Understanding Power Factor

In my opinion, the key to understanding the fundamentals of AC electricity is understanding the basic relationships in the “Power Triangle.”

RULE #1: Power Factor is NEVER determined by the SOURCE…but ONLY by the LOAD.

The Power Triangle is a comprehensive conceptual model as much as a mathematical one. It is a graphical representation and explanation of how each of its major components relate to one another. Since the model is a right triangle, each of the legs and hypotenuse can be calculated using the Pythagorean theorem, a2 + b2 = c2, provided two out of three values are known.

The center of attention in the Power Triangle is the “Power Factor” (PF) and everything revolves around it.

PF = Cos (Phase Angle) = KW / KVA

OR

PF = Sin (Phase Angle) = KVAR / KVA

Where: P = True Power [KW], S = Apparent Power [KVA], Q = Reactive Power [KVAR], Phase Angle = angle in degrees between Voltage and Current

By using basic trigonometry and geometry, we can manipulate different forms of the same electrical relationship as shown in the above diagram. Notice that since 3-phase relationships and Pythagorean equations are dealing with squares and the square root of 3, the relationships are quadratic (or exponential) functions…non-linear.

Causes and Effects

For the sake of visualizing how the Power Triangle works, the following causes and effects occur mathematically as a function of a square for a mostly “inductive” load. If the Reactive Power increases, KVA and the Phase Angle also increases. If Reactive Power decreases, KVA and the Phase Angle also decreases. If Reactive Power = 0, then KVA = KW, Phase Angle = 0 degrees, and Power Factor (PF) = 1 (“unity” Power Factor). NOTE: This is because any number divided by itself = 1 and Cos (0) = 1. It can be seen that Power Factor is always between 0 and 1, and 1 is best. These causes and effects are constantly in motion as the LOAD becomes more or less reactive (in this case, “inductive”).

For a mostly “capacitive” load, the triangle would be flipped downward as if the KW side was hinged with KVAR going down in the negative direction. Again, the same causes and effects are constantly in motion as the LOAD becomes more or less reactive (in this case, “capacitive”).

Some people compare this relationship to a glass of beer as follows: The foam is the KVAR, the beer is the KW, and the sum total level in the glass is the KVA. The only part that actually quenches the thirst is the beer, not the foam. So, the KVAR represents wasted power due to reactance. Facilities that run lots of induction motors have high levels of reactance which causes a low power factor (PF). Power companies will fine companies for running with a low Power Factor (PF) because they are wasting power that is not being paid for. Also, they are negatively affecting the power quality of their neighbors by creating high-reactance noise and excessive load to the grid. Excessive load due to wasted power can also cause unnecessary power outages and “brownouts.” To bring the Power Factor back up, the end user must install a capacitor bank to counter-act the effects of inductance by adding capacitance to the LOAD and make it less inductive. Thus, creating a more efficient electrical system. Kind of like having more ice-cold beer on a hot day with less foam.

An old analogy from my early school days uses a catchy phrase called “ELI the ICE man.” The acronyms, ELI and ICE stand for the following:

ELI = Voltage (E)…Inductance (L)…Current (I). This means when the LOAD is mostly inductive, the Power Factor is said to be “lagging”…because the current “lags” the voltage.

ICE = Current (I)…Capacitance (C)…Voltage (E). This means when the LOAD is mostly capacitive, the Power Factor is “leading”…because the current “leads” the voltage.

If an industrial plant runs many 3-phase induction motors, the primary load will be mostly Inductive. It is rare for the primary load to be mostly capacitive.

Therefore, using “ELI the ICE man”…

If KVAR is positive, the LOAD is mostly “Inductive” and the PF is “lagging.”

If KVAR is negative, the LOAD is mostly “Capacitive” and the PF is “leading.”

Remember RULE #1…Power Factor is NEVER determined by the SOURCE…but ONLY by the LOAD.