# How is the formula for the base current value derived in a three-phase per-unit system?

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?

• What is §b, Vb and Ib? – Andy aka Mar 10 '14 at 11:15
• Sorry about that, I was getting used to MathJax. – Seanny123 Mar 10 '14 at 11:45
• Are you ok with the sqrt 3 or is it the problem? – Andy aka Mar 10 '14 at 12:15
• The sqrt(3) is the problem. – Seanny123 Mar 10 '14 at 12:19
• 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. – Andy aka Mar 10 '14 at 13:08

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.