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

• Frequency containment reserve using wind farm and contingency state analysis. • An enhanced model of Frequency-constrained Contingency-State-Analysis is developed. • Both conventional generators and converter-interfaced generators as well as Under-Frequency-Load-Shedding are considered in the new models. • A set of new frequency dynamic indexes are calculated based on a Cross-Entropy-based Monte Carlo simulation. 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. [ABSTRACT FROM AUTHOR]