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Power Factor Improvement of an AC-DCConverter via Appropriate sPWM Technique

K. Georgakas, A. SafacasUniversity 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 achievedvia an AC-DC converter consisting of a rectifier bridge anda switching element operating by sPWM technique. The useof such a converter causes a lot of high harmonics at the ACside, which reduce the power factor and distort the gridvoltage. Using passive filter in the converter input to avoidthe 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 andexperimental investigation. The power factor correction isverified.

I. I NTRODUCTION

It is well known that the power control of a DC loadfeeding by the grid is achieved by the use of an AC-DCconverter structure operating through a sPWM technique.In figure 1 one can see such a converter structureconsisting of a MOSFET single phase rectifier bridge inseries connected with a switching MOSFET5. In the caseof an ohmic – inductive load a parallel freewheeling diodeis necessary. The rectification becomes by the parasitic

bridge MOSFET diodes, while the MOSFETs 1-4 enablethe 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 comparisonof a sinusoidal voltage waveform (U c)in phase to the gridvoltage (U g) with a high frequency triangular waveform inorder to obtain a switching pulse waveform. The pulseduration inside of a half sinusoidal period is not constantand the pulse of the maximum duration is located exact atthe middle of the half period, while the pulse of theminimum duration appears at the beginning of that, as itappears in figure 2a. Figure 3 shows the waveforms of thegrid voltage (50Hz) and the corresponding current pulse

waveforms (switching frequency 5 kHz). In case of anohmic DC load the basic harmonic of the grid current

pulse waveform (fig.3a) is in phase with the gridsinusoidal voltage waveform. If the DC load is ohmic-inductive one, then the basic current harmonic is shifted inrelation to the voltage waveform U g (fig.3b). In the casethat a sinusoidal waveform U c is leading upon the gridvoltage U g by an angle ‘a’ via comparison to the triangular

waveform (fig.2b), a grid current pulse waveform isobtained of which the basic harmonic is shifted to the gridvoltage. In this way the grid current basic harmonic can

becomes in phase with the grid sinusoidal voltage, if wehave an ohmic-inductive DC load. It means that the power factor can be corrected. In this paper an extensiveinvestigation of the influence of the leading or laggingangle ‘a’ to the power factor via simulation as well asexperimentally has been carried out.

2a

2b

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

3a

3b

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

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II. POWER FACTOR INVESTIGATION USINGSIMULINK /M ATLAB SIMULATION

The power factor calculation is achieved bySimulink/Matlab simulation using the appropriate modelsfor the system which is shown in figure 1. First, thesimulation has been carried out without input passivefilter for two different loads: a) ohmic load and b) ohmicinductive load (several values), by a switching frequencyf sw=5 kHz. The power factor as a function of the angle ‘a’mentioned above is depicted in the figures 4, 5 for aneffective load power of P=1200W. Figure 14 shows the

power factor in the case that a DC motor is used as aload. In figure 15 is PF=f(‘a’) by f sw=10 kHz. In figures11 and 12 the waveforms of the ac input voltage andcurrent are shown. The figures 6, 7, 8, 9 and 10 show thespectrum of the input current for characteristic values of the angle ‘a’. In the case of ohmic load (R=20 Ω) the

power factor gets its maximum value (PF max =0,6548) by‘a’=0°, which is relatively a low value because of thegreat current high harmonic content. If the load hasohmic-inductive character, the maximum PF value isobtained by a negative value of angle ‘a’. This happens

because the control voltage U c mentioned above isleading by the angle ‘a’ upon the grid voltage U g in order to achieve that the basic current harmonic is in phase withthe grid voltage. In this point it must be remarked that thesPWM procedure, controlled by the signal U c, leads tothe 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, thewaveforms of u in(t) and i in(t) get more similar to thewaveform of figures 13. But, by moving of the waveformiin(t) increase the high harmonic content, as it can beshown in the figures 6, 7, 8, 9 and 10, which are gettingthrough FFT analysis of the input current waveform i in(t)using the Origin software. It is obviously that the highharmonic content of i in(t), for example, by ‘a’=0° is lower than that by ‘a’=-45 o (fig.7 and 10). Beginning from

‘a’=0° and gradually going on to ‘a’=-45° the harmonicsof the 5 th, 7 th, 9 th and 11 th 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

P F [ % ]

' 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

P F [ % ]

'a' [ o]

L=10mH, R=20 Ω

L=30mH, R=20 Ω

L=50mH, R=20 Ω

L=100mH, R=20 Ω

L=200mH, R=20 Ω

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

inductive load as a parameter and switching frequency5 kHz without input filter (simulation results).

0 1 0 0 2 00 3 00 4 00 5 00 6 00 7 00 8 00 9 00 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 r e q u e n c y ( H z )

I [ A ]

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

(simulation results).

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


I [ A ]

Figure 7. Grid current harmonic content for angle ‘a’=0 ο and ohmic-

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

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


I [ A ]

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


0 1 0 0 2 00 3 00 4 00 5 00 6 00 7 00 8 00 9 00 1 0 0 00 2 00 0 0 30 0 0 0 4 0 0 00 5 00 0 00

1

2

3

Frequency (Hz)

I [ A ]

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


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


I [ A ]

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

L=30mH) (simulation results).

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0.20 0.21 0.22

-200

0

200

iin

uin

u ( t ) [ V ] ,

i ( t ) * 1 0 [ A ]

t [s]

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

inductive load (R=20 Ω, 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 ) * 1 0 [ A ]

t [s]

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

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

0.20 0.22

-200

0

200 Iin

Uin

u

( t ) [ V ] ,

i ( t ) * 1 0 [ A ]

t [s]

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

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

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

72

73

74

75

76

77

P F [ % ]

a [ o]

5 kHz10 kHz

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

motor load and switching frequency 5 kHz and 10 kHzwithout input filter (simulation results).

As mentioned above, the phase angle of the basiccurrent harmonic φ1 can be defined through the angle ‘a’.Using the values of the calculated power factor and of thespectrum analysis the value of φ1 can be calculated asfollow:

As the power factor of the basic harmonic is2k 2

1

1

Icos =PF 1+THD THD=

I,withϕ ⋅

∑ (1)

where I 1 = 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 knownvalues of PF, I 1 and I k , the values of cos φ1 and also φ1 can

be calculated. The results of such a calculation are shownin table I.

For example, for ‘a’=18°, ohmic-inductive load(R=20 Ω, L=30mH), f sw=5 kHz, U g=220 V, f g=50 Hz andP=1200W, the following values have been obtain:

I1=3,56 A, I 3=0,8918 A, I 5=0,16 A, …… I 100=1,112 A,I200=0,534 A, I 300=0,3 A, I 400=0,2 A, I 500=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 COS Φ1 USING THE SIMULATION RESULTS

(WITHOUT INPUT FILTER )

Angle ‘a’ PF cos φ1 φ1 [ο]‘18 ο’ (lag) 0,7827 0,8574 30,9‘9ο’ (lag) 0,7928 0,8792 28,45‘0ο’ 0,8009 0,8928 26,77‘-9 0’ (lead) 0,8069 0,8929 26,76‘-18 0’ (lead) 0,8108 0,8986 26,02‘-36 0’ (lead) 0,8128 0,9019 25,59‘-45 0’ (lead) 0,8113 0,9025 25,51‘-54 0’ (lead) 0,8085 0,9141 23,92‘-63 0’ (lead) 0,8042 0,8986 26,02

In the table I one can see that using the proposedoperation 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, itmeans that an improvement of 1,48% has been succeeded.Figure 15 shows the function PF=f(‘a’) by switchingfrequency f sw=10 kHz and P 1,2=1000W, 1600W. In thecase of this switching frequency value the results are verysimilar to the case of f sw=5 kHz.

If a passive filter with appropriate L-C values(L=100mH, C=1 μF) at the converter input is used, thesimulation results of the system are those which aredepicted in the figures 16, 17, 18, 19, 20, 21 and 22. ThePF values are increased in all cases, so that animprovement of about 10% is achieved (in comparison toPFmax in the two cases: with and without filter). Thespectrum analysis show that the high order harmonics(f k >800 Hz) doesn’t appear (fig.18,19 and 20). The currentwaveforms are different compared to those in case that nofilter is used, as the figures 21 and 22 show.

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

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

-50 -40 -30 -20 -10 080

81

88

89

90

1000 [W]

1500 [W]

P F [ % ]

degrees [ 0]

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

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

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

90

91

92

93

94

95

96

97

98

P F [ % ]

'a' [ o]

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

Figure 16. Power factor (PF) as a function of the angle ‘a’ byfive 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 -1 091

92

93

94

95

96

P F [ % ]

' a ' [ o ]

1 2 0 0 W5 0 0 W

Figure 17. Power Factor (PF) as a function of the angle ‘a’=0 o 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 00

1

2

3


I [ A ]

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

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

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


I [ A ]

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

filter and ohmic-inductive load (R=20 Ω, 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


I [ A ]

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

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

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

- 2 0 0

0

2 0 0

iin

u in

u ( t ) [ V ] ,

i ( t ) * 1 0 [ A ]

t [ s ]

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

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

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

- 2 0 0

0

2 0 0

iin

uin

u ( t ) [ V ] ,

i ( t ) * 1 0 [ A ]

t [ s ]

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

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

TABLE II.CALCULATION OF THE COS Φ1 USING THE SIMULATION RESULTS

(WITH INPUT FILTER )

Angle ‘a’ PF cos φ1 φ1 [o]‘0ο’ 0,8986 0,9334 21

‘-27o

’ (lead) 0,934 0,985 9,93‘-31,5 o’ (lead) 0,9381 0,9866 9,39‘-36 o’ (lead) 0,9388 0,9871 9,21‘-45 o’ (lead) 0,9349 0,9973 4,21‘-54 o’ (lead) 0,9179 ≈ 1 ≈ 0

III. EXPERIMENTAL RESULTS

A MOSFET converter has been designed andconstructed in the laboratory and its operation was

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

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

0,70

0,75

0,80

0,85

0,90

0,95

P F [ % ]

'a' [ o]

Figure 23. Power factor (PF) as a function of the angle ‘a’ for

ohmic-inductive load (R=180 Ω, 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

P F [ % ]

'a' [ o ]


ohmic-inductive load (R=180 Ω, L=30mH) andswitching 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

P F [ % ]

'a' [ o]


ohmic-inductive load (R=180 Ω, 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

P F [ % ]

'a' [ o]


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

-40 -30 -20 -10 0 10 2 0

0 ,94

0 ,95

0 ,96

0 ,97

0 ,98

0 ,99

1 ,00

1 ,01

P F [ % ]

'a' [ o ]

1 0 k H z5 k H z


ohmic load R=30 Ω and by switching frequency5 kHz with input filter (experimental results).

Figure 28. Grid voltage and current waveforms for ‘a’=0 o, ohmicload (R=180 Ω) and switching frequency 10 kHz

(experimental results).

Figure 29. Grid current waveform for ‘a’=0 o, ohmic-inductiveload (R=180 Ω, L=30mH) and switching freque-

ncy 2,5 kHz (experimental results).

In general, the differences between simulation andexperimental results are small. In all cases the power factor has high values (0,85…0,99) depended on theswitching 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 becomesmaximum. The value of this angle depends on the natureof the load, the output power, the input filter and theswitching frequency. A sinusoidal signal (voltage U c)created by microprocessor and leading upon the sinusoidalgrid voltage determines the sPWM converter operationand so the appropriate value ‘a’ can be achieved. Thetarget is to shift the grid current waveform relatively to the

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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, FrancescoGennaro, “Single Chip Integration for Motor Drive ConvertersWith Power Factor Capability”, IEEE TRANSACTION ONPOWER 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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