VSG Catastrophe Mechanism Based on Bifurcation and Catastrophe Theories

doi:10.11930/j.issn.1004-9649.202501032

Abstract

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

CLC Number:

TM712

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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URL: https://www.electricpower.com.cn/EN/10.11930/j.issn.1004-9649.202501032

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

Figures/Tables 18

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

Fig.2 Schematic of two bifurcations

Fig.3 Catastrophe manifolds and bifurcation sets

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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