For the EHV transmission lines with shunt reactors, the recovery voltage of fault phase exists the beat frequency phenomenon when transient fault occurred. The paper proposes a new automatic recognition scheme of single-phase adaptive reclosure based on Stochastic Subspace Identification(SSI). The scheme uses the recovery voltage of fault phase as characteristic quantity. Achieve system eigenvalues through EMD, stabilization diagram, SSI. Based on the distribution characteristics of system eigenvalues in the complex plane, define a decision space of fault characteristics, using the system eigenvalues as a reference point and permissible deviation of frequency as the radius. If the eigenvalues of fault signal all locate in the decision space, then the fault type is permanent fault, otherwise the fault type is transient fault. The quantitative index using to distinguish fault type is given in the paper in order to achieve automatic recognition of fault properties. Simulation results show that the proposed scheme can judge the fault property correctly and reliably without cross-regional discrimination results.