Topic > Calculation of phase angle diversity for variations over time...

1. IntroductionThe number and variety of nonlinear devices and installations used by residential and commercial customers are continually increasing. Therefore the effect of harmonics in the network is increasingly considered in both the design and operation of distribution systems. This analysis is not always easy, because multiple factors influence the emission and propagation of harmonics through the network, such as network impedance, voltage distortion and the variation over time in the number and type of connected equipment. One of the key aspects of realistic harmonic analysis is a correct representation of the sum of harmonic currents. The presence of different devices with different topologies at a connection point can cause a diversity of the harmonic phase angles of the current and subsequently can lead to a smaller magnitude of the vector sum than the arithmetic sum of the harmonic currents [1]. This is known as the diversity effect (or cancellation effect) and has a strong influence on the total harmonic distortion emitted by larger groups of nonlinear loads in the network. There are several indices such as sum exponent and diversity factor to quantify the effect. Most papers addressing the sum of harmonic currents only consider the effect of a few devices at a single moment of time or a perfect steady state of harmonics [e.g. [2-5]). If system, load and generation variations are considered, the problem becomes time-varying and further statistical post-processing is required to calculate the aggregate diversity indices. The parameters and methods used for post-processing can have a considerable impact on the calculated diversity index. Furthermore, the accuracy of these indices also depends on t...... half of the document ......l (3) always covers the entire dataset and is therefore also fixed for the study. In the case of the aggregation interval (1), three different cases were selected: no aggregation (10 period values), 1 minute aggregation and 10 minute aggregation. For the aggregation of the harmonic angles, the vector sum of the corresponding currents within the aggregation range was calculated and the resulting angle of this sum was used as the aggregate value. As evaluation quantile (4), the impact of the 95th compared to the 99th quantile is analyzed. Finally, different statistical calculation methods can be applied to find these quantiles (5). In this study the following two methods will be compared:• Method 1: and are calculated as quantiles based on the instantaneously calculated diversity factors and sum exponents.• Method 2: and are calculated based on the harmonic quantities and angular quantiles.