Development of combined Runge–Kutta Broyden's load flow approach for well‐ and ill‐conditioned power systems

Load flow (LF) is an extensively used tool in planning and operation of power systems. Formulation of LF problem can be assimilated as a set of autonomous ordinary differential equations, therefore, many numeric methods can be used to solve this problem. However, LF methods often need to compute one or more Jacobian matrix inversions in each iteration. Owing to this fact, these methods might not be computationally efficient. In this study, the authors propose combined Runge–Kutta Broyden's LF (RK4B) method in order to reduce the required Jacobian matrix inversion to only one in the first iteration. In this proposed method, Broyden's approach is employed in fourth‐order Runge–Kutta method. In addition, two modifications of the proposed method are presented to reduce the number of iterations and improve the computational performance. The proposed method and the two modifications are validated using several well‐ and ill‐conditioned cases. Results show that the combined approach has better computational performance than the classical multistage numeric methods, besides it preserves the robustness features of fourth‐order Runge–Kutta method.