The approximate analytical soution of an interconnected power system have been studied by using the Adomian decomposition method (ADM). Bifurcation diagram and phase diagram under different periodic load disturbance, chaotic characteristics of the system are studied by the MATLAB simulation based on the interconnected power system. Simulation results indicate that the chaotic oscillation will occur under a comparatively large periodic load disturbance. Finally, comparisons between the decomposition solutions and the fourth-order Runge–Kutta (RK4) numerical solutions are made for various time steps. Results show that compared with the RK4, Adomian decomposition method not only yields more accurate results and needs less calculation time, but also can improve the convergence speed.