A brief review on the application of the virtual impedance method in islanded alternating current microgrids to control reactive power sharing

Document Type : Research Paper

Author

1 Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

2 Smart Microgrid Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran

Abstract

To preserve power quality in islanded alternating current (AC) microgrids (MGs), precise line voltage regulation is crucial, especially in the presence of non-linear and unbalanced loads. Effective coordination among multiple distributed generation units is essential to meet the load requirements and maintain system stability. Disparities in line impedance often lead to unequal power distribution among distributed generation units in microgrids. This paper provides an overview of virtual impedance (VI) techniques and droop control. Typically, these techniques are combined to achieve equitable power distribution among dispersed generation units in microgrids with lines of varying impedances. In a stable state, the frequency of the distributed generation units within the microgrid remains uniform, facilitating accurate active power sharing. However, the voltage measurements from distributed generation units are often non-uniform, making reactive power sharing challenging in the microgrid. To address this issue, virtual impedance (VI) can be introduced by placing an additional impedance virtually between the inverter and the load in the physical circuit. This adjustment allows for modification of the inverter's control strategy. By integrating VI with droop control, the impedance observed at the converter's output is adjusted to counteract the coupling effects between active and reactive power, thus improving reactive power sharing and overall system performance in the microgrid.

Keywords

Main Subjects


[1] Fooladgar M, Fani B, Shahgholian G, et al. Evaluation of the trajectory sensitivity analysis of the DFIG control parameters in response to changes in wind speed and the line impedance connection to the grid DFIG. Journal of Intelligent Procedures in Electrical Technology. 2015;5(20):37–54.
[2] Hasan M. Energy economic expansion with production and consumption in BRICS countries. Energy Strategy Reviews. 2022;44:101005.
[3] Bagherian Farahabadi H, Kojoury-Naftchali M, Pahnabi A. High step-up converter with low voltage stress for fuel cell applications. Hydrogen, Fuel Cell & Energy Storage. 2022;9(2):117–132.
[4] Hosseini E, Shahgholian G. Different types of pitch angle control strategies used in wind turbine system applications. Journal of Renewable Energy and Environment. 2017;4(1):20–35.
[5] Shahgholian G. Modeling and simulation of a two-mass resonant system with speed controller. International Journal of Information and Electronics Engineering. 2013;3(5):448.
[6] Shahgholian G. Power system stabilizer application for load frequency control in hydroelectric power plant. Engineering Mathematics. 2017;2(1):21–30.
[7] Yan Z, Zhu X, Chang Y, Wang X, Ye Z, Xu Z, et al. Renewable energy effects on energy management based on demand response in microgrids environment. Renewable Energy. 2023;213:205–217.
[8] Shahgholian G. An overview of hydroelectric power plant: Operation, modeling, and control. Journal of Renewable Energy and Environment. 2020;7(3):14–28.
[9] Shahgholian G, Eshtehardiha S, Mahdavi-Nasab H, Yousefi M. A novel approach in automatic control based on the genetic algorithm in STATCOM for improvement power system transient stability. In: 2008 4th International IEEE Conference Intelligent Systems. vol. 1. IEEE; 2008. p. 4–14.
[10] Han Y, Ning X, Yang P, Xu L. Review of power sharing, voltage restoration and stabilization techniques in hierarchical controlled DC microgrids. IEEE Access. 2019;7:149202–149223.
[11] Islami MS, Urmee T, Kumara INS. Developing a framework to increase solar photovoltaic microgrid penetration in the tropical region: A case study in Indonesia. Sustainable Energy Technologies and Assessments. 2021;47:101311.
[12] Rahimi-Esbo M, Farahabadi MRFHB, Alizadeh E. Assessment of a novel photovoltaic electrolyzer fuel cell-ORC hybrid energy system for hydrogen and power production. Fuel cells. 2023;6:7.
[13] Shahgholian G, Khani K, Moazzami M. The Impact of DFIG based wind turbines in power system load frequency control with hydro turbine. Dam and Hedroelectric Powerplant. 2015;1(3):38–51.
[14] Shahgholian G, Izadpanahi N. Improving the performance of wind turbine equipped with DFIG using STATCOM based on input-output feedback linearization controller. Energy Equipment and Systems. 2016;4(1):65–79. Available from: https://www.energyequipsys.com/article_20128.html.
[15] Li Z, Chan KW, Hu J, Guerrero JM. Adaptive droop control using adaptive virtual impedance for microgrids with variable PV outputs and load demands. IEEE Transactions on Industrial Electronics. 2020;68(10):9630–9640.
[16] Jahangiri M, Haghani A, Raeisi HA, Mostafaeipour A. Generating electricity using pico hydro-based power plant in Koohrang county, Iran: effect of energy storage type. Hydrogen, Fuel Cell & Energy Storage. 2023;11(1):19–38.
[17] Shahgholian G. A brief review on microgrids: Operation, applications, modeling, and control. International Transactions on Electrical Energy Systems. 2021;31(6):e12885.
[18] Al-Saadi M, Al-Greer M, Short M. Strategies for controlling microgrid networks with energy storage systems: A review. Energies. 2021;14(21):7234.
[19] Jafari E, Marjanian A, Solaymani S, Shahgholian G. Designing an emotional intelligent controller for IPFC to improve the transient stability based on energy function. Journal of Electrical Engineering and Technology. 2013;8(3):478–489.
[20] Kiani A, Fani B, Shahgholian G. A multiagent solution to multi-thread protection of DGdominated distribution networks. International Journal of Electrical Power & Energy Systems. 2021;130:106921.
[21] Rathore B, Chakrabarti S, Srivastava L. A SelfRegulated Virtual Impedance control of VSG in a microgrid. Electric Power Systems Research. 2021;197:107289.
[22] Aghadavoodi E, Shahgholian G. A new practical feed-forward cascade analyze for close loop identification of combustion control loop system through RANFIS and NARX. Applied Thermal Engineering. 2018;133:381–395.
[23] Zeng Z, Yang H, Zhao R. Study on small signal stability of microgrids: A review and a new approach. Renewable and Sustainable Energy Reviews. 2011;15(9):4818–4828.
[24] Taleb M, Fani B, Shahgholian G, Mosavi A, Fathollahi A. Maintaining fuse in the presence of distributed generation sources in the distribution network to improve protection system. In: 2023 IEEE 17th International Symposium on Applied Computational Intelligence and Informatics (SACI). IEEE; 2023. p. 000455–000460.
[25] Haghshenas G, Mehdi Mirtalaei SM, Mordmand H, Shahgholian G. High step-up boost-fly-back converter with soft switching for photovoltaic applications. Journal of Circuits, Systems and Computers. 2019;28(01):1950014.
[26] Zhao X, Li YW, Tian H, Wu X. Energy management strategy of multiple supercapacitors in a DC microgrid using adaptive virtual impedance. IEEE Journal of Emerging and Selected Topics in Power Electronics. 2016;4(4):1174–1185.
[27] Shahgholian G, Fattollahi A. Improving power system stability using transfer function: A comparative analysis. Engineering, Technology & Applied Science Research. 2017;7(5):1946–1952.
[28] Taheri M, Shahgholian G, Fani B. Providing a protection method to support distributed generation against transient voltage instability. Iranian Electric Industry Journal of Quality and Productivity. 2023;12(1):22–30.
[29] Ahmed K, Hussain I, Seyedmahmoudian M, Stojcevski A, Mekhilef S. Voltage stability and power sharing control of distributed generation units in DC microgrids. Energies. 2023;16(20):7038.
[30] Van¸co WE, Silva FB, Monteiro JRB, de Oliveira CMR, Gomes LC. Theoretical-experimental analysis of the induction generator in the use of distributed generation. IEEE Latin America Transactions. 2021;19(3):396–403.
[31] Aderibigbe M, Adoghe A, Agbetuyi F, Airoboman A. Impact of distributed generations on power systems stability: A review. In: 2022 IEEE Nigeria 4th International Conference on Disruptive Technologies for Sustainable Development (NIGERCON). IEEE; 2022. p. 1–5.
[32] Adefarati T, Bansal RC. Integration of renewable distributed generators into the distribution system: a review. IET Renewable Power Generation. 2016;10(7):873–884.
[33] Taheri M, Shahgholian G, Fani B, Mosavi A, Fathollahi A. A Protection Methodology for Supporting Distributed Generations with Respect to Transient Instability. In: 2023 IEEE 17th International Symposium on Applied Computational
Intelligence and Informatics (SACI). IEEE; 2023. p. 000545–000550.
[34] Satapathy AS, Mohanty S, Mohanty A, Rajamony RK, Soudagar MEM, Khan TY, et al. Emerging technologies, opportunities and challenges for microgrid stability and control. Energy Reports. 2024;11:3562–3580.
[35] Hosseinpour H, MansourLakouraj M, Ben-Idris M, Livani H. Large-signal stability analysis of inverter-based AC microgrids: A critical and analytical review. IEEE Access. 2023;.
[36] Liu Y, Guan L, Guo F, Zheng J, Chen J, Liu C, et al. A reactive power-voltage control strategy of an AC microgrid based on adaptive virtual impedance. Energies. 2019;12(16):3057.
[37] Karimi H, Fani B, Shahgholian G. Coordinated protection scheme based on virtual impedance control for loop-based microgrids. Journal of Intelligent Procedures in Electrical Technology. 2021;12(46):15–32.
[38] Mohammadzamani F, Hashemi M, Shahgholian G. Adaptive control of nonlinear time-delay systems in the presence of output constraints and actuators faults. International Journal of Control. 2023;96(3):541–553.
[39] Mohammadzamani F, Hashemi M, Shahgholian G. Adaptive neural control of non-linear fractional order multi-agent systems in the presence of error constraints and input saturation. IET Control Theory & Applications. 2022;16(13):1283–1298.
[40] Farhang S, Shahgholian G, Fani B. Dynamic Behavior Improvement of Control System in Inverter-Based Island Microgrid by Adding a Mixed Virtual Impedance Loop to Voltage Control Loop. International Journal of Smart Electrical Engineering. 2022;1(1):27.
[41] Hoang TV, Lee HH. Virtual impedance control scheme to compensate for voltage harmonics with accurate harmonic power sharing in islanded microgrids. IEEE Journal of Emerging and Selected Topics in Power Electronics. 2020;9(2):1682–1695.
[42] Shahgholian G, Fathollahi A. Analyzing SmallSignal Stability in a Multi-Source Single-Area Power System with a Load-Frequency Controller Coordinated with a Photovoltaic System. AppliedMath. 2024;4(2):452–467.
[43] Shahgholian G, Moazzami M, Zanjani SM, Mosavi A, Fathollahi A. A Hydroelectric Power Plant Brief: Classification and Application of Artificial Intelligence. In: 2023 IEEE 17th International Symposium on Applied Computational Intelligence and Informatics (SACI). IEEE; 2023. p. 000141–000146.
[44] Shahgholian G, Dehghani M, Yousefi MR, Mirtalaei SMM. Small signal stability analysis and frequency control in a single-area multi-source electrical energy system. Hydrogen, Fuel Cell & Energy Storage. 2024;11(2):107–116.
[45] Shahgholian G. Comparison and Analysis of Dynamic Behavior of Load Frequency Control in Power System with Steam, Hydro and Gas Power Plants. Hydrogen, Fuel Cell & Energy Storage. 2023;10(4):311–325.
[46] Keyvani-Boroujeni B, Fani B, Shahgholian G, Alhelou HH. Virtual impedance-based droop control scheme to avoid power quality and stability problems in VSI-dominated microgrids. IEEE Access. 2021;9:144999–145011.
[47] An R, Liu Z, Liu J. Successive-approximationbased virtual impedance tuning method for accurate reactive power sharing in islanded microgrids. IEEE Transactions on Power Electronics. 2020;36(1):87–102.
[48] G¨othner F, Rold´an-P´erez J, Torres-Olguin RE, Midtg˚ard OM. Harmonic virtual impedance design for optimal management of power quality in microgrids. IEEE Transactions on Power Electronics. 2021;36(9):10114–10126.
[49] Budiwicaksana LA, Ardriani T, Furqani J, Rizqiawan A, Dahono PA. Improving inverter output current controller under unbalanced conditions by using virtual impedance. IEEE Access. 2021;9:162359–162369.
[50] Pompodakis EE, Strezoski L, Simic N, Paspatis AG, Alexiadis MC, Tsikalakis AG, et al. Short-circuit calculation of droop-controlled islanded AC microgrids with virtual impedance current limiters. Electric Power Systems Research. 2023;218:109184.
[51] He J, Li YW, Guerrero JM, Blaabjerg F, Vasquez JC. An islanding microgrid power sharing approach using enhanced virtual impedance control scheme. IEEE transactions on power electronics. 2013;28(11):5272–5282.
[52] Ekanayake UN, Navaratne US. A survey on microgrid control techniques in islanded mode. Journal of Electrical and Computer Engineering. 2020;2020(1):6275460.
[53] Karimi H, Shahgholian G, Fani B, Sadeghkhani I, Moazzami M. A protection strategy for inverter-interfaced islanded microgrids with looped configuration. Electrical Engineering. 2019;101(3):1059–1073.
[54] Tayab UB, Roslan MAB, Hwai LJ, Kashif M. A review of droop control techniques for microgrid. Renewable and Sustainable Energy Reviews. 2017;76:717–727.
[55] Abhishek A, Ranjan A, Devassy S, Kumar Verma B, Ram SK, Dhakar AK. Review of hierarchical control strategies for DC microgrid. IET Renewable Power Generation. 2020;14(10):1631–1640.
[56] Dixit S, Singh P, Ogale J, Bansal P, Sawle Y. Energy management in microgrids with renewable energy sources and demand response. Computers and Electrical Engineering. 2023;110:108848.
[57] Ali S, Zheng Z, Aillerie M, Sawicki JP, Pera MC, Hissel D. A review of DC Microgrid energy management systems dedicated to residential applications. Energies. 2021;14(14):4308.
[58] Shuai Z, Sun Y, Shen ZJ, Tian W, Tu C, Li Y, et al. Microgrid stability: Classification and a review. Renewable and Sustainable Energy Reviews. 2016;58:167–179.
[59] Rana MM, Uddin M, Sarkar MR, Meraj ST, Shafiullah G, Muyeen S, et al. Applications of energy storage systems in power grids with and without renewable energy integration—A comprehensive review. Journal of energy storage.
2023;68:107811.
[60] De La Cruz J, Wu Y, Candelo-Becerra JE, V´asquez JC, Guerrero JM. A review of networked microgrid protection: Architectures, challenges, solutions, and future trends. CSEE Journal of Power and Energy Systems. 2023;.
[61] Kumar K, Kumar P, Kar S. A review of microgrid protection for addressing challenges and solutions. Renewable Energy Focus. 2024;p. 100572.
[62] Akter A, Zafir EI, Dana NH, Joysoyal R, Sarker SK, Li L, et al. A review on microgrid optimization with meta-heuristic techniques: Scopes, trends and recommendation. Energy Strategy Reviews. 2024;51:101298.
[63] Khan B, Singh P. Selecting a meta-heuristic technique for smart micro-grid optimization problem: A comprehensive analysis. IEEE Access. 2017;5:13951–13977.
[64] Fani B, Shahgholian G, Alhelou HH, Siano P. Inverter-based islanded microgrid: A review on technologies and control. e-Prime-Advances in Electrical Engineering, Electronics and Energy. 2022;2:100068.
[65] Garc´ıa M, Aguilar J, R-Moreno MD. An Autonomous Distributed Coordination Strategy for Sustainable Consumption in a Microgrid Based on a Bio-Inspired Approach. Energies. 2024;17(3):757.
[66] Khan MZ, Ahmed EM, Habib S, Ali ZM. Multiobjective optimization technique for droop controlled distributed generators in AC islanded microgrid. Electric Power Systems Research. 2022;213:108671.
[67] Han Y, Ma R, Cui J. Adaptive higher-order sliding mode control for islanding and gridconnected operation of a microgrid. Energies. 2018;11(6):1459.
[68] Han Y, Li H, Shen P, Coelho EAA, Guerrero JM. Review of active and reactive power sharing strategies in hierarchical controlled microgrids. IEEE Transactions on Power Electronics. 2016;32(3):2427–2451.
[69] Ndeh SG, Ngwashi DK, Letting LK, Iweh CD, Tanyi E. Power sharing enhancement through a decentralized droop-based control strategy in an islanded microgrid. e-Prime-Advances in Electrical Engineering, Electronics and Energy.
2024;7:100433.

[70] Khanabdal S, Banejad M, Blaabjerg F, Hosseinzadeh N. Adaptive virtual flux droop control based on virtual impedance in islanded AC microgrids. IEEE Journal of Emerging and Selected Topics in Power Electronics. 2021;10(1):1095–1107.
[71] Khan MH, Zulkifli SA, Tutkun N, Ekmekci I, Burgio A. Decentralized Virtual Impedance Control for Power Sharing and Voltage Regulation in Islanded Mode with Minimized Circulating Current. Electronics. 2024;13(11):2142.
[72] Su H, Zhang Z, Wang S. Island microgrid power control system based on adaptive virtual impedance. Frontiers in Energy Research. 2023;10:974288.
[73] Rosini A, Labella A, Bonfiglio A, Procopio R, Guerrero JM. A review of reactive power sharing control techniques for islanded microgrids. Renewable and Sustainable Energy Reviews. 2021;141:110745.
[74] Keyvani B, Fani B, Karimi H, Moazzami M, Shahgholian G. Improved Droop Control Method for Reactive Power Sharing in Autonomous Microgrids. Journal of Renewable Energy and Environment. 2022;9(3):1–9.
[75] Wu T, Bao G, Chen Y, Shang J. A review for control strategies in microgrid. In: 2018 37th Chinese Control Conference (CCC). IEEE; 2018. p. 30–35.
[76] Lu Z, Wang L, Wang P. Review of voltage control strategies for DC microgrids. Energies. 2023;16(17):6158.
[77] Shahgholian G, Fani B, Keyvani B, Karimi H, Moazzami M. An Improvement in the Reactive Power Sharing by the Use
of Modified Droop Characteristics in Autonomous Microgrids. Energy Engineering and Management. 2019;9(3):64–71. Available from: https://energy.kashanu.ac.ir/article_113477.html.
[78] Sellamna H, Pavan AM, Mellit A, Guerrero JM. An iterative adaptive virtual impedance loop for reactive power sharing in islanded meshed microgrids. Sustainable Energy, Grids and Networks. 2020;24:100395.
[79] Issa W, Sharkh S, Abusara M. A review of recent control techniques of drooped inverter-based AC microgrids. Energy Science & Engineering. 2024;12(4):1792–1814.
[80] Yang C, Wu X, Song Q, Wu H, Zhu Y. An Enhanced Power Allocation Strategy for Microgrids Considering Frequency and Voltage Restoration. Electronics. 2024;13(10):1966.
[81] Shafiee Q, Nasirian V, Vasquez JC, Guerrero JM, Davoudi A. A multi-functional fully distributed control framework for AC microgrids. IEEE transactions on smart grid. 2016;9(4):3247–3258.
[82] Fathollahi A, Andresen B. Deep deterministic policy gradient for adaptive power system stabilization and voltage regulation. e-PrimeAdvances in Electrical Engineering, Electronics and Energy. 2024;9:100675.
[83] Fathollahi A, Andresen B. Adaptive Fixed-Time Control strategy of Generator Excitation and Thyristor-Controlled Series Capacitor in MultiMachine Energy Systems. IEEE Access. 2024;.
[84] Taha MQ, Kurnaz S. Droop control optimization for improved power sharing in AC islanded microgrids based on centripetal force gravity search algorithm. Energies. 2023;16(24):7953.
[85] Taheri D, Shahgholian G, Mirtalaei MM. The charging circuit of the energy storage system of the multi-input converter with high gain (Design, simulation and laboratory investigation). Technovations of Electrical Engineering in Green Energy System. 2023;2(6):26–35. Available from:sanad.iau.ir/fa/Article/904798.
[86] Dou C, Zhang Z, Yue D, Song M. Improved droop control based on virtual impedance and virtual power source in low-voltage microgrid. IET Generation, Transmission & Distribution. 2017;11(4):1046–1054.
[87] Gupta P, Ansari M. Analysis and control of AC and hybrid AC-DC microgrid: a review. In: 2019 2nd international conference on power energy, environment and intelligent control (PEEIC). IEEE; 2019. p. 281–286.
[88] Wang H, Wang X. Distributed reactive power control strategy based on adaptive virtual reactance. IET Renewable Power Generation. 2023;17(3):762–773.
[89] Yu Z, Ai Q, He X, Piao L. Adaptive droop control for microgrids based on the synergetic control of multi-agent systems. Energies. 2016;9(12):1057.
[90] Hu J, Duan J, Ma H, Chow MY. Distributed adaptive droop control for optimal power dispatch in DC microgrid. IEEE Transactions on Industrial Electronics. 2017;65(1):778–789.
[91] Kolluri RR, Mareels I, Alpcan T, Brazil M, de Hoog J, Thomas DA. Power sharing in angle droop controlled microgrids. IEEE Transactions on Power Systems. 2017;32(6):4743–4751.
[92] Suh J, Lee J, Jung S, Yoon M. Imbalance-based primary frequency control for converter-fed microgrid. IET Generation, Transmission & Distribution. 2022;16(2):247–256.
[93] Khaledian A, Aliakbar Golkar M. A new power sharing control method for an autonomous microgrid with regard to the system stability. Automatika: ˇcasopis za automatiku, mjerenje, elektroniku, raˇcunarstvo ikomunikacije. 2018;59(1):87–93.
[94] Baharizadeh M, Esfahani MSG, Kazemi N. Modified virtual frequency-voltage frame control scheme with zero sharing error for islanded AC microgrids. IET Generation, Transmission & Distribution. 2023;17(11):2576–2586.
[95] D’Arco S, Suul JA. Equivalence of virtual synchronous machines and frequency-droops for converter-based microgrids. IEEE Transactions on Smart Grid. 2013;5(1):394–395.
[96] Li Y, Li YW. Power management of inverter interfaced autonomous microgrid based on virtual frequency-voltage frame. IEEE Transactions on Smart Grid. 2011;2(1):30–40.
[97] Bevrani H, Habibi F, Babahajyani P, Watanabe M, Mitani Y. Intelligent frequency control in an AC microgrid: Online PSO-based fuzzy tuning approach. IEEE transactions on smart grid. 2012;3(4):1935–1944.
[98] Kamali M, Fani B, Shahgholian G, Gharehpetian GB, Shafiee M. Harmonic compensation and micro-grid voltage and frequency control based on power proportional distribution with adaptive virtual impedance method. Journal of
Intelligent Procedures in Electrical Technology. 2023;14(53):33–60.
[99] Buraimoh E, Aluko AO, Oni OE, Davidson IE. Decentralized virtual impedanceconventional droop control for power sharing for inverter-based distributed energy resources of a microgrid. Energies. 2022;15(12):4439.
[100] Keyvani B, Fani B, Shahgholian G. Preventing of Bifurcation Consequences in VSI-Dominated Micro-grids Using Virtual Impedance Theory. Computational Intelligence in Electrical Engineering. 2021;12(3):101–120.
[101] Elgamal M, Korovkin N, Menaem AA, Elmitwally A. An algorithm for power flow analysis in isolated hybrid energy microgrid considering DG droop model and virtual impedance control loop. Sustainable Energy, Grids and Networks.
2022;32:100875.
[102] Li C, Chaudhary SK, Savaghebi M, Vasquez JC, Guerrero JM. Power flow analysis for low-voltage AC and DC microgrids considering droop control and virtual impedance. IEEE Transactions on Smart Grid. 2016;8(6):2754–2764.
[103] Su H, Zhang Z, Wang S. Island microgrid power control system based on adaptive virtual impedance. Frontiers in Energy Research. 2023;10:974288.
[104] Rocabert J, Luna A, Blaabjerg F, Rodriguez P. Control of power converters in AC microgrids. IEEE transactions on power electronics. 2012;27(11):4734–4749.
[105] Wang X, Li YW, Blaabjerg F, Loh PC. Virtualimpedance-based control for voltage-source and current-source converters. IEEE Transactions on Power Electronics. 2014;30(12):7019–7037.
[106] Hoang TV, Lee HH. An adaptive virtual impedance control scheme to eliminate the reactive-power-sharing errors in an islanding meshed microgrid. IEEE Journal of Emerging and Selected Topics in Power Electronics. 2017;6(2):966–976.
[107] Mahmood H, Michaelson D, Jiang J. Accurate reactive power sharing in an islanded microgrid using adaptive virtual impedances. IEEE Transactions on Power Electronics. 2014;30(3):1605–1617.
[108] Vijay A, Parth N, Doolla S, Chandorkar MC. An adaptive virtual impedance control for improving power sharing among inverters in islanded AC microgrids. IEEE Transactions on Smart Grid. 2021;12(4):2991–3003.
[109] Hu Y, Xiang J, Peng Y, Yang P, Wei W. Decentralised control for reactive power sharing using adaptive virtual impedance. IET Generation, Transmission & Distribution. 2018;12(5):1198–1205.
[110] Tang M, Liu B, Zhou Z, Li LQ. Design and convergence analysis of an improved droop controller with adaptive virtual impedance. IEEE Access. 2021;9:128809–128816.
[111] Wong YCC, Lim CS, Cruden A, Rotaru MD, Ray PK. A consensus-based adaptive virtual output impedance control scheme for reactive power sharing in radial microgrids. IEEE Transactions on Industry Applications. 2020;57(1):784–
794.
[112] Liang X, Andalib-Bin-Karim C, Li W, Mitolo M, Shabbir MNSK. Adaptive virtual impedance-based reactive power sharing in virtual synchronous generator controlled microgrids. IEEE Transactions on Industry Applications. 2020;57(1):46–60.
[113] Ahmed M, Meegahapola L, Vahidnia A, Datta M. Adaptive virtual impedance controller for parallel and radial microgrids with varying X/R ratios. IEEE Transactions on Sustainable Energy. 2021;13(2):830–843.
[114] Deng F, Petucco A, Mattavelli P, Zhang X. An enhanced current sharing strategy for islanded ac microgrids based on adaptive virtual impedance regulation. International Journal of Electrical Power & Energy Systems. 2022;134:107402.
[115] Fan B, Li Q, Wang W, Yao G, Ma H, Zeng X, et al. A novel droop control strategy of reactive power sharing based on adaptive virtual impedance in microgrids. IEEE Transactions on Industrial Electronics. 2021;69(11):11335–11347.
[116] G¨othner F, Midtg˚ard OM, Torres-Olguin R, D’Arco S. Effect of including transient virtual impedance in droop-controlled microgrids. In: 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE
Industrial and Commercial Power Systems Europe (EEEIC/I&CPS Europe). IEEE; 2018. p.1–6.
[117] Alsafran AS, Daniels MW. Consensus control for reactive power sharing using an adaptive virtual impedance approach. Energies. 2020;13(8):2026.
[118] Chen Z, Luo A, Wang H, Chen Y, Li M, Huang Y. Adaptive sliding-mode voltage control for inverter operating in islanded mode in microgrid. International Journal of Electrical Power & Energy Systems. 2015;66:133–143.
[119] Zhang C, Xu D, Ma J, Chen H. A New Fast Control Strategy of Terminal Sliding Mode with Nonlinear Extended State Observer for Voltage Source Inverter. Sensors. 2023;23(8):3951.
[120] Wang Y, Tang J, Si J, Xiao X, Zhou P, Zhao J. Power quality enhancement in islanded microgrids via closed-loop adaptive virtual impedance control. Protection and Control of Modern Power Systems. 2023;8(1):10.