Power flow calculation is a key analytical tool in power system analysis. Traditional methods

such as the Newton-Raphson and PQ decomposition algorithms

are iterative and rely on the choice of initial values for convergence. To overcome these limitations

this paper proposes a recursive method

Holomorphic Embedding

has been proposed

which operates without reliance on initial guesses and consistently converges to an operable solution. However

current holomorphic embedding methods are mainly based on rectangular coordinates

requiring the solution of real and imaginary parts of voltages and reactive power injections at PV buses. In contrast

polar coordinate formulations involve fewer variables

but corresponding holomorphic embedding methods remain underexplored due to challenges posed by trigonometric functions like sine and cosine. To address this

this paper proposes a holomorphic embedding power flow method based on polar coordinates for the first time. Compared with rectangular-coordinate-based methods

the proposed approach uses fewer variables and provides a unified formulation for different bus types. Specifically

trigonometric functions are approximated using Taylor expansion to enable the embedding formulation

followed by the design of an embedding structure that facilitates initial solution acquisition. Recursive expressions are derived and illustrated with small-scale examples

and the method’s effectiveness and accuracy are validated through multiple test cases.