Three Phase A.C Supply: Explained

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SUMMARY

The discussion clarifies the relationship between line voltage and phase voltage in a three-phase AC supply system, specifically in the European context of 230V/400V. The voltage across any two lines is 400 volts due to the 120-degree phase shift, while the voltage across each line to ground is 230 volts. The calculation for line voltage is derived from the formula 2 x 230V x cos(30°), resulting in approximately 400 volts. Understanding this relationship is crucial for anyone working with three-phase systems.

PREREQUISITES
  • Understanding of three-phase AC supply systems
  • Familiarity with RMS voltage calculations
  • Knowledge of trigonometric functions in electrical engineering
  • Basic electrical circuit theory
NEXT STEPS
  • Study the derivation of line voltage in three-phase systems
  • Learn about the implications of phase shifts in AC circuits
  • Explore the differences between European and US three-phase systems
  • Investigate the use of phasor diagrams in electrical engineering
USEFUL FOR

Electrical engineers, technicians working with three-phase systems, and students studying electrical engineering concepts will benefit from this discussion.

FizixFreak
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i was reading three phase ac supply and this statement is quite confusing ''because of the 120 degrees phase shift the voltage across any two lines is 400 volts (the voltage across each of the lines connected to the terminals is 230 volts)
can anybody please explain it??
 
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FizixFreak said:
i was reading three phase ac supply and this statement is quite confusing ''because of the 120 degrees phase shift the voltage across any two lines is 400 volts (the voltage across each of the lines connected to the terminals is 230 volts)
can anybody please explain it??


What do you find confusing about it? How they came up with the 400 volts?

CS
 
Assuming you mean european 230v/415V - 3phase (the answer is slightly different for US 120v 3phase but by coincidence some of the numbers are close enough to be confusing.)

A single phase measured relative to the ground varies between 0 and about 325V - with an RMS value of 230V =peak voltage divided by root(2).
The maximum voltage difference between any two phases is about 400V = RMS voltage * root(3)
 
the line voltage is the voltage "difference" of two phase voltages... that means one phase voltage should be reversed and added to another phase.. than u'll have 2x230xcos(30) as the line voltage (\approx400)... (check for the attachment, then u'll get a better idea)
 

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Last edited:
Asok said:
the line voltage is the voltage "difference" of two phase voltages... that means one phase voltage should be reversed and added to another phase.. than u'll have 2x230xcos(30) as the line voltage (\approx400)... (check for the attachment, then u'll get a better idea)

rookie question
how do you came up with 2(230)cos(30) and why 30?
 
Asok drew a picture showing very nicely exactly where the 30º came from. Please look at the picture and if you don't understand that then ask a specific question about it.
 

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