A Power Flow Method for Power Distribution Systems Based on a Sinusoidal Transformation to a Convex Quadratic Form

The non-linearity and non-convexity of the AC power flow equations may induce convergence problems to the Newton-Raphson (NR) algorithm. Indeed, as shown by Thorp and Naqavi, the NR algorithm may exhibit a fractal behavior. Furthermore, under heavy loading conditions or if some of the line reactances are relatively large compared to the others, the Jacobian matrix becomes ill-conditioned, which may cause the divergence of this algorithm. To address the aforementioned problems for radial power distribution systems, we propose in this paper to apply a sinusoidal transform to map the AC power flow equations into a convex quadratic form, which includes node-based and Pythagorean equations. The good performance of the proposed approach is demonstrated via simulations carried out on several power distribution systems.