Why use cosine power factor?

Answer 1

Yes. Power factor is a cosine related function. To understand this, you need to understand volt-amps versus watts...

Volt-Amps (VA) is volts times amps, which may seem to be the same as watts (W). This is true only for resistive loads, where the phase angle of volts is the same as that of amps. In that case VA is the same as W.

What happens with non-resistive or reactive loads, however, is that amps are not in phase with volts. In an inductive load, such as a motor, amps lags volts; while in a capacitive load, amps leads volts. In both of these cases, you cannot just multiply volts and amps to get watts, due to a phenomenon known as power factor; power factor being the ratio of apparent power to true power.

To visualize this, you need to draw the power circle. Since WikiAnswers does not presently support graphic images, please take a piece of paper and follow along with me...

Draw a circle. To make it easy to do the math, draw it centered at the origin, and pretend that it has radius of one. This way, the trigonometry is easy.

Consider that the radius of the circle is VA. (Do not confuse this with the trigonometry trick where we also consider the radius to be one.)

Now, pick a point on the circle. Twelve O'Clock is a purely resistive load, where volts and amps are in phase. Nine O'Clock is a purely inductive load, where amps lags volts by 90 degrees. Three O'Clock is a purely capacitive load, where amps leads volts by 90 degrees. In "normal" trigonometry, zero degrees is at 3:00 O'Clock, but, by convention, zero degrees when dealing with reactive power is accepted to be 12:00 O'Clock. Just keep the trigonometric identities straight in your mind.

In practice, with normal electric motors and all other things considered, we see a point on the circle at about 10:30 or 11:00 O'Clock. Let's pick 10:30, to make the math easy. So, draw a line from the origin to the upper left at an angle of 45 degrees with respect to the Y-Axis. Label this line VA.

Notice that VA is constant, no matter what the phase angle may be.

Now, draw two more lines; one from the point on the circle at 10:30 O'Clock straight down, perpendicular to and stopping at the X-Axis - label this line W, and one from that same point to the right, perpendicular and stopping at the Y-Axis - label this line VAR.

Label the angle of the first line with respect to the Y-Axis as phase angle. Positive meaning inductive, and negative meaning capacitive. Notice that, if you had a 45 degree capacitive load, intersecting at 1:30 O'Clock, the magnitude of the VAR line would be the same, though positive instead of negative, and the W line would still be the same.

Now, power factor is W / VA, the ratio of apparent versus true. In this case, since we picked 45 degrees as the phase angle - to make it easy - the ratio is 0.707, or the cosine of the phase angle.

A typical power meter will register less than the actual power. In the worst case of a purely inductive load, the power meter would register zero, though the VA is still what it always was. The power meter is "lying", due to the power factor - energy is still being transferred - and the equipment must be sized to handle it - that is why Transformers and other things are often rated in VA instead of W. (Actually, KVA instead of KW.)

Now, if you are interested, and most power companies, engineers, and electricians are, then look at VAR. That is volts-amps reactive. There is a VAR power factor as well, simply the sine of the phase angle. In this case, again with 45 degrees, it is the same as the normal power factor, 0.707, however, we normally would call that -0.707, to differentiate between VAR (inductive) and VAR (capacitive).

Note that, if your phase angle is more than plus or minus 90 degrees, we are actually talking about a generator, instead of a load.

In practice, the phase angle is more like 20 to 30 degrees, so the power factor would be slightly higher, and the reactive power factor would be slightly lower. Power companies penalize large customers for poor power factors by measuring it and compensating their power meters or accounts to consider the perceived loss in energy or, more correctly, the increase in actual energy use. Also, poor power factor causes degradation of voltage on power lines, so power companies compensate with capacitor banks, shifting the phase angle back closer to zero

Answer 2

It's all to do with trigonometry. Apparent power is the vector-sum of true power and reactive power, and you can think of these three quantities forming a right-angled triangle (an oversimplification, but good enough for our purposes). Power factor is defined as the ratio of true power to apparent power, which corresponds to the ratio of adjacent to hypotenuse of this right-angled triangle. This ratio is called a cosine.