Distributionally Robust Model of Energy and Reserve Dispatch Based on Kullback–Leibler Divergence

Abstract

This paper proposes a distance-based distributionally robust energy and reserve (DB-DRER) dispatch model via Kullback-Leibler (KL) divergence, considering the volatile of renewable energy generation. Firstly, a two-stage optimization model is formulated to minimize the expected total cost of energy and reserve (ER) dispatch. Then, KL divergence is adopted to establish the ambiguity set. Distinguished from conventional robust optimization methodology, the volatile output of renewable power generation is assumed to follow the unknown probability distribution that is restricted in the ambiguity set. DB-DRER aims at minimizing the expected total cost in the worst-case probability distributions of renewables. Combining with the designed empirical distribution function, the proposed DB-DRER model can be reformulated into a mixed integer nonlinear programming (MINLP) problem. Furthermore, using the generalized Benders decomposition, a decomposition method is proposed and sample average approximation (SAA) method is applied to solve this problem. Finally, simulation result of the proposed method is compared with those of stochastic optimization and conventional robust optimization methods on the 6-bus system and IEEE 118-bus system, which demonstrates the effectiveness and advantages of the method proposed.

Research on power system flexibility considering uncertainties

“…The stochastic programming method requires the accurate distribution of random variables, but this is very unrealistic in practice. For example, incomplete data may lead to an inaccurate probability distribution, which may affect the decision-making results (Yang et al, 2019). The robust optimization method is different from stochastic programming.…”

“…where p and p 0 are probability distribution functions of the random variable ξ, and D KL (p|P 0 ) represents the Kullback-Leibler divergence from p to p 0 . The ambiguity set of a probability distribution based on Kullback-Leibler divergence is as follows (Yang et al, 2019):…”

Large Selective Kernel Network for Remote Sensing Object Detection

“…This has largely been achieved through the development of specialized detection frameworks, such as RoI Transformer [12], Oriented R-CNN [62] and R3Det [68], as well as techniques for oriented box encoding, such as gliding vertex [64] and midpoint offset box encoding [62]. Additionally, a number of loss functions, including GWD [70], KLD [72] and Modulated Loss [50], have been proposed to further enhance the performance of these approaches. However, despite these advances, relatively few works have taken into account the strong prior knowledge that exists in remote sensing images.…”

Danwei based community services : a case study of Tsinghua University

“…Visualization Results: Fig. 3 visually compares the results of KLD [37] and COBB. KLD's precision for the orientation of square-like objects is compromised by DA, whereas COBB accurately represents these objects, achieving strong performance by eliminating DA.…”

“…PIoU [1] and SCRDet [34] incorporate Intersection over Union (IoU) between prediction results and regression targets in their loss. GWD [36], KLD [37], and KFIoU [38] convert OBBs into Gaussian distributions for IoU calculation, introducing potential DA for square-like objects. While showing empirical effectiveness in reducing the impact of discontinuity, these approaches do not provide a theoretical resolution to the problem.…”