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   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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5. Detection and Localization of Faults in a Regional Power Grid: Faults in a Regional Power Grid

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   Kokoszka, Piotr; Rimkus, Mantautas; Hosur, Sanjay Sheshagiri; Duan, Dongliang; Wang, Haonan (July 2023, Austrian Journal of Statistics)

   The structure of power flows in transmission grids is evolving and is likelyto change significantly in the coming years due to the rapid growth ofrenewable energy generation that introduces randomness and bidirectionalpower flows. Another transformative aspect is the increasing penetrationof various smart-meter technologies. Inexpensive measurement devicescan be placed at practically any component of the grid. Using modeldata reflecting smart-meter measurements,we propose a two-stage procedure for detecting a fault in a regional powergrid. In the first stage, a fault is detected in real time. In the second stage,the faulted line is identified with a negligible delay. The approach uses onlythe voltage modulus measured at buses (nodes of the grid) as the input.Our method does not require prior knowledge of thefault type. The method is fully implemented in  R.Pseudo code and complete mathematical formulas are provided. 

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