On Over-Conservatism Under Low-Probability Extreme Events: A KL-Regularized Wasserstein Distributionally Robust Planning Method
Abstract
The increasing penetration of renewable energy makes power systems more vulnerable to low-probability extreme events, elevating system planning to a critical role in ensuring reliability. Distributionally robust optimization (DRO) based on the Wasserstein distance is widely used to address this challenge. However, we find that the conventional Wasserstein ambiguity set tends to excessively amplify the probabilities of low-probability extreme events, leading to over-conservative investment decisions. To mitigate this over-conservatism, this paper proposes a novel ambiguity set that modifies the Wasserstein distance with a Kullback-Leibler (KL) divergence regularization term. By leveraging the KL divergence's sensitivity to relative probability changes, the proposed set effectively curbs the unrealistic magnification of low-probability events. A two-stage distributionally robust planning model built upon this new ambiguity set is developed to optimize the installed capacity of photovoltaic, wind, and energy storage. The complex model is then reformulated as an equivalent exponential cone program with strict theoretical proofs, making it computationally tractable. Numerical results on the PJM 5-bus and IEEE 118-bus systems reveal the over-conservatism of standard Wasserstein DRO under low-probability extreme events and validate the effectiveness and efficiency of the proposed planning model and solution algorithm.
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BibTeX
@misc{shen2026overconservatism,
title = {{On Over-Conservatism Under Low-Probability Extreme Events: A KL-Regularized Wasserstein Distributionally Robust Planning Method}},
author = {Xinda Shen and Yifan Su and Bo Hu and Yanbo Chen and Changzheng Shao and Tao Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18290},
eprint = {2610.18290},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18290},
}
RIS
TY - UNPB
TI - On Over-Conservatism Under Low-Probability Extreme Events: A KL-Regularized Wasserstein Distributionally Robust Planning Method
AU - Xinda Shen
AU - Yifan Su
AU - Bo Hu
AU - Yanbo Chen
AU - Changzheng Shao
AU - Tao Wu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18290
UR - https://arxiv.org/abs/2610.18290
AB - The increasing penetration of renewable energy makes power systems more vulnerable to low-probability extreme events, elevating system planning to a critical role in ensuring reliability. Distributionally robust optimization (DRO) based on the Wasserstein distance is widely used to address this challenge. However, we find that the conventional Wasserstein ambiguity set tends to excessively amplify the probabilities of low-probability extreme events, leading to over-conservative investment decisions. To mitigate this over-conservatism, this paper proposes a novel ambiguity set that modifies the Wasserstein distance with a Kullback-Leibler (KL) divergence regularization term. By leveraging the KL divergence's sensitivity to relative probability changes, the proposed set effectively curbs the unrealistic magnification of low-probability events. A two-stage distributionally robust planning model built upon this new ambiguity set is developed to optimize the installed capacity of photovoltaic, wind, and energy storage. The complex model is then reformulated as an equivalent exponential cone program with strict theoretical proofs, making it computationally tractable. Numerical results on the PJM 5-bus and IEEE 118-bus systems reveal the over-conservatism of standard Wasserstein DRO under low-probability extreme events and validate the effectiveness and efficiency of the proposed planning model and solution algorithm.
ER -