This paper proposes 3 severity performance indices to detect transient instability of power systems and contingency ranking. The indices are based on state variables and transient energy function parameters such as kinetic and potential energy. They are tested and compared with other indices on the IEEE 9 and IEEE 39 test bus systems. Also in this paper, a comprehensive sensitivity and accuracy analysis is occurred to determine the severity index which has more appropriate performance to rank transient contingency of a power system. Then advantages and disadvantages of these indices are presented.