Due to the high risk of cascading failures, an online solution for N-2 failure control becomes increasingly important. Dual short-circuit fault, as one of the simplest N-2 failure, was studied in this article. Some explorations were made aiming at the composition rules of critical cluster (CC) and the relationship between the dual short-circuit fault's conservative control quantity and the individual fault's optimal control quantity. A theoretical derivation was made to investigate mutual influencing mechanism of individual faults based on EEAC theory. Definition for the classification of dual faults was given to study the composition of CC. Two rules were proposed to help searching control decisions of dual faults. The validity of all these conclusions and rules was evaluated in actual power system.