Stochastic bidding of volume and price in constrained energy and reserve markets

Natalia Romero, Koos van der Linden, German Morales-Espania, Mathijs de Weerdt

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
26 Downloads (Pure)


The power system is undergoing a significant change as it adapts to the intermittency and uncertainty from renewable generation. Flexibility from loads such as electric vehicles (EVs) can serve as reserves to sustain the supply-demand balance in the grid. Some reserve markets have rules for participation that are computationally challenging for aggregators of such flexible loads: they are asked to bid both volume and price, and on top of this there is a minimum-volume requirement, a constraint currently under discussion both in the US and European markets. Several state-of-the-art methods to find a bidding strategy for the demand scheduling of large fleets of flexible loads in the day-ahead and reserve market are adapted to deal with such a shared constraint, and are compared based on costs, unscheduled demand, and running time. The experimental analysis shows that although such a shared constraint significantly affects scalability, some of the proposed adaptations can deal with this without much loss in quality. This comparison also shows the importance of including good uncertainty models for dealing with the risk of not meeting the users’ demands, and that it is possible to find an optimal single price per time unit for scheduling a fleet of EVs.

Original languageEnglish
Article number106868
Pages (from-to)1-8
Number of pages8
JournalElectric Power Systems Research
Publication statusPublished - 2021


  • Electric vehicle (EV) aggregator
  • Energy market
  • Reserve market
  • Stochastic optimization


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