Analysis and simulation of small signal stability of parallel connection of virtual synchronous generators in a microgrid system
Subject Areas : Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering
1 - Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
Keywords: Small signal stability, System matrix modes, System microgrid, Parallel connection, Virtual synchronous generator,
Abstract :
The penetration of renewable energy sources into electrical networks using power electronic converters, due to their low inertia, causes electrical networks to respond negatively to load changes and the periodic nature of generation, which leads to increased frequency fluctuations and reduced power system stability. Synchronization of the inverter with the main grid is of great importance in inverter-based units, so that even in times of disruption or changes this synchronization with the grid must be maintained. Virtual synchronous generator (VSG) technology is used to simulate the characteristics of a synchronous generator to create damping and virtual inertia in a renewable energy-based power system in order to reduce frequency fluctuations and improve stability. Small-signal stability analysis using a small-signal model of parallel connection of two virtual synchronous generators is presented in this paper. For modeling, the second-order model of the virtual synchronous generator was used. The results of the dynamic behavior simulation are reviewed and analyzed by calculating the modes of the system matrix. Also, the participation coefficients are calculated to show the relationship between the system modes and state variables.
References:
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[25] Rajaguru, V., Annapoorani, K.I. (2023). Virtual synchronous generator based superco¬nd¬ucting magnetic energy storage unit for load frequency control of micro-grid using african vulture optimization algorithm. Journal of Energy Storage, 65, 107343.
[26] Alipoor, J., Miura, Y., Ise, T. (2015). Power system stabilization using virtual synchronous generator with alternating moment of inertia. IEEE Journal of Emerging and Selected Topics in Power Electronics, 3(2), 451-458.
[27] Ding, X., Cao, J. (2024). Deep and reinforc-ement learning in virtual synchronous gener-ator: A comprehensive review". Energies, 17(11), 2620.
[28] Zheng, T., Chen, L., Guo, Y., Mei, S. (2018). Comprehensive control strategy of virtual syn-chr¬onous generator under unbalanced voltage conditions. IET Generation, Transmi¬ssion and Distribution, 12(7), 1621-1630.
[29] Fang, J., Tang, Y., Li, H., Li, X. (2018). A battery/ultracapacitor hybrid energy storage system for implementing the power managem-ent of virtual synchronous generators. IEEE Trans. on Power Electronics, 33(4), 2820-2824.
[30] Wang, R., Chen, L., Zheng, T., Mei, S. (2017). VSG-based adaptive droop control for frequ-ency and active power regulation in the MTDC system. CSEE Journal of Power and Energy Systems, 3(3), 260-268.
[31] Hlaing, H.S., Liu, J., Miura, Y., Bevrani, H., Ise, T. (2019). Enhanced performance of a stand-alone gas-engine generator using virtual synchronous generator and energy storage system. IEEE Access, 7, 176960-176970.
[32] Rathore, B., Chakrabarti, S., Srivastava, L. (2021). A self-regulated virtual impedance control of VSG in a microgrid. Electric Power Systems Research, 197, 107289.
[33] Wang, H., Yang, C., Liao, X., Wang, J., Zhou, W., Ji, X. (2023). Artificial neural network-based virtual synchronous generator dual droop control for microgrid systems. Computers and Electrical Engineering, 111, 108930.
[34] Liang, J., Fan, H., Cheng, L., Rong, S., Li, T., Yu, T., Wang, L. (2024). Control strategy for improving the frequency response characteristics of photovoltaic and energy storage systems based on VSG control. Energy Reports, 11, 2295-2305.
[35] Jiang, W., Zhou, B. (2022). A virtual synchronous generator control strategy for microgrid based on harmonic current bypass control. International Transactions on Electrical Energy Systems, 1, 2516777.
[36] Liu, J., Miura, Y., Bevrani, H., Ise, T. (2017). Enhanced virtual synchronous generator control for parallel inverters in microgrids. IEEE Trans. on Smart Grid, 8(5), 2268-2277.
[37] Bo, Z., Xiangwu, Y., Yibin, H., Zhengnan, L., Xiangning, X. (2017). Stability control and inertia matching method of multi-parallel virtual synchronous generators. Transactions of China Electrotechnical Society, 32(10), 42-52.
[38] Mohamed, S.Y.A., Yan, X., Abdo, A.M.A. (2021). Parallel operation of virtual synchr-onous generators in a microgrid. Proceeding of the IEEE/ICCCEEE, Khartoum, Sudan, 1-6.
[39] Chen, M., Zhou, D., Wu, C., Blaabjerg, F. (2021). Characteristics of parallel inverters applying virtual synchronous generator control. IEEE Trans. on Smart Grid, 12(6), 4690-4701.
[40] Gao, X., Zhou, D., Anvari-Moghaddam, A., Blaabjerg, F. (2024). An adaptive control strategy with a mutual damping term for paralleled virtual synchronous generators system. Sustainable Energy, Grids and Networks, 38, 101308.
[41] Abou-Hussein, W.M., Dabour, S.M., Hamad, M.S., Rashad, E.M. (2023). Model predictive control based virtual synchronous generator for parallel-connected three-phase split-source con¬v¬erters in islanded ac microgrids. Energy Reports, 9, 1696-1706.
[42] Yang, Q., Yan, L., Chen, X., Chen, Y., Wen, J. (2023). A distributed dynamic inertia-droop control strategy based on multi-agent deep reinforcement learning for multiple paralleled VSGs. IEEE Trans. on Power Systems, 38(6), 5598-5612.
[43] Wang, Y., Chen, S., Yang, M., Liao, P., Xiao, X., Xie, X., Li, Y. (2025). Low-frequency oscillation in power grids with virtual synchronous generators: A comprehensive review. Renewable and Sustainable Energy Reviews, 207, 114921.
[44] Zhou, W. Xiaosong, Z. Xufeng, Y., Wei, X. (2020). Review on virtual synchronous generator technologies. Proceeding of the IEEE/ACDC, 744-751.
[45] Frasetyo, M.B., Wijaya, F.D., Firmansyah, E. (2021). Review on virtual synchronous generator model and control for improving microgrid stability. Proceeding of the IEEE/ICEES,Chennai, India, 397-402.
[46] Liu, Y., Hao, M., He, Y., Zang, C., Zeng, P. (2019). Review and applications of virtual synch¬ronous machines technologies. Proceeding of the IEEE/ISGT, Chengdu, China, 593-598.
[47] Li, H., Wang, K., Chen, Z., Peng, H., Tan, M. (2021). Parameters design in active power control of virtual synchronous generator consi-dering power-angle characteristic nonline¬arity. International Journal of Electrical Power and Energy Systems, 130, 106952.
[48] Shadoul, M., Ahshan, R., AlAbri, R.S., Al-Badi, A., Albadi, M., Jamil, M. (2022). A comprehensive review on a virtual-synchr-onous generator: topologies, control orders and techniques, energy storages, and applications. Energies, 15(22), 8406.
[49] Li, J., Wen, B., Wang, H. (2019). Adaptive virtual inertia control strategy of VSG for micro-grid based on improved bang-bang control strategy. IEEE Access, 7, 39509-39514.
[50] Sang, W., Guo, W., Dai, S., Tian, C., Yu, S., Teng, Y. (2022). Virtual synchronous generator, a comprehensive overview. Energies, 15(17), 6148.
[51] Yan, X., Mohamed, S.Y.A., Li, D., Gadalla, A.S. (2019). Parallel operation of virtual synchronous generators and synchronous generators in a microgrid. The Journal of Engineering, 16, 2635-2642.
[52] Liu, A. Liu, J., Wu, Q. (2023). Coupling stability analysis of synchronous generator and virtual synchronous generator in parallel under large disturbance. Electric Power Systems Research, 224, 109679.
[53] Cheema, K.M. (2020). A comprehensive review of virtual synchronous generator. International Journal of Electrical Power and Energy Systems, 120, 106006.
[54] Fani, B., Shahgholian, G., Alhelou, H.H., Siano, P. (2022). Inverter-based islanded mic¬ro¬grid: A review on technologies and control. e-Prime- Advances in Electrical Engineering, Electronics and Energy, 2, 100068.
[55] Awda, Y., Alowaifeer, M. (2024). Adaptive optimiz¬ation of virtual synchronous generator based on fuzzy logic control and differential evolution. Ain Shams Engineering Journal, 15(4), 4, 102606.
[56] Shi, T., Sun, J., Han, X., Tang, C. (2024). Research on adaptive optimal control strategy of virtual synchronous generator inertia and damping parameters. IET Power Electronics, 17(1), 121-133.
[57] Chen, J., O'Donnell, T. (2019). Analysis of virtual synchronous generator control and its response based on transfer functions. IET Power Electronics, 12(11), 2965-2977.
[58] Yang, D.Q., Li, M.J., Ma, T., Ni, J.W., Han, Z.Y. (2025). Study on adaptive VSG parame¬ters and SOC control strategy for PV-HESS primary frequency regulation. Energy, 314, 133909.
[59] Serban, I., Ion, C.P. (2017). Microgrid control based on a grid-forming inverter operating as virtual synchronous generator with enhanced dynamic response capability. International Journal of Electrical Power and Energy Systems, 89, 94-105.
[60] Ren, B., Li, Q., Fan, Z., Sun, Y. (2023). Adaptive control of a virtual synchronous generator with multiparameter coordination. Energies, 16(12), 4789.
[1] Mesrinejad, F., Yaghoubi, S., Fani, B. (2022). Secondary frequency control for improved dynamic performance in interconnected power system. Journal of Simulation and Analysis of Novel Technologies in Mechanical Enginee-ring, 14(3), 47-54.
[2] Babaei, M., Jahangiri, M., Raeiszadeh, F., Aboutalebi, G.R., Jafari, A., Nariman, A. (2023). The feasibility of using solar heating in the Yazd hospital: A case study. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 15(2), 17-28.
[3] Fathollahi, A., Andresen, B. (2024). Deep determi¬nistic policy gradient for adaptive power system stabilization and voltage regulation. e-Prime- Advances in Electrical Engineering, Electronics and Energy, 9, 100675.
[4] Shahgholian, G. (2020). An overview of hydroelectric power plant: Operation, modeling, and control. Journal of Renewable Energy and Environment, 7(3), 14-28.
[5] Wang, Z., Meng, F., Zhang, Y., Wang, W., Li, G., Ge, J. (2023). Cooperative adaptive control of multi-parameter based on dual-parallel virtual synchronous generators system. IEEE Trans. on Energy Conversion, 38(4), 2396-2408.
[6] Ghahramani, M., Heris, M.N., Zare, K., Ivatloo, B.M. (2016). Incorporation of demand response programs and wind turbines in optimal scheduling of smart distribution networks: A case study. International Journal of Smart Electrical Engineering, 5(4), 199-206.
[7] Mohamed, M.M., Zoghby, H.M., Sharaf, S.M., Mosa, M.A. (2022). Optimal virtual synchr-onous generator control of battery/sup¬ercap-acitor hybrid energy storage system for frequency response enhancement of photovoltaic/diesel microgrid. Journal of Energy Storage, 51, 104317.
[8] Mortazi, A., Saeed, S., Akbari, H. (2023). Optimizing operation scheduling in a microgrid considering probabilistic uncertainty and demand response using social spider algorithm. International Journal of Smart Electrical Engineering, 12(2), 113-125.
[9] Hosseinipour, A., Hojabri, H. (2018). Virtual inertia control of PV systems for dynamic performance and damping enhancement of dc microgrids with constant power loads. IET Renewable Power Generation, 12(4), 430-438.
[10] Zhang, P., Zhao, H., Cai, H., Shi, J., He, X. (2016). Power decoupling strategy based on ‘virtual negative resistor’ for inverters in low-voltage microgrids. IET Power Electronics, 9(5), 1037-1044.
[11] Zhang, B., Yan, X., Li, S., Zhang, X., Han, J., Xiao, X. (2018). Stable operation and small-signal analysis of multiple parallel DG inverters based on a virtual synchronous generator scheme. Energies, 11(1), 203.
[12] Jaklair, L., Yesuratnam, G., Sarma, P. (2024). Control algorithm for renewable energy standalone system with power quality and demand management. Majlesi Journal of Electrical Engineering, 18(1), 311-322.
[13] Suvorov, A., Askarov, A., Ruban, N., Rudnik, V., Radko, P., Achitaev, A., Suslov, K. (2023). An adaptive inertia and damping control strategy based on enhanced virtual synchronous generator model. Mathematics, 11(18), 3938.
[14] Cheema, K.M., Mehmood, K. (2020). Improved virtual synchronous generator control to analyse and enhance the transient stability of microgrid. IET Renewable Power Generation, 14(4), 495-505.
[15] Salama, H.S., Bakeer, A., Magdy, G., Vokony, I. (2021). Virtual inertia emulation through virtual synchronous generator based superconducting magnetic energy storage in modern power system. Journal of Energy Storage, 44, 103466.
[16] Shahgholian, G., Ebrahimi-Salary, M. (2012). Effect of load shedding strategy on interconnected power systems stability when a blackout occurs. International Journal of Computer and Electrical Engineering, 4(2), 212-216.
[17] Shahgholian, G., Moazaami, M., Honarvar, M.A. (2024). Small signal stability analysis of dynamic behavior of gas turbine power plant with secondary control loop in electric power system. Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering, 16(1), 23-35.
[18] Fathollahi, A., Andresen, B. (2024). Enhancing transient stability in multi-machine power systems through a model-free fractional-order excitation stabilizer. Fractal and Fractional, 8(7), 419.
[19] Shahgholian, G., Moazzami, M., Dehghani, M. (2025). A brief review of the application and control strategies of alternating current microgrids in the power system. Technovations of Electrical Engineering in Green Energy System, 4(2), 17-34.
[20] P. Saxena, N. Singh, A.K. Pandey, "Enhancing the dynamic performance of microgrid using derivative controlled solar and energy storage based virtual inertia system", Journal of Energy Storage, vol. 31, Article Number: 101613, Oct. 2020.
[21] Wu, W., Chen, Y., Luo, A., Zhou, L., Zhou, X., Yang, L. (2017). A virtual inertia control strategy for dc microgrids analogized with virtual synchronous machines. IEEE Trans. on Industrial Electronics, 64(7), 6005-6016.
[22] Zheng, F., Su, M., Liu, B., Liu, W. (2023). Adaptive virtual inertia control strategy for a grid-connected converter of dc microgrid based on an improved model prediction. Symmetry, 15(11), 2072.
[23] Lu, S., Zhu, Y., Dong, L., Na, G., Hao, Y., Zhang, G., Zhang, W., Cheng, S., Yang, J., Sui, Y. (2022). Small-signal stability research of grid-connected virtual synchronous generators. Energies, 15(19), 7158.
[24] Suvorov, A., Askarov, A., Bay, Y., Maliuta, B., Achitaev, A., Suslov, K. (2023). Comparative small-signal stability analysis of voltage-controlled and enhanced current-controlled virtual synchronous generators under weak and stiff grid conditions. International Journal of Electrical Power and Energy Systems, 147, 108891.
[25] Rajaguru, V., Annapoorani, K.I. (2023). Virtual synchronous generator based superco¬nd¬ucting magnetic energy storage unit for load frequency control of micro-grid using african vulture optimization algorithm. Journal of Energy Storage, 65, 107343.
[26] Alipoor, J., Miura, Y., Ise, T. (2015). Power system stabilization using virtual synchronous generator with alternating moment of inertia. IEEE Journal of Emerging and Selected Topics in Power Electronics, 3(2), 451-458.
[27] Ding, X., Cao, J. (2024). Deep and reinforc-ement learning in virtual synchronous gener-ator: A comprehensive review". Energies, 17(11), 2620.
[28] Zheng, T., Chen, L., Guo, Y., Mei, S. (2018). Comprehensive control strategy of virtual syn-chr¬onous generator under unbalanced voltage conditions. IET Generation, Transmi¬ssion and Distribution, 12(7), 1621-1630.
[29] Fang, J., Tang, Y., Li, H., Li, X. (2018). A battery/ultracapacitor hybrid energy storage system for implementing the power managem-ent of virtual synchronous generators. IEEE Trans. on Power Electronics, 33(4), 2820-2824.
[30] Wang, R., Chen, L., Zheng, T., Mei, S. (2017). VSG-based adaptive droop control for frequ-ency and active power regulation in the MTDC system. CSEE Journal of Power and Energy Systems, 3(3), 260-268.
[31] Hlaing, H.S., Liu, J., Miura, Y., Bevrani, H., Ise, T. (2019). Enhanced performance of a stand-alone gas-engine generator using virtual synchronous generator and energy storage system. IEEE Access, 7, 176960-176970.
[32] Rathore, B., Chakrabarti, S., Srivastava, L. (2021). A self-regulated virtual impedance control of VSG in a microgrid. Electric Power Systems Research, 197, 107289.
[33] Wang, H., Yang, C., Liao, X., Wang, J., Zhou, W., Ji, X. (2023). Artificial neural network-based virtual synchronous generator dual droop control for microgrid systems. Computers and Electrical Engineering, 111, 108930.
[34] Liang, J., Fan, H., Cheng, L., Rong, S., Li, T., Yu, T., Wang, L. (2024). Control strategy for improving the frequency response characteristics of photovoltaic and energy storage systems based on VSG control. Energy Reports, 11, 2295-2305.
[35] Jiang, W., Zhou, B. (2022). A virtual synchronous generator control strategy for microgrid based on harmonic current bypass control. International Transactions on Electrical Energy Systems, 1, 2516777.
[36] Liu, J., Miura, Y., Bevrani, H., Ise, T. (2017). Enhanced virtual synchronous generator control for parallel inverters in microgrids. IEEE Trans. on Smart Grid, 8(5), 2268-2277.
[37] Bo, Z., Xiangwu, Y., Yibin, H., Zhengnan, L., Xiangning, X. (2017). Stability control and inertia matching method of multi-parallel virtual synchronous generators. Transactions of China Electrotechnical Society, 32(10), 42-52.
[38] Mohamed, S.Y.A., Yan, X., Abdo, A.M.A. (2021). Parallel operation of virtual synchr-onous generators in a microgrid. Proceeding of the IEEE/ICCCEEE, Khartoum, Sudan, 1-6.
[39] Chen, M., Zhou, D., Wu, C., Blaabjerg, F. (2021). Characteristics of parallel inverters applying virtual synchronous generator control. IEEE Trans. on Smart Grid, 12(6), 4690-4701.
[40] Gao, X., Zhou, D., Anvari-Moghaddam, A., Blaabjerg, F. (2024). An adaptive control strategy with a mutual damping term for paralleled virtual synchronous generators system. Sustainable Energy, Grids and Networks, 38, 101308.
[41] Abou-Hussein, W.M., Dabour, S.M., Hamad, M.S., Rashad, E.M. (2023). Model predictive control based virtual synchronous generator for parallel-connected three-phase split-source con¬v¬erters in islanded ac microgrids. Energy Reports, 9, 1696-1706.
[42] Yang, Q., Yan, L., Chen, X., Chen, Y., Wen, J. (2023). A distributed dynamic inertia-droop control strategy based on multi-agent deep reinforcement learning for multiple paralleled VSGs. IEEE Trans. on Power Systems, 38(6), 5598-5612.
[43] Wang, Y., Chen, S., Yang, M., Liao, P., Xiao, X., Xie, X., Li, Y. (2025). Low-frequency oscillation in power grids with virtual synchronous generators: A comprehensive review. Renewable and Sustainable Energy Reviews, 207, 114921.
[44] Zhou, W. Xiaosong, Z. Xufeng, Y., Wei, X. (2020). Review on virtual synchronous generator technologies. Proceeding of the IEEE/ACDC, 744-751.
[45] Frasetyo, M.B., Wijaya, F.D., Firmansyah, E. (2021). Review on virtual synchronous generator model and control for improving microgrid stability. Proceeding of the IEEE/ICEES,Chennai, India, 397-402.
[46] Liu, Y., Hao, M., He, Y., Zang, C., Zeng, P. (2019). Review and applications of virtual synch¬ronous machines technologies. Proceeding of the IEEE/ISGT, Chengdu, China, 593-598.
[47] Li, H., Wang, K., Chen, Z., Peng, H., Tan, M. (2021). Parameters design in active power control of virtual synchronous generator consi-dering power-angle characteristic nonline¬arity. International Journal of Electrical Power and Energy Systems, 130, 106952.
[48] Shadoul, M., Ahshan, R., AlAbri, R.S., Al-Badi, A., Albadi, M., Jamil, M. (2022). A comprehensive review on a virtual-synchr-onous generator: topologies, control orders and techniques, energy storages, and applications. Energies, 15(22), 8406.
[49] Li, J., Wen, B., Wang, H. (2019). Adaptive virtual inertia control strategy of VSG for micro-grid based on improved bang-bang control strategy. IEEE Access, 7, 39509-39514.
[50] Sang, W., Guo, W., Dai, S., Tian, C., Yu, S., Teng, Y. (2022). Virtual synchronous generator, a comprehensive overview. Energies, 15(17), 6148.
[51] Yan, X., Mohamed, S.Y.A., Li, D., Gadalla, A.S. (2019). Parallel operation of virtual synchronous generators and synchronous generators in a microgrid. The Journal of Engineering, 16, 2635-2642.
[52] Liu, A. Liu, J., Wu, Q. (2023). Coupling stability analysis of synchronous generator and virtual synchronous generator in parallel under large disturbance. Electric Power Systems Research, 224, 109679.
[53] Cheema, K.M. (2020). A comprehensive review of virtual synchronous generator. International Journal of Electrical Power and Energy Systems, 120, 106006.
[54] Fani, B., Shahgholian, G., Alhelou, H.H., Siano, P. (2022). Inverter-based islanded mic¬ro¬grid: A review on technologies and control. e-Prime- Advances in Electrical Engineering, Electronics and Energy, 2, 100068.
[55] Awda, Y., Alowaifeer, M. (2024). Adaptive optimiz¬ation of virtual synchronous generator based on fuzzy logic control and differential evolution. Ain Shams Engineering Journal, 15(4), 4, 102606.
[56] Shi, T., Sun, J., Han, X., Tang, C. (2024). Research on adaptive optimal control strategy of virtual synchronous generator inertia and damping parameters. IET Power Electronics, 17(1), 121-133.
[57] Chen, J., O'Donnell, T. (2019). Analysis of virtual synchronous generator control and its response based on transfer functions. IET Power Electronics, 12(11), 2965-2977.
[58] Yang, D.Q., Li, M.J., Ma, T., Ni, J.W., Han, Z.Y. (2025). Study on adaptive VSG parame¬ters and SOC control strategy for PV-HESS primary frequency regulation. Energy, 314, 133909.
[59] Serban, I., Ion, C.P. (2017). Microgrid control based on a grid-forming inverter operating as virtual synchronous generator with enhanced dynamic response capability. International Journal of Electrical Power and Energy Systems, 89, 94-105.
[60] Ren, B., Li, Q., Fan, Z., Sun, Y. (2023). Adaptive control of a virtual synchronous generator with multiparameter coordination. Energies, 16(12), 4789.