Distributionally Robust Chance-Constrained AC-OPF for Integrating Wind Energy through Multi-Terminal VSC-HVDC

Li Yao, Xiuli Wang, Yujun Li, Chao Duan, Xiong Wu*

*Corresponding author for this work

Research output: Contribution to journalArticle


Using the multi-terminal VSC-HVdc (MTDC) system to collect far-distance offshore wind power into the main onshore ac grid has become one of the ideal transmission approaches for renewable energy integration. However, with traditional fixed dc droop control in MTDC system, the lack of the capability of regulating power flow might pose a great challenge to the system operation. Accordingly, a novel MTDC model has been established in this paper which establishes that the output power of onshore converters can be formulated as a linear function of the control variables, namely power initial set point of each onshore converter. Based on this model, considering the uncertainty from wind power forecast error, a distributionally robust chance-constrained AC-OPF model is proposed for the hybrid AC/MTDC system. Without any presumption on the probability distribution of uncertainty, this model ensures the secure operation by enforcing chance constraints under the worst-case probability distribution over an ambiguity set based on the Wasserstein-Moment metric. Aiming at obtaining a tractable chance-constraint reformulation, we first employ the partial linearization of ac power flow equations to yield a linear model which represents the system response under uncertainties. We then develop an efficient and scalable approach to derive the linear analytical reformulation of distributionally robust chance constraints. The performance of the proposed model is firstly tested on the 14-bus system for an illustrative purpose, and then on the 1354-bus system for demonstrating scalability.

Original languageEnglish (US)
Article number8756047
Pages (from-to)1414-1426
Number of pages13
JournalIEEE Transactions on Sustainable Energy
Issue number3
StatePublished - Jul 2020
Externally publishedYes


  • AC-OPF
  • Chance-constrained programming
  • Distributionally robust optimization (DRO)
  • Multi-terminal VSC-HVdc (MTDC)

ASJC Scopus subject areas

  • Renewable Energy, Sustainability and the Environment

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