Multiobjective power dispatch with line flow constraints using the fast Newton-Raphson method

The fast Newton-Raphson approach based on an alternative Jacobian matrix is proposed to solve the multiobjective power dispatch (MPD) problem with line flow constraints. Two conflicting objectives including minimization of fuel cost and environmental impact of emission are considered in this study. The Jacobian matrix is formulated by the incremental transmission loss in terms of the sensitivity factors, line flows, and line resistances. The sensitivity factors are obtained from line flow solutions based on a DC load now model. Moreover, the B-coefficients matrix and the Lagrange function can be shown as convex functions. Therefore, the existence and uniqueness of the solution for the nonlinear equation of the MPD problem can be proven. The proposed approach is tested on the IEEE 14- and 30-bus systems. Simulation results obtained from the proposed method confirm the advantage of computation rapidity and solution accuracy over that of the AC load flow method and the conventional B-coefficients method, respectively. The comparison confirms the capability of the proposed method in real-time implementation for the MPD problem.