Unsolvable power flow - restoring solutions of the electric power network equations

Unsolvable cases in power flow studies frequently occur if the system is heavily loaded or under contingency. This paper proposes an approach based on the left eigenvector associated with the eigenvalue of the Jacobian matrix in order to restore the real solutions of the load flow equations. The electric network equations are expressed in polar coordinates and the damped Newton-Raphson method is used to prevent divergence of the iterative process as well as to reach the surface between the solvable and unsolvable regions. Numerical results obtained with two power systems (including a real network) illustrate the proposed application.