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Urban demographics are changing, with more than half of the global population currently residing in urban areas. Traditionally, cities are often seen as passive energy consumers relying on external centralized systems. Motivated by the need to mitigate climate change, a shift is underway as cities actively shape energy systems. This shift involves decentralized power generation, electric vehicle (EV)-related electricity usage shifts, enhanced building energy efficiency, and increasing interaction between local power generation and load. This poses some challenges to distribution grid operation such as voltage violation, decreased power quality, equipment damage, power losses, and reliability issues. Addressing these issues requires load flow analysis, and to quantify the impacts based on load flow analysis, the hosting capacity concept has been introduced. Although traditional load flow analysis lacks uncertainty consideration, the growth of distributed photovoltaics (PV) generation and EVs demands enhanced accuracy through uncertainty modeling.

This thesis contributes to the knowledge of how uncertainty and correlation models can improve the quality of load flow and hosting capacity analysis for urban electricity distribution systems with high penetration of residential PV systems and EVs through the combination of methodological and case studies. Methodological studies propose uncertainty models for input variables and investigate their impact on load flow and hosting capacity assessment. Case studies demonstrate enhanced hosting capacity analysis quality through applied uncertainty models.

Results show that concentrated allocation of PV systems and EVs had more severe impacts, in particular at lower penetration levels, and smart charging in concentrated allocation had more significant benefits to reduce peak load and voltage drop. Results regarding residential building roofs show that the inclusion of more residential buildings when the PV penetration increases will require including a lot of less-optimal facets, and, hence, a novel method has been proposed to proportionally include less optimal roofs at every penetration level. The smart charging scheme, which has as its main objective to reduce the net-load variability, improves the electricity distribution system performance, and combined with PV curtailment, can further increase the hosting capacity. An increase in correlations between nodes is also observed due to this smart charging scheme. The city-level simulations show that the distribution system of the city can accommodate a 90% penetration level of PV with less than 1% risk of overvoltage and line loading does not limit the hosting capacity. The method used to model roof facet orientation proves effective for city level applications, given its simplicity and effectiveness.

In summary, this thesis concludes that the quality and knowledge of load flow and hosting capacity analysis for urban electricity distribution systems can be improved by several methods, including: the probabilistic model of PV power generation and EV charging profiles, the inclusion of EMS, the consideration of spatial allocation methods of PV and EV, the assessment of the correlation between PV and EV, and the consideration of rooftop tilt and azimuth uncertainties.