Complex Power

Power loss within a cable is calculated using the theory of Complex Power:

$S=Z\times I\times I^{*}$

where:
S = complex power ( = P + jQ ), in VA
Z = cable positive sequence impedance ( = R + jX ) in Ω
I = cable current (complex form), in A
* = the conjugate of the current

By applying the complex power cable, the losses in watts can be found by taking the real part of the result.  The reactive power requirement in VAr are given by the imaginary part.

The abve gives the power loss per core. For d.c. and a.c. single phase the power loss is twice that given above.  For three phase multiple by 3.

Power Loss Using Resistance

Power loss within a cable can also be estimated from the cable current and resistance:

$P=I^{2}R\times n$

where:
P        =        power loss, W
I         =        cable design current, A
R        =        cable resistance, Ω
n        =        factor depending on circuit type/number of conductors
                        = 2 for a.c. single phase, d.c. circuits
                        = 3 for a.c. three phase circuits (assumed balanced)

Note: for unbalance circuits the total power loss can be obtained by calculating the loss in conductor ( I_c²R_c ) and summing the losses in each conductor.