Digital Twin‐Driven Dynamic Probabilistic Power Flow in Distribution Networks via Semi‐Invariant Method

With the growing penetration of renewable energy, traditional power flow methods struggle to capture the multidimensional uncertainties and abrupt meteorological shifts in active distribution networks. To address this, the paper proposes a digital twin‐driven probabilistic power flow framework based on the semi‐invariant method and Gram–Charlier series expansion. In the modelling stage, real‐time data continuously calibrates Weibull, Beta and normal distribution parameters, transitioning grid evaluation to agile online tracking. A highly efficient convolution‐free engine utilises linear matrix mapping to directly derive nodal voltage semi‐invariants, whereas the Gram–Charlier expansion dynamically reconstructs continuous probability distributions. Simulation results on the IEEE 33‐bus system demonstrate that the proposed framework effectively quantifies the spatial accumulation of network uncertainties and the temporal evolution of operational risks, providing grid operators with dynamic probability boundaries of nodal voltage.