Frequency Limited & Weighted Model Reduction Algorithm With Error Bound: Application to Discrete-Time Doubly Fed Induction Generator Based Wind Turbines for Power System

Abstract

The state-space representations grant a convenient, compact, and elegant way to examine the physical systems, e.g., induction and synchronous generator-based wind turbines, with facts readily available for stability, controllability, and observability analysis. In this paper, the model order reduction of a stable doubly fed induction generator based variable-speed wind turbines model is performed with the aid of the proposed stability preserving balanced realization algorithm based on discrete frequency weights and limited frequency-interval. The frequency weighting and limited frequency-intervals-based model order reduction techniques presented by Enns's and Wang & Zilouchian produce an unstable reduced-order model at certain frequency weights and frequency intervals, respectively. To overcome this main drawback, many researchers provided a solution to preserve the stability of the reduced-order model. However, these existing approaches also produce an unstable reduced-order model in some conditions and produce a large variation to the original system; consequently, they provide a large approximation error. The proposed approach not only ensures the stability of the reduced-order model but also provides low approximation error as compared with other existing approaches and also provides an easily calculable a priori error bound formula. The proposed work produces steady and precise outcomes in contrast to conventional reduction methods, which shows the efficacy of the proposed algorithm.

Development of Frequency Weighted Model Order Reduction Techniques for Discrete-Time One-Dimensional and Two-Dimensional Linear Systems With Error Bounds

“…As a consequence, ROMs obtained are stable, and these techniques yield error bound formula [42]. Remark 8: Similarly, ROMs for decomposed systems (19) and (20) are obtained in similar way as in (49)(50) and (51-52) respectively. Moreover, ROMs obtained are stable and also yield error bound formula [42].…”

“…The frequency limited intervals for 1-D and 2-D systems are given in [48]. Similarly, frequency weighted and limited MOR approaches for power systems are given in [49]- [51].…”

New Feature Selection Algorithm Based on Feature Stability and Correlation

“…The authors showed that SFSS is fast and robust, with a higher classification accuracy, compression ratio, and extremely low computational time. In the work of Bashir et al [34], a model order reduction of a stable doubly fed induction generator based variablespeed wind turbine model was performed with the aid of the proposed stability-preserving balanced realization algorithm based on discrete frequency weights and a limited frequency interval. In contrast to conventional reduction methods, the proposed method produces steady and precise outcomes.…”

Corrections to “Frequency Limited & Weighted Model Reduction Algorithm With Error Bound: Application to Discrete-Time Doubly Fed Induction Generator Based Wind Turbines for Power System”

“…In the above article [1], two relevant references [2], [3] were missing. The last sentence of Section I-C. should read ''Proposed technique deals with frequency weighted and limited Gramians based MOR approach for the discrete-time systems.…”

“…The frequency weighted version of proposed work appears in [2] while frequency limited work appears in [3] for continuous time systems. Compared to [2], [3], mathematical model and simulations in [1] are done for frequency weighted and limited scenarios for discrete time systems. ''…”