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A key component in this technique is a relaxation\u2010based coarsening of the graph Laplacian given by the powergrid network and its weighted graph, which is represented by the admittance matrix. In this article, we use this coarsening strategy to develop a multigrid method for solving a static system of nonlinear equations that arises through Ohm's law, the so\u2010called powerflow equations. These static equations are tightly knitted to the dynamic model in that the full powergrid model is an algebraic\u2010differential system with the powerflow equations describing the algebraic constraints. We assume that the dynamic model corresponds to a stable operating powergrid, and thus, the powerflow equations are associated with a physically stable system. This stability permits the coarsening of the powerflow equations to be based on an approximate graph Laplacian, which is embedded in the powerflow system. By algebraically constructing a hierarchy of approximate weighted graph Laplacians, a hierarchy of nonlinear powerflow equations immediately becomes apparent. This latter hierarchy can then be used in a full approximation scheme (FAS) framework that leads to a nonlinear solver with generally a larger basin of attraction than Newton's method. Given the algebraic multigrid (AMG) coarsening of the approximate Laplacians, the solver is an AMG\u2010FAS scheme. Alternatively, using the coarse\u2010grid nodes and interpolation operators generated for the hierarchy of approximate graph Laplacians, a multiplicative\u2010correction scheme can be derived. The derivation of both schemes will be presented and analyzed, and numerical examples to demonstrate the performance of these schemes will be given.<\/jats:p>","DOI":"10.1002\/nla.2347","type":"journal-article","created":{"date-parts":[[2020,11,10]],"date-time":"2020-11-10T04:01:20Z","timestamp":1604980880000},"update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Algebraic multigrid for the nonlinear powerflow equations"],"prefix":"10.1002","volume":"28","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1948-7384","authenticated-orcid":false,"given":"Barry","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Mathematics Southern Methodist University Dallas Texas USA"}]},{"given":"Enrique","family":"Pereira Batista","sequence":"additional","affiliation":[{"name":"Department of Mathematics Southern Methodist University Dallas Texas USA"}]}],"member":"311","published-online":{"date-parts":[[2020,11,9]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Voltage stability of electric power systems","author":"Van Cutsem T","year":"2008"},{"key":"e_1_2_9_3_1","doi-asserted-by":"crossref","unstructured":"MakarovYV VyakaranamB WuD LeeB HouA ElbertS HuangZ. 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