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This paper presents a novel framework based on range arithmetic for solving power flow problems whose input data are specified within real compact intervals. Reliable interval bounds are computed for the power flow problem, which is represented as an optimization model with complementary constraints to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. It is demonstrated that the lower and upper bounds of the power flow solutions can be obtained by solving two determinate optimization problems. Several numerical results are presented and discussed, demonstrating the effectiveness of the proposed methodology and comparing it to a previously proposed affine arithmetic based solution approach.
Vaccaro et al. (2012) studied this question.