Design and HIL Validation of Van der Pol-based Virtual Oscillator Control for Two Parallel Inverters

Duy Thai Ha, Thanh Trung Lai, Trong Minh Tran, Hoang Phuong Vu, Viet Phuong Pham

Received	Revised	Accepted	Published
07 May 2026	27 Aug 2026	15 Sep 2026	26 Sep 2026

Citation :

Duy Thai Ha, Thanh Trung Lai, Trong Minh Tran, Hoang Phuong Vu, Viet Phuong Pham, "Design and HIL Validation of Van der Pol-based Virtual Oscillator Control for Two Parallel Inverters," International Journal of Electrical and Electronics Engineering, vol. 13, no. 9, pp. 148-158, 2026. Crossref, https://doi.org/10.14445/23488379/IJEEE-V13I9P112

Abstract

Islanded AC microgrids with parallel inverters require coordinated voltage formation and load sharing. This study presents a Van der Pol-based virtual oscillator controller for two parallel single-phase voltage-source inverters. The voltage reference of each inverter is generated from its local output-current measurement, and no communication channel is used between the two control units. The controller parameters are selected from the inverter power rating, nominal voltage and frequency, allowable frequency variation, transient requirement, and third-harmonic constraint. The proposed method is evaluated in a MATLAB/Simulink model and then executed on a TMS320F28379D DSP connected to a Typhoon HIL 402 real-time simulator. The test cases include resistive-load operation with equal 1:1 and unequal 1:2 current-sharing conditions, resistive load steps, and a nonlinear rectifier-load case. For the tested conditions, the inverter voltages settle near 220 V RMS, and the current waveforms follow the selected sharing settings in both the simulation and Controller-Hardware-in-the-Loop (CHIL) results. Under the nonlinear load, the inverter currents are distorted, whereas the inverter voltages remain synchronized and nearly sinusoidal. The results show that the controller can be implemented on the selected DSP-HIL platform for communication-free parallel-inverter operation.

Keywords

Virtual Oscillator Control, Van der Pol oscillator, Parallel inverters, Islanded AC microgrid, Hardware in the Loop (Typhoon HIL).

References

Qiang Lin et al., “Field Demonstration of Parallel Operation of Virtual Synchronous Controlled Grid-Forming Inverters and a Diesel Synchronous Generator in a Microgrid,” IEEE Access, vol. 10, pp. 39095-39107, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
Vikash Gurugubelli, Arnab Ghosh, and Anup Kumar Panda, “Parallel Inverter Control using Different Conventional Control Methods and an Improved Virtual Oscillator Control Method in a Standalone Microgrid,” Protection and Control of Modern Power Systems, vol. 7, no. 1, pp. 1-13, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
Hua Han et al., “Review of Power Sharing Control Strategies for Islanding Operation of AC Microgrids,” IEEE Transactions on Smart Grid, vol. 7, no. 1, pp. 200-215, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
M.C. Chandorkar, D.M. Divan, and R. Adapa, “Control of Parallel Connected Inverters in Standalone Ac Supply Systems,” IEEE Transactions on Industry Applications, vol. 29, no. 1, pp. 136-143, 1993.
[CrossRef] [Google Scholar] [Publisher Link]
Qing-Chang Zhong, and Yu Zeng, “Universal Droop Control of Inverters with Different Types of Output Impedance,” IEEE Access, vol. 4, pp. 702-712, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
Vivek Khatana, Soham Chakraborty, and Murti V. Salapaka, “A Plug and Play Distributed Secondary Controller for Microgrids with Grid-Forming Inverters,” IECON 2024 - 50^th Annual Conference of the IEEE Industrial Electronics Society, Chicago, IL, USA, pp. 1-6, 2024.
[CrossRef] [Google Scholar] [Publisher Link]
Qing-Chang Zhong, “Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel,” IEEE Transactions on Industrial Electronics, vol. 60, no. 4, pp. 1281-1290, 2013.
[CrossRef] [Google Scholar] [Publisher Link]
Zilin Li et al., “Adaptive Droop Control using Adaptive Virtual Impedance for Microgrids with Variable PV Outputs and Load Demands,” IEEE Transactions on Industrial Electronics, vol. 68, no. 10, pp. 9630-9640, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
Brian B. Johnson et al., “Synthesizing Virtual Oscillators to Control Islanded Inverters,” IEEE Transactions on Power Electronics, vol. 31, no. 8, pp. 6002-6015, 2016.
[CrossRef] [Google Scholar] [Publisher Link]
Siyi Luo et al., “A New Virtual Oscillator Control without Third-Harmonics Injection For DC/AC Inverter,” IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10879-10888, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
Mingshen Li et al., “Advanced Synchronization Control for Inverters Parallel Operation in Microgrids using Coupled Hopf Oscillators,” CPSS Transactions on Power Electronics and Applications, vol. 5, no. 3, pp. 224-234, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
Brian B. Johnson et al., “Synchronization of Parallel Single-Phase Inverters with Virtual Oscillator Control,” IEEE Transactions on Power Electronics, vol. 29, no. 11, pp. 6124-6138, 2014.
[CrossRef] [Google Scholar] [Publisher Link]
Mohit Sinha et al., “Uncovering Droop Control Laws Embedded within the Nonlinear Dynamics of Van Der Pol Oscillators,” IEEE Transactions on Control of Network, vol. 4, no. 2, pp. 347-358, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
Minghui Lu et al., “Comparison of Droop Control and Virtual Oscillator Control Realized by Andronov-Hopf Dynamics,” IECON 2020 The 46^th Annual Conference of the IEEE Industrial Electronics Society, Singapore, pp. 4051-4056, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
Roberto Rosso et al., “Grid-Forming Converters: Control Approaches, Grid-Synchronization, and Future Trends-A Review,” IEEE Open Journal of Industry Applications, vol. 2, pp. 93-109, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
Sara Anttila et al., “Grid Forming Inverters: A Review of the State of the Art of Key Elements for Microgrid Operation,” Energies, vol. 15, no. 15, pp. 1-30, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
Yuting Teng et al., “Review on Grid-Forming Converter Control Methods in High-Proportion Renewable Energy Power Systems,” Global Energy Interconnection, vol. 5, no. 3, pp. 328-342, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
Brian Johnson et al., “Comparison of Virtual Oscillator and Droop Control,” 2017 IEEE 18^th Workshop on Control and Modeling for Power Electronics (COMPEL), Stanford, CA, USA, pp. 1-6, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
Dayan B. Rathnayake et al., “Grid Forming Inverter Modeling, Control, and Applications,” IEEE Access, vol. 9, pp. 114781-114807, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
Gab-Su Seo et al., “Dispatchable Virtual Oscillator Control for Decentralized Inverter-Dominated Power Systems: Analysis and Experiments,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, pp. 561-566, 2021.
[CrossRef] [Google Scholar] [Publisher Link]
Langella, Roberto, Testa, Alfredo, and, Alii, “IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems,” IEEE Recommended Practice, 2014.
[Google Scholar] [Publisher Link]
F. Blaabjerg et al., “Overview of Control and Grid Synchronization for Distributed Power Generation Systems,” IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398-1409, 2006.
[CrossRef] [Google Scholar] [Publisher Link]
M. Ali, H.I. Nurdin, and J.E. Fletcher, “Synthesizing Averaged Virtual Oscillator Dynamics to Control Inverters with an Output LCL Filter,” IECON 2020 - 46^th Annual Conference of the IEEE Industrial Electronics Society, Singapore, pp. 3265-3270, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
Minghui Lu, Sairaj Dhople, and Brian Johnson, “Benchmarking Nonlinear Oscillators for Grid-Forming Inverter Control,” IEEE Transactions on Power Electronics, vol. 37, no. 9, pp. 10250-10266, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
Minghui Lu et al., “Adaptation of Commercial Current-controlled Inverters for Operation with Virtual Oscillator Control,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, pp. 3427-3432, 2019.
[CrossRef] [Google Scholar] [Publisher Link]

[1] Qiang Lin et al., “Field Demonstration of Parallel Operation of Virtual Synchronous Controlled Grid-Forming Inverters and a Diesel Synchronous Generator in a Microgrid,” IEEE Access, vol. 10, pp. 39095-39107, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[2] Vikash Gurugubelli, Arnab Ghosh, and Anup Kumar Panda, “Parallel Inverter Control using Different Conventional Control Methods and an Improved Virtual Oscillator Control Method in a Standalone Microgrid,” Protection and Control of Modern Power Systems, vol. 7, no. 1, pp. 1-13, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[3] Hua Han et al., “Review of Power Sharing Control Strategies for Islanding Operation of AC Microgrids,” IEEE Transactions on Smart Grid, vol. 7, no. 1, pp. 200-215, 2016.
[CrossRef] [Google Scholar] [Publisher Link]

[4] M.C. Chandorkar, D.M. Divan, and R. Adapa, “Control of Parallel Connected Inverters in Standalone Ac Supply Systems,” IEEE Transactions on Industry Applications, vol. 29, no. 1, pp. 136-143, 1993.
[CrossRef] [Google Scholar] [Publisher Link]

[5] Qing-Chang Zhong, and Yu Zeng, “Universal Droop Control of Inverters with Different Types of Output Impedance,” IEEE Access, vol. 4, pp. 702-712, 2016.
[CrossRef] [Google Scholar] [Publisher Link]

[6] Vivek Khatana, Soham Chakraborty, and Murti V. Salapaka, “A Plug and Play Distributed Secondary Controller for Microgrids with Grid-Forming Inverters,” IECON 2024 - 50^th Annual Conference of the IEEE Industrial Electronics Society, Chicago, IL, USA, pp. 1-6, 2024.
[CrossRef] [Google Scholar] [Publisher Link]

[7] Qing-Chang Zhong, “Robust Droop Controller for Accurate Proportional Load Sharing Among Inverters Operated in Parallel,” IEEE Transactions on Industrial Electronics, vol. 60, no. 4, pp. 1281-1290, 2013.
[CrossRef] [Google Scholar] [Publisher Link]

[8] Zilin Li et al., “Adaptive Droop Control using Adaptive Virtual Impedance for Microgrids with Variable PV Outputs and Load Demands,” IEEE Transactions on Industrial Electronics, vol. 68, no. 10, pp. 9630-9640, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[9] Brian B. Johnson et al., “Synthesizing Virtual Oscillators to Control Islanded Inverters,” IEEE Transactions on Power Electronics, vol. 31, no. 8, pp. 6002-6015, 2016.
[CrossRef] [Google Scholar] [Publisher Link]

[10] Siyi Luo et al., “A New Virtual Oscillator Control without Third-Harmonics Injection For DC/AC Inverter,” IEEE Transactions on Power Electronics, vol. 36, no. 9, pp. 10879-10888, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[11] Mingshen Li et al., “Advanced Synchronization Control for Inverters Parallel Operation in Microgrids using Coupled Hopf Oscillators,” CPSS Transactions on Power Electronics and Applications, vol. 5, no. 3, pp. 224-234, 2020.
[CrossRef] [Google Scholar] [Publisher Link]

[12] Brian B. Johnson et al., “Synchronization of Parallel Single-Phase Inverters with Virtual Oscillator Control,” IEEE Transactions on Power Electronics, vol. 29, no. 11, pp. 6124-6138, 2014.
[CrossRef] [Google Scholar] [Publisher Link]

[13] Mohit Sinha et al., “Uncovering Droop Control Laws Embedded within the Nonlinear Dynamics of Van Der Pol Oscillators,” IEEE Transactions on Control of Network, vol. 4, no. 2, pp. 347-358, 2017.
[CrossRef] [Google Scholar] [Publisher Link]

[14] Minghui Lu et al., “Comparison of Droop Control and Virtual Oscillator Control Realized by Andronov-Hopf Dynamics,” IECON 2020 The 46^th Annual Conference of the IEEE Industrial Electronics Society, Singapore, pp. 4051-4056, 2020.
[CrossRef] [Google Scholar] [Publisher Link]

[15] Roberto Rosso et al., “Grid-Forming Converters: Control Approaches, Grid-Synchronization, and Future Trends-A Review,” IEEE Open Journal of Industry Applications, vol. 2, pp. 93-109, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[16] Sara Anttila et al., “Grid Forming Inverters: A Review of the State of the Art of Key Elements for Microgrid Operation,” Energies, vol. 15, no. 15, pp. 1-30, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[17] Yuting Teng et al., “Review on Grid-Forming Converter Control Methods in High-Proportion Renewable Energy Power Systems,” Global Energy Interconnection, vol. 5, no. 3, pp. 328-342, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[18] Brian Johnson et al., “Comparison of Virtual Oscillator and Droop Control,” 2017 IEEE 18^th Workshop on Control and Modeling for Power Electronics (COMPEL), Stanford, CA, USA, pp. 1-6, 2017.
[CrossRef] [Google Scholar] [Publisher Link]

[19] Dayan B. Rathnayake et al., “Grid Forming Inverter Modeling, Control, and Applications,” IEEE Access, vol. 9, pp. 114781-114807, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[20] Gab-Su Seo et al., “Dispatchable Virtual Oscillator Control for Decentralized Inverter-Dominated Power Systems: Analysis and Experiments,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, pp. 561-566, 2021.
[CrossRef] [Google Scholar] [Publisher Link]

[21] Langella, Roberto, Testa, Alfredo, and, Alii, “IEEE Recommended Practice and Requirements for Harmonic Control in Electric Power Systems,” IEEE Recommended Practice, 2014.
[Google Scholar] [Publisher Link]

[22] F. Blaabjerg et al., “Overview of Control and Grid Synchronization for Distributed Power Generation Systems,” IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1398-1409, 2006.
[CrossRef] [Google Scholar] [Publisher Link]

[23] M. Ali, H.I. Nurdin, and J.E. Fletcher, “Synthesizing Averaged Virtual Oscillator Dynamics to Control Inverters with an Output LCL Filter,” IECON 2020 - 46^th Annual Conference of the IEEE Industrial Electronics Society, Singapore, pp. 3265-3270, 2020.
[CrossRef] [Google Scholar] [Publisher Link]

[24] Minghui Lu, Sairaj Dhople, and Brian Johnson, “Benchmarking Nonlinear Oscillators for Grid-Forming Inverter Control,” IEEE Transactions on Power Electronics, vol. 37, no. 9, pp. 10250-10266, 2022.
[CrossRef] [Google Scholar] [Publisher Link]

[25] Minghui Lu et al., “Adaptation of Commercial Current-controlled Inverters for Operation with Virtual Oscillator Control,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), Anaheim, CA, USA, pp. 3427-3432, 2019.
[CrossRef] [Google Scholar] [Publisher Link]