The rapidly growing market for electric vehicles (EVs) and chargers has a considerable influence on the operation of the distribution network. Accurate evaluation of the number of EVs penetrating the distribution network, that is, the hosting capacity (HC) of EVs, is beneficial to distribution network planning and efficient operation. Further, EVs have uncertainties in terms of arrival time, departure time, battery state of charge (SOC), and choice of charging station, which collectively affect the system difficult, but important, step of modeling EV uncertainties on system performance. This paper presents a methodology to model how many EVs can penetrate a low voltage distribution network, especially microgrid. First, EV load modeling incorporating uncertainties is performed by applying interval and affine arithmetic. Second, to analyze the effects of voltage, the same arithmetic methods are extended to perform power flow calculation. Thirdly, interval undervoltage probability (IUP) is introduced to evaluate the HC of the EVs. Subsequently, a voltage violation index (VVI) is introduced, and an EV HC evaluation method is proposed, assisting in the flexible operation of the network based on VVI. The utility of the proposed method is demonstrated by modeling the network of Seoul National University in South Korea, which is subsequently compared with the conventional approach of determining EV HC. The model incorporated Seoul National University's practical cable data, load data, and vehicle access data, along with the number of EVs penetrating the target network.INDEX TERMS Affine arithmetic, distribution network, electric vehicle, electric vehicle hosting capacity, interval arithmetic, uncertainties, under voltage probability.