Three Phase A.C Supply: Explained

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Discussion Overview

The discussion revolves around the concept of three-phase AC supply, specifically addressing the voltage relationships between phases, including the confusion surrounding the 120-degree phase shift and the resulting line voltages of 230 volts and 400 volts.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants express confusion about the statement regarding the 120-degree phase shift and how it leads to a line voltage of 400 volts while each line voltage is 230 volts.
  • One participant clarifies that in a European context, the 230V/415V three-phase system is being discussed, noting that the maximum voltage difference between any two phases is approximately 400V, calculated as RMS voltage multiplied by the square root of 3.
  • Another participant explains that the line voltage is derived from the voltage difference between two phase voltages, suggesting a calculation involving the cosine of 30 degrees.
  • A participant questions the derivation of the formula 2(230)cos(30) and the relevance of the angle 30 degrees, indicating a need for further clarification.
  • A later reply mentions a visual aid provided by another participant to illustrate the origin of the 30-degree angle in the calculations.

Areas of Agreement / Disagreement

Participants generally agree on the basic principles of three-phase AC supply but express differing levels of understanding regarding the calculations and concepts involved, indicating that the discussion remains unresolved in terms of clarity for some participants.

Contextual Notes

There are assumptions regarding the definitions of line and phase voltages, and the discussion does not resolve the specific mathematical steps or the reasoning behind the use of the cosine function in the voltage calculations.

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)
 

Attachments

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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