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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摘要

研究表明锁相环成为导致双馈风电机组低频和次/超同步振荡和同步失准的重要因素。虽然当前模型降阶成为实时仿真和控制器设计的重要手段并得到了广泛的研究,但是传统模型降阶技术多关注于模型精度和模型计算复杂度,无法实现特定参数或控制环节的机理保留。因此,本文提出一种基于平衡截断的锁相环完整结构保留的双馈风电机组降阶模型构建方法。该方法完整保留了风电机组的动态特性,并解决了降阶系统响应曲线在特定频段内无法贴合全阶系统的问题。首先建立并联双馈风电机组全阶小信号模型。其次,分别将锁相环结构与系统解耦并分离为解耦子系统与解耦主系统。然后,将锁相环中含有的状态变量保留在解耦子系统中,并对解耦主系统应用平衡截断。最后将解耦子系统与降阶解耦主系统恢复耦合,完成锁相环完整结构的保留和系统降阶。文章以20台双馈风机并联的风电机组为例,验证所提锁相环完整结构保留降阶方法的有效性。

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关键词 ：双馈风机, 锁相环, 小信号稳定性, 降阶模型, 平衡截断

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 (include 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 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

收稿日期: 2024-12-30

PACS:

TM712

基金资助:

国家自然科学基金（52307194,5247072151）和国家重点研发计划（2023YFF0615000）资助

通讯作者: 王睿男,1993年生,副教授,博士生导师,研究方向为风光储集成化微电网的稳定分析与运行控制。E-mail：wangrui@ise.neu.edu.cn

作者简介: 于潇寒男,2001年生,博士研究生,研究方向为新型电力系统的稳定分析与致稳控制。E-mail：13840165130@163.com

引用本文:

于潇寒, 王睿, 邹亮, 孙秋野. 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[J]. 电工技术学报, 0, (): 250440-. Yu Xiaohan, Wang Rui, Zou Liang, Sun Qiuye. Construction of Reduced Order Model of Doubly-Fed Wind Turbines with The Preservation of Complete Phase-Locked Loop Structure Based on Balanced Truncation. Transactions of China Electrotechnical Society, 0, (): 250440-.

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