Artificial Dynamic Theory based Optimal Power Flow

The efficiency and reliability of the power system operation are highly dependent on the solution of the non-linear Optimal Power Flow (OPF) problem. However, the ill-conditioning of the Jacobian poses a serious issue on the solution mechanism as matrix inversion is required. To avoid the Jacobian inversion, this paper introduces a Lyapunov theory-based approach for solving the nonlinear OPF problem. The aim is to transform the static equations of OPF into an artificial dynamic system, such that the equilibrium points of the dynamic system coincide with the optimal solutions of OPF. The variables of OPF are designed as a state vector of an autonomous nonlinear system and variation of these state vectors are developed in such a way that they give a stable vector field. Moreover, nonlinear complementary functions are used to handle the complementary conditions emerging from the Lagrangian formulation. The adapted solution methodology surmounts the shortcomings associated with the Hessian matrix inversion. Also, unlike already existing similar works, our approach gives the primal and dual solution of OPF problem. Simulations on standard IEEE test systems are carried out to show the efficiency of the proposed methodology.