Application of asymptotic numerical method with homotopy techniques to power flow problems

• Method associates Newton homotopy with ANM to solve power flow equations.
• To provide a reliable way to study ill-conditioned power flow problems.
• To propose an efficient method to study multiple solutions of power flow equations.

Traditional power flow methods such as the Newton-like methods are locally convergent and may be ineffective in some circumstances. In this paper, we propose a novel computational approach which associates a Newton homotopy with an asymptotic numerical method (ANM) to solve the nonlinear power flow equations. ANM is a family of algorithms based on the computation of Taylor series expansion per step. With ANM, as the homotopy path has been expressed into a closed analytical form section by section, the multiple power flow solutions on the path are computed by solving a simple polynomial equation. The proposed method provides a reliable way to study the ill-conditioned power flow problems thanks to the use of homotopy transformation and higher-order predictor of ANM. Numerical examples of several power systems are presented to validate the effectiveness of the method.

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