Preliminary analysis of MV over-headlines models for high frequency harmonic penetration studies in the new scenario of smart grids

In the new scenario of Smart Grids, the distribution systems and Micro-grids will use more and more Power Electronics devices to interface loads, dispersed generation, storage systems and other single components or sub-systems. The switching frequencies adopted by new generation power electronic apparatus are increasing, thanks to the availability of faster high power switches, to increase efficiency and controllability. This trend is changing the scenario of the harmonic pollution analyses and the traditional interval of frequencies of interest (0 - 2.5 kHz), recently extended (2.5 - 9.0 kHz), should be substituted by a wider interval (0 -100 kHz). One of the main problems for the assessment of the high frequency harmonic penetration in the networks is modeling traditional and new components at higher frequencies accounting for phenomena (skin effects, proximity effects, capacitive couplings, parameter variability with frequency, ...) that do not play a relevant role in the low frequency traditional range. In the paper, the behavior of MV over-head lines is considered in the frequency range from 0 to 100 kHz for positive and zero sequences. First a comparison of DP model with N models based on concentrated equivalent Π circuits in cascade is reported and then a very simple case-study based on time domain simulation and referred to a typical case in smart grids is commented. The main outcomes of the paper are: • in the frequency range from 2.5 kHz to 9 kHz, which is the upper limit of the low-frequency range considered by IEC Standards, only one Π equivalent is not enough to assure a satisfying accuracy; • for numerical simulation purposes, Distributed Parameters models, when available, are suggested because of their accuracy and computational efficiency; • for the experimental emulation of MV lines (e.g. for small scale Smart Grids prototypes), models based on cascade of numerous Π equivalent circuits are needed to obtain acceptable accuracy levels: up to 9 kHz, cascades of few equivalent circuits seem to be enough in terms of accuracy to model the first low frequency resonances; up to 100 kHz, cascades of equivalents by tens are necessary to model the numerous series and parallel resonances that are present.