Recursive power flow calculation based on polar coordinates holomorphic embedding method

• A novel Polar-HEM is proposed for power flow calculation for the first time. • The polar-coordinate formulation eliminates trigonometric terms via angle addition expansion, enabling an analytically tractable holomorphic embedding framework. • The proposed method derives a recursive power flow solution directly in voltage magnitude and phase angle variables, avoiding dependence on initial guesses. A unified recursive formulation is developed for both PQ and PV buses, reducing model dimensionality and simplifying derivation compared with classical rectangular HE methods. • Extensive simulations on IEEE benchmark systems verify the method’s accuracy, linear convergence, and robustness under heavy-load conditions, outperforming traditional Newton–Raphson and rectangular-coordinate HE methods. Power flow calculation is a fundamental tool for power system analysis. Traditional power flow calculation methods predominantly rely on iterative algorithms, such as the Newton-Raphson method, whose convergence depends critically on the selection of initial points. To address the limitations of iterative algorithms, the holomorphic embedding (HE) method has emerged as a recursive power flow solution technique in recent years. This method eliminates dependence on initial points and guarantees reliable convergence to a high-voltage (operable) solution. However, all existing HE methods are formulated based on power flow equations in rectangular coordinates, where the unknown variables typically include the real and imaginary parts of the bus voltages, as well as the reactive power injections at PV buses. This paper introduces a HE method formulated in polar coordinates, referred to as Polar-HEM. Initially, the trigonometric functions in the polar coordinates power flow equations are expanded using angle addition formulas, facilitating the systematic construction of the HE formulation. Subsequently, a formulation with a readily obtainable germ solution is developed. The recursive relationships are rigorously derived and explicitly demonstrated using a 3-bus test system. Extensive validation across multiple test cases demonstrates the effectiveness of the proposed method and its ability to diagnose convergence issues.