In this paper there are given a few mathematical relations for the power analysis in un-sinusoidal regime. If the voltage is sinusoidal and the current is unsinusoidal, the apparent power will be ascertained by the active power, the fundamental displacement factor and on the current distortion factor. If the voltage and the current are un-sinusoidal, there will exist the optimum values for real parts of harmonics impedances that will minimize the apparent power. More interesting is the possibility of minimization the apparent power at constant mechanical powe