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Real Power, Apparent Power

Power Factor

Power Factor is a measure of how effectively electrical power is being used. A high power factor (approaching unity) indicates efficient use of the electrical distribution system while a low power factor indicates poor use of the system.


Many loads in industrial electrical distribution systems are inductive.


Examples include motors, transformers, fluorescent lighting ballasts, and induction furnaces.


The line current drawn by an inductive load consists of two components: 

Magnetizing Current 
The magnetizing current is the current required to sustain the electro-magnetic flux or field strength in the machine. This component of current creates reactive power that is measured in kilovolt-amperes reactive (kVAR). Reactive power doesn’t do useful “work,” but circulates between the generator and the load. It places a heavier drain on the power source, as well as on the power source’s distribution system.

Power Producing Current
The real (working) power-producing current is the current that reacts with the magnetic flux to produce the mechanical output of the motor.  

Real Power
is measured in kilowatts (kW) and can be read on a wattmeter.

Apparent Power is the total of Real (working) power and Reactive power together.  Apparent power is measured in kilovolt-amperes (kVA) 

Power Factor is the ratio of real power to apparent power.

To determine power factor (PF), divide real power (kW) by apparent power (kVA).

Power Factor triangle

The Power Triangle

In a sinusoidal system, the result is also referred to as the cosine. 

Another way to visualize power factor and demonstrate the relationship between kW, kVAR and kVA, is the right “power” triangle.


The hypotenuse of the triangle represents the apparent power (kVA) which is simply the system voltage multiplied by the amperage times the square root of three (for a three-phase system) divided by 1,000.


The right side of the triangle represents the reactive power (kVAR).


The base of the triangle represents the real or working power, measured in kW. The angle between the kW and kVA legs of the triangle is the phase angle cosine. 

Power factor is also referred to as leading or lagging. In the case of the magnetizing current, the power factor is lagging, in that the current follows the voltage waveform.


The amount of lag is the electrical phase angle between the voltage and the current. Power Factor is equal to the cosine of the phase angle between the voltage and current waveforms.

Excerpts taken from “Energy Management for Motor Driven Systems”,  Office of Industrial Technologies, Energy efficiency and renewable energy, US Department of Energy, Chapter 8 Power Factor Correction


Other great resources are: the US Motor Challenge Fact Sheet, “Reducing Power Factor Cost”, a Program of the Department of Energy and Railcar and Power Triangle from Con Edison website

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