ABSTRACT Coordinating transmission system operators (TSOs) and distribution system operators (DSOs) under high renewable penetration demands probabilistic frameworks that faithfully capture the non‐Gaussian uncertainty introduced by wind forecast errors. Existing approaches either assume Gaussian distributions, losing critical information about distributional asymmetry and tail behavior, or employ computationally expensive scenario‐based methods that scale poorly to multi‐area systems. To address these limitations, this paper proposes a hierarchical probabilistic coordination framework with three integrated components. First, a Cornish–Fisher‐based risk metric is derived that embeds all four statistical moments—mean, variance, skewness and kurtosis—directly into the coordination objective, enabling explicit penalization of distributional asymmetry and tail heaviness without auxiliary variables or scenario aggregation. Second, a two‐level analytical target cascading (ATC) algorithm with augmented Lagrangian penalty updates is developed, where each DSO reports only five scalars (risk cost, mean, standard deviation, skewness and kurtosis) to the TSO, preserving network privacy while enabling area‐specific non‐Gaussian risk assessment. Third, a systematic risk differentiation mechanism distinguishes area‐level risk contributions based on their individual distributional characteristics, enabling targeted reserve allocation that variance‐only or three‐moment methods cannot achieve. Case studies on a 118‐bus TSO with 9‐bus and 7‐bus DSOs using 100 scenarios per iteration, ten 50 MW TSO wind farms, and one wind farm per DSO compare four methods: deterministic, variance‐only, three‐moment and the proposed higher‐order moment (HOM) approach. The HOM method achieves a risk‐adjusted cost 12% below deterministic coordination, with 91% OPF feasibility across 1500 scenario solves. Results confirm that area‐level non‐Gaussian features—particularly strong skewness and excess kurtosis at the DSO level—drive meaningful risk differentiation that variance‐only methods miss.
Nawaz et al. (Thu,) studied this question.