Risk-Based Distributionally Robust Optimal Power Flow With Dynamic Line Rating

Abstract

In this paper, we propose a risk-based data-driven approach to optimal power flow (DROPF) with dynamic line rating. The risk terms, including penalties for load shedding, wind generation curtailment and line overload, are embedded into the objective function. To hedge against the uncertainties on wind generation data and line rating data, we consider a distributionally robust approach. The ambiguity set is based on second-order moment and Wasserstein distance, which captures the correlations between wind generation outputs and line ratings, and is robust to data perturbation. We show that the proposed DROPF model can be reformulated as a conic program. Considering the relatively large number of constraints involved, an approximation of the proposed DROPF model is suggested, which significantly reduces the computational costs. A Wasserstein distance constrained DROPF and its tractable reformulation are also provided for practical large-scale test systems. Simulation results on the 5-bus, the IEEE 118-bus and the Polish 2736-bus test systems validate the effectiveness of the proposed models.

Optimization under uncertainty in the era of big data and deep learning: When machine learning meets mathematical programming

“…However, there are few papers on its PSE applications in the existing literature [117,119]. As the trend of big data has fueled the increasing popularity of datadriven stochastic programming in many areas, DRO emerges as a new data-driven optimization paradigm which hedges against the worst-case distribution in an ambiguity set, and has various applications in power systems, such as unit commitment problems [125][126][127][128], and optimal power flow [129,130].…”

Risk-Based Distributionally Robust Real-Time Dispatch Considering Voltage Security

“…For the W-DRO, [23] tackles the reserve and energy joint dispatch problem considering wind power uncertainties based on the W-DRO. A W-DRO model for OPF problems is established in [24], which considers dynamic line rating and line overload risk. [25] studies a W-DRO-based optimal gas-power flow problem with uncertain wind generation.…”

Distributionally Robust Co-Optimization of Power Dispatch and Do-Not-Exceed Limits

“…are commonly applied (see, e.g., [24]- [27]). Other distributional information based on, e.g., the Wasserstein distance [28], [29], the φ-divergence [11], [30], and the unimodality [16], [31], [32], have also been proposed to characterize the ambiguity set. Accordingly, DRO formulates a robust counterpart of SP and hedges against the worstcase probability distribution within the ambiguity set.…”