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The swing equation is essential for modelling and analyzing the power system dynamics, after being disturbed. Two types of stability i.e., voltage and power angle stability are considered to be vital in the study stability of power system. Power angle stability is being considered as matter of concern in this work. Power angle stability can be measured by analyzing the dynamics of swing equation. The existence of chaos in swing equation is a fact in power system. Chaos can drive the system power angle into instability, as chaos is a fundamental aspect of a nonlinear dynamical system. Instability can also result in a total shutdown of the system. This work presents a novel approach for stability analysis of multi-machine system using swing curve derived from an equation. The proposed method provides advanced techniques to detect instability in power system using swing dynamics and analyze their impact on stability. It reduces qualitative changes in dynamic systems when parameters vary, leading to shifts in stability and the emergence of new states. The stability and security of power systems are crucial for ensuring reliable electricity supply to consumers.