Bifurcation points and loadability limits as solutions of constrained optimization problems

In this paper the problem of power system loadability limits with adequate representation of generation overexcitation limits is examined. Based on the exact penalty function approach, an equality and inequality constrained optimization problem is formulated. Any solution of the proposed problem is a loadability limit of the power system, irrespective of whether the loadability limit is a bifurcation point, or a breaking point due to the excitation limits. A simple power system example is given to illustrate the points raised. Finally, a means for the direct calculation of the normal vector to the loadability surface is given in terms of the Lagrange multipliers of the proposed optimization problem.