Recent studies on the power systems collapse prevention and the mechanism of cascading failures have shown that the self-organized criticality（SOC） is the character of power system blackouts. The theory of extreme value mainly studies extreme value， which traditionally can be used as a tool forecasting tsunami， earthquake and flood. By applying the theory of extreme value in the SOC of power system blackouts， the paper proves that the limit of the size extreme value distribution of the blackouts based on the scale-frequency power-law distribution is convergent to theⅠformula. As an example， the calculation of extremes analysis of the blackouts data of the Northeast and Northwest China power grid is presented.