Traditional OPA model and its improved models can simulate the cascading failures and reveal the macro-scale of self-organized criticality of the power grid， but lack for considering the effect of the evolvement of topology of the power grid. For the purpose of studying the mechanism of blackouts， an improved OPA model is proposed， in which the structure evolvement of power grid is added to the slow dynamics. Simulation results from two typical complex networks show power grid always organizes itself to criticality in evolving model of small-world network as well as scale-free network. Moreover， from the comparison results between the power grids with two different growth ways， it can be found that the characteristic of small-world power grid makes power loss larger than that in scale-free power grid， and cascading failure in scale-free power grid often lead to lines outage in small scale and ends with little power loss， which can help to release the system stress and decrease the probability of large blackouts. These results can be beneficial in major disturbance mitigation and system planning and upgrading.