# Calculation of Phase Angle Diversity for Time-Varying Harmonic Currents from Grid Measurement

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1. Introduction

Number and variety of non-linear devices and installations used by residential and commercial customers are increasing continuously. Therefore the effect of harmonics in the network is more and more considered in both the planning and the operation of distribution systems. This analysis is not always easy, because multiple factors influence the emission and propagation of harmonics through the network, like the network impedance, the voltage distortion and the time-variation of number and type of connected equipment.

One of the key aspects of a realistic harmonic analysis is a correct representation of summation of harmonic currents. The presence of different devices with different topologies at one connection point can cause a diversity of current harmonic phase angles and subsequently may lead to a lower magnitude of vector sum than the arithmetical sum of the harmonic currents [1]. This is known as diversity effect (or cancellation effect) and has a high influence on the total harmonic distortion emitted by larger groups of non-linear loads into the grid. Different indices like summation exponent and diversity factor exist to quantify the effect.

Most of the papers that address the summation of harmonic currents consider only the effect of few devices in a single moment of time or a perfect steady state of harmonics [e.g. [2-5]). If variation of system, load and generation are considered, the problem becomes time-varying and an additional statistical post-processing is required in order to calculate aggregated diversity indices. The parameters and methods used for the post-processing can have a considerable impact on the calculated diversity index. Furthermore, the accuracy of these indices depends also on t...

... middle of paper ...

...l (3) covers always the whole dataset and is therefore also fix for the study.

In the case of aggregation interval (1), three different cases were selected: No aggregation (10 period values), 1min aggregation and 10min aggregation. For the aggregation of harmonic angles, the vector sum of the corresponding currents inside the aggregation interval was calculated, and the resulting angle of this sum was used as the aggregated value. As assessment quantile (4) the impact of 95th vs. 99th quantile are analyzed. Finally different statistical calculation methods (5) can be applied to find those quantiles. In this study the following two methods will be compared:

• Method 1: and are calculated as quantiles based on the instantaneous calculated diversity factors and summation exponents.
• Method 2: and are calculated based on harmonic magnitudes and angle quantiles.

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