Editing Power-flow study (section)

==Other power-flow methods==
* [[Gauss–Seidel method]]: This is the earliest devised method. It shows slower rates of convergence compared to other iterative methods, but it uses very little memory and does not need to solve a matrix system.
* [[Fast-decoupled-load-flow method]] is a variation on Newton–Raphson that exploits the approximate decoupling of active and reactive flows in well-behaved power networks, and additionally fixes the value of the [[Jacobian matrix and determinant|Jacobian]] during the iteration in order to avoid costly matrix decompositions. Also referred to as "fixed-slope, decoupled NR". Within the algorithm, the Jacobian matrix gets inverted only once, and there are three assumptions. Firstly, the conductance between the buses is zero. Secondly, the magnitude of the bus voltage is one per unit. Thirdly, the sine of phases between buses is zero.  Fast decoupled load flow can return the answer within seconds whereas the Newton Raphson method takes much longer. This is useful for real-time management of power grids.<ref>{{Cite journal|last1=Stott|first1=B.|last2=Alsac|first2=O.|date=May 1974|title=Fast Decoupled Load Flow|journal=IEEE Transactions on Power Apparatus and Systems|language=en-US|volume=PAS-93|issue=3|pages=859–869|doi=10.1109/tpas.1974.293985|bibcode=1974ITPAS..93..859S |issn=0018-9510}}</ref>
* [[Holomorphic embedding load flow method]]: A recently developed method based on advanced techniques of complex analysis. It is direct and guarantees the calculation of the correct (operative) branch, out of the multiple solutions present in the power-flow equations.
* [[Backward-Forward Sweep (BFS) method]]: A method developed to take advantage of the radial structure of most modern distribution grids. It involves choosing an initial voltage profile and separating the original system of equations of grid components into two separate systems and solving one, using the last results of the other, until convergence is achieved. Solving for the currents with the voltages given is called the backward sweep (BS) and solving for the voltages with the currents given is called the forward sweep (FS).<ref>Petridis, S.; Blanas, O.; Rakopoulos, D.; Stergiopoulos, F.; Nikolopoulos, N.; Voutetakis, S. An Efficient Backward/Forward Sweep Algorithm for Power Flow Analysis through a Novel Tree-Like Structure for Unbalanced Distribution Networks. ''Energies'' 2021, ''14'', 897. https://doi.org/10.3390/en14040897, https://www.mdpi.com/1996-1073/14/4/897</ref>
* [[Laurent Power Flow (LPF) method]]: Power flow formulation that provides guarantee of uniqueness of solution and independence on initial conditions for electrical distribution systems. The LPF is based on the current injection method (CIM) and applies the Laurent series expansion. The main characteristics of this formulation are its proven numerical convergence and stability, and its computational advantages, showing to be at least ten times faster than the BFS method both in balanced and unbalanced networks.<ref>Giraldo, J. S., Montoya, O. D., Vergara, P. P., & Milano, F. (2022). A fixed-point current injection power flow for electric distribution systems using Laurent series. Electric Power Systems Research, 211, 108326. https://doi.org/10.1016/j.epsr.2022.108326</ref> Since it is based on the system's admittance matrix, the formulation is able to consider radial and meshed network topologies without additional modifications (contrary to the compensation-based BFS<ref>Shirmohammadi, D., Hong, H. W., Semlyen, A., & Luo, G. X. (1988). A compensation-based power flow method for weakly meshed distribution and transmission networks. IEEE Transactions on power systems, 3(2), 753-762. https://doi.org/10.1109/59.192932</ref>). The simplicity and computational efficiency of the LPF method make it an attractive option for recursive power flow problems, such as those encountered in time-series analyses, metaheuristics, probabilistic analysis, reinforcement learning applied to power systems, and other related applications.