Analytical Analyze of Power Factor Improvement for Power Converter

Ionel Horea Baciu and Serban Lungu

Applied Electronics Department, Technical University of Cluj Napoca ionel.baciu@ael.utcluj.ro

Abstract: This paper present a study about a power supply but which can be extrapolate to all power converter. This study about power factor correction can be utilized in learning process. The study is based on mathematical equations for Flyback converter. I made a case study about the comparison between two types of conduction mode for a power supply converter. In this case study I observe a real difference in a positive sense. This case study was realized from two reasons. First is to help the student in learning process to understand the difference between two different types of a converter working. Second is to see a simple method to improve the power factor for power converter. The difference between the two types of conduction mode was demonstrate applying the mathematical results in Matlab graphics and the improvement of power factor true an input filter was realized in Pspice.

1. INTRODUCTION

In almost 90 % of circuits we need a continuous power to supply it. That power is obtained from a sinusoidal power with a rectifier circuit and, to reduce ripple, a capacitive filter. In ideal case the load must emulate a pure resistor in which case the reactive power is zero. The current waveform, from the input, is totally in the phase with input voltage, but in this case it isn’t. These types of circuit introduce on the power line some harmonics which are very pollutant for nearby electrical circuit network. These types of pollutant represent in fact the real power transmitted from the off-line power line to electronic gadget. To compensate this type of load we must introduce an inductive element to minimize looses.

I made analytic numerical calculations to determine the dependencies between power factor and voltage transfer ratio. I start the study from modulation of mathematical equations for Flyback Converter. I demonstrate the difference between Continuous Conduction Mode (CCM) and Discontinuous Conduction Mode (DCM) true the Matlab graphics. In Pspice I obtain some tables with harmonics components in two situations. First situation, without input filter and second with input filter. In paper will see an important difference.

Time

40ms 45ms 50ms 55ms 60ms 65ms 70ms 75ms 80msI(R2)

-1.0A

0A

1.0A

SEL>>

V(R2:1,D4:2)-20V

0V

20V

Fig. 1. Input waveform for a rectifier circuit with capacitive

filter: a) Power line voltage; b) Input current.

Time

40ms 45ms 50ms 55ms 60ms 65ms 70ms 75ms 80msI(R2)

-200mA

0A

200mAV(R2:1,D3:1)

-20V

0V

20V

SEL>>

Fig. 2. Input waveform for a rectifier circuit without

capacitive filter: a) Power line voltage; b) Input current.

In function of current waveform true inductor element we have two situations. First is when the values of current don’t touch zero value, that means Continuous Conduction Mode (CCM) and second when the zero value is touch, when we have Discontinuous Conduction Mode (DCM).

978-1–4577–2112–0/2011/$ 26.00 © 2011 IEEE 457 34th Int. Spring Seminar on Electronics Technology

Fig. 3. Waveform of inductor current

for continuous conduction mode.

2. THEORETICAL MODEL

First, before to calculate different values of components I must to specify that the Flyback converter is like Buck – Boost converter with a difference. To the input the voltage have value Ui/n where the n is transformer ratio.

Fig. 4. a) Flyback Converter; b) Buck-Boost Converter.

2.1. Continous Conduction Mode (CCM)

We have two situations. When the transistor is ON and diode is OFF and when transistor is OFF and diode is ON.

When T is ON

Si

ii DTnLU

ii ==Δ max (1)

When T is OFF

So

ii TDL

Uii )1(min −==Δ (2)

From these relations we will obtain:

nU

DDU i

o −=

1 (3)

From this relation we can observe the output voltage in direct proportion with input voltage. That value can go to a unitary power factor.

DDM−

=1

(4)

where: M = nU0/Ui – transfer factor of voltage.

2.2. Discontinuous Conduction Mode (DCM)

Fig. 5. Waveform of inductor current for

discontinuous conduction mode.

In this case when T is ON we have:

Si

ii DTnLUii ==Δ max (5)

But when T is OFF we have:

So

i TDL

Ui '=Δ (6)

From this two relations we obtain:

DM

DnUUD i 1'

0

== (7)

⎟⎠⎞

⎜⎝⎛ +=+=

ML

Tn

UDDDIi

i

iimed

112

)'(2

2

max (8)

From Pin = Pout result:

RU

ML

Tn

UD

nU

i

i20

2

112

=⎟⎠⎞

⎜⎝⎛ + (9)

And obtain for M:

2

3212

−+= L

TRD

M (10)

To obtain the relation of power factor we need to realize a analytic numerical calculations. The power factor relation is represented in equation 11.

978-1–4577–2112–0/2011/$ 26.00 © 2011 IEEE 458 34th Int. Spring Seminar on Electronics Technology

rmsirmsi

in

IVPFP

,,

.. = (11)

In this equation we have:

( ) ( ) ( )∫=π

ωπ 0

1 tdtitvP iiin (12)

( ) ( )∫=π

ωπ 0

2,

1 tdtiI irmsi (13)

The input current results from equation 8. In this case i(t) is:

( ) ( ) ( )⎟⎠⎞

⎜⎝⎛ += t

Mt

L

Tn

UDti

i

i ωω sin11sin2

2

(14)

The input voltage contains just a fundamental component but no dc or harmonics and we can say 0...320 ==== VVV .

( ) ( )tn

UtU ii ωsin= (15)

And result:

2, nU

U irmsi = (14)

2

2

,1

831

38

21

2 MML

Tn

UDI

i

rmsi ++=π

(16)

⎟⎠⎞

⎜⎝⎛ +

⎟⎠⎞

⎜⎝⎛

=ML

Tn

UDP

i

in1

34

22

22

ππ

(17)

And we obtain:

21

831

38

21

134

22..

MM

MFP++

+=

π

π

π (18)

3. MATLAB SIMULATIONS

I made a study in MATLAB based on several relations before this chapter. I made a comparison between relations obtained for CCM and DCM for

voltage transfer function. The relations represented in figure 6 are equation 4 and equation 10.

Fig. 6. DCM and CCM control characteristic.

Also, I made a representation for Power Factor based on equation 18 obtained from analytical demonstration.

Fig. 7. Variation of Power Factor.

4. PSPICE SIMULATIONS

I made a simulation to a Flyback converter which was supply from a sinusoidal source.

C1

100n

R1

100

C3

2.2n

0

I

R4

68k

R2

10MEG

R3

1

C2

220u

D5

MBR1540D6

MBR1540

R5

1V1

FREQ = 50VAMPL = 15VOFF = 0

C4

100u

D1

MBR1540

D4

MBR1540

V3

TD = 50u

TF = 1uPW = 45uPER = 100u

V1 = 0

TR = 1u

V2 = 5

D3

MBR1540TX1

+-

+

-

S1

S

VON = 1.0VVOFF = 0.0VD2

MBR1540

Fig. 8. Flyback Converter Circuit.

978-1–4577–2112–0/2011/$ 26.00 © 2011 IEEE 459 34th Int. Spring Seminar on Electronics Technology

To determine the power factor I made a comparison of harmonic component of input current in two situations. First a simple circuit and second with an improvement. That improvement was realized true an input filter.

Tab. 1. The Harmonic Component for Input Current of Flyback Converter Without Input Filter.

Tab. 2. The Harmonic Component for Input Current of Flyback Converter With Input Filter.

What we can see from table 1 is a very bad Power

Factor. That can be observing from below pictures. In that picture I represent the power harmonic spectrum.

Fig. 9. The harmonic component for input

current without input filter.

From table 2 we can observe an important modification of power harmonics components. In this

case the total harmonic distortion factor is low. From this result a high Power Factor.

Fig. 10. The harmonic component for input

current with input filter.

5. CONCLUSIONS

With Flyback converter in Continuous Conduction Mode (CCM) we can obtain a very high value for Power Factor (near 1) but is very hard to control and is necessary to have a complex control circuit. This thing result from nonlinearity of blue characteristic represent in figure 6.

From figure 6 we can say the control characteristic of Flyback Converter in both modes of commutation. We can observe in Discontinuous Conduction Mode (DCM), based on equation 10, a family of linear characteristics in function of 2RT/L. In this case the converter is easily to control.

In figure 7 I represent the power factor calculated in equation 18. That equation is available for the DCM function mode. We can see for some values of n*Uo/Ui a Power Factor near 1. That is the reason because we don’t need a specialized circuit for Power Factor Correction.

REFERENCES

[1] Baciu I.H., Lungu S.,”Advanced CAD Methods for Designing High Quality Power Systems”, 2006.

[2] Pop O., Lungu S.,“Sepic Converter Analyses in Discontinous Current Mode Operation with Applications in Power Factor Correction“,2004.

[3] Dorin Petreus, Lungu Serban, Surse in Comutatie, Ed.Mediamira, Cluj Napoca 1999.

[4] Serban Lungu, Ovidiu Pop, „Modelarea circuitelor electronice“, Casa Cartii de Stiinte, Cluj Napoca, 2006.

[5] Robert W. Erickson, Fundamentals of Power Electronics, 1999.

[6] The Math Works, Inc, „Matlab User’s Guide“, 1993.

978-1–4577–2112–0/2011/$ 26.00 © 2011 IEEE 460 34th Int. Spring Seminar on Electronics Technology