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Power flow analysis is the backbone of power system analysis and design. They are necessary for planning, operation, economic scheduling and exchange of power between utilities. The principal information of power flow analysis is to find the magnitude and phase angle of voltage at each bus and the real and reactive power flowing in each transmission lines. Power flow analysis is an importance tool involving numerical analysis applied to a power system. In this analysis, iterative techniques are used due to there no known analytical method to solve the problem. To finish this analysis there are methods of mathematical calculations which consist plenty of step depend on the size of system. Load flow studies are used to ensure that electrical power transfer from generators to consumers through the grid system is stable, reliable and economic. Conventional techniques for solving the load flow problem are iterative, using the Newton-Raphson or the Gauss-Seidel methods.
Introduction- Power flow study is a fundamental task of power system operation and planning. various methods developed in commercial package for power flow study, the Newton-Raphson method is the most successful one. It is however well recognized that the NR method may diverge in power flow study. In this paper, we numerically study the convergence regions of power flow solutions using Newton-Raphson(NR) method. This study of convergence region is motivated by the need to determine an initial guess which converges to one of the power flow solution. It will be numerically shown that the convergence region of NR method, if exist, has a fractal boundary and is hence sensitive to initial conditions. Several fractal features will be investigated considering the convergence regions of power flow at the base case and at various loading conditions, and with different load models.
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