The energy system is being transitioned to increase sustainability. This transition has been accelerated by the increased awareness about the adverse effects of the greenhouse gas (GHG) emissions into the atmosphere. The transition includes switching to electricity as the energy carrier in some sectors, e.g., transportation, increasing the contribution of renewable energy sources (RES) to the grid, and digitalizing the grid services. Electric vehicles (EVs) are promoted and subsidized in many countries among the sustainability initiatives. Consequently, the global sales of EVs rapidly increased in the recent years. Many EV owners might charge their EVs only at home, thereby increasing the residential load. The residential load might further increase due to the initiatives to electrify the heating/cooling sector. This thesis contributes to the knowledge about the operation of the future energy system by modeling the spatial charging load of private EVs in cities, and by proposing a forecasting model to predict the residential load. Both models can be used to evaluate the impacts of both technologies on the local electricity grid. In addition, demand response (DR) schemes can be proposed to reduce the adverse effects of both the charging load of EVs and the residential load. A case study of the EV model on the Herrljunga city grid showed that 100% EV penetration with 3.7 kW (charging rate of 14.8 km/h) chargers will not cause voltage violations in the grid. Winter load is responsible for 5% voltage drop at the weakest bus, and EVs add only 1% to this drop. In a Swedish city, charging EVs will require adding extra 1.43 kW/car to the grid capacity—assuming 22 kW (charging rate of 88 km/h) residential chargers. If the EV charging is not restricted to residential locations, an increase of 1.23 kW/car is expected. The proposed forecasting model is comparable in accuracy to previously developed models. As an advantage, the model produces a probability density function (PDF) describing the model’s certainty in the forecast. In contrast, many previous contributions provided only point forecasts.