optimal distribution of primary control participation with respect to voltage stability

in competitive electricity markets the transmission system will at times be heavily loaded. at these occasions prevention of voltage instability is an important objective that the system operator has to meet. in this paper a method for finding the primary control participation that maximizes the margin from an operating point to the saddle-node bifurcation surface is proposed. the arising optimization problem is solved using a steepest descent method. the proposed method can find its applications both in generation planning and in real-time operation of electric power systems.