Power Factor

Why Power Factor Matters

Until fairly recently, power factor has only been of concern to industrial users and electricity providers.  Residential consumers are generally unaware of it because the grid utility does not directly charge them for it.  In most countries, residential users only pay for true power in watts (not apparent power in volt-amps) so an appliance having a poor power factor is not considered a disadvantage.  Thus, the power factor for such appliances has only been improved due to legislation.

However, with the proliferation of inverter-type generating capacity, poor power factor becomes an issue when a residential user is also the electricity producer (typically via photovoltaic panels).

If you want to charge your EV battery using a portable power station, the charger's power factor matters.

Displacement versus Harmonic Power Factor

Historically, factories with large (and/or many) induction motors were concerned with displacement power factor.  This is due to the motor's demand for current not being in perfect alignment (phase) with the supplied voltage.  That is, the current sine wave lagged the voltage sine wave due to inductance.  From the “displacement” of these two waveforms, power factor could be calculated.  Displacement power factor can be improved by installing the correct capacitance in parallel with the load.  This is called passive power factor correction (PFC).

However, power factor also suffers when a load uses power discontinuously.  This happens in things like switched-mode power supplies, inverter-driven variable speed motors, and the topic of our concern today, modern battery chargers.  Here, power factor is degraded due to the load “gulping” current in a rapid on/off fashion.  This fast pulsating consumption produces harmonic distortion that is detrimental to achieving a good power factor.  In this case, simply putting a capacitor in parallel with the load will not fix the problem — active PFC is required.  Active PFC aims to time small gulps to closely follow the shape of the incoming sine wave.  An active PFC demonstration board I worked with in the mid-1990s is show in the header photo.

Numerically, power factor can vary from one (perfect energy utilization) down to zero (no energy utilization) and is typically between 0.5 and 0.75 for the devices mentioned above when they are under load.  But this number can and does vary greatly during operation.

Power Factor—The Beer Glass Analogy

I did not originate this analogy but do like it.  If my brief summary below is insufficient, I'd encourage you to seek out a YouTube version.  But be forewarned, they will concentrate on displacement power factor and may not even mention harmonics.  

Consider a glass of beer drawn from a tap.  It is part liquid and part foam. 

• The liquid beer is what we actually drink.  This is real power (measured in watts).  It's also called active power and does useful work.

• The foam takes up space in the glass, but you don't drink it.  This is reactive power (measured in volt-amps-reactive).  It does not do any useful work, but is required nonetheless.  It sloshes back and forth between the source and the load at twice the line frequency.

• The total volume in the glass is apparent power (measured in volt-amps).  This is what the utility’s generators, transformers, and wiring must provide.  Thus, the glass must be large enough to hold the foam as well as the beer

To continue the analogy, with a power factor of one, the glass contains all beer.  With a power factor of zero, the glass contains all foam.  Usually, the glass will contain a mixture.  Power factor correction can achieve a nearly full (0.99+) glass of liquid.

Written succinctly, power factor is the ratio of real power to apparent power (including all harmonics).

Finally, in case it's not obvious, power factor has no applicability to DC circuits.

A Tale of Two Chargers

The eight photos below were taken of measurements made with a Fluke 39 power meter.  They show the operating characteristics of two chargers.  The old-school charger for an Electric Motion 5.7 lacks power factor correction.  The modern charger for a Mecatecno Dragonfly employs active PFC.  Although the display on the Fluke 39 is a low-resolution LCD (you can see the individual pixels) the images and a bit of explanatory text are telling.

The EM 5.7's charger exhibited a power factor of about 0.65 when the photos were taken (but this does change depending on loading).  The Dragonfly's power factor fluctuated between 0.99 and 1.0 regardless of load.  

Note that the voltage waveforms look about the same for both the 5.7 and the Dragonfly.  Neither is a perfect sine wave, which also shows that grid power at its point of use is imperfect.  (I have included a photo farther below of an oscilloscope trace that better illustrates this.) 

Notice the 5.7 shows an AC-line voltage 120.4V whereas the Dragonfly shows 122.2V.  The line-voltage droop for the 5.7's charger is actually greater despite the Dragonfly's charger consuming more power (0.77 kW) than the 5.7's charger (0.63 kW) at the time the photos were taken.  This is due to the 5.7's charger requiring a higher RMS current (7.80 A) versus the Dragonfly's charger (6.56 A).  The higher current causes a greater I×R voltage drop in the wiring.  This is one ramification of a poor power factor.

Now compare the shapes of the current waveforms.  The Dragonfly's charger is much closer to looking like a sine wave than 5.7's.  This is the key to seeing a good power factor from a “gulping” current consumption. 

The waveforms for power show the final result.  Again, the Dragonfly's charger is much closer to being a sine wave.  The reason the power waveforms do not go below zero is simple mathematics.  Multiplying the negative half-cycle voltage by the negative half-cycle current yields a positive power.

The final two screenshots from the Fluke 39 give a quantitive comparison of the harmonic distortion present in the input current waveforms.  The Dragonfly's charger shows only the fundamental frequency (60 Hz).  This is excellent and representative of a perfect power factor.  The 5.7 charger's distribution shows significant content for the odd harmonics (3rd, 5th, 7th, etc.) and even some content for the even harmonics (DC, 2nd, 4th, 6th, and 8th).  This is a validation of its poor power factor number.

Real-World Example

I recently bought a Bluetti AC200L power station to run my refrigerator in case of a power outage.  It's a nice unit where solar power can charge a LiFePO4 battery pack which then discharges through an inverter to run AC-powered appliances.

In testing the unit, I decided to charge the motorcycle batteries.  Although I can not find anywhere in Bluetti's documentation that says this, the AC output power displayed actually measures volt-amps rather than watts.  So power factor is already considered.  This makes a lot of sense and is quite useful — and it's very accurate. 

It was easy to see the 5.7's charger drained the power station's battery much faster than the Dragonfly's charger.  That difference has everything to do with power factor.

To summarize, given the same amount of energy transfer, the battery in a portable power station will last twice as long operating a charger that has a power factor of 1 than if the charger's power factor is only 0.5.