Understanding Power Factor-cd00003904

8/13/2019 Understanding Power Factor-cd00003904

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APPLICATION NOTE

UNDERSTANDING POWER FACTOR

by L. Wuidart

AN523/1093 1/5

1. INTRODUCTION

The majority of electronics designers do notworry about Power Factor (PF); PF issomething that you learnt one day at school

in your electrotechnics course as beingthe cos f, the phase angle between the

voltage and current waveforms. However,this conventional definition is only valid whenconsidering ideal sinusoidal signals for bothcurrent and voltage waveforms, and in reality

most off-line power supplies draw a non-sinusoidal current.

Many off-line systems will typically have afront end section consisting of a rectifierbridge and an input filter capacitor, which

act as a peak detector - see figure 1. Acurrent flows to charge the capacitor onlywhen the instantaneous AC voltage exceeds

the voltage of the capacitor. A single phaseoff-line supply draws a current pulse during

a small fraction of the half-cycle duration.Between those current peaks, the load drawsthe energy stored in the input capacitor.

The phase lag and also the harmoniccontent of the pulsed current waveformproduce additional RMS currents, affecting

the real power available from the mains. SoPower Factor is much more than cos!

The P.F. value measures how much themains efficiency is affected by both the

phase lag and the harmonic content of theinput current. In this context, the EuropeanStandard EN 60555 only defines the limit of

current harmonics in mains suppliedequipment.


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2.2 Non-ideal sinusoidal currentAssuming that the mains voltage is an idealsinusoidal voltage waveform, its RMS value

is:

VRMSVpeak

=2

If the current has been distorted in some

way (for example as in figure 1) into aperiodic non-sinusoidal waveform, applying

a Fourier transform gives:IRMS(total)= I0+ I21RMS+ I22RMS + .... + I2nRMS

where I0is the DC component of the current,I1RMS the fundamental of the RMS current

(that is the component at the frequency ofthe voltage input) and I2RMS ... InRMSare theharmonics created by the distortion.

For a pure AC signal, there is no DC

component and so I0= 0.

The fundamental of the RMS current can be

modelled as in section 2.1 above as an in-phase component I1RMSP and a quadraturecomponent I1RMSQ, and so the RMS currentcan be expressed as:

IRMS(total)= I0+ I21RMS P+ I21RMS Q + I2nRMSThen, the Real Power is given by the RMSvoltage multiplied by the in-phase current:

P = VRMS. I1RMS P

Figure 1:Full-Wave Rectifier

P = VRMS. IRMSCOS: In-Phase or Real Power

Q = VRMS. IRMSSIN: Reactive or QuadrativePower

S = VRMS. IRMS: Total Apparent Power

2. THEORETICAL MEANING

The Power Factor is defined by:

2.1 Ideal sinusoidal signals

For ideal sinusoidal voltage and currentwaveforms, if there is a phase difference between the voltage and current waveforms,

the total apparent power can be modelledas being composed of two components:

one in phase with the input voltage, and theother 90 out of phase (in quadrature) with it- see figure 2.

Then by definition,

P.F. =P

S = COS

P.F. = =P

S

REAL POWER

APPARENT POWER

Figure 2: Power vectors of ideal sinusoidal signals

n=2

P

Q

S

Imains

Vmains

LOAD

VDC

VDC

Vmains

ImainsT/2 T

t

APPLICATION NOTE


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P = Real Power

= VRMS. IRMS. COS

Q = Reactive Power

= VRMS. IRMS. SIN

S1 = Apparent Fundamental Power

= VRMS. I1RMS

D = Distortion Power

= VRMS. I2nRMSS = TOTAL APPARENT POWER

= VRMS. IRMS (total)

As 1 is the displacement angle betweenthe input voltage and the in-phasecomponent of the fundamental current:

I1RMS P= I1RMSCOS 1

so

P = VRMS. IRMSCOS 1

As the total apparent power is given by:

S = VRMS. IRMS total

the Power Factor can be calculated as :

P.F. =P

S

COS=

I1 RMS

IRMS (total)

. 1

If the phase angle between I1RMSand IRMS(total)is defined as :

COS =I1 RMS

IRMS (total)

is linked to the harmonic content of thecurrent; as the harmonic content of IRMS(total)approaches zero,approaches 0 and cos

approaches 1.2.3 Summary

Finally then, the Power Factor can be

expressed as:

P.F. = COS. COS1

and the representation of the power vectorsbecomes that shown in figure 3.

1is the conventional displacement angle(phase lag) between the voltage and the

fundamental component of the current, while is the distortion angle caused by theharmonic content of the current.

Both the reactive power, Q, and the distortion

power, D, produce extra RMS currents,giving additional losses and reducing theefficiency of the mains supply network.

Figure 3: Power vectors with non-sinusoidal signals.

n=2

P

Q

S1

1

D

S

APPLICATION NOTE


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Improving the Power Factor means reducingboth elements:

10 means COS 11:

reduction of the phase lag between I and V,

0 means COS 1:

reduction of harmonic content of I.

3. PRACTICAL IMPLICATIONS OFPOWER FACTOR

3.1 Benefits of reduced Power Factor

Both the user and the electricity supply

company can benefit from a reduction inPower Factor. Adding a PFC also reducesthe component costs in a downstream

converter.

3.1.1 Benefits to the user

At the minimum line voltage (85VAC), astandard 115VACwall socket should be ableto deliver the nominal 15A to a common

load. However, an SMPS without a PowerFactor Corrector (PFC), which will typically

have a Power Factor of 0.6, reduces theavailable current to around 9A.

As an example, a single wall socket willsupply four 280W computers equipped withPFCs, but only two without.

3.1.2 Benefits to the distribution company

Both the reactive power Q and the distortionpower D give rise to extra RMS currents,

significantly reducing the efficiency of themains supply network. This means that the

copper distribution wires must be thickerthan would otherwise be necessary.

Delivering power at frequencies other thanthe line frequency (ie the distortion powerD) also causes difficulties. The distortiondisturbs the zero voltage crossing detection

systems, and generates overcurrent in theneutral line and resonant overvoltages.

In Europe, the standard EN 60555 and theinternational project IEC 555-2 limit the

harmonic content of the current of mainssupplied equipment.

3.1.3 Reduction of component costs in the

downstream converter

For the same output power capability, aconventional converter using an input mainsvoltage doubler has primary RMS current

1.8 times higher than one employing a PFCregulator. Consequently, if a PFC is used ina system using Power MOSFET switches,

the on-resistance (RDS(ON)) of the switchescan be up to three times higher than in asystem without PFC, allowing significantly

cheaper parts to be used.The size of the converter transformer canbe reduced not only because the thicknessof the windings is smaller, but also because

of the regulation of the DC bulk voltagedelivered by the PFC pre-regulator.

The PFC provides an automatic mainsselection on a wide range of voltages from

85VAC up to 265VAC. Compared to theconventional doubler front-end section thesame hold-up time can be achieved with a

bulk storage capacitor 6 times smaller. Forexample, to achieve a 10ms hold-up time, a100W converter in doubler operation requires

a series combination of two 440F capacitorswithout a PFC, but only a single 130F with.

3.2 RFI filter

However, the size and cost optimisation ofthe PFC has to take the RFI filter intoconsideration. A PFC circuit generates more

high frequency interference to the mains

than a conventional rectifier front-end - seefigure 4. Thus the use of a PFC means that

additional filtering is required. For this reason,modulation techniques and mode ofoperation for the PFC have to be carefully

adapted to the requirements of theapplication.

APPLICATION NOTE


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Figure 4: SMPS with (a) conventional rectifier front-end, and

(b) PFC front-end.

4. CONCLUSIONS

For new designs, SMPS designers will haveto take into account the IEC 555-2 standard.In practice, this will require the use of a PFC

on the front end of much mains suppliedequipment. The additional cost of the PFCis compensated by the significant reduction

in the cost of components for thedownstream converter. The PFC alsoprovides additional functions such as

automatic mains voltage selection andconstant output voltage.

Smaller

EMI filter

Larger

EMI filter

PFC

C i

0.1F

C i

220F

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