With the penetration of PV on the distribution system continually increasing, new advanced simulation methods are necessary to model the potential technical impacts of PV to the equipment and operation of the distribution system. With distributed PV, a timeseries analysis approach is necessary to more fully capture the time-varying nature of solar energy and the interaction with distribution system operations. The objective of the research is to streamline the PV interconnection process by providing more accurate methods that require less time for both the PV interconnection screening criteria and the PV interconnection impact study process. To improve the computational speed of timeseries simulations, an equivalent circuit reduction method is developed to simplify the circuit to a reduced-order model. The reduced circuit is equivalent during timeseries simulations, but it solves in a fraction of the time. The algorithm works with unbalanced multi-phase complex distribution system models, and it is shown to have high accuracy when validated against the full feeder models. An advanced PV hosting capacity simulation tool is developed and used to quantify system impacts for many PV interconnection scenarios, configurations, and locations, which can be generalized to develop improved future interconnection screening criteria. The advanced tools quantify location-specific impacts and the locational hosting capacity of potential PV interconnection locations on the feeder, including PV impact signatures and zones. A set of 50 different real distribution systems is analyzed in detail to demonstrate the range of scenarios and impacts that can occur depending on the feeder characteristics and topology. Specific methods are developed for time-series analysis, faster simulation times, distribution system equivalent circuit reduction, and PV hosting capacity analysis. The advancements presented in this thesis assist in streamlining PV interconnection studies with faster interconnection analysis times and more accurate screening criteria.