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• A dynamic equivalent modelling approach for the representation and analysis of the dynamic performance of distribution networks with high penetration of Electric Vehicles (EVs) is developed. • The influence of EV charger control parameters on the resulting dynamic responses and modelling needs is investigated. • The impact of EV penetration level on the dynamic behavior of distribution networks is analysed. • The variability of model parameters under different EV penetration levels is presented. During the last few years, there is a worldwide drive for the electrification of the transportation sector to achieve reduced carbon emissions. In this context, the global fleet of electric vehicles (EVs) is steadily increasing. Consequently, in the near future, EVs will become a significant part of the overall power demand. Therefore, the distinct characteristics of the power converters, used in EV charging stations, will have a clear impact on power system dynamics. Therefore, new methods and models are required to simulate and analyse the dynamic performance of distribution networks (DNs) hosting EVs as well as to represent their aggregated dynamic behaviour for transmission level dynamic studies. Towards this objective, in this paper, an equivalent model, based on variable order transfer functions, is proposed to analyse the dynamic properties of EVs as well as to simulate the dynamic behavior of EV-rich DNs. Initially, a sensitivity analysis is performed to quantify the influence of the different control settings of the EV chargers on the resulting dynamics. The analysis reveals that control settings affect considerably the underlying dynamics. Nevertheless, in all cases the proposed equivalent model provides very accurate estimates. Moreover, the impact of EV penetration level on DN dynamics is quantified using a set of metrics. Additionally, a parametric analysis is conducted to verify the applicability of the proposed equivalent model for the dynamic analysis of DNs under specific EV penetration levels. Finally, guidelines for the derivation of generic parameters for the developed equivalent model are proposed. [ABSTRACT FROM AUTHOR]