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This paper attempts to integrate the hidden failure model into structural vulnerability analysis of large power grid. A new concept, characteristic path length in a complex power grid is defined. The impact of characteristic path length on power grid vulnerability is analyzed via different attacks: random attack and heavy loaded based attack. Simulation results on IEEE 300 system and its evolving networks have been presented. Conclusions such as small characteristic path length can increase the vulnerability of power grid and also the probability of size of blackouts, etc have been drawn. Discussion on application of the characteristic path length to improve the power system stability is also made.