Interval Holomorphic Embedding Load Flow Method: A novel approach for interval analysis considering load and generation uncertainties

This paper presents an interval approach for the Holomorphic Embedding Load Flow Method (HELM) considering load , generation uncertainties. In the proposed method, power flow equations are considered as holomorphic complex functions, being their solutions determined recursively based on the expansion in Maclaurin series and analytical continuation using Pade approximants. The concepts of the interval arithmetic are applied into the HELM equations assuming active and reactive powers as uncertain data to obtain interval values associated with the voltage phasors for all the system buses. The procedures to calculate interval results are described along the paper including the use of interval arithmetic concepts applied into the HELM equations. IEEE test systems such as 6, 14, 30 and 57-bus are used for computational simulations, being the results compared with Monte Carlo (MC) approach, Krawczyk method, Taylor series, affine arithmetic and the traditional interval power flow. As important contribution, a novel interval power flow technique is presented allowing to compute interval values closer to the ones determined by MC simulations than other alternative methods. Results are obtained in a computational time approximately 500 times faster than the MC approach considering 20,000 simulations and the interval sensitivities are, at least, twice lower than other interval methods.