This work aims at allowing for increased penetration of renewable distributed generation (DG) in the power distribution system (DS). The means to achieve this goal is changing the DS topological structure, i.e. by network reconfiguration (NR). In this work, first, a method is presented to determine the maximum allowable DG capacity based on steady-state bus voltage and line current operating limits. DS meshed topology is then investigated as a potential solution to allow for an increased installed DG capacity. This is motivated by the impacts of meshed configuration on DS stiffness, which represents the relative strength of the DS at the DG Point of Interconnection (POI). A novel NR problem is then formulated to allow for higher DG penetration while maintaining operating constraints. Although conventional NR formulations include the constraint to keep a radial topology, the radiality constraint is relaxed in this work to consider both radial and meshed configurations. Moreover, in order to minimize the impacts of variable and intermittent DG output on system bus voltages, the relationship between the DS bus impedance matrix and bus voltage variations due to power output changes is derived and incorporated in the proposed NR problem formulation. Minimization of voltage variations at the POI and at remote buses of interest (e.g. voltage-sensitive loads or voltage regulating devices) are considered. The proposed NR method is then evaluated under various test cases, including different locations of DG installation, single and multi-DG cases, different DG power factors, and DS loading conditions. The presented NR scheme shows several added benefits, including robustness to system loading conditions, with consequent reduction in switching actions, and minimized operations of voltage regulating devices.