® APPLICATION NOTE UNDERSTANDING POWER FACTOR

by L. Wuidart

1. INTRODUCTION The majority of electronics designers do not the of the . A single phase worry about Power Factor (PF); PF is off-line supply draws a current pulse during something that you learnt one day at school a small fraction of the half-cycle duration. in your “electrotechnics course” as being Between those current peaks, the load draws the cos οf ϕ, the phase angle between the the energy stored in the input capacitor. voltage and current waveforms. However, The phase lag ϕ and also the harmonic this conventional definition is only valid when content of the pulsed current waveform considering ideal sinusoidal signals for both produce additional RMS currents, affecting current and voltage waveforms, and in reality the real power available from the mains. So most off-line power supplies draw a non- Power Factor is much more than cos ϕ! sinusoidal current. The P.F. value measures how much the Many off-line systems will typically have a mains efficiency is affected by both the front end section consisting of a phase lag ϕ and the harmonic content of the bridge and an input filter capacitor, which input current. In this context, the European act as a peak detector - see figure 1. A Standard EN 60555 only defines the limit of current flows to charge the capacitor only current harmonics in mains supplied when the instantaneous AC voltage exceeds equipment.

AN523/1093 1/5 APPLICATION NOTE

Figure 1: Full-Wave Rectifier

VDC LOAD Imains

VDC Vmains Vmains t Imains T/2 T

2. THEORETICAL MEANING The Power Factor is defined by: 2.2 Non-ideal sinusoidal current Assuming that the mains voltage is an ideal P REAL POWER P.F. = = sinusoidal voltage waveform, its RMS value S APPARENT POWER is:

2.1 Ideal sinusoidal signals Vpeak VRMS= For ideal sinusoidal voltage and current 2 waveforms, if there is a phase difference ϕ If the current has been distorted in some between the voltage and current waveforms, way (for example as in figure 1) into a the total apparent power can be modelled periodic non-sinusoidal waveform, applying as being composed of two components: a Fourier transform gives: one in phase with the input voltage, and the other 90° out of phase (in quadrature) with it 2 2 2 IRMS(total) = √I0 + I 1RMS + I 2RMS + .... + I nRMS - see figure 2. Then by definition, where I0 is the DC component of the current, I1RMS the fundamental of the RMS current P (that is the component at the frequency of P.F. = = COS ϕ S the voltage input) and I2RMS ... InRMS are the harmonics created by the distortion. Figure 2: Power vectors of ideal sinusoidal signals For a pure AC signal, there is no DC component and so I0 = 0. P The fundamental of the RMS current can be ϕ modelled as in section 2.1 above as an in-

phase component I1RMSP and a quadrature Q component I1RMSQ, and so the RMS current S can be expressed as:

∞ 2 2 2 IRMS(total) = √I0 + I 1RMS P + I 1RMS Q + Σ I nRMS n=2 P = VRMS . IRMS COS ϕ: In-Phase or Real Power Then, the Real Power is given by the RMS ϕ Q = VRMS . IRMS SIN : Reactive or Quadrative voltage multiplied by the in-phase current: Power

S = VRMS . IRMS: Total Apparent Power P = VRMS . I1RMS P

2/5 APPLICATION NOTE

As ϕ 1 is the displacement angle between θ is linked to the harmonic content of the the input voltage and the in-phase current; as the harmonic content of IRMS(total) component of the fundamental current: approaches zero, θ approaches 0 and cos θ approaches 1. I1RMS P = I1RMS COS ϕ1 2.3 Summary so Finally then, the Power Factor can be ϕ P = VRMS . IRMS COS 1 expressed as: As the total apparent power is given by: P.F. = COS θ . COS ϕ1

S = VRMS . IRMS total and the representation of the power vectors the Power Factor can be calculated as : becomes that shown in figure 3.

ϕ1 is the “conventional” displacement angle P I . COS 1 (phase lag) between the voltage and the P.F. = = 1 RMS S IRMS (total) fundamental component of the current, while θ is the distortion angle caused by the If the phase angle between I1RMS and IRMS(total) harmonic content of the current. is defined as θ: Both the reactive power, Q, and the distortion I power, D, produce extra RMS currents, θ 1 RMS COS = giving additional losses and reducing the IRMS (total) efficiency of the mains supply network.

Figure 3: Power vectors with non-sinusoidal signals.

P = Real Power P = V . I . COS ϕ ϕ1 RMS RMS θ Q = Reactive Power Q = V . I . SIN ϕ S1 RMS RMS

S1 = Apparent Fundamental Power S = VRMS . I1RMS D D = Distortion Power ∞ = V . √ Σ I2 RMS n=2 nRMS S = TOTAL APPARENT POWER

=VRMS . IRMS (total)

3/5 APPLICATION NOTE

Improving the Power Factor means reducing harmonic content of the current of mains both elements: supplied equipment. → → ϕ1 → 0 means COS ϕ1 → 1: 3.1.3 Reduction of component costs in the reduction of the phase lag between I and V, downstream converter θ → 0 means COS θ → 1: For the same output power capability, a conventional converter using an input mains reduction of harmonic content of I. voltage doubler has primary RMS current 1.8 times higher than one employing a PFC regulator. Consequently, if a PFC is used in 3. PRACTICAL IMPLICATIONS OF a system using Power MOSFET , POWER FACTOR the on-resistance (RDS(ON)) of the switches 3.1 Benefits of reduced Power Factor can be up to three times higher than in a Both the user and the electricity supply system without PFC, allowing significantly company can benefit from a reduction in cheaper parts to be used. Power Factor. Adding a PFC also reduces The size of the converter can the component costs in a downstream be reduced not only because the thickness converter. of the windings is smaller, but also because 3.1.1 Benefits to the user of the regulation of the DC bulk voltage delivered by the PFC pre-regulator. At the minimum line voltage (85VAC), a The PFC provides an automatic mains standard 115VAC wall socket should be able to deliver the nominal 15A to a common selection on a wide range of from load. However, an SMPS without a Power 85VAC up to 265VAC. Compared to the Factor Corrector (PFC), which will typically conventional doubler front-end section the have a Power Factor of 0.6, reduces the same hold-up time can be achieved with a available current to around 9A. bulk storage capacitor 6 times smaller. For example, to achieve a 10ms hold-up time, a As an example, a single wall socket will 100W converter in doubler operation requires supply four 280W computers equipped with a series combination of two 440µF PFCs, but only two without. without a PFC, but only a single 130µF with. 3.1.2 Benefits to the distribution company 3.2 RFI filter Both the reactive power Q and the distortion However, the size and cost optimisation of power D give rise to extra RMS currents, the PFC has to take the RFI filter into significantly reducing the efficiency of the consideration. A PFC circuit generates more mains supply network. This means that the high frequency interference to the mains copper distribution wires must be thicker than a conventional rectifier front-end - see than would otherwise be necessary. figure 4. Thus the use of a PFC means that Delivering power at frequencies other than additional filtering is required. For this reason, the line frequency (ie the distortion power modulation techniques and mode of D) also causes difficulties. The distortion operation for the PFC have to be carefully disturbs the zero voltage crossing detection adapted to the requirements of the systems, and generates overcurrent in the application. neutral line and resonant . In Europe, the standard EN 60555 and the international project IEC 555-2 limit the

4/5 APPLICATION NOTE

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

Smaller C EMI filter i 220µF

Larger C i EMI filter 0.1µF

PFC

4. CONCLUSIONS For new designs, SMPS designers will have in the cost of components for the to take into account the IEC 555-2 standard. downstream converter. The PFC also In practice, this will require the use of a PFC provides additional functions such as on the front end of much mains supplied automatic mains voltage selection and equipment. The additional cost of the PFC constant output voltage. is compensated by the significant reduction

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