Quantifying frequency containment reserve using cross-entropy frequency-constrained contingency-state-analysis model

Yiping Yuan, Zhou Liu*, Zhe Chen, Kim Hoej Jensen, Marjan Popov

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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With the increasing penetration of converter-interfaced generators, the frequency containment reserve (FCR) from conventional generators keeps going down, leading to a potential risk of frequency instability under contingencies. Consequently, Converter-interfaced generators are required to provide FCR and participate in the corrective rescheduling. Nevertheless, how to assess the FCR and quantify the adequacy of FCR under contingencies is a big challenge in modern new power system. To address this challenge, a cross-entropy-based frequency-constrained contingency-state-analysis (FC-CSA) model is proposed in this paper. Notably, both frequency control (FC) of units (i.e., conventional synchronous generators and converter-interfaced generators), and under frequency load shedding (UFLS) are incorporated in the primary frequency response. Then a unified system frequency response (SFR) function representing frequency dynamic is derived. This SFR function is extracted and reformulated as a group of mixed-integer linear constraints and participates in the traditional CSA model. Moreover, a set of frequency dynamic indexes, i.e., Expectation of UFLS risk, Expectation of FCR from conventional and converter-interfaced generators, is extended to depict the FCR that the power system requires. These indexes are calculated by the FC-CSA in a cross-entropy-based monte carlo simulation (CE-MCs). Case studies on a modified IEEE 6-bus test system and IEEE 118-bus test system are carried out to demonstrate the effectiveness of the proposed FC-CSA model.

Original languageEnglish
Article number108705
Pages (from-to)1-12
Number of pages12
JournalInternational Journal of Electrical Power and Energy Systems
Publication statusPublished - 2023

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  • Contingency-State-Analysis
  • Cross-Entropy-based Monte Carlo simulation
  • Frequency Containment Reserve
  • Frequency Control
  • Under-frequency Load Shedding


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