to the

Proceedings of the 15th Mediterranean Conference onControl & Automation, July 27 - 29, 2007, Athens - Greece

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grid voltage in order to be the basic current harmonic in phase with the grid voltage.

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[13]. Alfio Consoli, Mario Cacciato, Antonio Testa, Francesco Gennaro, “Single Chip Integration for Motor Drive Converters With Power Factor Capability”, IEEE TRANSACTION ON POWER ELECTRONICS, VOL.19, NO.6, November, 2000, pp. 1372-1379.

[14]. Jean-Christophe Crebier, Bertrand Revol, and Jean Paul Ferrieux “Boost-Chopper-Derived PFC Rectifiers: Interest and Reality”, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL.52, NO.1, FEBRUARY, 2005.

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Proceedings of the 15th Mediterranean Conference onControl & Automation, July 27 - 29, 2007, Athens - Greece

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