A novel characterization of saddle-node bifurcation points for general nonlinear systems with decoupled parameters

The authors develop a new characterization for saddle-node bifurcations for a specific class of nonlinear dynamical systems. These particular dynamical systems depend on a parameter which is mathematically decoupled from the system states. The new characteristic equation is (n + 1)-dimensional and therefore computationally more efficient than the standard (2n + 1)-dimensional formulation generally utilized for n-dimensional general nonlinear systems. A new test function is proposed and shown to be monotonical in the vicinity of a saddle-node bifurcation point and therefore it is possible to monitor the approach to the saddle-node bifurcation point during the solution process, offering in this manner a definite advantage over the conventional approach in terms of control over the solution process. Some simulation results on a 234-bus power system are presented