A grid harmonic summation method based on the probability assessment of harmonic phase angles

The summation of two harmonic voltage vectors at same frequency is only certain if their amplitudes and phase angles are well known. Therefore, there are many cases where the difference of phase angles between harmonic voltage vectors is unknown. In calculation of the steady state rating of the a.c. harmonic filter equipment, algebraic summation method is often used in determining maximal harmonic level. This summation law is very conservative as it may result in high cost of equipment ratings. Actually, a compromise should be made in taking into account the equipment safety and the risk of overrating as well as excessive costs. Based on uniform distribution of difference in phase angles, the paper provides an algorithm to calculate the probability upon which the magnitude of summation vector of two harmonic voltages may exceed a given value. This result may be applied in passive harmonic filter design in order to cut down the excessive over cost, and may be served as harmonic assessment guidance used in evaluating and setting grid power quality commitment.