Currently, the large-scale integration of renewable energy sources (RESs) such as wind and solar photovoltaic generators is profoundly altering the dynamic behaviors of electrical grids, notably by reducing their inertia and making transient stability more critical. The originality of this work lies in its systematic exploration of the nonlinear dynamics of electrical networks, analyzing in depth the impact of RESs integration on grid stability and focusing on frequency response and rotor angle dynamics. This work proposes a methodology for evaluating and optimizing power system stability index, focusing on two major indicators: the Critical Clearing Time (CCT) and the Rate of Change of Frequency (ROCOF). The IEEE 39-bus test system is used as a test bench to simulate different renewable energy injection and microgrid (MG) location scenarios. Three-phase faults are applied to several grid lines to determine the corresponding CCTs and assess the system's ability to recover a stable state after disturbance. An automated approach was developed to calculate the CCT, enabling faster convergence and simultaneous testing of multiple fault locations. Variations in the ROCOF were also measured to quantify the effect of microgrids on frequency stability. The results show that high renewable energy penetration tends to reduce the CCT and increase the ROCOF, indicating a loss of dynamic robustness. However, optimizing the microgrid location to include an energy storage system (ESS) improves overall stability. These observations are supported by comparative simulations with and without renewable energy integration. Ultimately, this work highlights the importance of optimally locating distributed units and using CCT and ROCOF indices as diagnostic and optimization tools for modern power grids with high renewable energy penetration.