Aritméticas intervalares aplicadas à solução do problema de fluxo de potência via equações de injeção de corrente

Abstract

Power flow analysis typically uses a given set of generation and loading profiles to determine steady state operating conditions of electric power systems. When the input data are imprecise, several scenarios need to be analysed to cover the range of uncertainties. Under these conditions, it is necessary to utilise algorithms to incorporate the effect of the uncertainties within the power flow analysis. As an alternative solution to this issue, a new method has been proposed, based on the use of affine arithmetic. This alternative technique has been developed to improve the self-validated numerical analysis. Within affine arithmetic, the quantities of interest are represented by affine combinations of certain primitive variables. The affine combinations can signify both the source of the uncertainties in the data and the approximations during calculations. This technique is incorporated at the power flow which is expressed in terms of current injection equations, with the voltages represented in the rectangular form. The proposed results are later compared with the Monte Carlo Simulation and interval arithmetic, both of which solve the same issue: uncertainties in the power flow analysis of electric power grids.