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To give more insights of the low-frequency oscillations, we mainly investigate the dynamical and geometrical properties of boundaries of Small Signal Stability Region (SSSR) composed of Hopf bifurcation points in power injection space. First, we investigate the characteristics of boundaries composed of Hopf bifurcation points in power injection space. By investigating the two-dimensional cross-sections of the boundaries of a typical system, we find the boundaries whose critical oscillation modes have similar frequency are likely symmetrical in geometry. Then, to improve the precision of computing the boundary of SSSR, we investigate the difference of boundaries when considering the saturation of generator, and we find the SSSR becomes a little bigger than not considering the saturation of generator. Based on the result above, we find that the generators are all saturated at the practical boundary of SSSR. So we suggest using the saturated parameters of generator to compute the boundary of SSSR.