Analysis and Design of a High Power Factor AC/DC Converter with an Active Ripple Filter

Pisit Wisutmetheekorn1,2 and Viboon Chunkag2 1 Dept. of Control Instrumentation and Mechatronic Eng. Mahanakorn University of Technology

Bangkok Thailand; pisit@mut.ac.th 2 Dept. of Electrical Engineering, King Mongkut’s University of Technology North Bangkok

Bangkok Thailand, s5010190048@kmutnb.ac.th, vck@kmutnb.ac.th

Abstract—This paper presents analysis and design of a high power factor AC/DC converter with an active ripple filter by using supercapacitors as energy storage. In the normal operating mode, the AC/DC converter feeds power to load and charges supercapacitors. The supercapacitors are charged from the output of the AC/DC converter through a bidirectional DC/DC converter. If supercapacitors voltage is between 70 to 90 percent of its rated value, the bidirectional DC/DC converter is controlled as an active ripple filter for reducing ripple voltage at the output end of the AC/DC converter. In case of an ac line is interrupted, the stored energy in the supercapacitors is fed to load. The later operating mode is called the backup operating mode. In this paper the proposed system is investigated by software simulation. The results from MATLAB/Simulink show the proposed system offer a fast transient response in output voltage control and a lower ripple voltage at the output end of the AC/DC converter.

Keywords—power factor correction, active ripple filter,backup power supply,supercapacitor

I. INTRODUCTION In the industrial plant, programmable logic controllers (PLC) and process instruments are normally installed. These equipments are usually powered by dc voltage source from the switching power supplies. In case of a power failure, the PLC and the process instrument of the critical system should be back up the process data on their memories before they safely shut down. The uninterruptible power supply (UPS) is widely used as a back up power supply for various systems such as computer system, telecommunication system and industrial control system [1]. A battery bank is used as the energy storage in the UPS. When the utility line is interrupted, energy in the battery is fed to load by a power converter. In the UPS, the DC/DC converter is required for step up battery voltage to higher level for input of the inverter then the inverter converts dc voltage to ac voltage at output of the UPS. How ever in case of dc load the inverter is not required. The back up time of the UPS is dependent on batteries capacity. However the controllers in the process control system require only a short time to back up some data before the system is shut down then the high capacity battery is not necessary. Recently supercapacitors are applied in many applications. From its high capacitance value, so that it can be used as an energy storage device and has more advantage than the battery such as higher power density, long life cycle, environmental safety, maintenance free and easy to charge [2]-[3]. In this paper, the high power factor AC/DC converter with the energy storage is

presented. The proposed system consists of a CUK topology based AC/DC converter and a bidirectional DC/DC converter interface between the supercapacitors and output dc bus of the AC/DC converter. In the proposed system, the supercapacitors and the bidirectional DC/DC converter are also controlled as an active ripple filter which is used to reduce the output ripple voltage of the AC/DC converter. The rest of this paper is organized as follows: Section II presents the system description. Section III shows the transfer function and controller design of the proposed system. Simulations are then presented in Section IV. Finally, conclusion is drawn in Section V.

II. SYSTEM DESCRIPTION

A. System Configuration The proposed system is shown in Fig. 1. It’s consists of the AC/DC converter, the bidirectional DC/DC CUK converter and the system controller. In the normal operating mode the AC/DC converter transfers energy from the ac line to the output end and the bidirectional DC/DC converter is controlled to charge or discharge the supercapacitors. If the supercapacitors voltage in the normal operating mode is between 70 to 90 percent of its rated value, the system controller will control the bidirectional DC/DC converter as an active ripple filter to reduce the load ripple voltage. In the backup operating mode, the system controller controls the bidirectional DC/DC converter to transfer energy from the supercapacitors to load. Functions of the system controller are control the output voltage and calculate current commands of the power converters in each operating mode.

B. The Power Circuit From Fig. 1, the CUK topology with an input-output isolation transformer is selected as a single phase AC/DC active power factor correction (PFC). Because of the CUK converter has inductors at the end of input and output then the input-output current can be smooth by these inductors. The current controller HC1 is used to control the input current of the AC/DC converter to track the rectified voltage at input of the converter for power factor correction purpose [4]. The bidirectional DC/DC CUK converter is used to transfer energy between the output dc bus and the supercapacitors SCC by control the power switches SW2 and SW3.

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vO

L12

iL12

SW2 SW3

D2D3

L22

iL22

iCO

iO

C3

iL22

vSCCsc

iL11

L11

SW1

L21

iL21

C1 C1

D1

1 : nCO RO

iL21

kPW1

iL11ref

iload

iL11

iL12

iref

DIR

EN

PW2

iL22 PW3

iSC

HC1

HC2

HC3

vac

System Controller

vacvOiloadvSCiL12

irefiL11ref DIR EN

iS

Fig. 1. Systems configuration

The fixed band hysteresis current controllers HC2 and HC3 are used to control the inductor current of the bidirectional converter in discharge and charge mode respectively. To charge the supercapacitors from dc bus, the power circuit of the bidirectional DC/DC converter of this mode is shown in Fig. 2. In charge mode the direction signal DIR is set to ‘0’ then the signal PW2 always ‘0’ and the power switch SW2 is off. To control the inductor current 22Li in charge mode, the power switch SW3 is controlled by the current controller HC3. Fig.3 shows the bidirectional DC/DC converter in discharge mode. The inductor current 12Li is controlled by the current controller HC2.

C. Current Commands Calculation In the proposed system, the current commands of the bidirectional DC/DC converter and the AC/DC converter are dependent on the system operating mode and they are calculated by the system controller. From concept of power balance control technique [5], the output power of the AC/DC converter is summation of power at the bidirectional DC/DC converter and load power at the output end.

iL12

SW2 SW3

D2

iL22vSC

iL12

iref = iL22ref

DIR = 0

EN = 1

PW2=0

iL22

PW3HC2

HC3

= 1

Csc

L22C3L12iSC

vOiCO

CO RO

iL22

iload

Fig. 2. The bidirectional DC/DC converter in charge mode

L12

iL12

SW2

D2D3

L22

iL22

C3

vSC

iL12

iref = iL12ref

DIR=1

EN=1

PW2

iL22

PW3=0

iSC

HC2

HC3

= 0

Csc vOiCO

CO RO

iload

Fig. 3. The bidirectional DC/DC converter in discharge mode However in a half period of the ac line, the load power is equal to the input power of the AC/DC converter. The peak inductor current 11

ˆLI of the AC/DC converter is calculated

from (1).

g

OloadL V

vii ⋅⋅= 2ˆ11 (1)

Where gV is rms value of the ac line voltage.

The current command of the AC/DC converter refLI 11ˆ is

calculated from summation of the output signal of voltage loop controller contv and the peak inductor current 11

ˆLI in (1). The

current command refLI 11ˆ is written as in (2).

contg

OloadrefL v

VviI +⋅⋅= 2ˆ

11 (2)

The PI controller is used to control the output voltage. Similar to inductor current calculation in (1), the inductor current 22Li of the bidirectional DC/DC converter is calculated from (3).

O

LSCL v

ivi 12

22⋅

= (3)

To achieve high input power factor of the AC/DC converter, the input current Si in Fig. 1 is controlled to be sinusoidal shape and in-phase with ac line voltage. The input power of the AC/DC converter is given in (4).

)2cos1()( tIVtp Srmsgin ω−= (4)

Where ω is an angular frequency of the ac voltage source. By neglects power loss in the AC/DC converter, the output current of the AC/DC converter )(tiO is calculated from (5).

ttv

IVtv

IVti

O

Srmsg

O

SrmsgO ω2cos

)(

)()( ⋅−= (5)

The output current )(tiO consists of dc current and sinusoidal ac current term. Both components of the current )(tiO are

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dependent on the input ac line voltage, input ac line current and the output voltage. The ac component of the current )(tiO

causes the output ripple voltage. Therefore the output ripple voltage can be reduced by inject ac current which is out of phase with the ac current term of the AC/DC converter. From previous idea, the bidirectional DC/DC converter is controlled to eliminate the ac current term at the output of the AC/DC converter.

A proportional (P) controller is used to control the supercapacitors voltage in an appropriate range. The inductor current command )(22 ti refL is calculated from summation of output signal of P controller Pscv and the ac current component of the current )(tiO as shown in (6).

)(2cos)(

)(22 tvttv

IVti Psc

O

SrmsgrefL +⋅= ω (6)

The operating mode of the bidirectional DC/DC converter is dependent on the sign of the current command )(22 ti refL . For

negative value of )(22 ti refL , the power switch SW3 is controlled and the system controller generates the current command )(tiref as given in (7).

)()( 22 titi refLref = (7)

If the current command )(22 ti refL is positive, the power switch SW2 is controlled to feed energy from the supercapacitors to the output. The current command )(tiref is equal to )(12 ti refL and calculated from (8).

)()()(2cos

)()()()()( 22 tv

tvtvt

tvIV

tvtvtiti Psc

SC

O

SC

Srmsg

SC

OrefLref ⋅+⋅=⋅= ω (8)

The diagram of current command calculation for control the bidirectional DC/DC converter as an active ripple filter is shown in Fig. 4. In the backup operating mode, only energy from the supercapacitors is transferred to load at the output. From input output power balance, the inductor current 12Li of the bidirectional DC/DC converter is calculate in form of load power as in (9).

)()()()(12 tv

titvtiSC

OOL

⋅= (9)

Similar to control the AC/DC converter in the normal operating mode using power balance control technique, the current command of the bidirectional DC/DC converter in the backup operating mode is calculated from (10) and the diagram is shown as in Fig. 5.

contvtv

titvtiSC

OOrefL

)()()()(12 +⋅= (10)

III. TRANSFER FUNCTION AND CONTROLLER DESIGN The average small signal analysis [6] is used to find the

transfer function of the proposed system. However the proposed system has two operating modes and each mode has a

tovSrmsIgV

ω2cos⋅

Vg

ISrms

vO

GainvSCref

vSC

+

-

iL22ref

iL12ref

+

+

iref

sign( )

%

vPsc

Fig. 4 An active ripple filter current command calculation

vO

iO

vOref+

-vSC

% +

+iref

PI Controller

vCont

Fig. 5 Current command calculation for the DC/DC bidirectional converter in the backup operating mode

different transfer function. At the output end in Fig. 1, the dynamic equation is shown in (9).

loadO

OO idt

dvCi += (11)

Where Oi is summation of the output inductor current 21Li and 22Li .In the normal operating mode, the supercapacitors is

charged and power is fed from ac line to load and the supercapacitors. The power balance equation of the normal operating mode is shown in (10).

OLOloadgL vivi

VI⋅−⋅= 22

11

2

ˆ (12)

The current equation at the output node is:

2221 LOL iii −= (13) From (11) and relation of the inductor current 21Li and 11Li of the AC/DC converter, the power balance equation is arranged as:

)(2

ˆ22

11LOO

gL iivVI

−=⋅

(14)

Apply the perturbations in (6) and (11)-(14). Then the small signal approximation is performed. The results are as follows.

contLrefL vII ~~ˆ

~ˆ

1111 += (15)

sCiiv

O

loadOO

~~~ −= (16)

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OO

OLLL

O

go v

VIIiI

V

Vi ~)(~~

ˆ2

~ 222211 ⋅−++= (17)

gL

LOloadOOLloadg

L vIiViVvIIV

I ~2

~~~)(2~ˆ 11

222211 −−+−= (18)

Where OV means a steady state value and Ov~ means a small signal value. From (15)-(18), using block diagram reduction technique and set loadi~ , 22

~Li and gv~ equal to zero, the small

signal block diagram of OrefO vv ~/~ is shown in Fig. 6. The

OrefO vv ~/~ transfer function is shown in (19).

)()(1)()(

~~

1

1

sGsGksGsG

vv

PVCfb

PVC

Oref

O

⋅+⋅= (19)

fbk is output voltage feedback gain. )(sGVC and )(1 sGP are voltage loop controller and plant

transfer function as shown in (18)-(19).

sksksG iP

VC+=)( (20)

sVCV

sGOO

gP

2/)(1 = (21)

Pk and ik are proportional and integral gain of a PI controller. In the backup operating mode, only energy from the supercapacitors is fed to load. The power balance equation of the backup operating mode is in (22).

OloadSCL vivi ⋅=⋅12 (22)

Due to only the bidirectional DC/DC converter supplies energy to load then the output current Oi equal to inductor current 22Li . Equation (23) shows the relation between the input and output current of the DC/DC bidirectional converter in the normal operating mode.

SC

OOL v

vii ⋅=12 (23)

Similar to the analysis in the normal mode, the perturbation is applied to (22)-(23). After approximated by the small signal approximation, the results are in (24)-(25).

O

OL

VII −22

sCO

1

fbk

+Ov~

O

g

VV2

++

+

g

Lload

VII )(2 22−

+

-Orefv~

Voltage controller

vcont

Fig. 6. Control system block diagram of the normal operating mode

)~~~(1~2212 SCLloadOOload

SCL vIiVvI

Vi −⋅+⋅= (24)

)~~~(1~1222 SCLOOLSC

OO vIvIiV

Vi ⋅+⋅−⋅= (25)

From (8) the inductor current command refLi 12

~ˆ of the

bidirectional DC/DC converter is shown in (26).

contLrefL vii ~~ˆ

~ˆ

1212 += (26)

From (24)-(26), set SCv~ and loadi~ to zero and the small signal transfer function OrefO vv ~/~ of the backup mode is shown in (27).

)()(1)()(

~~

2

2

sGsGksGsG

vv

PVCfb

PVC

Oref

O

⋅+⋅= (27)

Where )(2 sGP is the plant transfer function of the backup operating mode.

sVCVsG

OO

CSP =)(2 (28)

Where SCV is nominal value of the supercapacitors voltage OV is output voltage at the steady state OC is output filter capacitor From the previous analysis, the plant transfer function in the backup mode is different from the transfer function of the normal operating mode. Therefore the parameters of the controller must be adapted to the appropriate values for each operating mode. The controller parameters are designed by frequency method [7]. The required phase margin and cutoff frequency of the compensated system are specified then the proportional gain and integral gain are calculated. In the normal mode the proposed system is designed to have a cross over frequency at 15 Hz and 75 of a phase margin at cross over frequency. For the backup operating mode, the cross over frequency is 40 Hz and 75 of a phase margin.

IV. SIMULATION RESULTS

The proposed system was verified by MATLAB/Simulink. The power converters were modeled on basic of the converter dynamic equations. The parameters of the converters in the proposed system are:

11L = 3mH, 21L = 1mH, F22000F,121 μμ === OCCC 12L = 0.3mH, 22L = 0.3mH, F5.03 μ=C

F29=SCC / 30V (maximum voltage) and Ω= 038.0ESRR Feedback gain 4.2/1=fbk Rated power of the AC/DC converter 250 W Output voltage = 24 V, AC input voltage = 220 Vrms

The continuous time controller in (20) was transformed in to a discrete form with 250 sμ sampling rate. The controller of the normal operating mode is in (29).

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1

1

17365.0741.0)( −

−

−−=

zzzGVC (29)

The controller of the backup operating mode is in (30).

1

1

111.1537.15)( −

−

−−=

zzzGVC (30)

A. Transient response of the normal operating mode Fig. 7. shows the transient response of the proposed system

that operated in the normal operating mode with charge the supercapacitors through the bidirectional DC/DC converter. The load condition of results in Fig. 7 is as follows

Between t=0 to t=0.4 s load equal to 50 W t = 0.4 to t = 0.6 s load equal to 200 W t = 0.6 to t = 0.8 s load equal to 50 W t = 0.8 to t = 1 s load equal to 200 W

In this mode the supercapacitors are charged with constant current and the supercapacitors voltage is increased linearly. At t= 0.4 s load is changed from 50 W to 200 W, the output ripple voltage is increased with ripple less than 0.5 volt peak. The response time of voltage loop control is fast and can observe from Fig. 7 at time equal to 0.4, 0.6, and 0.8 s. Fig. 8 shows the steady state ac line current of the proposed system in the normal operating mode compared with ac line voltage. The ac line current is in phase with the ac line voltage. Thus the input power factor is nearly unity.

In Fig. 9 shows the simulation results of the proposed system with the bidirectional DC/DC converter and the supercapacitors are controlled as an active ripple filter to reduce a ripple voltage at the output.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 121.9

22

22.1

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 123.52424.5

28

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-202

Time (s)

Output voltage (V)

Supercapacitor current (A)

Load current (A)

Supercapacitor voltage (V)

Fig. 7. Simulation results of the normal mode with out an active ripple

filter

0.54 0.56 0.58 0.6 0.62 0.64 0.66-4

-3

-2

-1

0

1

2

3

4

Time (s)

AC line voltage (100V/div)

AC line current (1A/div)

Fig.8. AC input line current and voltage in the normal mode operating mode

start active ripple filter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 121.995

22 22.005

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10

010

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 123.52424.5

28

Time (s)

Output voltage (V)

Supercapacitor current (A)

Load current (A)

Supercapacitor voltage (V)

Fig. 9. Simulation results of the normal mode with an active ripple filter

The load condition in Fig. 9 are 200 W at t= 0 to 0.6 s, 50W at t = 0.6 to 0.8 s and back to 200 W at t = 0.8 s. The bidirectional DC/DC converter is controlled as an active ripple filter at t = 0.4 s and the output ripple voltage is reduced. In Fig. 9 the negative and positive values of the supercapacitors current SCI shows the energy has been transfer between the supercapacitors and the output dc bus of the AC/DC converter. However the supercapacitors voltage still increased a little bit due to the supercapacitors voltage controller.

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B. Transient response of the backup operating mode The backup operating mode of the proposed system will

start when ac line is failed. From the simulation results as shown in Fig. 10 and Fig. 11, the input ac voltage is loss at time t = 0.45 s and the system controller controls the bidirectional DC/DC converter to feed stored energy in the supercapacitors to load at the output end. While the supercapacitors supplied energy to load, the output ripple voltage is lower than the output voltage in the normal operating mode that can observe from output voltage waveform as in Fig. 10 at time more than 0.45 s.

V. CONCLUSIONS

The analysis and design of the AC/DC converter with using the supercapacitors as energy storage has been presented. A power balance control technique and the average small signal model have been applied to voltage loop control design. The bidirectional DC/DC converter and the supercapacitors have been used to supply energy to load when the utility line interrupted. In the normal operating mode, the bidirectional DC/DC converter can be controlled as an active ripple filter to reduce the output ripple voltage. The simulation results show the proposed system has fast response in output voltage control and peak ripple voltage is not more than 0.5 V peak or about 2% of the output voltage value incase of the active ripple filter is inactive. At full load and the active ripple filter is started, the output ripple voltage is not more than 0.1 V peak or 0.4% of the output voltage.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

5

10

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-10

0

10

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 127.8

28

28.2

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 123.524 24.5

26

Time (s)

Output voltage (V)

Supercapacitor current (A)

Load current (A)

Supercapacitor voltage (V)

Fig. 10. Simulation results of the backup operating mode at t = 4.5 s

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-300-200-100

0 100200 300

Time (s)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-5-4-3-2-1012345

Time (s)

AC input voltage (V)

AC input current (A)

Fig. 11 Line voltage and current in the backup operating mode

REFERENCES [1] A. Emadi, A. Nasiri, S.B. Bekiarov, Uninterruptible Power Supplies and

Active Filters, CRC Press LLC, 2005. [2] I. Galkin, A. Stepanov, J. Laugis,"Outlook of Usage of Supercapacitors

in Uninterruptible Power Supplies",in Proc. BEC 2006 Conf., 2006,pp. 1-4

[3] A. Stepanov, I. Galkin, L. Bisenieks,” Implementation of supercapacitors in uninterruptible power supplies”, in Proc. EPE 2007 Conf., 2007,pp. 1-7.

[4] W. Zhang, G. Feng, Y.-F. Liu, and B. Wu,” A Digital Power Factor Correction (PFC) Control Straegy Optimized for DSP,” IEEE Transaction on Power Electronics, Vol.19, No. 6, pp 1474-1485,Nov 2004.

[5] U. Kamnarn and V. Chunkag “Power Balance Control Technique of The Modular Three-Phase AC to DC Converter with Fast Transient Response,” ARTICLE Electric Power Systems Research, Vol. 77,Issue 12, pp.1585-1594,October 2007

[6] R. W. Errickson, D. Maksimovic, Fundamentals of Power Electronics, 2nd. Edition, Kluwer Academic Publishers, 2001. [7] N. S. Nise, Control Systems Engineering, 3rd. Edition, John-Wiley &

Sons, Inc., 2000.

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