Affine arithmetic-based dynamic operating reserve quantification considering correlated load and renewable uncertainties

Shivani Garg, Sumanth Yamujala, Parul Mathuria, Rohit Bhakar*, Harpal Tiwari

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


Operating reserves (OR), alongside other ancillary services, are essential for mitigating the increasing uncertainty in generation from Intermittent Renewable Energy Sources (IRES). Traditional OR are determined based on rules of thumb, such as reliability considerations (N - 1 or N - k ), and they neglect the uncertainty between dispatch intervals. Load–generation imbalances lead to excessive reliance on regulation reserves and out-of-merit dispatch. Highlighting this, recent literature has focused on developing models for dynamic reserve quantification. While the models significantly enhance the traditional static reserve quantification, they heavily rely on probabilistic approaches. Despite their effectiveness, probabilistic approaches are computationally complex and necessitate precise historical data. Furthermore, most studies do not consider the correlation between load and IRES when determining reserves, leading to inaccurate estimation and impacting the system’s economics. Affine arithmetic-based models emerge as a promising solution, offering the ability to estimate correlated uncertainties with reduced computational complexity. This paper contributes to developing affine arithmetic models for OR quantification, considering IRES and load correlated uncertainties. Two distinct approaches to reserve quantification are explored: (1) deterministic scheduling with exogenous OR quantification, and (2) affine arithmetic-based scheduling framework to quantify and allocate OR endogenously. A comparative analysis is conducted with probabilistic scenario-based method and interval arithmetic scheduling. The effectiveness of the models is analyzed on the Great Britain test system with 40% renewable integration. Numerical results highlight that around 99% of the probabilistic net-load scenarios are within the net-load bounds generated by the proposed methodology. The reserve requirement is minimized by approximately 8% during peak hours and 35% during off-peak hours with correlated uncertainty. Furthermore, AA-based approach achieved a 15% reduction in total operating cost during the considered operational time-frame, compared to interval arithmetic optimization.
Original languageEnglish
Article number110513
JournalElectric Power Systems Research
Number of pages16
Publication statusPublished - 2024


  • Affine auertaintyrithmetic
  • Endogenous reserve
  • Exogenous reserve
  • Intermittent renewable energy sources
  • Reserve quantification
  • Uncertainty modeling


Dive into the research topics of 'Affine arithmetic-based dynamic operating reserve quantification considering correlated load and renewable uncertainties'. Together they form a unique fingerprint.

Cite this