The mélange of terms in the title of this post have been used by others to explain power factor. Most of them are awful analogies, and that is what sparked me to attempt to figure this out for myself and explain it, both with more relevance and clarity.

But first, why does power factor matter? Because, contrary to what most people would say, bad power factor wastes energy and requires a larger capacity for generation and delivery of electricity.

## Mathematical Power Factor

A couple weeks ago in Power Factor and Toenail Fungus, I provided a brief overview of what causes power factor with a physical demonstration in a video. In that post, I described one cause, or source, of poor power factor – lightly loaded motors. A lightly loaded motor can be one that is far oversized for its load or one that drives constant torque loads, which requires over-sizing for starting.

On a microsecond scale, lightly loaded motors take a surge of electricity, store it momentarily in the motor, and then release it back to the grid[2].

Electronics often require non-linear loads, resulting in a distorted wave form and poor power factor. Nearby, you can see what I mean from an image in the referenced Wikipedia page. That shows the current draw, in cyan, for a computing load.

- Linear: smooth sine wave in yellow
- Non-linear: a distorted spiky curve in cyan

For simplicity, let’s stick with the smooth linear load of a motor, using a cartoon I developed a couple weeks back, shown again below. This time, I am showing the original and three additional cases of degrading power factor.

Hopefully, It is obvious to you from observation that these are showing different cases of voltage and current.

### Apparent Power

Apparent power is the dumb multiplication of voltage and current that we covered in Power Factor and Toenail Fungus. That is, measure the current and voltage independently and multiply them together.

As shown in these charts (look at them now), the current peaks at 3 and the voltage peaks at 5[3]. The apparent (dumb) power is 15 Watts[4], or 3 x 5.

### Real Power

The real power is the multiplication of volts and amps at one instant. The definition of power factor is real power divided by apparent power.

Shown above, we get the following real power table.

You can see the concept of these results by looking at the charts above. The voltage and current get more out of phase, where the multiplication of voltage and amperage at any given time (real power) is less and less with each successive chart. To facilitate the visualization, I added a vertical line showing the same point in time for all cases. You can see that multiplying voltage and current at that point results in different values depending on the power factor shown.

### Fake Power

Fake power is the difference between apparent power and real power. Many sources call this reactive power, but that is a misnomer. The word power insinuates energy consumption over time. There is no reactive power; only reactive current. It is stored momentarily and released back to the grid.

## Why Does Power Factor Matter and Where is the Waste?

Power factor matters because we need to put more current on the system to get the real work we need. Putting more current on the system results in a bunch of undesirable requirements.

- No conductor (highline) is perfect. Just as there are friction losses in pipes that require pumps to keep moving water, some resistance exists in conductors, and that resistance causes losses in the form of heat. We call these I-squared-R losses or I^2 x R losses, which is the phenomenon that lights a filament in an incandescent light bulb or the burner on an electric stove. More current on the conductors means more losses, means more power generation required.

- Everything from the generator to the load, including conductors, transformers, and substations has to be larger to handle the losses and carry more current. Operating expenses are higher, and infrastructure costs are higher.

So tell me, why is power factor correction not included in any demand-side management program? If we correct power factor, we get the same exact benefits as efficiency measures: lower capital and operating cost.

## Power Factor Correction

Power factor can be corrected at the load. Power factor correction allows the generator, transmission, and distribution system to deliver real power, only.

Power factor is most commonly corrected by using magical electrical doohickeys called capacitors. Like an inductive motor, a capacitor will store electrical energy for a split second and then release it at just the right time. Therefore, if a motor that has a crappy power factor needs a shot of reactive current and fake power, the capacitor will deliver it at the right time. The capacitor delivers locally, so the generator, transmission, and distribution system don’t have to.

[1] This is the grand finale; the crescendo of power factor ecstasy

[2] https://en.wikipedia.org/wiki/Power_factor

[3] A current of 3 amps is not unusual, although voltage in commercial and most industrial circuits is 120, 208, 277, or 480. These are combinations of the three legs in three phase power discussed in Grid Power Generation.

[4] There is a square root of three factor that is irrelevant for this discussion.

[…] the “dumb” meters. The fact that electromechanical meters measure real power, accounting for power factor is not short of amazing. There is easily as much creative ingenuity in that design as there is in a […]