Computation of bifurcation and maximum loading limit in electrical power systems

In this paper, we propose a more efficient method to calculate the nose point of PV curve by means of Newton Raphson's iteration procedures. A problem of the nose point of PV curve under an operating condition is formulated as the maximization of system loads with constraints corresponding to system operating conditions. A quadratic form with respect to state vector expresses the objective function. Network operating conditions are formulated by quadratic equations with respect to state vector in equality constraints. The problem of maximization of system load is formulated with an objective function and several number of equality constraints in power systems for the nose point of PV curve. The Lagrange's multiplier method is the most common method to the maximizing problem for the nose point of PV curve with the specified constraints for power system operating conditions. It is known that we can obtain the optimal point of the nonlinear programming problem is null point of the gradients of Lagrange function. The proposed method is composed of the Newton Raphson's iteration-procedure to find out the optimal point, where the Karush Kuhn Tucker condition is satisfied. Newton Raphson's technique has great advantages in fast quadratic convergence and less computer time. Numeric examples of the closest bifurcation, the nose point of PV curve and their applications are demonstrated with use of several model systems for the examination of proposed methods.