Power Factor

       Power factor is one of the most important topics in the field of electrical engineering, because of  its direct impact on the cost of energy. Before we can derive a definition of power factor, we must distinguish between three types of electrical power.

First: the apparent power (S)   

current triangle 

     It represents the total electric power which giving to the loads to execute its function., It calculated by multiplying the voltage by  the current, so it measured in volt ampere (VA) or kilo volt ampere (KVA). For example, a 500  KVA transformer means that,  the direct product of  the current and the voltage across its terminal is equal to 500,000 (usually transformer capacity measured in kilo volt ampere because the transformer is a static device, don't consumes the current, its input is voltage and current, and its output is voltage and current). 

Second: the Active or True or Real power (P) 

      It represents the true power which converted into motion in motors,light in lamps, heat in heaters, etc . For a single phase ac circuit, the active power is equal to the product of the current and the voltage and cosine phi (where phi is the angle between the voltage wave and the current wave). It measured in watt (W) or kilo watt (KW). For example, a 100 watt 220 volt tungsten bulb means that, the bulb consumes current equal to 100 watt divided by the product of  voltage and cosine phi =100/(220*1) = 0.45 ampere, to emit a specific amount of light. While if the bulb is 150 watt, it consume a higher current =150/(220*1) = 0.68 ampere, to emit a higher amount of light.

 Third: the Reactive power (Q) 

power triangle 

       It represents the power which consumed by the load without converting into useful power. For example, the power consumed in magnetizing coils in induction motors is reactive power, because the motor consumes it without translate it into motion. It measured in volt ampere reactive (VAR) or kilo volt ampere reactive (KVAR). It equal to the product of the voltage and the current and sine phi (where phi is the angle between the voltage wave and the current wave).

 Power factor (pf)
       Now we can easily  derive the power factor definition, power factor is the ratio of the active power which  can be used practically as light or motion or heat to the apparent  power.
pf = VI cos phi / VI = cos phi.

Power triangle 
         The current in ac circuits divided into two components, the active current and the reactive current. The directional summation of the two components give the total consumed current. This shown in the figure "current triangle". Now we can derive another definition for the power factor, power factor is the ratio of the active current to the total current.
pf = I cos phi / I = cos phi.
        The power triangle generated by multiplying each side of the current triangle by V, so the ratio between the active current and the total current, is equal to the ratio between the active power and the apparent power. Power factor is a dimensionless quantity, its value ranging between 0 and 1,so it can be expressed in decimal or  percentage.Thus power factor of 0.8 is the same as 80 percent.