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New energy power systems with high-permeability photovoltaic and wind power are high-dimensional dynamic large-scale systems with nonlinear, uncertain and complex operating characteristics. The uncertainty of new energies creates challenges in detailed analyses of operating conditions and the efficient planning of distribution networks. Probabilistic power flows (PPFs) are effective tools for uncertainty analyses of distribution networks, and they can be applied in stochastic programming, risk assessment and other fields. We propose different forms of PPFs, which are origin moments rather than means and variances, based on point estimation. We design a stochastic programming model suitable for new energy planning in practice, and the PPF results can be used to improve energy stochastic programming methods by considering the principle of maximum entropy (POME) and quadratic fourth-order moment (QFM) estimation. The origin moments of PPFs are transformed into central moments as inputs of QFM based on probability theory. QFM can efficiently estimate the constraint probability levels of stochastic optimal planning models, and the proposed method is verified based on an IEEE 33-node distribution network.

Statistical Machine Learning Model for Uncertainty Planning of Distributed Renewable Energy Sources in Distribution Networks