A second order dynamic power flow model

•This paper proposes a novel dynamic approach aimed at solving the power flow equations.•We formulated the power flow equations by a set of ordinary differential equations.•The power flow solutions are obtained by finding the equilibrium points of a dynamic system.•We will demonstrate that the dynamic power flow model is stable.•Detailed numerical results demonstrate the effectiveness of the proposed methodology.

In this paper a novel second order power flow solution paradigm based on artificial dynamic models is proposed. The idea is to derive the second order optimality conditions for the power flow problem by reformulating the system equations into a set of ordinary differential equations, whose equilibrium points represent the problem solutions. Starting from the Lyapunov Theory we will demonstrate that the structure of this artificial dynamic model is stable with an exponential asymptotic convergence to the equilibrium points. The application of this technique for solving both unconstrained and constrained power flow problems is explained in details, and several numerical results are presented and discussed, demonstrating the effectiveness of the proposed methodology.