This paper focuses on a comprehensive stability study of a two-area power system with wind power integration and synthetic inertia control in each area, considering the effects of varying the interconnection link. Normally, synthetic inertia proposals are analyzed in one-area systems, in which stability is tested without considering transmission system phenomena, such as coherency. As modern power systems are progressively becoming interconnected, the possibility of forming two or more non-coherent areas is likely, which poses a challenge to synthetic inertia control techniques that use system frequency as a main feedback signal. In this context, this work addresses a crucial gap in the existing literature and provides a valuable starting point for studying more complex interconnected power systems with wind power integration. Simulations were performed in Matlab-Simulink considering a data-driven frequency dynamics model of the Chilean Electric System, and a wind power model with synthetic inertia control H2 norm minimization in each area. The results showed that it is possible to find local optimal feedback gains, preserving the stability of the global system under significant variations in the interconnection link. RoCoF and Nadir indicators are provided, highlighting the benefits of synthetic inertia control, particularly in low-inertia situations.