![]() The stochastic optimal planning of distribution networks has become one of the key problems in the development of smart grids. The impact of new energy uncertainty on the operation optimization of distribution networks cannot be ignored, and high requirements for planning and design have been proposed. Hydrogen production from renewable energy has become a hot spot of new energy application because of its low energy consumption ( Zhang et al., 2021). In the context of smart grids and low-carbon power, the broad application of intermittent renewable distributed generation (DG) has led to uncertainty in distribution network planning ( Injeti and Thunuguntla, 2020). 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. The origin moments of PPFs are transformed into central moments as inputs of QFM based on probability theory. 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. We propose different forms of PPFs, which are origin moments rather than means and variances, based on point estimation. 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. The uncertainty of new energies creates challenges in detailed analyses of operating conditions and the efficient planning of distribution networks. ![]() 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. 2State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (North China Electric Power University), Beijing, China.1College of Information and Electrical Engineering, China Agricultural University, Beijing, China.
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