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• The purpose of this article is to study a power flow algorithm with strong convergence, initial value adaptability, and efficiency. • This paper proposes a two-part alternating iterative framework based on dynamic equivalent admittance. • The proposed algorithm has universality for well-and ill-conditioned systems. • The proposed method combines the convergence characteristics of the Z-bus Gauss method and Newton's method, so it is easy to implement based on existing program codes. Power flow is an extensively used tool in various operations and planning of power systems. In this paper, we propose an efficient hybrid method for solving the power flow problems in ill-conditioned power systems. This method is implemented in a framework of two-part alternating iteration. In Part I of this method, PV bus voltages are regarded as constant and PQ bus voltages are updated by the Z-bus Gauss method. In Part II of this method, PQ bus loads are equivalent to dynamic admittances, and PV bus voltage angles are updated by Newton's method. The values of PQ bus voltage magnitudes and PV bus voltage angles are passed between Part I and Part II. The proposed method is validated in well- and ill-conditioned systems and compared with several well-known power flow methods. Results show that the proposed method is robust and efficient to address the issues related with large-scale ill-conditioned power systems and it is not significantly affected by the considered initial guess. [ABSTRACT FROM AUTHOR]