Analysis of Electrical Power Systems with Newton-Type Accelerated Numerical Methods

Abstract

The non-linear algebraic equations that model the load flow in an electrical network are non-linear and depend on the voltage and the complex power. In this paper, two three-step Newton-type numerical methods were reformulated to solve the non-linear equations modeling the load flow in an electrical network; the objective is to accelerate their convergence and reduce the execution time. Utilizing the Taylor series expansion of the original Newton-Raphson formula, an over-relaxation function was calculated and applied to two and three-step Newton-type numerical methods, and with the selection of an over-relaxation factor, the simulation time of the developed FORTRAN programs was reduced. With the modified techniques, the IEEE test systems of 30 and 118 nodes were solved, finding differences in the magnitude of the voltages of 0.32 percent and reducing, with a two-step method, the execution time from 1817 to 202 milliseconds for the 118-node system. For the test systems used, the low-order methods with over-relaxation present better characteristics from the point of view of execution time. From the results obtained, the load flow problem was successfully solved by applying the over-relaxation function to the reformulated Newton-type methods.