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Proceedings of the 14th International Middle East Power Systems Conference (MEPCON’10), Cairo University, Egypt, December 19-21, 2010, Paper ID 154.

217

Review of Passive and Active Circuits for Power

Factor Correction in Single Phase, Low Power AC-

DC Converters

H.Z.Azazi*, E. E. EL-Kholy**, S.A.Mahmoud* and S.S.Shokralla* * Electrical Engineering Department, Faculty of Engineering, Menoufiya University, Shebin El-Kom, Egypt

** King Abdulaziz University, Faculty of Engineering, Electrical Engineering Department, Saudi Arabia

Email: [email protected]

Abstract :- The increasing growth in the use of electronic

equipment in recent years has resulted in a greater need to

ensure that the line current harmonic content of any

equipment connected to the ac mains is limited to meet

regulatory standards. This requirement is usually satisfied

by incorporating some form of Power Factor Correction

(PFC) circuits to shape the input phase currents, so that

they are sinusoidal in nature and are in phase with the

input phase voltages. There are multiple solutions in whichline current is sinusoidal. This paper provides a concise

review of the most interesting passive and active circuits of

power factor correction, for single phase and low power

applications.The major advantages and disadvantages are

highlighted.

Keywords: Converter, Power factor correction, Harmonic

currents.

1. INTRODUCTION

Power factor correction (PFC) is necessary for ac-to-dcconverters in order to comply with the requirements of

international standards, such as IEC 61000–3–2 and IEEE-519. PFC can reduce the harmonics in the line current,

increase the efficiency and capacity of power systems, andreduce customer’s utility bill [1-2].

Single phase diode rectifiers are widely used for industrial

applications. Many conventional switching power supplies indata processing equipment and low power motor drive

systems operate by rectifying the input ac line voltage and

filtering with large electrolytic capacitors. The capacitor draws

current in short pulses. This introduces several problemsincluding reduction in the available power and increase losses.

This process involves both nonlinear and storage elements,

and results in the generation of harmonics in the line current[3-5] .The non linear characteristics of loads such as

televisions, computers, faxes and variable speed motor drives

(used in air-conditioning) have made harmonic distortion in

electrical distribution systems. However, when operating inlarge numbers, the cumulative effect of these loads has the

capability of causing serious harmonic distortions. This results

in a poor power quality, voltage distortion, poor power factor at input ac mains, slowly varying rippled dc output at load end

and low efficiency [3]. The input current has narrow pulses which in turn increase

its r.m.s value. Buildings with a large number of computers

and data processing equipments also experience large neutral

currents rich in third harmonic currents. Therefore, the

reduction in input current harmonics and the improvement of

power factor operation of motor drives are necessary for

energy saving. Many methods have been proposed to solve the problem of a poor power factor, which can be classified as

active and passive methods.

The non-ideal character of these input currents creates anumber of problems for the power distribution network and

for other electrical apparatuses in the neighborhood of therectifier systems. This approach has many disadvantages,

including:1) High-input harmonic current components.

2) Low rectifier efficiency due to large rms value of the input

current.

3) Input ac mains voltage distortion because of the associated

peak currents.

4)Maximum input power factor is approximately 0.6, while a

larger filter inductor is required for a high-input power factor [4].

Unless some correction circuit is used, the input rectifier

with a capacitive filter circuit will draw pulsating currentsfrom the utility grid, resulting in poor power quality and high

harmonic contents that adversely affect other users. Thesituation has drawn the attention of regulatory bodies around

the world. Governments are tightening regulation, setting newspecifications for low harmonic currents, and restricting the

amount of harmonic currents that can be generated. As a

result, there is a need for a reduction in line harmonics currentnecessitating the need for power factor correction (PFC) and

harmonic reduction circuits [5].

2. DEFINITION OF POWER FACTOR

Power factor (PF) is defined as the ratio of the real power

(P) to apparent power (S), or cosine (for pure sine wave for

both current and voltage) the phase angle between the current

and voltage waveforms.

PF = Real Power / Apparent Power (1)

Real power (watts) produces real work; this is the energy

transfer component . Reactive power is the power required to

produce the magnetic fields (lost power) to enable the real

work to be done, where apparent power is considered the total power that the power company supplies. This total power is

the power supplied through the power mains to produce the

required amount of real power.



218

If both current and voltage are sinusoidal and in phase,the power factor is 1.0. If both are sinusoidal but not in phase,

the power factor is the cosine of the phase angle. In

elementary courses in electricity, this is sometimes taught asthe definition of the power factor, but it applies only in the

special case, where both the current and voltage are pure sine

waves. This occurs when the load is composed of resistive,

capacitive and inductive elements and all are linear (invariantwith current and voltage).

Fig. 1- Diode bridge rectifier

Switched-mode power supplies present a non-linear

impedance to the mains, as a result of the input circuitry. Theinput circuit usually consists of a half-wave or full-wave

rectifier followed by a storage capacitor (similar to Fig. 1).

The capacitor maintains voltage of approximately the peak voltage of the input sine wave until the next peak comes along

to recharge it. In this case, current is drawn from the input

only at the peaks of the input waveform, and this pulse of current must contain enough energy to sustain the load until

the next peak. This is done by dumping a large charge into the

capacitor during a short time, after which the capacitor slowly

discharges the energy into the load until the cycle repeats. It is

not unusual for the current pulse of 10% to 20% of the cycleduration, meaning that the current during the pulse must be 5

to 10 times of the average current as illustrated by fig. 2 .

Figure 3 shows the harmonic content of the current waveform.The fundamental (in this case 50 Hz) is shown with a

reference amplitude of 100%, and the higher harmonics are

then given with their amplitudes (shown as percentages of the

fundamental amplitude). Note that, the even harmonics are barely visible; this is a result of the symmetry of the

waveform. The power factor of this power supply is

approximately 0.6 [6].

Fig. 2- Input Characteristics of a typical switched-mode power supply without

PFC

Fig. 3- Harmonic contents of the current waveform in Figure 2

Assuming an ideal sinusoidal input voltage source, the

power factor can be expressed as the product of the distortion

factor and the displacement factor, as given by equation (3).The distortion factor K d ,is the ratio of the fundamental root-

mean-square (RMS) current (I rms(1)) to the total RMS current

(I rms). The displacement factor k θ is the cosine of the

displacement angle (φ) between the fundamental input current

and the input voltage. For sinusoidal voltage and non-

sinusoidal current, equation (1) can be expressed as:

PF=rmsrms

rmsrms

I V

I V ϕ cos,1

= ϕ cos

,1

rms

rms

I

I

=K d cosφ (2)

PF=K d K θ

(3)

The distortion factor K d is given by the following equation:

K d = I rms(1) / I rms (4)

The displacement factor K θ

is given by the following

equation:

K θ

= cos φ (5)

The displacement factor k θ can be made unity with a

capacitor or inductor, but making the distortion factor K d unity

is more difficult. When a converter has less than unity power

factor, it means that the converter absorbs apparent power

higher than the active power. This means that the power source has a higher VA rating than what the load needs. In

addition, the harmonic currents generated by the converter in

the power source affects other equipment [7].

Power Factor vs. Harmonic Reduction:

The following equations link total harmonic distortion to

power factor.

11

100(%)2

−×=d K

THD (6)

2

100

(%)1

1

⎟ ⎠

⎞⎜⎝

⎛ +

=THD

K d (7)

Therefore, when the fundamental component of the inputcurrent is in phase with the input voltage, K θ = 1. Then we

have,

d d K K K PF == θ (8)

Then:



219

2

100

(%)1

1

⎟ ⎠

⎞⎜⎝

⎛ +

=THD

PF (9)

The purpose of the power factor correction circuit is to

minimize the input current distortion and make the current in

phase with the voltage.When the power factor is not equal to 1, the current waveform

does not follow the voltage waveform. This result not only in

power losses, but may also cause harmonics that travel downthe neutral line and disrupt other devices connected to the line.

3. POWER FACTOR CORRECTION CIRCUITS

The classification of single-phase PFC topologies is

shown in Fig. 4.The diode bridge rectifier (similar to Fig. 1) has no

sinusoidal line current. This is because most loads require a

supply voltage V2 with low ripple, which is obtained by using

a correspondingly large capacitance of the output capacitor Cf

. Consequently, the conduction intervals of the rectifier diodesare short and the line current consists of narrow pulses with an

important harmonic contents [8].

There are several methods to reduce the harmoniccontents of the line current in single-phase systems.

Fig. 4- Classification of single-phase PFC topologies.

3.1. PASSIVE METHODS OF PFC

3.1.1. Rectifier with AC-side inductor

Passive methods of PFC use additional passive

components in conjunction with the diode bridge rectifier (Fig.

1). One of the simplest methods is to add an inductor at theAC-side of the diode bridge, in series with the line voltage as

shown in Fig. 5(a). The maximum power factor that can beobtained by this configuration is 0.76.

(a)

0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88-400

-300

-200

-100

0

100

200

300

400

(b)

Fig. 5- Rectifier with AC-side inductor: a) Schematic; b) Line voltage and line

current with V1=220Vrms , resistive load R=500Ω , Cf =470μF , andLa=130mH.

Simulated results of the rectifier with AC-side inductor are

presented in Fig. 5(b), where the inductance La has been

chosen to maximize the power factor. The line current has

K d=0.888, cos φ=0.855 and PF=0.759 [7].

3.1.2. Rectifier with DC-side inductor

The inductor can be also placed at the DC-side, as shownin Fig.6. (a) [8]. The inductor current is continuous for a large

enough inductance Ld . In the theoretical case of near infiniteinductance, the inductor current is constant, so the inputcurrent of the rectifier has a square shape and the power factor

is 0.9 . However, operation close to this condition would

require a very large inductor, as illustrated by the simulated

line current waveform, for Ld 1H (without Ca), shown inFig. 6 (b). For lower inductance Ld, the inductor current

becomes discontinuous. The maximum power factor that can

be obtained in such a case is 0.76, the operating mode beingidentical to the case of the AC-side inductor, which is

previously discussed. An improvement of the power factor can

be obtained by adding the capacitor Ca as shown in Fig. 6.

(a), which compensates the displacement factor, cos φ. Adesign for K d and unity displacement factor cos φ is possible,

leading to a maximum obtainable power factor 0.905 [9]. This

is shown in Fig.6 (b) by the simulated line current for Ld

275mH and Ca 4.8µF.

(a)

(b)

Fig. 6- Rectifier with DC-side inductor: a) Schematic; b) Line voltage and line

current with V1=220Vrms , resistive load R=500Ω and Cf =470μF.

Line Voltage Line Current

With Ca Without Ca



220

In Figure 6, With Ld=1H and without Ca , the line currenthas K d=0.897, cos φ=0.935 and PF=0.839, and output voltage

is V2=200V. With Ld=275mH and with Ca =4.8 μF, the line

current has K d=0.905 , cos φ=0.999 and PF=0.904, and outputvoltage is V2=230V.

3.1.3. Rectifier with series-resonant band-pass filter

The shape of the line current can be further improved byusing a combination of low-pass input and output filters [10].

There are also several solutions based on resonant networks

which are used to attenuate harmonics. For example, a band-

pass filter of the series resonant type, tuned at the line-frequency, is introduced in-between the AC source and the

load. Figure (7-a) shows the schematic diagram, and figure (7-

b) shows the simulated results. For 50Hz networks, largevalues of the reactive elements are needed.

(a)

0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88-400

-300

-200

-100

0

100

200

300

400

(b)

Fig. 7- Rectifier with series-resonant band-pass filter: a) Schematic; b) Line

voltage and line current with V1=220Vrms, resistive load R=500Ω ,

Cf=470μF, Ls=1.5H and Cs=6.75 μF.

The line current has K d=0.993, cos φ=0.976 and PF=0.969,

and output voltage is V2=250V.

3.1.4. Rectifier with parallel-resonant band-stop filter

The solution uses a band-stop filter of the parallel-resonant type [4]. Figure 8 shows the schematic diagram and

the simulated waveforms. The filter is tuned at the third

harmonic, hence it allows for lower values of the reactiveelements when compared to the series-resonant band-pass

filter.

(a)

0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88-400

-300

-200

-100

0

100

200

300

400

(b)

Fig. 8- Rectifier with parallel-resonant band-stop filter: a) Schematic; b) Line

voltage and line current with V1=220Vrms, resistive load R=500Ω , Cf =470μF,

L p=240mH and C p=4.7 μF.

The line current has K d=0.919, cos φ=0.999 and PF=0.918,and output voltage is V2=260V.

3.1.5. Rectifier with harmonic trap filter

Another possibility is to use a harmonic trap filter. Theharmonic trap consists of a series-resonant network, connected

in parallel to the AC source and tuned at a harmonic that must

be attenuated [11]. For example, the filter shown in Fig. 8 has

two harmonic traps, which are tuned at the 3rd

and 5th

harmonic, respectively. As seen from Fig. 9 (b), the line

current is improved, at the expense of increased circuit

complexity. Harmonic traps can be used also in conjunctionwith other reactive networks, such as a band-stop filter .

(a)

0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88-400

-300

-200

-100

0

100

200

300

400

(b)

Fig. 9- Rectifier with harmonic trap filter: a) Schematic; b) Line voltage and

line current

In Fig.9, with V1=220Vrms, resistive load R=500Ω , Cf =470μF,

L1=400mH , L3=200mH , C3=5.6 μF , R 3=0.1 Ω , L5=100mH ,

C5=4.04 μF , and R 5=0.1 Ω; The line current has K d=0.999,

cos φ=0.999 and PF=0.998, and output voltage is V2=290V.

3.1.6. Rectifier with an additional inductor, capacitor and

diode (LCD):

The rectifier with an additional inductor, capacitor, and

diode – LCD rectifier – is shown in Fig. 10, together withsimulated waveforms. The added reactive elements have

relatively low values. The circuit changes the shape of the


Line VoltageLine Current




221

input current, while only a limited reduction of the harmoniccurrents can be obtained [12].

In Fig.10, with V1=220Vrms, resistive load R=500Ω ,

Cf =470μF, C1=40 μF and Ld=10mH ; The line current has K d=0.794, cos φ=0.998 and PF=0.792, and output voltage is

V2=300V.

(a)

0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.88-400

-300

-200

-100

0

100

200

300

400

(b)

Fig. 10- Rectifier with an additional inductor, capacitor and diode (LCD): a)

Schematic; b) Line voltage and line current.

Passive methods of power factor correction have certainadvantages, such as simplicity, reliability and ruggedness,

insensitivity to noise and surges, no generation of high-frequency electro magnetic interface (EMI) and no high

frequency switching losses. On the other hand, they also haveseveral drawbacks. Solutions based on filters are heavy and

bulky, because the line-frequency reactive components are

used. They also have a poor dynamic response, lack voltageregulation and the shape of their input current depends on the

load. Even though line current harmonics are reduced, thefundamental component may show an excessive phase shift

that reduces the power factor. Moreover, circuits based onresonant networks are sensitive to the line-frequency. In

harmonic trap filters, series-resonance is used to attenuate a

specific harmonic. However, parallel-resonance at differentfrequencies occurs too, which can amplify other harmonics

[11].

3.2. ACTIVE METHODS OF PFC

The active methods of PFC, which involve the shaping of

the line current, using switching devices such as MOSFETs

and IGBTs, is a result of advances in power semiconductor

devices.

3.2.1. LOW-FREQUENCY ACTIVE METHODS OF PFC

Three representative solutions are presented in Fig. 11.

The phase-controlled rectifier and its control signals are

shown in Fig.11. (a) and Fig.11. (b) respectively. It is derivedfrom the rectifier with a DC-side inductor (Fig.6), where

diodes are replaced with thyristors. According to Ref. [13],

depending on the inductance Ld and the firing-angle α , a near-

unity distortion factor K d or displacement factor cosφ can be

obtained. However, the overall power factor PF is always less

than 0.7. In Ref. [14], the inductance Ld and firing angle α arechosen to maximize K d. This implies a lagging displacement

factor, cosφ that is compensated by additional an input

capacitance, C a . This approach is similar to that used for thediode bridge rectifier with a DC-side inductor. This solution

offers controllable output voltage, it is simple, reliable, and

uses low-cost thyristors. On the negative side, the outputvoltage regulation is slow and a relatively large inductance Ld

is still required.

The low-frequency switching Boost converter is shown in

Fig.11. (c). The active switch S is turned on for the durationT on , as illustrated in Fig.11. (d), to enlarge the conduction

interval of the rectifier diodes [2]. It is also possible to have

multiple switching per half line-cycle, at low switching

frequency, in order to improve the shape of the line current

[15]. Nevertheless, the line current has a considerable ripplecontent.

The low-frequency switching Buck converter is shown in

Fig.11.(e). Theoretically, the inductor current is constant for anear-infinite inductance Ld . The switch is turned on for the

duration T on and the on-time intervals are symmetrical with

respect to the zero-crossings of the line voltage, as illustrated

in Fig.11. (f). The line current shape is square, with adjustableduty-cycle. For lower harmonic contents of the line current,

multiple switching per line-cycle can be used. However, the

required inductance Ld is large and impractical [16].To conclude, low-frequency switching PFC offers the

possibility to control the output voltage within certain limits.In such circuits, switching losses and high-frequency EMI are

negligible. However, the reactive elements are large and theregulation of the output voltage is slow.

(a)

(b)

(c)




222

(d)

(e)

(f) Fig. 11- Low frequency active circuits of PFC: a) Controlled rectifier with

DC-side inductor, with b) phase-control; c) Boost converter, with d) one

commutation per half line-cycle; e) Buck converter, with f) one commutation

per half line-cycle.

3.2.2. HIGH-FREQUENCY ACTIVE METHODS OF

PFC

The PFC stage can be realized by using a diode bridgeand a DC/DC converter with a switching frequency much

higher than the line-frequency. In principle, any DC/DC

converter can be used for this purpose, if a suitable control

method is used to shape its input current, or if it has inherentPFC properties.

The converters can operate in Continuous Inductor Current Mode – CICM, where the inductor current never

reaches zero during one switching cycle, or Discontinuous

Inductor Current Mode - DICM, where the inductor current is

zero during intervals of the switching cycle.

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 12- high-frequency active circuits of PFC: a) Buck converter, with b)waveforms; c) Boost converter, with d) waveforms; e) Buck-Boost converter,

with f) waveforms.



223

The converters are shown in Fig. 12 together withwaveforms relevant for a PFC application, assuming operation

in CICM.

Buck Converter:

The Buck converter, shown in Fig. 12 (a), has a step-

down conversion ratio. Therefore, it is possible to obtain an

output voltage V 2 lower than the input voltage (V 1 ). However,the converter can operate only when the instantaneous input

voltage v1 is higher than the output voltage V 2. Hence, the line

current of a power factor correction based on a Buck converter has crossover distortions, as illustrated in Fig. 12 (b).

Moreover, the input current of the converter is discontinuous.

Consequently, even in CICM, the input current has a

significant high-frequency component that increases EMI andfilter is required. Some PFC applications based on this

topology are reported in Ref [17-18].

Boost Converter:

The boost converter, is the most common topology used

for power factor correction, and it can operate in two modes –

continuous conduction mode (CCM) and discontinuous

conduction mode (DCM). The Boost converter is shown inFig. 12 (c). It has a step-up conversion ratio; hence the output

voltage V 2 is always higher than the input voltage V 1.

Operation is possible throughout the line-cycle, so the inputcurrent does not have crossover distortions. As illustrated in

Fig. 12 (d), the input current is continuous. Hence, an input

current with reduced high-frequency content can be obtained

when operating in CICM. For medium and higher power applications, where the input filter requirements dominate the

size of the magnetic elements, the CCM boost converter is a better choice, due to lower peak current (which reduces

conduction losses) and lower ripple current (which reduces

input filter requirements and inductor AC losses). For these

reasons, the Boost converter operating in CICM is widely used

for PFC [19-22].

Buck-Boost Converter:

The Buck-Boost converter, shown in Fig. 12 (e), canoperate either as a step-down or a step-up converter. This

means that the output voltage V 2 can be higher or lower than

the amplitude V 1 of the input voltage, which gives freedom in

specifying the output voltage. Operation is possiblethroughout the line-cycle and a sinusoidal line current can be

obtained. However, the output voltage is inverted, which

translates into higher voltage stress for the switch. Moreover,similar to the Buck converter, the input current is

discontinuous with significant high-frequency contents, as

illustrated in Fig. 12 (f). Thus, the input current has a

significant high-frequency component that increases EMI andfiltering requirements [7].

In addition to these basic converters, the two switches

Buck - Boost converter shown in Fig. 13 [23] is an interestingsolution. It operates as a Buck converter when the input

voltage is higher than the output voltage and as a Boost

converter when the input voltage is lower than the outputvoltage. Therefore, operation is possible throughout the line-

cycle and the output voltage can be varied in a wide range, in

a similar manner of the Buck-Boost converter. Another positive aspect is that, due to its non-inverted output voltage,

the voltage stress of the switches is lower than in a Buck-

Boost converter. However, this topology has an increasednumber of switches, which leads to higher cost and conduction

losses.

Fig. 13- Two- switches Buck- Boost converter

PWM rectifier:Another non-isolated PFC topology is the PWM rectifier

[24-25], shown in Fig. 14. The topology in Ref [24] can

supply the step-up or step-down outputs like the buck-boostcircuit. A full-bridge PWM rectifier in Ref [25] provides the

step-up output. The PWM rectifier circuit needs two [24] or

four [25] power switches to achieve the unity power factor,

because it employs a half- or full-bridge configuration. It alsoneeds more complicated control than the boost topology.

Fig. 14- PWM rectifier

The use of active techniques of PFC results in one or more

of the following advantages:

• Lower harmonic contents in the input current in

comparison to the passive techniques.

• Reduced r.m.s current rating of the output filter capacitor.

• Unity power factor is possible to achieve.

• For higher power levels, active techniques of PFC will

result in size, weight and cost benefits over passivetechniques of PFC.

4. CONCLUSIONS

As we have seen, conventional AC rectification is a very

inefficient process, resulting from a waveform distortion of the

current drawn from the power line. It produces a largespectrum of harmonic signals that may disturb other

equipments.

It is concluded that the harmonics may be reduced and thesupply can be mad more efficient by additional circuits at the

input of the converter.

Many solutions for ac-dc power factor correction have

been discussed. Examples have been provided for passive



224

techniques. Passive power factor correction circuits havecertain advantages, such as simplicity, reliability and

ruggedness, insensitivity to noise and surges, no generation of

high-frequency EMI and no high frequency switching losses.On the other hand, they also have several drawbacks.

Active PFC solutions are more suitable options for

achieving near unity power factor and sinusoidal input current

waveform with extremely low harmonic distortion. In theseactive solutions, a converter with switching frequencies higher

than the AC line frequency is placed in between the output of

the diode bridge rectifier and the bulk capacitor. The reactiveelements of this converter are small, because their size

depends on the converter switching frequency rather than the

AC line frequency.

5. REFERENCES

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