capacitor compensator

7/28/2019 Capacitor Compensator

1/7

Abstract--This paper explorers techniques for minimizing

zero-crossing distortion in single-phase PFC converters

from the angle of topologies. Zero-crossing distortions of

typical single-phase PFC topologies are compared in theory

to reveal that cusp distortion is predominant responsible for

zero-crossing distortion. PWM rectifier with the capability

of bi-directional current can minimum and eliminate zero-crossing distortion even though there is phase displacement

in current loop at the cost of increasing switching loss and

larger boost inductor. Then, a simple switched capacitor

compensation scheme with low voltage rating switching

devices and low switching frequency is presented to

minimum zero-crossing distortion. Furthermore, the

proposed switched capacitor circuit can be added to existing

single-phase PFC converters without modification of

original topologies and controllers, hence it is economically

feasible. Numerical simulations are given to validate the

theoretical analysis and effectiveness of the proposed

scheme. With switched capacitor compensator, single-phase

PFC converters demonstrate good input performance.

Index Terms-- Cusp distortion, harmonic current, single-

phase PFC converters, switched capacitor compensator,

zero-crossing distortion.1

I. INTRODUCTION

Single-phase power factor correction (PFC) convertershave been widely used in AC-DC power supply systemdue to their advantages of unit input power factor andmuch less input current distortion, compared with simplediode rectifiers. However, the input current distortion atthe zero crossing of the input voltage is an inherent

behavior and becomes more serious with increasing input

line frequency. Especially in medium-frequency powersupply applications ranging from 360Hz-800Hz in futurecommercial aircrafts, zero-crossing distortion may causesingle-phase PFC converters not to be able to meetstringent harmonic regulatory requirements as DO-160Dlisted in Table I [1]. Therefore, a great number of single-

phase PFC topologies [2]-[4] and control methods [5]-[7]have been proposed to solve this problem.

The major causes for zero-crossing distortion insingle-phase PFC converters can be divided into two

parts: discontinues conduction mode (DCM) distortionand cusp distortion. The DCM distortion occurs beforethe zero crossing of the input voltage and it is mainly

This work was supported by Open Project Program of State KeyLab. of Electrical Insulation and Power Equipment.

determined by the current leading phase relative to theinput voltage in the current loop. Good current loopdesign or phase compensation [2] can reduce andeliminate DCM distortion in theory. The cusp distortionoccurs right after the zero crossing of the input voltageand it is mainly related to the inductance of the boost

inductor. A smaller inductor can reduce the cuspdistortion. Literature [3] proposed multi-level techniquesto reduce the zero-crossing distortion. However, thedrawbacks are their control complexity and additionalneutral-point potential balancing for output capacitors.Furthermore, they cant eliminate cusp distortioninherently. In this paper, zero-crossing distortions oftypical single-phase PFC converters are analyzed andcompared from the angle of topologies to reveal that cuspdistortion is the predominant responsible for zero-crossing distortion. PWM rectifier with the capability of

bi-directional current flow can reduce, and eliminateDCM distortion and cusp distortion even though there is

phase displacement in current loop.

TABLEIDO-160HARMONIC CURRENT LIMITATION FORAIRBORNE EQUIPMENT

Harmonic Order Single phase

Odd triplen harmonics(h=3,6,9,15,......,39)

Ih=0.15I1/h

Odd non-triplen harmonics(h=5,7,11,13,......,37)

Ih=0.3I1/h

Even Harmonics(h=2,4)

Ih=0.01I1/h

Even Harmonics(h=6,8,,40)

Ih=0.0025I1

Based on analysis in section II, bi-directional current

flow or enough charging voltage of the boost inductor atzero-crossing of input voltage is the key to reducing inputcurrent zero-crossing distortion. Then, the next section

presents a simple switched capacitor compensationscheme with low switching frequency to reduce, eveneliminate zero-crossing distortion in theory. The designand operation principles of switched capacitor circuit, thetheoretical reduction of zero-crossing distortion areanalyzed in details. Numerical simulations are given tovalidate the theoretical analysis and effectiveness of the

proposed scheme. Furthermore, comparison of traditionalsingle-phase PFC converters using switched capacitorcompensator with PWM rectifier with bi-polar pulse-

width modulation shows that proposed compensationscheme demonstrates good input performance and it isalso economically feasible.

A Simple Switched Capacitor Compensator toMinimize Zero-Crossing Distortion in

Single-Phase PFC ConvertersYan Zhang, Jinjun Liu, and Chaoyi Zhang

Department of Electrical Engineering, Xian Jiao Tong University, China

Email: [email protected]

8 t h I n t e r n a t i o n a l C o n f e r e n c e o n P o w e r E l e c t r o n i c s - E C C E A s i a

M a y 3 0 - J u n e 3 , 2 0 1 1 , T h e S h i l l a J e j u , K o r e a

9 7 8 - 1 - 6 1 2 8 4 - 9 5 7 - 7 / 1 1 / $ 2 6 . 0 0 2 0 1 1 I E E E

[ W e E 1 - 2 ]


2/7

II. COMPARISONOFZERO-CROSSINGDISTORTION

As previously mentioned, four kinds of typical single-phase PFC topologies shown in Fig.1 (a)-(d) are to beinvestigated. Traditional single-phase PFC (a) is the mostwidespread in power supply system due to its simple

main circuit and mature control methods; the recentlyproposed high step up ratio DC-DC topology with lowerinput current ripples [8] can be applied in single PFC as agood choice for reduction of zero-crossing distortion.This converter is referred as diode-assisted single-phasePFC (b) in this study. Three-level single-phase PFC (c) is

presented in literature [3] to minimize zero-crossingdistortion. Bridgeless single-phase PWM rectifier (d) [9]with the capabilities of bi-directional current flow caneliminate zero-crossing distortion, but it requires somecosts, such as complicated control, high switching lossand larger boost inductor, which will be discussed.

For zero-crossing distortion comparison, different

single phase PFC converters are controlled by the samecurrent loop design: average current control with varyingleading phase angle at different input line frequency [2]or nonlinear current control (such as one cycle control)with minimum phase displacement [6]. Meantime, wefurther assume that the boost inductors of PFC convertersoperate in the continuous conduction mode (CCM) overthe entire line cycle and output capacitor voltage isconstant in one switching period. To compare typicalsingle-phase PFC topologies on reduction of zero-crossing distortion, some parameters that are necessaryfor derivation are as follows:

Po maximum output power of single-phase PFC;Vi input voltage of single-phase PFC;Vm peak input voltage of single-phase PFC;Im peak input current of single-phase PFC;fline input line frequency;fs switching frequency; phase displacement in the current loop.

As described in literature [3], zero-crossing distortionof traditional single-phase PFC converter (a), includingDCM distortion and cusp distortion, are analyzed andquantified in details. Furthermore, the boost inductor

design should be considered because it is importantresponsible for zero-crossing distortion. In general, the

boost inductor is designed according to the input currentripples. With the model and the analyses presented inliterature [3], the mathematical expression of currentripples (I), DCM distortion interval (DCM) and cusp

distortion interval (C) for typical single-phase PFCconverters can be obtained and listed in Table 1. Thedetailed derivation is given in the Appendix.

(a) Traditional single-phase PFC.

(b) Diode-assisted single-phase PFC

(c) Three-level single-phase PFC

(d) Bridgeless single-phase PWM rectifierFig. 1. Typical single-phase PFC topologies

TABLEIIDO-160SUMMARY OF TYPICAL SINGLE-PHASE PFCTOPOLOGIES FORZERO-CROSSING DISTORTION

Single-phase PFC Traditional PFC Diode-assisted PFC Three-level PFCBridgeless PWM rectifier

Uni-polar PWM Bi-polar PWM

Current ripples

( I' )( | |) | |

o i i

o s

V V V

V Lf

( | |) | |

( | |)

o i i

o in s

V V V

V V Lf

( 2 | |) | |

2

o i i

o s

V V V

V Lf

( | |) | |o i i

o s

V V V

V Lf

2 2( | | )

2

o i

o s

V V

V Lf

DCM distortion

interval ( DCMM )

2

1 1 1

22m

p p q

V

1 ( 2 )o m s mp V V Lf I 2

1 8 s m o mq Lf I V V T

2

2 2 2

2 (2 )m s m m

p p q

V Lf I V

2 2 ( )o m s m o mp V V Lf I V V T

28 (2 )

s m o m s m mq Lf I V V Lf I V T

2

3 3 3

24m

p p q

V

3( 4 )

m s m op V Lf I V

2


2

1 1 1

22m

p p q

V

1( 2 )

o m s mp V V Lf I

2


2

4 4 4

22 m

p p q

V

4 4 s m op Lf I V 2

4 4 ( 4 )m o o s mq V V V Lf I T

Cusp distortion

interval ( CM )

2

5 5 5

2 mp p q

V

5 5( 4 , 16 )line m line m mp Lf I q Lf I VS S T

2

6 6 6

2 m

p p q

V

6 4 2line m op Lf I VS

6 16 line m mq Lf I V S T


3/7

Based on analysis above, a comparison example isconducted with following parameters: Vm = 162V; Vo =200-400V; fline = 360-800Hz; Im = 12A; Po = 1kW; fs =

100kHz. Fig.2 and Fig.3 show the relationship of DCMdistortion interval and cusp distortion interval versusinput inductor value respectively for traditional PFC

converter at 400Hz and 800Hz line frequency, where isthe varying phase displacement for different current loopcontrol and input line frequency. It is clear that phasedisplacement is the essential cause for DCM distortionand zero phase displacement can eliminate DCMdistortion in theory. The cusp distortion is main part forzero-crossing distortion and the DCM distortion can beignored with good current loop design.

Fig.4 shows boost inductor design for different single-phase PFC converters. With the same input currentripples, diode-assisted PFC and three-level PFC canadopt smaller boost inductor. That is the essential reasonwhy they can reduce zero-crossing distortion. The cusp

distortion comparison shown in Fig.5 reflects that diode-assisted PFC and three-level PFC are good choice toreduce cusp distortion. Three-level PFC demonstratesminimize zero-crossing distortion, however, it increasesthe control complexity, including the neutral-point

potential balancing for output capacitors.

0.2 0.4 0.6 0.8 1 1.2 1.40

5

10

15

20

L (mH

DCM

(DEG)

= 0

= 5

= 10

Fig. 2. DCM interval versus inductor value for traditional single-phasePFC.

0.5 1 1.50

10

20

30

40

50

60

L (mH)

C

(DEG)

fline=400Hz

fline=800Hz

= 0

= 5

= 10

Fig. 3. Cusp distortion interval versus inductor value for traditionalsingle-phase PFC.

5 10 15 200

0.5

1

1.5

2

2.5

Maximum current ripple (%)

L(mH)

T PFC

D PFC

TL PFC

Fig. 4. The maximum current ripples versus inductor value. ( T PFC:traditional PFC; D PFC: diode-assisted PFC; TL PFC: three level PFC )

Even though diode assisted PFC converter and three-level PFC converter can reduce zero crossing distortion,

but they cant eliminate zero-crossing distortion in theory.Single-phase PWM rectifier can eliminate zero-crossingdistortion, but it needs special control scheme. With uni-

polar pulse-width modulation [10], S1 is always turned

on and S2, S4 are commutated alternatively to realize theinductor charging and discharging in the positive half-wave; in the negative half-wave, S3 is always turned onand S2, S4 are commutated alternatively to realize theinductor charging and discharging. In essence, the DCMdistortion interval and cusp distortion interval is the sameas traditional single-phase PFC. With bi-polar pulse-width modulation [10], S1 S4 and S2 S3 are commutatedalternatively in one switching period, the terminal voltageof boost inductor changes between Vi+Vo and Vi-Vo.Reverse direction current is allowed to avoid the inputcurrent being clamped to zero before the zero crossing ofthe input voltage. Meantime, the output voltage is reverse

connected in the primary loop to supply enough slow rateof the inductor current after the zero crossing of the inputvoltage. Besides all the switches working in highfrequency, this control scheme also requires largerinductor due to higher input current ripples shown inFig.6. The relationships of cusp distortion interval versus

5 10 15 200

20

40

60

80


C

(DEG)

C PFC (400Hz)

C PFC (800Hz)

D PFC (400Hz)

D PFC (800Hz)

TL PFC (400Hz)

TL PFC (800Hz)

Fig. 5. Cusp distortion interval versus input current ripples. ( T PFC:traditional PFC; D PFC: diode-assisted PFC; TL PFC: three level PFC )

5 10 15 200

1

2

3

4

5


L(mH)

Uni-polar PWM

Bi-polar PWM

Fig. 6. The maximum current ripples versus inductor value for PWMrectifier.

5 10 15 200

20

40

60

80


C

(DEG)

Bi-polar PWM

Uni-polar PWM

= 0

= 5

= 10

Fig. 7. Cusp distortion interval versus maximum current ripples forPWM rectifier.


4/7

input current ripples for single-phase PWM rectifier withdifferent control methods are shown in Fig.7. It is clearthat PWM rectifier with bi-polar PWM demonstratesminimum zero-crossing distortion.

III. SIMPLESWITCHEDCAPACITORFOR

MINIMIZINGZERO-CROSSINGDISTORTIONFrom analysis in above section, a simple switched

capacitor circuit is series connected in the ac powersupply link to improve input current performance shownin Fig.8. Two bidirectional switches (S2, S3) are used tocontrol the switching capacitor to minimize zero-crossingdistortion and maintain charge balancing for the capacitorin one input line frequency. Bidirectional switches canuse two unidirectional switching devices in practicalapplication. The corresponding operation principle anddrive signals for S2 and S3 are shown in Fig.9. In theduration [0, /2], S3B is turned on, the positive voltage(VC+) of the capacitor supplies the enough current slow

rate so the current can ramp up to follow the reference.Meantime, the capacitor discharges from VC+ and thenrecharges in reverse direction to VC- (|VC+| = |VC-|). In theduration [/2, ], S2B is turned on, capacitor is bypassedand the input current in the primary loop is the same astraditional single-phase PFC. In the duration [, 3/2],S3A is turned on, the negative voltage (VC-) of thecapacitor supplies enough current slow rate through diodeD2, D4. Meantime, the capacitor discharges from VC- andthen recharges in reverse direction to VC+ (|VC+| = |VC-|).In the duration [3/2, 2], S2A is turned on, capacitor is

bypassed and the input current in the primary loop is thesame as traditional single-phase PFC. Therefore, the

capacitor does not need backup power supply and theabsolute value ofVC+ is equal to that ofVC- in one inputline frequency. There is one note here, switching actionsof S2 S3 occur at the zero crossing of the input current toavoid the input current clamed to zero before the zero

Fig. 8. Simple switched capacitor compensator used in traditional

single-phase PFC converters.

0 0.5 1 1.5 2

-10

0

10

Iin

(A)

0 0.5 1 1.5 2

-50

0

50

Vc

(V)

0 0.5 1 1.5 2-0.5

00.5

11.5

S3drive

SB SA

0 0.5 1 1.5 2-0.5

00.5

11.5

Time(ms), fline

=800Hz

S2drive

SB SA

Fig.9. Control signals for S2 and S3.

-crossing of the input voltage. So the simple switchedcapacitor circuit can reduce, even eliminate zero-crossingdistortion with good current loop design in theory.Furthermore, the blocking voltage of one switchingdevice in the switched capacitor compensator is half ofthe maximum capacitor (C) voltage in steady state. And

the required charging voltage of the boost inductor atzero-crossing of input voltage is much smaller thanoutput voltage. Therefore, low voltage rating switchingdevices may be used. With low voltage rating switchingdevices operating in low switching frequency, the designcost and efficiency of single-phase PFC converters maynot be seriously deteriorated.

In one input line frequency, the slow rate of inputcurrent achieves maximum at zero-crossing point, so therequired minimum charging voltage across the capacitorcan be calculated as follows:

m

ttIi

rec LI

dt

diLV

m

Z

ZZ

0),sin(

(1)

In the duration [0, /2], the capacitor discharge fromVC+ and then recharge in reverse direction to VC- and theabsolute value ofVC+ should be equal to that ofVC-

CmCmC VCI

VtIC

VZ

Z

S 2/

0

)sin(1

(2)

The required capacitance of the capacitor is:

LfLC

line

222max 8

1

2

1

SZ (3)

IV. SIMULATIONANDVERIFICATION

Numerical simulations using matlab/simulink havebeen performed to confirm above switched capacitorcompensation scheme shown in Fig.8. The single-phasePFC uses the following parameters: input boost inductorL=800uH; input (rms) voltage Vi =115V; input linearfrequencyfline = 360-800Hz; input powerPo=1kW; outputvoltage Vo=200-400V; switching frequency fs=100kHz.According to above equation (1)-(3), the requiredcharging voltage (Vrec) of inductor at zero-crossing pointis 50V and a suitable capacitance of the capacitor is about25uF.

Fig.10 and Fig.11 show simulated input waveforms

and current spectrum analysis for traditional single-phasePFC in order to quantify the effects of switched capacitorcompensation scheme in reducing input current harmonicdistortion with typical current close loop designs: averagecurrent control with linear PI compensator [2] andnonlinear current control (such as one cycle control) [6].As can be seen, the input current of traditional single-

phase PFC is clamped and could not follow the currentreference at zero-crossing point. Therefore, the currentcontains a large amount of 3th, 5th, 7th, 9th harmonics.The total harmonic distortion (THD) is 6.46% at 400Hzwith about 8o phase displacement in current loop and7.14% at 800Hz with nonlinear one cycle control, which

causes single-phase PFC not to be able to meet strongharmonic regulatory requirements. When a switchedcapacitor compensator is applied, these odd harmonic are


5/7

9 9.5 10 10.5 11 11.5 12-20

-16

-12

-8

-4

0

4

8

12

16

20

Time (ms)

Inp

utcurrent(A)

Iref

Iin

9 9.5 10 10.5 11 11.5 12-200

-100

0

100

200

Inputvoltage(V)

Vi

9 9.5 10 10.5 11 11.5 12-20

-16

-12

-8

-4

0

4

8

12

16

20

Time (ms)

Inp

utcurrent(A)

Iref

Iin

9 9.5 10 10.5 11 11.5 12-200

-100

0

100

200

Inputvoltage(V)

Vi

0 1 3 5 7 9 11 13 15 17 19 21 23 25

Harmonic order

6

4

2

0

Fundamental (400Hz) = 11.82 , THD=6.46%

Fig.10. Input voltage, current and spectrum analysis with linear current PI compensator. (Left: without switched capacitor compensator.Right: withswitched capacitor compensator;Iref: input current reference;Iin: actual input current; Vi: input voltage; Vo = 400V; fs = 100kHz; fline = 400Hz; =8

o )

8 8.5 9 9.5 10-20

-16

-12

-8

-4

0

4

8

12

16

20

Time (ms)

Inputcurrent(A)

Iref

Iin

8 8.5 9 9.5 10-200

-100

0

100

200

Inputvoltage(V)

Vi

8 8.5 9 9.5 10-20

-16

-12

-8

-4

0

4

8

12

16

20

Time (ms)

Inputcurrent(A)

Iref

Iin

8 8.5 9 9.5 10-200

-100

0

100

200

Inputvoltage(V)

Vi

Mag(%ofFundamental)

3

2

1

00 1 3 5 7 9 11 13 15 17 19 21 23 25

Harmonic order

Fundamental (800Hz) = 11.92 , THD=2.53%

Fig.11. Input voltage, current and spectrum analysis with nonlinear current compensator (one cycle control). (Left: without switched capacitorcompensator.Right: with switched capacitor compensator;Iref: input current reference;Iin: actual input current; Vi: input voltage; Vo = 400V; fs =100kHz; fline = 800Hz)

TABLEIII

COMPARISON EXAMPLE OF TRADITIONAL PFCWITH SWITCHED CAPACITOR

Power devices &Power converter

MOSFETSPW20N60(600V 20A)

MOSFETBSZ067N06(60V 20A)

DIODEIDP23E60

(600V 23A)

Switchingdevices

design cost(US dollar)

Efficiency(%)

THD (%)(400Hz)

Unit Price $3.48 $0.47 $ 1.12

Traditional single-phase PFC

1 \ 5 $9.1 90.7 6.46

Traditional PFC withswitched capacitor

1 4 5 $11.0 89.9 2.04

PWM Rectifier withbi-polar modulation

4 \ 4 $18.4 85.3 1.69

significantly reduced and the input current distortion is

minimized to a large extent. In theory, the input currentperformance of single-phase PFC with switched capacitoris close to that of PWM rectifier with bi-polar modulation.

Efficiency and design cost are the important criterion

for power converter. In order to quantify the effects ofadditional switched capacitor compensator on cost andefficiency, 1kW single-phase PFC converters analyzed


6/7

above are considered using Infineon power devices as areference. The switching devices design cost, efficiencyand total harmonic distortion (THD) of traditional single-

phase PFC and PWM rectifier with bi-polar modulationare listed in Table III. The price of switching devices isobtained from Infineon product notes [11] and the

electronic components distributors [12] on April 2, 2011.For efficiency comparison, only switching devices powerlosses are considered. Given the certain switching devices,the efficiency of power converters can be obtained. Thedetailed power MOSFET and DIODE loss calculationmethods can be found in literatures [13] [14]. Seen fromTable III, PWM Rectifier with bi-polar modulationdemonstrates the best input performance, but its designcost and efficiency is not outstanding. With switchedcapacitor compensator, the input current performance oftraditional single-phase PFC can be improved to a largeextent, while the efficiency is reduced by less than 1%using low voltage-rating power MOFET. Therefore, as a

zero-crossing distortion compensation scheme, theadditional switched capacitor compensator has evidentadvantages of cost and efficiency compared with PWMrectifier with bi-polar modulation.

V. CONCLUSION

A theoretical analysis and comparison of single-phasePFC converters show that reduction of the inductor valueand input current ripples with different topologies is aneffective way to minimize zero-crossing distortion.Diode-assisted single-phase PFC and three-level single-

phase PFC can reduce zero-crossing distortion indifferent degree, but cant eliminate. Single-phase PWM

rectifier can eliminate zero-crossing distortion at cost ofhigh switching loss, lager boost inductor and design cost.

This paper presents a simple switched capacitorcompensator, which can be used in all these kinds ofsingle-phase PFC converters to minimize zero-crossingdistortion. With simple control, it can avoid input current

being clamped to zero before the zero crossing of theinput voltage and supply enough input current risingslope after zero crossing of the input voltage. Numericalsimulations are given to verify the effectiveness and thevalidity of the proposed scheme. With simple switchedcapacitor compensator, single-phase PFC convertersdemonstrate good input performance. Furthermore, withlow voltage-rating switching devices, the compensationscheme has evident advantages of cost and efficiencycompared with PWM rectifier with bi-polar pulse-widthmodulation.

APPENDIX

1) Traditional single-phase PFC:a) Input current ripple IAs to the traditional single-phase PFC, the duty cycle

can be expressed as:

o

io

V

VVD

(4)

The input current ripple can be calculated by thecurrent increase when switching device is turned on.

isL VD

IfL

dt

diL

'| (5)

so

iio

LfV

VVVI

)( ' (6)

b) DCM distortion interval DCM and cusp distortioninterval C

As described in literature [3], the critical value DCMoftraditional PFC meets the following equation:

)sin(2

sin)sin(TM

DCMm

so

DCMmDCMmo IfLV

VVV (7)

And the critical value Cmeets:

)sin()cos1(2

TMMS

CmCline

m ILf

V (8)

Because DCM and C are always very small value, thefollowing assumptions are applied to simple calculation:

21cos,sin

2MMMM || (9)

The resulted obtainable DCM

and C

are:

2

222

2

8)2()2(

m

momsomsmmsmo

DCMV

VVILfVILfVILfVV TM

|

(10)

m

mmlinemlinemline

CV

VILfILfILf

2

16)4(4 2 TSSSM

| (11)

The error between the approximate values and theaccurate value ofDCMand C is less than 2%.

2) Diode-assisted single-phase PFCa) Input current ripple IAs described in literature [8], the duty cycle of diode-

assisted PFC can be expressed as:

io

io

VV

VVD

(12)

The expression of current ripple can be written as:

sio

iio

LfVV

VVVI

)(

)(

' (13)


Similarly, the critical value DCM of diode-assistedPFC meets the following equation:

)sin()sin(2

sin)sin(

TMM

MM

DCMm

sDCMmo

DCMmDCMmo

IfVVL

VVV (14)

DCMcan be calculated by sampling equation (14).

)2(2

2

2

22

mmsm

DCMVILfV

qpp

|M (15)

Where: )(22 Tmomsmo VVILfVVp

)2(82 mmsmoms VILfVVILfq T

As to cusp distortion interval C, the calculationequation of diode-assisted PFC is the same as that (11) oftraditional PFC.


3) Three-level single-phase PFC


7/7

a) Input current ripple IThe duty cycle of three-level PFC can be expressed as:

o

io

V

VVD

(16)

The expression of current ripple is:

so

iio

LfV

VVVI

2

)2( ' (17)


The critical value DCMof three-level PFC meets:

)sin(4

sin)sin2(TM

MM

DCMm

so

DCMmDCMmo IfLV

VVV

(18)DCMcan be calculated by sampling equation (18).

2

22

33

4

32

m

moms

DCMV

VVILfpp TM

| (19)

Where: )4(3 msmo ILfVVp

And the expression of C for three-level PFC is thesame as that (11) of traditional PFC.


4) PWM rectifier with uni-polar pulse-width modulationThe expressions of input current ripple, DCM

distortion interval and cusp distortion interval for PWMrectifier with uni-polar pulse-width modulation are thesame as that of traditional PFC.

5) PWM rectifier with bi-polar pulse-width modulation

a) Input current ripple IThe duty cycle of PWM rectifier with bi-polar pulse-width modulation can be expressed as:

o

io

V

VVD

2

(20)

The expression of current ripple is:

so

io

LfV

VVI

2

)(22

' (21)


Similarly, the critical value DCMmeets:

)sin(4

)sin( 22

TMM

DCMm

so

DCMmo

IfLV

VV

(22)

And the critical value Cmeets:

)sin(2

)cos1(TM

S

Cm

line

CoCm ILf

VV (23)

DCM and C can be calculated by sampling equation(12) and (23).

2

22222

2

)4(4164

m

msoomomsoms

DCMV

ILfVVVVIfLVILf TM

|

(24)

m

mmlineomlineomline

C

V

VILfVILfVILf

2

16)24(24 2 TSSSM

|

(25)


REFERENCES

[1] Environmental conditions and test procedures for airborneequipment,RTCADO-160D, Section 16, Issue5, May 2000.

[2] J. Sun, On the Zero-Crossing Distortion Single-PhasePFC Converters, IEEE Trans. Power Electronics, vol.19,pp. 685 - 692, May 2004.

[3] X. Qu, X. Ruan, A Scheme for Improving Input CurrentZero-Crossing Distortion of Single-Phase Power-Factor-Correction Converters, PESC '06. 37th IEEE, pp. 1- 6,June 2006.

[4] Muhammad Mansoor Khan, A Modified Boost Topologyto Minimize Distortion in PFC Rectifier, IPEMC 2004,vol. 3, pp. 1248 - 1252, Aug. 2004.

[5] M. Chen, J. Sun, Feedforward Current Control of BoostSingle-phase PFC Converters, IEEE Trans. PowerElectronics, vol. 21, pp. 338 - 345, March 2006.

[6]

M. Chen, A. Mather and J. Sun, Nonlinear CurrentControl of Single-Phase PFC Converters, IEEE Trans.Power Electronics, vol. 22, pp. 2187 - 2194, Nov. 2007.

[7] K.P.Louganski, J. Lai, Current Phase Lead Compensationin Single-Phase PFC Boost Converters with A ReducedSwitching Frequency to Line Frequency Ratio,APEC '06.Twenty-First Annual IEEE, pp. 7, March 2006.

[8] H. Nomura, K. Fujiwara and M. Yoshida, A New DC-DCConverter Circuit with Larger Step-up/down Ratio,PESC'06, pp. 1 - 7, June 2006.

[9] O. Stihi and B. Ooi, A Single-phase Controlled-CurrentPWM Rectifier,IEEE Transactions on Power Electronics,Vol.3, No.4, pp. 453-459, Oct. 1988

[10]S. Halasz, Comparison of Sinusoidal PWM Methods,Periodica Polytechca, Ser. El. Eng. Vo1.37, No.4, pp. 273

- 290, 1993.[11]Infineon Product Note [Online]. http://www.infineon.com[12]Digi-Key, Product Index of Digi-Key, pp. 1567 - 1573,

Nov. 2010. Available: http://www.digikey.com[13]Duan Graovac, Marco Prschel, MOSFET Power Losses

Calculation Using the Data-Sheet Parameters InfineonTech. Rep, Appl. notes pp. 6 - 10, July 2006.

[14]F. Blaabjerg, J. Pedersen, and A. Elkjaer, An ExtendedModel of Power Losses in Hard-switched IGBT Inverters,Proceeding of IAS96, pp.14541463. Oct. 1996.

capacitor compensator

Documents