Hongjin Du

Weijie Xia, James Ciyu Qin, Edgar Mauricio Salazar Duque et al.

Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC) based power flow (PF) simulations or simplified analytical approximations. While MC approaches are computationally intensive and demand substantial data storage, analytical approximations often compromise accuracy. In this paper, we propose a novel analytical PPF framework that eliminates the dependence on MC-based PF simulations and, in principle, enables an approximation of the analytical form of arbitrary voltage distributions. The core idea is to learn an explicit and invertible mapping between stochastic power injections and system voltages using invertible neural networks (INNs). By leveraging the Change of Variable Theorem, the proposed framework facilitates direct approximation of the analytical form of voltage probability distributions without repeated PF computations. Extensive numerical studies demonstrate that the proposed framework achieves state-of-the-art performance both as a high-accuracy PF solver and as an efficient analytical PPF estimator.

Hongjin Du, Aleksandra Lekić

The integration of massive offshore wind into hybrid AC-HVDC grids demands robust DC voltage regulation, yet conventional fixed-gain droop controllers struggle under severe stochastic volatility. This paper bridges the gap between system-level economic dispatch and converter-level control by proposing a novel Stochastic Optimal Power Flow (SOPF)-based adaptive droop framework. Rather than relying on heuristic or reactive tuning, wind forecast uncertainty is modeled using a zone-wise Beta distribution that accurately captures the heteroscedastic nature of wind errors across low, mid, and high power regimes. By leveraging Polynomial Chaos Expansion (PCE) within a chance-constrained SOPF, the system's stochastic states are formulated analytically. Crucially, the optimal adaptive droop gain is extracted directly from the first-order PCE coefficients via a Jacobian-free sensitivity analysis, embedding statistical voltage-security guarantees directly into the local converter control. Validation on a 4-terminal AC-HVDC system demonstrates that scenario-adaptive gains significantly outperform standard fixed-coefficient approaches, effectively minimizing active-power tracking errors during extreme wind disturbances.