The controllers of wind parks that are connected to weak grids can induce unstable oscillations near the fundamental frequency. Such phenomenon can be studied with equivalent impedances of the wind generators, which depend on their operational setpoints at the fundamental frequency. The feasibility of such setpoint, i.e., solution to the power flow, does not depend on the control parameters. However, oscillations from unfeasible setpoints and control instabilities both occur at weak grids and near the fundamental frequency. This letter presents an exploratory study to map the conditions where both phenomena occur, using sensitivity studies comprising multiple setpoints and control parameter tunings. The results are visually presented as the regions which inform the configurations leading to unfeasible setpoints, and unstable control interaction scenarios. Amongst the results, it can be observed that the trajectory of the eigenvalues in the Nyquist plots towards an unfeasible setpoint approaches a fundamental frequency instability.