Power grids constitute an essential infrastructure providing and distributing electrical energy. The grid structure is currently subject to rapid changes due to the integration of renewable energy sources. In this development one is confronted with several challenges and opportunities as, for instance, the reduction of inertial masses in the system, the strongly increasing decentralisation of generators, and the fluctuating power feed-in by generators relying on renewable energy sources. In this thesis, models are studied that describe the non-linear power-grid dynamics in the presence of fluctuating power feed-in from renewable energy sources, primarily wind turbines. Realistic features of wind-power feed-in are captured by using real data measured at a research platform located in the North Sea. This approach is applied to test systems provided by the Institute of Electrical and Electronics Engineers (IEEE), in which one conventional generator is replaced by a wind turbine. It is found that so-called dead ends and other weakly coupled network parts are particularly prone to power fluctuations and perturbations. In contrast to previous studies, the often pronounced heterogeneities of the power grid elements are taken into account when solving the non-linear power-flow and swing equations. Also reactances between locations of power generation and power feed-in are considered, which causes the link topology in the power grid to correspond to a full graph, where all nodes are effectively connected. Both the grid heterogeneities and the additional generator reactances have a decisive impact on power grid stability. Some structures considered as particularly stable in simplified models are prone to perturbations when utilising the more realistic model and vice versa. By the analysis of various quantities characterising functional grid operation, it is shown that a reliable assessment of power grid stability requires the consideration of heterogeneities and generator reactances.