Harmonic summation and assessment based on probability distribution of phase angle

At the point of common coupling (PCC), 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 phase angle difference between harmonic voltage vectors is unknown. In practice, for example, in calculating the steady state rating of the a.c. passive harmonic filter, arithmetic 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. On the basis of the probability and the given harmonic value, harmonic summation can be assessed. This may also result in a recommendation of another harmonic summation method for the standard IEC/TR 61000-3-6.