基于分岔和突变理论的VSG突变机理研究

doi:10.11930/j.issn.1004-9649.202501032

摘要/Abstract

摘要：

虚拟同步发电机（virtual synchronous generator，VSG）在运行过程中会因为突变现象而出现系统分岔曲线改变和VSG电压骤降或骤升等问题，不利于VSG的稳定运行。针对这个问题，首先，建立了以直流母线电容器电压方程为摆幅方程的VSG数学模型；其次，基于分岔和突变理论分别讨论了在内部参数和外部运行工况变化下VSG中出现的突变现象并揭示了突变机制；然后，划分了参数稳定区域并用时域仿真验证了所划分区域的正确性；最后，分析了突变对VSG电压支撑能力的影响。结果表明，突变是通过鞍结分岔点发生的，不同参数变化引起的突变是不同的，当发生电压骤降的突变时，VSG电压支撑能力会提高；当发生电压骤升的突变时，VSG电压支撑能力会减弱；在参数稳定区域内，VSG不会出现突变现象。

关键词: 分岔理论, 突变理论, 三相电压源逆变器, 虚拟同步发电机, 电压突变

Abstract:

The virtual synchronous generator (VSG) may have problems that the system bifurcation curve changes and the VSG voltage drops or rises due to catastrophe phenomena during operation, which is not conducive to the stable operation of the VSG. To address these problems, a VSG mathematical model with direct current bus capacitor voltage equation as the swing equation was firstly established. Secondly, the catastrophe phenomenon occurring in the VSG under the variations of internal parameters and external operating conditions were respectively discussed and the catastrophe mechanism was revealed based on the bifurcation and catastrophe theories. Then, the parameter stability regions were partitioned and the correctness of the partitioned regions were verified by time-domain simulation. Finally, the effect of catastrophe on VSG's voltage support capacity was analyzed. The results show that the catastrophe occurs through saddle-node bifurcation points and changes with different parameters; the VSG voltage support capability increases when catastrophe occurs with voltage dropping, while the VSG voltage support capability decreases when catastrophe occurs with voltage swelling; within the parameter stability regions, the VSG is not subject to catastrophe.

Key words: bifurcation theory, catastrophe theory, three-phase voltage source inverter, virtual synchronous generator, voltage catastrophe

中图分类号:

TM712

马晓阳, 杨顺, 刘宇, 王晓冰, 汪颖. 基于分岔和突变理论的VSG突变机理研究[J]. 中国电力, 2025, 58(7): 91-104.

MA Xiaoyang, YANG Shun, LIU Yu, WANG Xiaobing, WANG Ying. VSG Catastrophe Mechanism Based on Bifurcation and Catastrophe Theories[J]. Electric Power, 2025, 58(7): 91-104.

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链接本文: https://www.electricpower.com.cn/CN/10.11930/j.issn.1004-9649.202501032

https://www.electricpower.com.cn/CN/Y2025/V58/I7/91

图/表 18

图 1 三相VSI主电路和d-q轴等效电路

Fig.1 Circuit and d-q equivalent circuit of three-phase VSI

图 2 2种分岔的示意

Fig.2 Schematic of two bifurcations

图 3 突变流形和分岔集

Fig.3 Catastrophe manifolds and bifurcation sets

图 4 (u, v)参数空间和对应分岔

Fig.4 (u, v) parameter space and corresponding bifurcations

表 1 仿真参数

Table 1 Simulation parameters

参数		数值
R/mΩ		100
Y/S		0.033
C/μF		240
D_abc		0.6
u_q/V		1
Z_g/Ω		100

图 5 不同Is下以ud为分岔参数的分岔现象

Fig.5 Bifurcation phenomenon with ud as bifurcation parameter for different Is

表 2 Is、L和ξSCR变化导致突变现象的结果

Table 2 Catastrophe results caused by Is, L and ξSCR changes

案例	分岔点	突变位置	电压变化
I_s=1 A	HB
I_s=2 A	HB, SNB	u_d= –1.661 V（正向）	25.432→9.773 V
I_s=2 A	HB, SNB	u_d = –1.695 V（反向）	13.829→32.982 V
I_s=3 A	HB, SNB	u_d = –0.752 V（正向）	43.651→3.609 V
I_s=3 A	HB, SNB	u_d = –1.363 V（反向）	9.821→71.256 V
L=0.023 H	HB
L=0.06 H	HB, SNB	u_d = –0.368 V（正向）	12.426→5.453 V
L=0.06 H	HB, SNB	u_d = –0.383 V（反向）	7.340→15.621 V
L=0.1 H	HB, SNB	u_d =0.313 V（正向）	14.423→1.455 V
L=0.1 H	HB, SNB	u_d =0.057 V（反向）	3.626→23.068 V
ξ_SCR=2.5	HB
ξ_SCR=3	HB
ξ_SCR=3.5	HB, SNB	u_d =1.419 V（正向）	14.983→0.337 V
ξ_SCR=3.5	HB, SNB	u_d =0.381 V（反向）	1.677→26.918 V

图 6 ud正向变化时系统分岔与时域的叠加（Is = 3 A）

Fig.6 Superposition of the system bifurcation with the time-domain for positive changes in ud (Is = 3 A)

图 7 ud反向变化时系统分岔与时域的叠加（Is = 3 A）

Fig.7 Superposition of the system bifurcation with the time-domain for inverse changes in ud (Is = 3 A)

图 8 不同L下以ud为分岔参数的分岔现象

Fig.8 Bifurcation phenomenon with ud as bifurcation parameter for different L

图 9 ud正向变化时系统分岔与时域的叠加（L = 0.1 H）

Fig.9 Superposition of the system bifurcation with the time-domain for positive changes in ud (L = 0.1 H)

图 10 ud反向变化时系统分岔与时域的叠加（L = 0.1 H）

Fig.10 Superposition of the system bifurcation with the time-domain for inverse changes in ud (L = 0.1 H)

图 11 不同ξSCR下以ud为分岔参数的分岔现象

Fig.11 Bifurcation phenomenon with ud as bifurcation parameter for different ξSCR

图 12 ud正向变化时系统分岔与时域的叠加（ξSCR = 3.5）

Fig.12 Superposition of the system bifurcation with the time-domain for positive changes in ud (ξSCR = 3.5)

图 13 ud反向变化时系统分岔与时域的叠加（ξSCR = 3.5）

Fig.13 Superposition of the system bifurcation with the time-domain for inverse changes in ud (ξSCR = 3.5)

图 14 在区域内取不同运行点时的系统时域仿真

Fig.14 Time-domain simulation of the system at different operating points in the region

图 15 在区域外取不同运行点时的系统时域仿真

Fig.15 Time-domain simulation of the system at different operating points outside the region

图 16 系统发生突变和未发生突变时的机端电压波形

Fig.16 Machine-side voltage waveforms with and without catastrophe

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