Fluxo de potência holomórfico intervalar: uma nova abordagem para o tratamento de incertezas em sistemas elétricos de potência

Abstract

Due to the introduction of energy sources with high variability, new types of load, meter inaccuracy and uncertain data in the electrical sector, it is necessary to develop computational methods capable of correctly modeling the uncertainties inherent to the power flow. In this context, this dissertation presents an interval approach for the Holomorphic Embedding Load Flow Method (HELM), considering load and generation uncertainties. In the proposed method, the power flow equations are written as holomorphic complex functions, being their solution determined recursively based on the MacLaurin series’ expansion and maximum analytical continuation using Padé approximants. Concepts of interval arithmetic are applied to HELM equations, assuming active and reactive powers as uncertain data to obtain interval values associated with voltage phasors for all buses in the system. Test systems, such as those with 6, 14, 30 and 57-buses, are used for computational simulations, being the results compared to the Monte Carlo (MC) approach, the Krawczyk method, the Taylor series and the affine arithmetic. As a relevant contribution, a novel interval power flow technique is presented, allowing computation of interval values closer to those determined by MC simulations than other methodologies published in the literature. Computational time is approximately 300 times faster than the MC approach considering 20.000 simulations and the interval sensitivities are, at least, two times smaller than those obtained by other interval methods. Additionally, an important contribution is presented to consider the treatment of reactive power generation limits regarding generation units, which significantly impacts the interval analysis applied to power flow equations.