I am confused as to whether or not I should use the line to line voltage on a 3 phase motor or the line to neutral voltage to calculate power? Would someone please be able to fill me in, and possibly offer an explanation as to why? I do believe there are explanations explaining how the L-L and L-N voltages are related, but I need to know which one is used to calculate power. Thank you.
You can use both voltages to calculate power, but it yields to a different expression. If \$U_f\$ is the line to neutral voltage and \$i_L\$ the current in one the lines, then:
Now because line to line voltage \$U_L\$ is related to \$U_f\$ by \$U_L=\sqrt 3 U_f\$, then after substituting in the previous expression we have:
$$P=\sqrt 3U_Li_L\cos \phi$$