Sensitivity of Transient Stability Critical Clearing Time

Once the critical clearing time of a fault leading to transient instability has been computed, it is desirable to quantify its dependence on system parameters. We derive, for a general power system model a new and exact formula for the first-order sensitivity of the critical clearing time with respect to any system parameter. The formula is evaluated by integrating variational equations forward in time along the base case fault-on trajectory and integrating adjoint variational equations backward in time along the postfault trajectory. The computation avoids recomputing the critical clearing time for each parameter change and gives insight into how parameters influence power system transient stability. The computation of the sensitivity of the critical clearing time with respect to load impedances and generator inertias is illustrated on a 39-bus system.