直驱风机并网非线性振荡形态挖掘与机理剖析

doi:10.16182/j.issn1004731x.joss.25-0611

摘要/Abstract

摘要：

以直驱风机并网系统为例，构建了包含原动机控制、机侧与网侧变流器控制、多重限幅及控制切换等非线性环节的综合模型，提出一种基于密度聚类算法并结合人工鉴别的非线性振荡形态筛选方法。结果表明：该方法能高效识别近似等幅振荡、倍周期振荡和混沌振荡等多种典型形态；由控制切换、限幅碰撞及限幅饱和等非线性因素主导的振荡，其本质是相关环节由被动响应转变为振荡的主动驱动源，通过非光滑或非对称特性向系统注入能量；倍周期振荡与桨距角变化率限幅的非对称性及多重限幅耦合密切相关。

关键词: 饱和限幅, 控制切换, 非线性振荡, 密度聚类, 稳定现象挖掘, 批量时域仿真, 机理剖析

Abstract:

Taking a grid-connected direct-drive wind turbine system as an example, a comprehensive model is developed that incorporates nonlinear elements such as prime mover control, machine-side and grid-side converter control, multiple limiters, and control switching. A nonlinear oscillation pattern identification method based on density clustering and manual identification is proposed. The results show that the proposed method can efficiently identify various typical patterns, including quasi-constant amplitude oscillations, period-doubling oscillations, and chaotic oscillations. Oscillations dominated by nonlinear factors such as control switching, limiter collision, and limiter saturation are essentially caused by the transition of the associated components from passive responses to active sources of oscillations, which inject energy into the system through nonsmooth or asymmetric characteristics. Period-doubling oscillations are closely related to the asymmetry of pitch rate limiting and the coupling of multiple limiters.

Key words: saturation limiting, control switching, nonlinear oscillation, density clustering, stability phenomena identification, batch time-domain simulation, mechanism analysis

中图分类号:

TP391.9

文立斌,唐绍普,胡宪法等 . 直驱风机并网非线性振荡形态挖掘与机理剖析[J]. 系统仿真学报, 2026, 38(6): 1734-1748.

Wen Libin,Tang Shaopu,Hu Xianfa,et al . Pattern Identification and Mechanism Analysis of Nonlinear Oscillations in Grid-connected Direct-drive Wind Turbines[J]. Journal of System Simulation, 2026, 38(6): 1734-1748.

图/表 16

图1

图2

图3

图4

表1

表2

图5

图6

表3

直驱风机并网系统原模型参量及参数值

参量	数值
单机容量S_base/MVA	2
直流电压V_dc/kV	1.45
额定运行频率f_req/Hz	60
直流电容C/µF	15 000
最大电流值I_max	1.1 p.u.
网侧PLL中PI比例系数k_{p_pll}	50
网侧DVC中PI比例系数k_{p_DVC}	1.0
网侧AVC中PI比例系数k_{p_AVC}	0.75
网侧无功环控制比例系数k_{p_Q}	1.0
网侧ACC中d/q轴PI比例系数k_{p_I}	0.5
网侧ACC的q轴指令值I_q,_G_{_}_lim限幅值	±1.1
机侧ACC的q轴指令值I_q,_T_{_}_lim限幅值	±1.1
无功控制指令Q_lim限幅值	±0.6
网侧ACC中PI输出限幅	±0.7
桨距角增长变化率限值/((˚)/s)	15
并网点电压V_t/kV	0.69
额定风速v_nom/(m/s)	12
机侧额定运行频率f_{req_PM}/Hz	30
并网电感L_f/mH	0.335
穿越控制电压偏差阈值ΔU	±0.1 p.u.
网侧PLL中PI积分系数k_i_{_pll}	100
网侧DVC中PI积分时间常数T_i_{_DVC}	0.02
网侧AVC中PI积分时间常数T_i_{_AVC}	0.1
网侧无功环控制积分时间常数T_i_{_Q}	0.02
网侧ACC中d/q轴PI积分时间常数T_i_{_I}	0.05
网侧ACC的d轴指令值I_d,_{G_lim}限幅值	$± I G, m a x 2 - I q, G_o r d 2$
机侧ACC的d轴指令值I_d,_{T_lim}限幅值	$± I T, m a x 2 - I q, T_o r d 2$
网侧PLL输出频率上限f_G_,_max/Hz	72
网侧PLL输出频率上限f_G_,_min/Hz	48
机侧PLL输出频率上限f_T_,_max/Hz	36
机侧PLL输出频率上限f_T_,_min/Hz	24
桨距角可调范围/(˚)	0~28
网侧ACC中PI输出限幅	±0.8
桨距角减小变化率限值/((˚)/s)	5

表3

图7

图8

图9

图10

图11

图12

表4

非线性振荡形态-作用环节-机理总结

参数变化	主导/强参与环节	非线性参与类型	功率振荡现象	$Δ θ$ 形态	振荡机理
网侧无功控制的PI积分时间常数T_{i_}_Q减小	穿越控制	控制切换	近似等幅振荡	近似等幅振荡	周期性穿越控制反复投退
网侧PLL带宽增加	PLL限幅	限幅碰撞	近似等幅振荡	近似等幅振荡	PLL输出频率周期性限幅碰撞
网侧ACC的PI中的积分时间常数T_{i_}_I减小	网侧ACC的d轴限幅、机侧PLL限幅	限幅碰撞限幅饱和	近似等幅振荡后崩溃	振荡后达2π	周期性限幅碰撞致近似等幅振荡，限幅饱和致系统崩溃
并网电感L_f增大至一定范围	机侧ACC的d轴限幅、穿越控制	限幅碰撞控制切换	I型倍周期振荡	倍周期振荡	系统等效阻尼降低，多非线性因素作用
直流电压环PI积分时间常数T_{i_}_D减小	桨距角变化速率	限幅饱和	II型倍周期振荡	倍周期振荡	机侧注入的非对称限幅特性引起的强迫振荡
并网电感L_f增大，如本文提及的0.9 mH	穿越控制、机侧d轴ACC限幅	控制切换限幅饱和	混沌振荡	混沌振荡	系统等效阻尼严重降低，进入临界状态
进一步增大并网电感L_f	输入PWM参考电压幅值限幅、穿越控制	限幅饱和控制切换	振荡发散或崩溃	振荡后达到2π 或快速达到2π	系统等效阻尼极度削弱，进入不稳定状态

表4

参考文献 25

[1]	谢小荣, 王路平, 贺静波, 等. 电力系统次同步谐振/振荡的形态分析[J]. 电网技术, 2017, 41(4): 1043-1049.
	Xie Xiaorong, Wang Luping, He Jingbo, et al. Analysis of Subsynchronous Resonance/Oscillation Types in Power Systems[J]. Power System Technology, 2017, 41(4): 1043-1049.
[2]	樊陈, 姚建国, 张琦兵, 等. 英国"8·9"大停电事故振荡事件分析及思考[J]. 电力工程技术, 2020, 39(4): 34-41.
	Fan Chen, Yao Jianguo, Zhang Qibing, et al. Reflection and Analysis for Oscillation of the Blackout Event of 9 August 2019 in UK[J]. Electric Power Engineering Technology, 2020, 39(4): 34-41.
[3]	邱伟, 孙凯祺, 丁肇豪, 等. 西葡"4·28"停电事故原因初探及对中国电力系统发展的启示[J]. 电力系统自动化, 2025, 49(24): 1-11.
	Qiu Wei, Sun Kaiqi, Ding Zhaohao, et al. Preliminary Exploration of Causes of Spain-portugal Blackout on April 28,2025 and Its Enlightenment for Development of China's Power System[J]. Automation of Electric Power Systems, 2025, 49(24): 1-11.
[4]	吴恒, 阮新波, 杨东升. 弱电网条件下锁相环对LCL型并网逆变器稳定性的影响研究及锁相环参数设计[J]. 中国电机工程学报, 2014, 34(30): 5259-5268.
	Wu Heng, Ruan Xinbo, Yang Dongsheng. Research on the Stability Caused by Phase-locked Loop for LCL-type Grid-connected Inverter in Weak Grid Condition[J]. Proceedings of the CSEE, 2014, 34(30): 5259-5268.
[5]	季一宁, 王海风. 包含串补的并网直驱风电场振荡稳定性及可行域分析[J]. 电工技术学报, 2024, 39(3): 686-698.
	Ji Yining, Wang Haifeng. Analysis of Oscillation Stability and Feasible Region of Parameters in Grid-connected Direct-drive Wind Farm with Series Compensation[J]. Transactions of China Electrotechnical Society, 2024, 39(3): 686-698.
[6]	毕天姝, 孔永乐, 肖仕武, 等. 大规模风电外送中的次同步振荡问题[J]. 电力科学与技术学报, 2012, 27(1): 10-15.
	Bi Tianshu, Kong Yongle, Xiao Shiwu, et al. Review of Sub-synchronous Oscillation with Large-scale Wind Power Transmission[J]. Journal of Electric Power Science and Technology, 2012, 27(1): 10-15.
[7]	栗然, 卢云, 刘会兰, 等. 双馈风电场经串补并网引起次同步振荡机理分析[J]. 电网技术, 2013, 37(11): 3073-3079.
	Li Ran, Lu Yun, Liu Huilan, et al. Mechanism Analysis on Subsynchronous Oscillation Caused by Grid-integration of Doubly Fed Wind Power Generation System via Series Compensation[J]. Power System Technology, 2013, 37(11): 3073-3079.
[8]	黄林彬. 高比例电力电子装备电力系统的同步稳定分析与控制设计[D]. 杭州: 浙江大学, 2020.
	Huang Linbin. Synchronization Stability and Control of Power Systems with High-penetration Power Electronics[D]. Hangzhou: Zhejiang University, 2020.
[9]	Fu Ruiqing, Wang Xiaoru, Li Longyuan, et al. Analytic Quantification of Controllers Interaction of Weak Grid Tied VSC in Current Control Timescale[J]. IEEE Transactions on Energy Conversion, 2024, 39(1): 191-204.
[10]	Huang Linbin, Xin Huanhai, Li Zhiyi, et al. Grid-synchronization Stability Analysis and Loop Shaping for PLL-based Power Converters with Different Reactive Power Control[J]. IEEE Transactions on Smart Grid, 2020, 11(1): 501-516.
[11]	刘巨, 姚伟, 文劲宇. 考虑PLL和接入电网强度影响的双馈风机小干扰稳定性分析与控制[J]. 中国电机工程学报, 2017, 37(11): 3162-3173.
	Liu Ju, Yao Wei, Wen Jinyu. Small Signal Stability Analysis and Control of Double-fed Induction Generator Considering Influence of PLL and Power Grid Strength[J]. Proceedings of the CSEE, 2017, 37(11): 3162-3173.
[12]	Mohammadreza Fakhari Moghaddam Arani, Abdel-Rady I Mohamed Yasser. Analysis and Performance Enhancement of Vector-controlled VSC in HVDC Links Connected to very Weak Grids[J]. IEEE Transactions on Power Systems, 2017, 32(1): 684-693.
[13]	Wang Dong, Liang Liang, Shi Lei, et al. Analysis of Modal Resonance Between PLL and DC-link Voltage Control in Weak-grid Tied VSCs[J]. IEEE Transactions on Power Systems, 2019, 34(2): 1127-1138.
[14]	姜齐荣, 赵崇滨. 并网逆变器的电磁暂态同步稳定问题[J]. 清华大学学报(自然科学版), 2021, 61(5): 415-428.
	Jiang Qirong, Zhao Chongbin. Electromagnetic Transient Synchronization Stability with Grid-connected Inverters[J]. Journal of Tsinghua University(Science and Technology), 2021, 61(5): 415-428.
[15]	曾平, 张琛, 李征. 电网故障期间全功率风电机组的暂态同步稳定控制策略[J]. 中国电机工程学报, 2022, 42(16): 5935-5947.
	Zeng Ping, Zhang Chen, Li Zheng. Control Strategy of Transient Synchronization Stability of Full-scale Wind Turbines During Grid Faults[J]. Proceedings of the CSEE, 2022, 42(16): 5935-5947.
[16]	张宇, 蔡旭, 张琛, 等. 并网变换器的暂态同步稳定性研究综述[J]. 中国电机工程学报, 2021, 41(5): 1687-1701.
	Zhang Yu, Cai Xu, Zhang Chen, et al. Transient Synchronization Stability Analysis of Voltage Source Converters: A Review[J]. Proceedings of the CSEE, 2021, 41(5): 1687-1701.
[17]	张宇, 张琛, 蔡旭, 等. 并网变换器的暂态同步稳定性分析:稳定域估计与镇定控制[J]. 中国电机工程学报, 2022, 42(21): 7871-7883.
	Zhang Yu, Zhang Chen, Cai Xu, et al. Transient Grid-synchronization Stability Analysis of Grid-tied Voltage Source Converters: Stability Region Estimation and Stabilization Control[J]. Proceedings of the CSEE, 2022, 42(21): 7871-7883.
[18]	薛安成, 王子哲, 付潇宇, 等. 基于非光滑分叉的直驱风机次同步振荡机理分析[J]. 电力系统自动化, 2020, 44(7): 87-92.
	Xue Ancheng, Wang Zizhe, Fu Xiaoyu, et al. Mechanism Analysis of Subsynchronous Oscillation in Direct-driven Wind Turbine Based on Non-smooth Bifurcation[J]. Automation of Electric Power Systems, 2020, 44(7): 87-92.
[19]	Xue Ancheng, Fu Xiaoyu, Wang Zizhe, et al. Analysis of Sub-synchronous Band Oscillation in a DFIG System with Non-smooth Bifurcation[J]. IEEE Access, 2019, 7: 183142-183149.
[20]	薛安成, 王永杰, 付潇宇, 等. 含SVG的双馈系统切换型次同步振荡及其非光滑分岔特性分析[J]. 电网技术, 2021, 45(3): 918-925.
	Xue Ancheng, Wang Yongjie, Fu Xiaoyu, et al. Analysis of Switched Subsynchronous Oscillation and Its Non-smooth Bifurcation Characteristics in Doubly-fed System with SVG[J]. Power System Technology, 2021, 45(3): 918-925.
[21]	黄桦, 陆宇烨, 潘学萍, 等. 基于限幅环节动作时间的直驱永磁风电场等值建模[J]. 河海大学学报(自然科学版), 2019, 47(1): 88-94.
	Huang Hua, Lu Yuye, Pan Xueping, et al. Equivalent Modelling of the DDPMSG-based Wind Farm Based on Action Time Clustering of Limiting Component[J]. Journal of Hohai University(Natural Sciences), 2019, 47(1): 88-94.
[22]	吴天昊, 谢小荣, 贺静波, 等. 限幅状态下并网变流器的同步稳定问题[J]. 中国电机工程学报, 2025, 45(17): 6886-6896.
	Wu Tianhao, Xie Xiaorong, He Jingbo, et al. Synchronization Stability Issues of Grid-tied Converters with Saturation Nonlinearities[J]. Proceedings of the CSEE, 2025, 45(17): 6886-6896.
[23]	纪君奇, 杨黎晖, 马西奎. 基于虚拟同步发电机控制的并网逆变器切换型振荡及其非光滑分岔特性[J]. 电工技术学报, 2024, 39(24): 7860-7873.
	Ji Junqi, Yang Lihui, Ma Xikui. Switched Oscillation and Its Non-smooth Bifurcation Characteristics in Grid-connected Inverter Based on Virtual Synchronous Generator Control[J]. Transactions of China Electrotechnical Society, 2024, 39(24): 7860-7873.
[24]	薛静玮, 林毅, 叶荣, 等. 正阻尼直驱风电系统限幅持续饱和引起的振荡分析[J]. 电力系统及其自动化学报, 2023, 35(2): 45-52.
	Xue Jingwei, Lin Yi, Ye Rong, et al. Analysis of Oscillation Caused by Continuous Saturation of Limit for Positive Damping PMSG System[J]. Proceedings of the CSU-EPSA, 2023, 35(2): 45-52.
[25]	范宏, 彭瑞, 张树卿, 等. 基于多次密度空间聚类算法的多逆变器并网同步稳定物理表征[J]. 南方电网技术, 2025, 19(6): 173-183.
	Fan Hong, Peng Rui, Zhang Shuqing, et al. Physical Characterization of Grid-connected Synchronous Stability of Multiple Inverters Based on Multiple Density Spatial Clustering Algorithm[J]. Southern Power System Technology, 2025, 19(6): 173-183.

环节	输入		参数	限值	输出
机侧有功控制	x_in,0	P_G	k_p_{_}_P	I_d,_T_{_}_min	I_d,_{T_ord}
机侧有功控制	x_in,1	P_ref	k_i_{_}_P	I_d,_T_{_}_max	I_d,_{T_ord}
机侧电压控制	x_in,0	V_ref_{_}_T	k_p_{_V}_m	I_q,_T_{_}_min	I_q,_{T_ord}
机侧电压控制	x_in,1	V_{rms_T}	k_i_{_V}_m	I_q,_T_{_}_max	I_q,_{T_ord}
机侧d轴电流控制	x_in,0	I_d_{,T_ord}	k_p,TI_{_d}	V_d,_TI_{_}_min	V_d,_TI
机侧d轴电流控制	x_in,1	I_d_,T	k_i,TI_{_d}	V_d,_TI_{_}_max	V_d,_TI
机侧q轴电流控制	x_in,0	I_q_{,T_ord}	k_p,TI_{_q}	V_q,_TI_{_}_min	V_q,_TI
机侧q轴电流控制	x_in,1	I_q_,T	k_i,TI_{_q}	V_q,_TI_{_}_max	V_q,_TI
网侧DVC	x_in,0	E_dc	k_p_{_}_DVC	I_d,_G_{_}_min	I_d,_{G_ord}
网侧DVC	x_in,1	E_{dc_ref}	k_i_{_}_DVC	I_d,_G_{_}_max	I_d,_{G_ord}
网侧端电压控制	x_in,0	V_t_{_}_rms	k_p_{_}_AVC	Q_min	-Q_ref
网侧端电压控制	x_in,1	V_{t_ref}	k_i_{_}_AVC	Q_max	-Q_ref
网侧无功控制	x_in,0	Q_ref	k_p_{_}_Q	I_q,_G_{_}_min	I_q,_{G_ord}
网侧无功控制	x_in,1	Q_G	k_i_{_}_Q	I_q,_G_{_}_max	I_q,_{G_ord}
网侧d轴ACC	x_in,0	I_d_{,G_ord}	k_p,GI_{_d}	V_d,_GI_{_}_min	V_d,_GI
网侧d轴ACC	x_in,1	I_d_,G	k_i,GI_{_d}	V_d,_GI_{_}_max	V_d,_GI
网侧q轴ACC	x_in,0	I_q_{,G_ord}	k_p,GI_{_q}	V_q,_GI_{_}_min	V_q,_GI
网侧q轴ACC	x_in,1	I_q_,G	k_i,GI_{_q}	V_q,_GI_{_}_max	V_q,_GI

控制环节	切换特性
穿越控制
Chopper电路控制