Weakness analysis based on grid strength assessment is useful for identifying potential weak grid issues. However, when taking into account the impact of the interactions among Renewable Energy Sources (RESs), the weakness analysis becomes computationally challenging. Different combinations of PointsofInterconnections (POIs) of RESs may have different impacts on grid strength at each POI. Due to the combination nature, such weakness analysis may be time-consuming when identifying the weakest combination of POIs from a large number of potential candidate locations in realistic power grids. This dissertation addresses the topic of determination of the weakest RESs combinations. Based on impedance ratios as a criterion, the dissertation shows that the impacts of impedance ratios magnitudes and angles are ‘quasi-mutually exclusive’. Such a concept is then used to reduce the computational burden with a fast screening algorithm. To further understand the impact of network components on grid strength, vector-based interaction analysis is developed based on the concepts of operational transfer impedances and operational interaction operators. In particular, this dissertation shows how mathematical models of interaction of multiple RESs can be simplified by replacing them with equivalent impedances, allowing us to simplify the mathematical expressions that quantify interactions among RESs. The conclusions and concepts established based on simplified models are statistically tested for their applicability to the generalized interaction model. The result would be a more simplified mathematical representation of interaction among RESs. Finally, a new technique is presented to efficiently update the Bus Impedance Matrix (Zbus) following changes in the series impedance of a branch. Conventionally, such update requires redundant recalculations, which involve matrix inversion operations (i.e., inverting the Bus Admittance Matrix, Ybus) and thus cause high computational burden because of potential matrix ill-conditioning, especially for largescale power grids. This dissertation overcomes these shortcomings by deriving an analytical expression for changes in Zbus in terms of its old elements and the variation of the impedance of a given branch. Hence, the computation overhead is comparatively small, and no issues arise due to the new Ybus being ill-conditioned. Such contribution helps facilitate real-time applications of methods that rely on Zbus.