A Novel Higher-Order Numerical Scheme for System of Nonlinear Load Flow Equations

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Power flow problems can be solved in a variety of ways by using the Newton–Raphson approach. The nonlinear power flow equations depend upon voltages Vi and phase angle δ. An electrical power system is obtained by taking the partial derivatives of load flow equations which contain active and reactive powers. In this paper, we present an efficient seventh-order iterative scheme to obtain the solutions of nonlinear system of equations, with only three steps in its formulation. Then, we illustrate the computational cost for different operations such as matrix–matrix multiplication, matrix–vector multiplication, and LU-decomposition, which is then used to calculate the cost of our proposed method and is compared with the cost of already seventh-order methods. Furthermore, we elucidate the applicability of our newly developed scheme in an electrical power system. The two-bus, three-bus, and four-bus power flow problems are then solved by using load flow equations that describe the applicability of the new schemes.