Pattern Identification and Mechanism Analysis of Nonlinear Oscillations in Grid-connected Direct-drive Wind Turbines

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

Abstract

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

CLC Number:

TP391.9

Wen Libin, Tang Shaopu, Hu Xianfa, Xi Jinji, Zhang Tongtong, Hu Hong, Zhang Weijie. 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.

Figures/Tables 16

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Table 1

Table 2

Fig. 5

Fig. 6

Table 3

Original model parameters and parameter values of grid-connected direct-drive wind turbine system

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

Table 3

Fig. 7

Fig. 8

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Table 4

Nonlinear oscillation patterns-affected components-mechanisms

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

Table 4

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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