The closest load flow limit in electrical power systems by Monte Carlo simulation

This paper describes a method of obtaining a point in voltage vector space for the shortest distance between normal operation and a critical point of load flow in electrical power systems by means of Monte Carlo simulation. It also presents the characteristics of the power distance, voltage distance, and inner products of eigenvectors and voltage differences with respect to the point on the trajectory of minimum search. The critical point is characterized by the zero determinant of the Jacobian matrix. The point is known as the saddle node bifurcation. We propose a method of calculating the critical point under the bus constraints of the load flow equation. A new set of voltages is given by a random generator for a step of the Monte Carlo simulation. We calculate the power distance and draw a trajectory for the closest bifurcation by a random process. The result shows that the right eigenvector is parallel to the normal line to the tangential planes at the closest bifurcation. (C) 2004 Wiley Periodicals, Inc.