Distributionally Robust Generation Expansion Planning With Unimodality and Risk Constraints

Farzaneh Pourahmadi, Jalal Kazempour

Research output: Contribution to journalJournal articleResearchpeer-review


As more renewables are integrated into the power system, capacity expansion planners need more advanced longterm decision-making tools to properly model short-term stochastic production uncertainty and to explore its effects on expansion decisions. We develop a distributionally robust generation expansion planning model, accounting for a family of potential probability distributions of wind forecast error uncertainty. Aiming to include more realistic distributions, we construct more informed moment-based ambiguity sets by adding structural information of unimodality. We include operational-stage unit commitment constraints and model the risk of operational limit violations in two distinct forms: chance and conditional value-at-risk (CVaR) constraints. In both forms, the resulting expansion planning model is a mixed-integer second-order cone program. Using a thorough out-of-sample numerical analysis, we conclude: (i) the distributionally robust chance-constrained generation expansion planning model exhibits a better out-ofsample performance only if sufficiently accurate information about the first- and the second-order moments as well as the mode location of potential distributions is available; (ii) conversely, if such accurate information is unavailable, the distributionally robust CVaR-constrained generation expansion planning model outperforms; (iii) these two models have a similar performance when unimodality information is excluded.
Original languageEnglish
JournalIEEE Transactions on Power Systems
Number of pages15
Publication statusAccepted/In press - 2021


  • Distributionally robust optimization
  • Chance constraints
  • CVaR constraints
  • Generation expansion planning
  • Unimodality information

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