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Intermittent distributed generation and stochastic loads cause uncertainty in power flow in distribution networks. To construct the relationship between power injections and node voltages over a long time scale and a wide operational region, an interval mapping model is proposed in this paper, which is composed of multiple affine power flow calculations and interval regression via quadratic programming. An acceleration mechanism using parallel processing and iterative acceleration is designed to improve modeling efficiency. The application of the interval model in overvoltage prevention coordinated control is further discussed. Numerical results tested by a modified IEEE 33-bus system demonstrate that the interval mapping model has good performance in assessing the impact boundaries of power injections on uncertain voltage responses. The acceleration mechanism for the modeling process gives the interval mapping model the potential for online application; the effect of overvoltage prevention control in simulation further shows its practical value.
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Chen et al. (2017) studied this question.
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