Distributionally Robust Chance-Constrained Generation Expansion Planning

Farzaneh Pourahmadi, Jalal Kazempour, Christos Ordoudis, Pierre Pinson, Seyed Hamid Hosseini

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    Abstract

    This paper addresses a centralized generation expansion planning problem, accounting for both long- and shortterm uncertainties. The long-term uncertainty (demand growth) is modeled via a set of scenarios, while the short-term uncertainty (wind power generation) is described by a family of probability distributions with the same first- and second-order moments obtained from historical data. The resulting model is a distributionally robust chance-constrained optimization problem, which selects the conventional generating units to be built among predefined discrete options. This model includes a detailed representation of unit commitment constraints. To achieve computational tractability, we use a tight relaxation approach to convexify unit commitment constraints and solve the model with linear decision rules, resulting in a mixed-integer second-order cone program. It is observed that the proposed model exhibits better out-of-sample performance in terms of total expected system cost and its standard deviation compared to a chanceconstrained model that assumes a Gaussian distribution of shortterm uncertainty. A similar observation is made when comparing the proposed model against a chance-constrained program that uses empirical renewable power generation data with unknown type of distribution, recasting as either a robust optimization or a stochastic program.
    Original languageEnglish
    JournalIEEE Transactions on Power Systems
    Volume35
    Issue number4
    Pages (from-to)2888 - 2903
    ISSN0885-8950
    DOIs
    Publication statusPublished - 2020

    Keywords

    • Distributionally robust chance-constrained optimization
    • Conic programming
    • Linear decision rules
    • Generation expansion planning
    • Out-of-sample analysis
    • Unit commitment

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