隨著全球碳排減量目標的推動，傳統大型燃料發電廠逐漸被小型分散式再生能源系統所取代，例如太陽能和風力發電系統。這些再生能源系統通常通過電力電子轉換器連接到電網，但這種方式導致系統缺乏慣性且發電不穩定，從而造成電網的高度變動。低慣量系統在電流切載時會面臨過大的頻率變動，傳統的電流追隨控制方法已無法應對。構網型控制的出現改善了這些問題，成為未來電力系統發展的重要方向。本研究針對構網型控制中的新興技術——虛擬振盪器，進行深入研究。於論文中介紹了各類振盪器的振盪原理以及多部機同步條件和穩定性分析，並且針對傳統虛擬震盪器，如死區震盪器、范德波爾震盪器進行比較。最後，透過對死區振盪器和可調變振盪器的離線及即時模擬，驗證虛擬振盪器的應用性。

Driven by global carbon reduction goals, traditional large-scale fuel power plants are gradually being replaced by small-scale distributed renewable energy systems, such as solar and wind power systems. These renewable energy systems typically connect to the grid via power electronic converters, which result in a lack of inertia and unstable power generation, leading to high volatility in the grid. Low inertia systems face excessive frequency variations during load shedding, rendering traditional current-following control methods inadequate. The emergence of grid-forming control has mitigated these issues and has become a crucial direction for future power system development. This study delves into the emerging technology of virtual oscillators within grid-forming control. The paper presents the oscillation principles of various oscillators, as well as the synchronization conditions and stability analysis for multiple units. Finally, the applicability of virtual oscillators is verified through off-line and real-time simulations of dead-zone oscillators and dispatchable oscillators.

[1] X. Lin, Y. Zheng, Z. Liang and Y. Kang, ”The suppression of voltage overshoot
and oscillation during the fast recovery process from load short-circuit fault for
three-phase stand-alone inverter,” IEEE Journal of Emerging and Selected Topics
in Power Electronics, vol. 9, no. 1, pp. 858-871, Feb. 2021.
[2] C. Smith, A. Gargoom, M. T. Arif and M. E. Haque, ”Control techniques for grid
forming inverters: a comparative analysis,” IEEE Industry Applications Society
Annual Meeting (IAS), pp. 1-9, 2022.
[3] D. B. Rathnayake et al., ”Grid forming inverter modeling, control, and applica-
tions,” IEEE Access, vol. 9, pp. 114781-114807, 2021.
[4] N. Mohammed, H. H. Alhelou and B. Bahrani, Grid-forming power inverters:
control and applications, 1st ed. Boca Raton FL USA: CRC Press, 290 p, 2023.
[5] R. Rosso, X. Wang, M. Liserre, X. Lu and S. Engelken, ”Grid-forming convert-
ers: an overview of control approaches and future trends,” IEEE Energy Convers.
Congr. Expo.(ECCE) , Oct. 2020, pp. 4292-4299.
[6] J. Rocabert, A. Luna, F. Blaabjerg and P. Rodr´ıguez, ”Control of power converters
in AC microgrids,” IEEE Trans. Power Electronics, vol. 27, no. 11, pp. 4734-4749,
Nov. 2012.
[7] N. Mohammed, H. Udawatte, W. Zhou, D. J. Hill and B. Bahrani, ”Grid-Forming
Inverters: A Comparative Study of Different Control Strategies in Frequency and
Time Domains,” IEEE Open Journal of the Industrial Electronics Society, vol. 5,
pp. 185-214, 2024.
[8] B. B. Johnson, S. V. Dhople, A. O. Hamadeh and P. T. Krein, ”Synchronization of
parallel single-phase inverters with virtual oscillator control,” IEEE Trans. Power
Electronics, vol. 29, no. 11, pp. 6124-6138, Nov. 2014.
51
[9] B. B. Johnson, S. V. Dhople, J. L. Cale, A. O. Hamadeh and P. T. Krein,
”Oscillator-based inverter control for islanded three-phase microgrids,” IEEE
Journal of Photovoltaics, vol. 4, no. 1, pp. 387-395, Jan. 2014.
[10] E. Oviedo, N. V´azquez and R. Femat, ”Synchronization Technique of Grid-
Connected Power Converters Based on a Limit Cycle Oscillator,” IEEE Trans.
Industrial Electronics, vol. 65, no. 1, pp. 709-717, Jan. 2018.
[11] B. B. Johnson, S. V. Dhople, A. O. Hamadeh and P. T. Krein, ”Synchronization of
Nonlinear Oscillators in an LTI Electrical Power Network,” IEEE Trans. Circuits
and Systems I: Regular Papers, vol. 61, no. 3, pp. 834-844, March 2014.
[12] B. B. Johnson, M. Sinha, N. G. Ainsworth, F. D¨orfler and S. V. Dhople, ”Synthe-
sizing virtual oscillators to control islanded inverters,” IEEE Trans. Power Elec-
tronics, vol. 31, no. 8, pp. 6002-6015, Aug. 2016.
[13] M. Lu, S. Dhople and B. Johnson, ”Benchmarking nonlinear oscillators for grid-
forming inverter control,” IEEE Trans. Power Electronics, vol. 37, no. 9, pp.
10250-10266, Sept. 2022.
[14] S. Luo, W. Wu, E. Koutroulis, H. S. -H. Chung and F. Blaabjerg, ”A new un-
balanced voltage compensation method based on HOPF oscillator for three-phase
DC/AC inverters with unbalanced loads,” IEEE Trans. Smart Grid, vol. 13, no. 6,
pp. 4245-4255, Nov. 2022.
[15] M. Li, Y. Gui, Y. Guan, J. Matas, J. M. Guerrero and J. C. Vasquez, ”Inverter paral-
lelization for an islanded microgrid using the Hopf oscillator controller approach
with self-synchronization capabilities,” IEEE Trans. Industrial Electronics, vol.
68, no. 11, pp. 10879-10889, Nov. 2021.
[16] M. Li, B. Wei, J. Matas, J. M. Guerrero and J. C. Vasquez, ”Advanced synchro-
nization control for inverters parallel operation in microgrids using coupled Hopf
oscillators,” CPSS Trans. Power Electronics and Applications, vol. 5, no. 3, pp.
224-234, Sept. 2020.
52
[17] M. Colombino, D. Groß, J. -S. Brouillon and F. D¨orfler, ”Global phase and mag-
nitude synchronization of coupled oscillators with application to the control of
grid-forming power inverters,” IEEE Trans. Automatic Control, vol. 64, no. 11,
pp. 4496-4511, Nov. 2019.
[18] L. A. B. Tˆorres, J. P. Hespanha and J. Moehlis, ”Synchronization of identical os-
cillators coupled through a symmetric network with dynamics: a constructive ap-
proach with applications to parallel operation of inverters,” IEEE Trans. Automatic
Control, vol. 60, no. 12, pp. 3226-3241, Dec. 2015.
[19] G. -S. Seo, M. Colombino, I. Subotic, B. Johnson, D. Groß and F. D¨orfler, ”Dis-
patchable virtual oscillator control for decentralized inverter-dominated power
systems: analysis and experiments,” 2019 IEEE Applied Power Electronics Con-
ference and Exposition , Anaheim, CA, USA, pp. 561-566, 2019.
[20] D. Groß, M. Colombino, J. -S. Brouillon and F. D¨orfler, ”The effect of
transmission-line dynamics on grid-forming dispatchable virtual oscillator con-
trol,” IEEE Trans. Control of Network Systems, vol. 6, no. 3, pp. 1148-1160, Sept.
2019.
[21] M. Lu, ”Virtual oscillator grid-forming inverters: state of the art, modeling, and
stability,” IEEE Trans. Power Electronics, vol. 37, no. 10, pp. 11579-11591, Oct.
2022.
[22] M. Lu, S. Dutta, V. Purba, S. Dhople and B. Johnson, ”A grid-compatible virtual
oscillator controller: analysis and design,” IEEE Energy Convers. Congr. Expo.
(ECCE), 2019, pp. 2643-2649.
[23] S. Luo, W. Chen, X. Li and Z. Hao, ”A new virtual inertial strategy for An-
dronov–Hopf oscillator based grid-forming inverters,” IEEE Journal of Emerging
and Selected Topics in Power Electronics, vol. 12, no. 2, pp. 1995-2005, April
2024.
[24] V. Gurugubelli, A. Ghosh and A. K. Panda, ”Design and implementation of op-
timized Andronov-Hopf oscillator control method for parallel inverters in stan-
53
dalone microgrid,” IEEE Trans. Industry Applications, vol. 59, no. 6, pp. 7013-
7026, Nov.-Dec. 2023.
[25] M. H. Ravanji, W. Zhou, N. Mohammed and B. Bahrani, ”Comparative analysis of
the power output capabilities of grid-following and grid-forming inverters consid-
ering static, dynamic, and thermal limitations,” IEEE Trans. Power Systems, vol.
39, no. 2, pp. 2693-2705, March 2024.
[26] H. Ahmed, S. -A. Amamra and M. Bierhoff, ”Frequency-locked loop-based esti-
mation of single-phase grid voltage parameters,” IEEE Trans. Industrial Electron-
ics, vol. 66, no. 11, pp. 8856-8859, Nov. 2019.
[27] M. Maghenem, E. Panteley and A. Lor´ıa, ”Singular-perturbations-based analysis
of dynamic consensus in directed networks of heterogeneous nonlinear systems,”
IEEE Trans. Automatic Control, 2023.
[28] M. Dalboni and A. Soldati, ”On the synchronization of parallel power converters
via emulation of linear mechanical oscillators,” IEEE/ASME Trans. Mechatronics,
vol. 29, no. 2, pp. 1088-1099, April. 2024.
[29] R. Rosso, X. Wang, M. Liserre, X. Lu and S. Engelken, ”Grid-forming convert-
ers: control approaches, grid-synchronization, and future trends—a review,” IEEE
Open Journal of Industry Applications, vol. 2, pp. 93-109, 2021.