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This work deals with the application of tensor methods based on a quadratic model, to solve a set of nonlinear equations. Particular attention is given to the power flow problem, with emphasis on the modelling of the steady state electric network equations in rectangular coordinates. Two formulations of the power flow problem are used for the application of tensor methods. The first is the conventional approach based on active and reactive power mismatches. The second includes the equations of both power injection and the current injection balances. It is shown that the use of tensor models increases the robustness and can speed up the power flow iterative process if the computational effort for calculating the quadratic term is reduced. Numerical results obtained with power systems ranging from 6 to 1916 buses illustrate the application of the proposed methodology.