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The authors describe a method for taking uncertainty into account during power flow solutions with uncertain input data. The method is based on interval arithmetic which takes into consideration the uncertainty of the nodal information, and is able to provide strict bounds for the solutions to the problem: all possible solutions are included within the bounds given by interval arithmetic. Results are compared with those obtainable by Monte Carlo simulations and by the use of stochastic power flows. Object-oriented programming techniques make it possible to use interval arithmetic with minimal modifications to existing software. However, to reduce the conservatism inherent in all interval arithmetic computations, an iterative method used to obtain the hull of the solution set is described.>
Wang et al. (Wed,) studied this question.