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

   https://doi.org/10.1109/PESGM46819.2021.9637963  

   Valinejad, Jaber ; Mili, Lamine ; Xu, Yijun ( July 2021 , 2021 IEEE Power & Energy Society General Meeting (PESGM))

   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 nodebased and Pythagorean equations. The good performance of the proposed approach is demonstrated via simulations carried out on several power distribution systems. 

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   https://doi.org/10.1109/IAS44978.2020.9334785  

   Chowdhury, Md Mahmud-Ul-Tarik ; Kamalasadan, Sukumar ( October 2020 , 2020 IEEE Industry Applications Society Annual Meeting)