Symmetrical three-phase power flow problem, √3
The \$\sqrt(3) \$ comes from resolving 3phase power when the voltage is in line voltage NOT phase voltage.

As you wrote: 


  For symmetrical thee-phase power systems, the equation for complex
  power is:
  
  \$S=\sqrt3UI∗\$
  
  where U is the voltage between two conductors. This voltage between
  conductors is always the value referred to, when talking about the
  voltage level of an electric distribution network.


The power in a 3phase system is 3*I*V where I is the phase current and V is the phase voltage.  Your statement is with regards to line-line voltage. line-line voltage is \$\sqrt3\$ larger THUS

\$P = 3 \frac{U}{\sqrt3}I \$  where U is line-line voltage, I is phase voltage

via surds: \$\frac{3}{\sqrt3}= \sqrt3 \$ 

Thus \$P = 3 \frac{U}{\sqrt3}I = \sqrt3UI\$