Dynamic sensitivity functions and the stability of power systems with FACTS controllers

The reliability of an electric power supply is of vital importance as systems become more stressed. Both small-signal and transient stability in power systems are crucial components of dynamic security assessment. This dissertation presents a new method for the evaluation of transient stability of a power system using dynamic sensitivity functions. This method has an advantage over previous methods in that there are no limits on the model complexity. In particular, the differential-algebraic models are handled very easily. Contingencies can be ranked according to their severity using the sensitivity of system trajectories to system parameters or pre-fault loading conditions. The more stressed the system is, the greater are the sensitivities. This provides a useful indicator of system stress and by normalization, one can compare different contingencies. It is well known that Hopf bifurcations cause system voltage instability before saddle-node bifurcations occur as system loading increases. The impact on the Hopf bifurcation point is investigated in this dissertation for systems which include flexible alternating current transmission system (FACTS) controllers. It is found that FACTS controllers can delay the onset of Hopf bifurcations and, thus, improve voltage stability. Sensitivity theory is also applied to a system with a differential-algebraic model, which includes a FACTS controller. It is found that the FACTS variables can be among the most sensitive to parameter variations.