Distributionally robust hierarchical multi-objective voltage risk management for unbalanced distribution systems

Shida Zhang, Shaoyun Ge, Hong Liu, Bo Zhao, Chouwei Ni, Zhengyang Xu, Chenghong Gu

Research output: Contribution to journalArticlepeer-review

7 Citations (SciVal)


The large-scale integration of renewable energy generators (REGs) is key to reducing carbon emissions. However, the intermittency of REG outputs poses operational risk challenges on distribution systems (DSs). This paper proposes a novel Wasserstein-based distributionally robust assessment for the voltage risk index that represents both likelihood and non-linearly increasing severity of voltage violations. We propose a hierarchical DRO model for risk management that integrates a multi-objective distributionally robust optimization (DRO) at the distribution system operator (DSO) level and a basic DRO at the user level. Then, a systematic solution method is developed, where the proposed model is equivalently reformulated into tractable bilevel mixed-integer convex programs. The effectiveness, advantages, and scalability of the proposed method are validated on the IEEE 33-bus system and unbalanced IEEE-123-bus system.

Original languageEnglish
Article number109446
Number of pages21
JournalInternational Journal of Electrical Power and Energy Systems
Early online date2 Sept 2023
Publication statusPublished - 31 Dec 2023

Bibliographical note

Funding Information:
This work is supported by Key Technology Project of State Grid Corporation of China (Key technology research and application of prefecture-level carbon and electricity coordinated grid regulation and control with a high proportion of distributed clean energy, 5100-202119565A-0-5-SF).


  • Carbon tax
  • Distributionally robust optimization
  • Renewable energy generators
  • Security risk management
  • Unbalanced distribution systems
  • Voltage risk assessment

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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