Power flow calculation by combination of Newton-Raphson method and Newton's method in optimization

In this paper, the application of the Newton's method in optimization for power flow calculation is considered. Convergence conditions of the suggested method using an example of a three-machine system are investigated. It is shown, that the method allows to calculate non-existent state points and automatically pulls them onto the boundary of power flow existence domain. A combined method which is composed of Newton-Raphson method and Newton's method in optimization is presented in the paper.