Market-clearing with stochastic security - Part I: Formulation

François Bouffard, Francisco D. Galiana, Antonio J. Conejo

    Research output: Contribution to journalArticlepeer-review


    The first of this two-paper series formulates a stochastic security-constrained multi-period electricity market-clearing problem with unit commitment. The stochastic security criterion accounts for a pre-selected set of random generator and line outages with known historical failure rates and involuntary load shedding as optimization variables. Unlike the classical deterministic reserve-constrained unit commitment, here the reserve services are determined by economically penalizing the operation of the market by the expected load not served. The proposed formulation is a stochastic programming problem that optimizes, concurrently with the pre-contingency social welfare, the expected operating costs associated with the deployment of the reserves following the contingencies. This stochastic programming formulation is solved in the second companion paper using mixed-integer linear programming methods. Two cases are presented: a small transmission-constrained three-bus network scheduled over a horizon of four hours and the IEEE Reliability Test System scheduled over 24 h. The impact on the resulting generation and reserve schedules of transmission constraints and generation ramp limits, of demand-side reserve, of the value of load not served, and of the constitution of the pre-selected set of contingencies are assessed. © 2005 IEEE.
    Original languageEnglish
    Pages (from-to)1818-1826
    Number of pages8
    JournalIEEE Transactions on Power Systems
    Issue number4
    Publication statusPublished - Nov 2005


    • Deterministic/probabilistic security criteria
    • Electricity markets
    • Expected load not served
    • Failure rate
    • Reserve
    • Stochastic programming
    • Transmission limits
    • Unit commitment
    • Value


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