Because of the limitations imposed by the physical structure of the excitation systems of synchronous generators， the voltage output of the system has saturation elements（magnitude modulation element）. This effect inevitably introduces nonlinear characteristics to the excitation voltage output. A novel approach is presented to determine the boundary of the small signal stability region（SSSR） using the volume of the ellipsoidal region of attraction（RA） as the criteria in linear optimal excitation control（LOEC） system with the saturation element. The SSSR defined in injection space is studied using the proposed method. Results demonstrate that the SSSR calculated based on the proposed algorithm is approximately equal to the one obtained using Hopf bifurcation theory when the criteria of RA or the stabilized disturbance is very small， and the proposed algorithm gets smaller SSSR when the criteria of RA or the stabilized disturbance is enlarged. These results show that SSSR may consider the disturbance， which enlarges the facet of studies on SSSR.