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When analysing a power system using the per-unit system for a three phase system, why is \$S_b = \sqrt{3}*V_b*I_b\$, where as shown in the link, \$S_b\$ is the base power value, \$V_b\$ is the base voltage value and \$I_b\$ is the base current value?

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    \$\begingroup\$ What is §b, Vb and Ib? \$\endgroup\$
    – Andy aka
    Commented Mar 10, 2014 at 11:15
  • \$\begingroup\$ Sorry about that, I was getting used to MathJax. \$\endgroup\$
    – Seanny123
    Commented Mar 10, 2014 at 11:45
  • \$\begingroup\$ Are you ok with the sqrt 3 or is it the problem? \$\endgroup\$
    – Andy aka
    Commented Mar 10, 2014 at 12:15
  • \$\begingroup\$ The sqrt(3) is the problem. \$\endgroup\$
    – Seanny123
    Commented Mar 10, 2014 at 12:19
  • \$\begingroup\$ Do you understand why sqrt3 is used in regular 3 phase for converting phase voltage to line voltage? In other words is this a general 3-phase question about sqrt3. I'm asking this because I'm not familiar with the per-unit system but I know standard 3-phase stuff. \$\endgroup\$
    – Andy aka
    Commented Mar 10, 2014 at 13:08

1 Answer 1

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Three phase circuits in power systems can be connected in two ways, delta connection or a wye connection. Luckily, both of these circuits have the same equation for apparent power.

\$S=\sqrt{3}VI\text{*}\$

It is this insight that allows for the current formula, despite the relation between line/phase voltage/current being different for the delta and the wye circuit.

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  • \$\begingroup\$ It's better to emphasise the voltage is phase-to-phase. \$\endgroup\$
    – Edward
    Commented Sep 30, 2021 at 12:40

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