基于平衡截断的锁相环完整结构保留双馈风电机组降阶模型构建

doi:10.19595/j.cnki.1000-6753.tces.242362

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Abstract Phase-locked loop (PLL) has gradually become an important factor that causes low frequency and sub-/super-synchronous oscillation and synchronous misalignment of doubly-fed wind turbines (DFWTs). Many time-domain state-space models have been studied for the wide band oscillation of DFWTs caused by the mismatch of the PLL. However, these models are often difficult to analyze for their high order. At the same time, the method of reduced order model analysis is unable to analyze the mechanism of the instability caused by the PLL, as the specific structure can not be retained at the present stage. Therefore, in order to retain the advantages of the state space analysis method with the discrimination of instable characteristic root and the advantages of reduced order model with small amount and high computation efficiency, a method to construct a reduced-order model for DFWTs with complete structure preservation of PLL based on balanced truncation is proposed.
Firstly, the full-order small signal model of parallel DFWTs is established in the form of state space presentation. Secondly, the PLL structure is decoupled from the system and the system is separated into decoupled subsystem (including PLL) and decoupled main system. The general idea is to reduce the order of the decoupled main system without PLL, and then integrate the model of the reduced order model of decoupled main system with the PLL structure to form a reduced order model with the PLL. Then, the state variables contained in the PLL are retained in the decoupled subsystem. Thus, an improved balanced truncation is applied to the decoupled main system. In this paper, the traditional balanced truncation based model order reduction method is improved. The prerequisite condition that the state matrix of the model to be order-reduced must be Hurwitz is improved, so that the balanced truncation based model order reduction can be carried out for any unstable state matrix. In this paper, a positive constant is introduced into the Laplace transform to form two Laplace variables. By applying the new variable Laplace variable in Laplace transform and Laplace inverse transform, the state matrix of the adjusted system can be kept Hurwitz. At this time, the adjusted system state matrix satisfies Hurwitz and can be used for the balanced truncated based model order reduction of the system. The reduced order model of the original system can be obtained by Laplace inverse transformation. The positive constant introduced in the whole process is eliminated in the transformation, which has no effect on the subsequent processing. The improved balanced truncation eliminates the premise assumption of system stability in the traditional model reduction technology. Finally, the decoupled subsystem and the decoupled main system are combined, and the complete structure of PLL is preserved. In this paper, a method of complete PLL structure preserved model order reduction based on balanced truncation is given, and a set of pseudo code of model order reduction with PLL structure preserved is given which can be directly used for other parallel wind farms. In this paper, 20 wind turbines with DFWTs in parallel are taken as an example to verify the effectiveness of the proposed PLL complete structure preservation model order reduction method. The time-domain output errors between the reduced-order model and the full-order model are demonstrated. In order to demonstrate the response characteristics of the reduced order model of DFWTs with complete PLL structure preserved, the amplitude-frequency/phase-frequency response curves of each element in the transfer function matrix of the reduced order model and the full-order model are presented respectively in the full frequency domain. In addition, the amplitude-frequency characteristic curves of the main diagonal elements in the transfer function matrix of the reduced order model are shown in the full frequency domain under the presence of small wind velocity perturbations. The dynamic effectiveness of the proposed PLL preserved model order reduction method based on balanced truncation is demonstrated.

Key words： Wind turbines phase-locked loop small-signal stability reduced order model balanced truncation

Received: 30 December 2024

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TM712

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	Yu Xiaohan
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	Zou Liang
	Sun Qiuye

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Yu Xiaohan,Wang Rui,Zou Liang等. Construction of Reduced Order Model of Doubly-Fed Wind Turbines with the Preservation of Complete Phase-Locked Loop Structure Based on Balanced Truncation[J]. Transactions of China Electrotechnical Society, 2026, 41(3): 898-911.

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