An effort is made to determine how line flow changes affect the robustness of the system using the energy margin sensitivities to power generation shifts and power flow distribution factors. A method to obtain stability constrained line flow limits is proposed. The major difference between this research work and other research in transient energy function sensitivity techniques for line flow limits is that this research allows for line flow changes caused by unspecified machines. Previous research dealt with line flow limits due to a generation shift at a single specified machine. However, it is possible that a generation shift at another machine or combination of machines may consume the energy margin less quickly and thus result in large stability constrained transaction capability.