Power Factor 

By on

ComplexPower
Power Factor
Power factor is the ratio between the real power (P in kW) and apparent power (S in kVA) drawn by an electrical load. 

The reactive power (Q in kVAr) causes the real and apparent power to be displaced from each other.  Reactive power provides the necessity for electric and magnetic fields to enable the power system to work.

In addition to being the ratio of real power to apparent power, the power factor can also be express as the cosine of the angle between the two.

image03

If the reactive power of the load is inductive, the real power will lag the apparent power and the power factor will be lagging.  If the reactive power is capacitive the power factor will be leading.

In it's simplest form power factor, can also be considered a measure of the useful work obtained from a power system

Three phase power factor and single phase power factor follow the same concepts

For a theoretical discussion of power factor, see the section on Complex Power on the Alternating Current Circuits note.

Typical Power Factors

Average Power Factor values for the most commonly used plant, equipment and appearances:

plant and appliances cos φ tan φ
induction motor - loaded at 0% 0.17 2.80
induction motor - loaded at 25% 0.55 1.52
induction motor - loaded at 50% 0.73 0.94
induction motor - loaded at 75% 0.80 0.75
induction motor - loaded at 100% 0.85 0.62
lamps incandescent 1.0 0
lamps fluorescent (uncompensated) 0.5 1.73
lamps fluorescent (compensated) 0.93 0.39
lamps discharge 0.4 to 0.6 2.29 to 1.33
oven resistance elements 1.0 0
oven induction heating (compensated) 0.85 0.62
oven dielectric heating 0.85 0.62
resistance type soldering machines 0.8 to 0.9 0.75 to 0.48
arc-welding fixed 1-phase 0.5 1.73
arc-welding motor-generator set 0.7 to 0.9 1.02 to 0.48
arc-welding transformer-rectifier set 0.7 to 0.8 1.02 to 0.75
arc furnace 0.8 0.75

Source: Groupe Schneider - Electrical installation guide
(According to IEC International Standards), 1996

Harmonic Distorted Waveforms

Example - true power factor

A load is operating with a displacement power factor of 0.875 and THD of 13.4%.  What is the true power factor?

The distortion power factor is given by:

Image(41) 

Resulting in a true power factor of:

Image(42)

Power factor as set up above assumes a sinusoidal wave form.  In a modern power system with the growth of power electronic devices, the waveform is generally not sinusoidal.  In this instance the definition of power factor becomes a little more complicated. 

  • displacement power factor - is the power factor of the 50 Hz fundamental for a harmonic distorted waveform
  • distortion power factor - is the amount the displacement power is reduced due to harmonic content
  • true power factor - is the actual power factor, taking into account the harmonic distortion

In a non-sinusoidal waveform the harmonic content reduces the power delivered to the load.  True power factor will always be less than the displacement power factor. The ratio of the true power factor to the displacement power factor is the distortion power factor.  For purely sinusoidal waveforms the distortion power factor is always 1. 

If the total harmonic distortion is know, then the distortion power factor can be found from:

Image(39)

Image(40)

Power Factor Correction

Calculation of Required kVAr

Existing Situation is defined as load P in kW with power factor pf1  (assume lagging)

Leading  to, complex power S1 in kVA
image12

Current Phase angle φ1 is given by: 
image13

The desired situation is defined as new power factor pf2
New Phase angle φ2 is give by: 
image14

Required compensation Q2 in kVAr: 
image15  and image16 

Numerical Example

Existing Situation: P = 450 kW pf1 = 0.83
S1 = 450/0.83 = 542 kVA

φ1 = cos-1(0.83) = 33.9 degrees

Desired Situation: pf2 = 0.95 
φ2 = cos-1(0.95) = 18.2 degrees

Calculation Results:
Q2 = 450 * (tan(33.9)-tan(18.2)) = 154 kVAr

S2 = 450/0.95 = 473 kVA (12.7% reduction)

By improving the power factor, power supply authorities need to generate less reactive power and power distribution systems become more efficient.  Power supply authorities often charge a penalty for power factor and it can be financially beneficial for the owner of equipment to provide systems to improve their power factor.

Power factor correction is typically carried out by the addition of capacitors – creating reactive power 180o out of phase with that created by the loads (typically inductive).

Power factor correction may be applied as bulk correction at the main plant switchboard or installed locally at each load.

 image04

 

image05

 

image06

If the kW is to remain constant then:

 image07

and

image08

giving:

image09

image10

image11

Power Factor Correction Tool

0042_PFC
Power Factor
Correction Unit

The calculation of the amount of reactive power required to achieve a given improvement is relatively easy to calculate.

To assist in the calculation of required power factor compensation we have added a power factor correction calculation tool to our site. See the links below for details.



Steven McFadyen's avatar Steven McFadyen

Steven has over twenty five years experience working on some of the largest construction projects. He has a deep technical understanding of electrical engineering and is keen to share this knowledge. About the author

myElectrical Engineering

comments powered by Disqus

  1. Sinnadurai's avatar Sinnadurai says:
    7/11/2012 11:56 AM

    Why is the pfc disconnected when a standby generator feeds the load?

    • Steven's avatar Steven says:
      7/11/2012 12:38 PM

      It is not the power factor correction per say, but the possibility of leading power factors which are not good for generators. Generators have a limited ability to absorb real or reactive power (as opposed to normal power systems which are usually much bigger than any load).

      Best thing is to manage the power factor well. Switching off seems an easy approach, but you need to be careful that the actual power factor is not so low as to exceed the generator kVA rating.


Comments are closed for this post:
  • have a question or need help, please use our Questions Section
  • spotted an error or have additional info that you think should be in this post, feel free to Contact Us



HTML Symbol Entities

HTML supports a variety of entity symbols which can be entered using either numbers or an entity name.  The number or name is preceded by the ‘&’ sign...

Cost Performance and Time

Often us engineers get so bogged down in equations, using software, producing drawings and writing specifications that this becomes the sole focus.   ...

Hazardous Areas – IEC and NEC/CEC Comparison

Depending where in the world you work, you are likely following one of two standards International Electrotechnical Commission (IEC) National...

Cable Sheath and Armour Loss

When sizing cables, the heat generated  by losses within any sheath or armour need to be evaluated. When significant, it becomes a factor to be considered...

Generation of a Sine Wave

A fundamental concept behind the operation of alternating current systems is that voltage and current waveforms will be sinusoidal – a Sine Wave. This...

Capacitor Theory

Capacitors are widely used in electrical engineering for functions such as energy storage, power factor correction, voltage compensation and many others...

Surface Treatment – Ladders, Trays and Baskets

Steel ladders, trays and baskets form the backbone of cable containment systems. Often these items need some form of surface treatment to prevent corrosion...

Microsoft OneNote

A couple of months ago I came Microsoft's OneNote and downloaded the 60 day free trail. Since then I have been using it regularly and now have a full license...

Arc Flash Calculations

Working in the vicinity of electrical equipment poses an hazard. In addition to electric shock hazard, fault currents passing through air causes Arc Flash...

Voltage Levels to IEC 60038

The standard aims to consolidate AC and traction voltages within the industry and defines the following bands: band 1 - A.C. systems 100 V to 1...

Have some knowledge to share

If you have some expert knowledge or experience, why not consider sharing this with our community.  

By writing an electrical note, you will be educating our users and at the same time promoting your expertise within the engineering community.

To get started and understand our policy, you can read our How to Write an Electrical Note