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1. Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

   https://doi.org/10.1109/TPEC60005.2024.10472209  

   Barati, Masoud (February 2024, IEEE)

   This manuscript presents a novel approach utilizing computational graph strategies for solving the power flow equations through the synergistic use of Newton-Raphson (NR) and Gradient Descent (GD). As a foundational element for operational and strategic decision-making in electrical networks, the power flow analysis has been rigorously examined for decades. Conventional solution techniques typically depend on second-order processes, which may falter, especially when faced with subpar starting values or during heightened system demands. These issues are becoming more acute with the dynamic shifts in generation and consumption patterns within modern electrical systems. Our research introduces a dual-mode algorithm that amalgamates the principles of first-order operation. This inventive method is adept at circumventing potential local minima traps that hinder current methodologies, thereby reinforcing the dependability of power flow solutions. We substantiate the effectiveness of our advanced algorithm with comprehensive testing on established IEEE benchmark systems. Our findings reveal that our approach not only expedites the convergence process but also ensures consistent performance across diverse system states, signifying a meaningful progression in the realm of power flow computation. 

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2. Introducing a Concise Formulation of the Jacobian Matrix for Newton-Raphson Power Flow Solution in the Engineering Curriculum

   https://doi.org/10.1109/PECI51586.2021.9435220  

   Conlin, Elijah; Dahal, Niraj; Rovnyak, Steven M.; Rovnyak, James L. (April 2021, 2021 IEEE Power and Energy Conference at Illinois (PECI))

   null (Ed.)

   The power flow computer program is fundamentally important for power system analysis and design. Many textbooks teach the Newton-Raphson method of power flow solution. The typical formulation of the Jacobian matrix in the NR method is cumbersome, inelegant, and laborious to program. Recent papers have introduced a method for calculating the Jacobian matrix that is concise, elegant, and simple to program. The concise formulation of the Jacobian matrix makes writing a power flow program more accessible to students. However, its derivation in the research literature involves advanced manipulations using higher dimensional derivatives, which are challenging for dual level students. This paper presents alternative derivations of the concise formulation that are suitable for undergraduate students, where some cases can be presented in lecture while other cases are assigned as exercises. These derivations have been successfully taught in a dual level course on computational methods for power systems for about ten years. 

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3. The importance of the counter-cation in reductive rare-earth metal chemistry: 18-crown-6 instead of 2,2,2-cryptand allows isolation of [Y ^II (NR ₂ ) ₃ ] ¹⁻ and ynediolate and enediolate complexes from CO reactions

   https://doi.org/10.1039/C9SC05794C  

   Ryan, Austin J.; Ziller, Joseph W.; Evans, William J. (February 2020, Chemical Science)

   The use of 18-crown-6 (18-c-6) in place of 2.2.2-cryptand (crypt) in rare earth amide reduction reactions involving potassium has proven to be crucial in the synthesis of Ln( ii ) complexes and isolation of their CO reduction products. The faster speed of crystallization with 18-c-6 appears to be important. Previous studies have shown that reduction of the trivalent amide complexes Ln(NR 2 ) 3 (R = SiMe 3 ) with potassium in the presence of 2.2.2-cryptand (crypt) forms the divalent [K(crypt)][Ln II (NR 2 ) 3 ] complexes for Ln = Gd, Tb, Dy, and Tm. However, for Ho and Er, the [Ln(NR 2 ) 3 ] 1− anions were only isolable with [Rb(crypt)] 1+ counter-cations and isolation of the [Y II (NR 2 ) 3 ] 1− anion was not possible under any of these conditions. We now report that by changing the potassium chelator from crypt to 18-crown-6 (18-c-6), the [Ln(NR 2 ) 3 ] 1− anions can be isolated not only for Ln = Gd, Tb, Dy, and Tm, but also for Ho, Er, and Y. Specifically, these anions are isolated as salts of a 1 : 2 potassium : crown sandwich cation, [K(18-c-6) 2 ] 1+ , i.e. [K(18-c-6) 2 ][Ln(NR 2 ) 3 ]. The [K(18-c-6) 2 ] 1+ counter-cation was superior not only in the synthesis, but it also allowed the isolation of crystallographically-characterizable products from reactions of CO with the [Ln(NR 2 ) 3 ] 1− anions that were not obtainable from the [K(crypt)] 1+ analogs. Reaction of CO with [K(18-c-6) 2 ][Ln(NR 2 ) 3 ], generated in situ , yielded crystals of the ynediolate products, {[(R 2 N) 3 Ln] 2 (μ-OCCO)} 2− , which crystallized with counter-cations possessing 2 : 3 potassium : crown ratios, i.e. {[K 2 (18-c-6) 3 ]} 2+ , for Gd, Dy, Ho. In contrast, reaction of CO with a solution of isolated [K(18-c-6) 2 ][Gd(NR 2 ) 3 ], produced crystals of an enediolate complex isolated with a counter-cation with a 2 : 2 potassium : crown ratio namely [K(18-c-6)] 2 2+ in the complex [K(18-c-6)] 2 {[(R 2 N) 2 Gd 2 (μ-OCHCHO) 2 ]}. 

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4. 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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5. Mean‐standard deviation model for minimum cost flow problem

   https://doi.org/10.1002/net.22135  

   Gokalp, Can; Boyles, Stephen D.; Unnikrishnan, Avinash (December 2022, Networks)

   We study the mean-standard deviation minimum cost flow (MSDMCF) problem, where the objective is minimizing a linear combination of the mean and standard deviation of flow costs. Due to the nonlinearity and nonseparability of the objective, the problem is not amenable to the standard algorithms developed for network flow problems. We prove that the solution for the MSDMCF problem coincides with the solution for a particular mean-variance minimum cost flow (MVMCF) problem. Leveraging this result, we propose bisection (BSC), Newton–Raphson (NR), and a hybrid (NR-BSC)—method seeking to find the specific MVMCF problem whose optimal solution coincides with the optimal solution for the given MSDMCF problem. We further show that this approach can be extended to solve more generalized nonseparable parametric minimum cost flow problems under certain conditions. Computational experiments show that the NR algorithm is about twice as fast as the CPLEX solver on benchmark networks generated with NETGEN. 

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