The state-space representations grant a convenient, compact, and elegant way to examine the induction and synchronous generator-based wind turbines, with facts readily available for stability, controllability, and observability analysis. The state-space models are used to look into the functionality of different wind turbine technologies to fulfill grid code requirements. This paper deals with the model order reduction of the Variable-Speed Wind Turbines model with the aid of improved stability preserving a balanced realization algorithm based on frequency weighting. The algorithm, which is in view of balanced realization based on frequency weighting, can be utilized for reducing the order of the system. Balanced realization based model design uses a full frequency spectrum to perform the model reduction. However, it is not possible practically to use the full frequency spectrum. The Variable-Speed Wind Turbines model utilized in this paper is stable and includes various input-output states. This brings a complicated state of affairs for analysis, control, and design of the full-scale system. The proposed work produces steady and precise outcomes such as in contrast to conventional reduction methods which shows the efficacy of the proposed algorithm.

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 article, 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.

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.”