The goal of this study is to evaluate the instability that current power systems are susceptible to as a result of integrating new components like power electronics, electric vehicles, and renewable energy production. Today, the stability and security of the electrical network are impacted by the growing development of renewable energy sources. The purpose of this research is to assess the various stabilities which concerns the electricity system utilizing a feature selection and DLNN technique. Nigerian 28 bus system and IEEE9 bus system data contingencies were generated using DIgSILENT. The Relief-F feature selection method is used to construct a data processing pipeline for feature selection. This investigation is conducted using the DIgSILENT/Python program, which is run on an Intel Pentium core i5 2GHz CPU. The suggested model's improved performance is evaluated on the Nigeria 28 bus system and IEEE 9 bus system. For the Nigeria 28 bus system and the IEEE 9 bus system, the findings show evaluation performance metrics for accuracy, precision, sensitivity, f1-score, specificity, mean squared error, and root mean square error. The evaluation metrics of the IEEE 9 bus system and the Nigeria 28 bus system were compared with other publications in the corresponding literature. This study demonstrates the utility of the DLNN technique for online, real-time evaluation of transient stability and small signal stability.