The Closest Load Flow Limit in Electrical Power Systems by Monte Carlo Simulation

This paper describes a method to obtain a point for the shortest distance between a normal operation and a critical point of load flow in electrical power systems by means of Monte Carlo simulation. It also presents characteristics of power distance, voltage distance, and inner products of eigenvectors and voltage difference with respect to the point on the trajectory of minimum search. The critical point is characterized by the zero determinant of Jacobian matrix. The point is known as saddle node bifurcation. We propose a method to calculate the critical point under bus constraints of the load flow equation. A new set of voltages is give by random generator for a step of Monte Carlo simulation. We calculate the power distances and draw a trajectory for the closest bifurcation by the random process. The result shows that the right eigenvector is parallel to the normal line of tangential planes at the closest bifurcation.