A novel application of sensitivity analysis to evaluate solar photovoltaic (PV) impacts on power distribution systems is proposed. The fast Quasi-Static Time Series (QSTS) algorithm, developed in this work, accurately estimates both the voltage and current-related solar PV impacts in distribution feeders with various voltage regulation (VR) devices, including load tap changing transformers, line voltage regulators, switching capacitor banks and smart inverters. The sensitivity coefficients for each node are estimated using a novel regression based perturb-and-observe technique, which is scalable to any number of input time series profiles and VR devices. These sensitivity coefficients represent a local linearization of the nonlinear AC power flow manifold (PFM), and allow for a quick estimation of the nodal voltage and branch current magnitude. Furthermore, the impact of VR device operation on the PFM is extensively investigated. It is shown that a change in VR device state causes discontinuities in the PFM, which requires recomputation of the network sensitivities. The proposed algorithm shows an average speed gain of 150 times over the brute-force QSTS method while maintaining low error thresholds. These findings suggest that linear sensitivities can be leveraged to accurately analyze distributed generation impacts. ; Ph.D.