Comparison of robust, optimal, and lightweight learning-based controllers for frequency and voltage regulation in inverter-dominated microgrids
In inverter-dominated microgrids with high renewable penetration, frequency and voltage regulation are strongly affected by load steps, source variability, and reduced inertia, which raises the question of how different control strategies trade off tracking accuracy, dynamic stress, power quality, and control effort under identical operating conditions. We conducted a systematic and reproducible comparison of six representative controllers, including active disturbance rejection control, sliding mode control, model predictive control, fuzzy proportional--integral--derivative control, and two lightweight learning-assisted approaches based on extreme learning machines and least-squares support vector machines. All controllers were evaluated on the same control-oriented microgrid model using stochastic renewable profiles, step load disturbances, measurement noise, and multiple Monte Carlo realizations. Performance was assessed using quantitative metrics covering frequency tracking, transient response, rate of change of frequency, voltage deviation, harmonic distortion, and control activity. The results show that fuzzy proportional--integral--derivative control achieved the best overall tracking performance with a root mean square error of 0.00753 Hz and an integral absolute error of 0.05586 Hz, while maintaining a moderate control effort of 0.200 p.u. Sliding mode control yielded the lowest voltage total harmonic distortion at 3.30\%, whereas model predictive control produced the smoothest control signal with a mean control effort of 0.017 p.u., but it suffers from significantly larger tracking errors, with a root mean square error of 0.07488 Hz. These results demonstrate that controller performance is strongly metric-dependent and that no single strategy is universally optimal for all operational objectives.
- Musca R, Vasile A, Zizzo Grid-forming converters. A critical review of pilot projects and demonstrators. Renewable and Sustainable Energy Reviews. 2022;165:112551. https://www.doi.org/10.1016/j.rser.2022.112551
- Teng Y, Deng W, Pei W, et Review on grid-forming converter control methods in high-proportion renewable energy power systems. Global Energy Interconnection. 2022;5(3):328-342. https://www.doi.org/10.1016/j.gloei.2022.06.010
- Rathnayake DB, Akrami M, Phurailatpam C, et al. Grid Forming Inverter Modeling, Control, and IEEE Access. 2021;9:114781-114807. https://www.doi.org/10.1109/ACCESS.2021.3104617
- Gu Y, Green Power System Stability With a High Penetration of Inverter-Based Re-sources. Proc IEEE. 2023;111(7):832-853. https://www.doi.org/10.1109/jproc.2022.3179826
- Sajadi A, Kenyon RW, Hodge Synchronization in electric power networks with inherent het-erogeneity up to 100% inverter-based renewable generation. Nat Commun. 2022;13(1). https://www.doi.org/10.1038/s41467-022-30164-3
- Cheema A comprehensive review of virtual synchronous generator. International Journal of Electrical Power & Energy Systems. 2020;120:106006. https://www.doi.org/10.1016/j.ijepes.2020.106006
- Kannan A, Nuschke M, Dobrin BP, et al. Frequency stability analysis for inverter dominated grids during system split. Electric Power Systems Research. 2020;188:106550. https://www.doi.org/10.1016/j.epsr.2020.106550
- He X, Huang L, Suboti´c I, et al. Quantitative Stability Conditions for Grid-Forming Converters With Complex Droop IEEE Trans Power Electron. 2024;39(9):10834-10852. https://www.doi.org/10.1109/TPEL.2024.3404251
- Zhang H, Yu S, Xiong L, et al. Power instruction correction based frequency response strategy for grid forming inverter in islanded microgrids. International Journal of Electrical Power & Energy Systems. 2024;155:109551. https://www.doi.org/10.1016/j.ijepes.2023.109551
- Ordono A, Sanchez-Ruiz A, Zubiaga M, et Current limiting strategies for grid forming inverters under low voltage ride through. Renewable and Sustainable Energy Reviews. 2024;202:114657. https://www.doi.org/10.1016/j.rser.2024.114657
- Abudyak YH, Rezaei MH, Abdelnabi AAB, et al. Grid-Forming Inverters Review: Control, Stability, and the Next Stage With Artificial Intelligence and Digital Twins. IEEE Open J Power Electron. 2026;7:351-387. https://www.doi.org/10.1109/OJPEL.2026.3654526
- IEEE Standard for Interconnection and Interoperability of Inverter-Based Resources Interconnecting with Associated Transmission Electric Power. https://www.doi.org/10.1109/IEEESTD.2022.9762253
- Elbouchikhi E, El Moubarek AB, Abouloifa A, et al. Active disturbance rejection control for four-wire inverters in standalone renewable resources-based microgrid — islanded microgrids ADRC-based control. ISA Transactions. 2025;156:290. https://www.doi.org/10.1016/j.isatra.2024.11.006
- Li J, You H, Liu S, et Active disturbance rejection distributed secondary control for DC microgrids. High Voltage. 2024;9(1):241-251. https://www.doi.org/10.1049/hve2.12398
- Liu S, You H, Li J, et Active disturbance rejection control based distributed secondary control for a low-voltage DC microgrid. Sustainable Energy, Grids and Networks. 2021;27:100515. https://www.doi.org/10.1016/j.segan.2021.100515
- Ning B, Han QL, Ding L. Distributed Secondary Control of AC Microgrids With Ex-ternal Disturbances and Directed Communication Topologies: A Full-Order Sliding-Mode Approach. IEEE/CAA J Autom Sinica. 2021;8(3):554-564. https://www.doi.org/10.1109/JAS.2020.1003315
- Wu L, Liu J, Vazquez S, et al. Sliding Mode Control in Power Converters and Drives: A Re-view. IEEE/CAA J Autom Sinica. 2022;9(3):392- https://www.doi.org/10.1109/JAS.2021.1004380
- Rosero CX, Rosero F, Tapia F. Fully Decentralized Sliding Mode Control for Frequency Regulation and Power Sharing in Islanded Microgrids. Energies. 2025;18(20):5495. https://www.doi.org/10.3390/en18205495
- Qi X, Zheng J, Mei F. Model Predictive Control–Based Load-Frequency Regulation of Grid-Forming Inverter–Based Power Front Energy Res. 2022;10. https://www.doi.org/10.3389/fenrg.2022.932788
- Ullah Q, Costa Resende E, Carlos Gomes Freitas L, et al. Enhancing voltage stability of grid forming power converters based on model predictive controller. International Journal of Electrical Power & Energy Systems. 2024;163:110317. https://www.doi.org/10.1016/j.ijepes.2024.110317
- Heydari R, Young H, Flores-Bahamonde F, et al. Model-Free Predictive Control of Grid-Forming Inverters With LCL Filters. IEEE Trans Power Electron. 2022;37(8):9200-9211. https://www.doi.org/10.1109/TPEL.2022.3159730
- Meng J, Zhang Z, Zhang G, et al. Adaptive model predictive control for grid-forming converters to achieve smooth transition from islanded to grid-connected mode. IET Generation Trans & Dist. 2023;17(12):2833-2845. https://www.doi.org/10.1049/gtd2.12859
- Dangeti LSN, Marimuthu R. Distributed model predictive control strategy for microgrid frequency Energy Reports. 2025;13:1158-1170. https://www.doi.org/10.1016/j.egyr.2024.12.071
- Lin Y, Zhu J, He F, et A Data-Driven Model-Free Predictive Voltage Control Strategy for Grid-Forming Inverters. IEEJ Transactions Elec Engng. 2025;20(12):2045-2052. https://www.doi.org/10.1002/tee.70078
- Al Kez D, Foley AM, Ahmed F, et al. Overview of frequency control techniques in power systems with high inverter-based resources: Challenges and mitigation measures. IET Smart Grid. 2023;6(5):447-469. https://www.doi.org/10.1049/stg2.12117
- Khan M, Wu W, Li Grid-forming control for inverter-based resources in power systems: A review on its operation, system stability, and prospective. IET Renewable Power Gen. 2024;18(6):887-907. https://www.doi.org/10.1049/rpg2.12991
- Shahgholian G, Moradian M, Fathollahi Droop control strategy in inverter-based microgrids: A brief review on analysis and application in is-landed mode of operation. IET Renewable Power Gen. 2025;19(1). https://www.doi.org/10.1049/rpg2.13186
- Mohammed N, Ali M, Ciobotaru M, et al. Accurate control of virtual oscillator-controlled is-landed AC microgrids. Electric Power Systems Research. 2023;214:108791. https://www.doi.org/10.1016/j.epsr.2022.108791
- Sowa I, Tran TT, Heins T, et al. An Average Consensus Algorithm for Seamless Synchronization of Andronov-Hopf Oscillator Based Multi-Bus IEEE Access. 2021;9:90441-90454. https://www.doi.org/10.1109/ACCESS.2021.3090657
- Zhao Q, Han Z, Wang S, et al. Coordinated control of multiple converters in model-free AC/DC distribution networks based on reinforcement Front Energy Res. 2023;11. https://www.doi.org/10.3389/fenrg.2023.1202701
- Xing L, Shu Z, Fang J, et Distributed control of DC microgrids: A relaxed upper bound for constant power loads. Automatica. 2025;173:112021. https://www.doi.org/10.1016/j.automatica.2024.112021
- Said SM, Aly M, Hartmann B, et Coordinated fuzzy logic-based virtual inertia con-troller and frequency relay scheme for reliable operation of low-inertia power system. IET Renewable Power Gen. 2021;15(6):1286-1300. https://www.doi.org/10.1049/rpg2.12106
- Wang X, Li J, Guo Q, et al. Parameter Design of Half-Bridge Converter Series Y-Connection Microgrid Grid-Connected Filter Based on Improved PSO-LSSVM. Singh AR, International Trans-actions on Electrical Energy Systems. 2023;2023:1-13. https://www.doi.org/10.1155/2023/9534004
- Kondaiah VY, Saravanan B, Sanjeevikumar P, et A review on short-term load forecasting models for micro-grid application. The Journal of Engineering. 2022;2022(7):665-689. https://www.doi.org/10.1049/tje2.12151
- Xing X, Jia L. Energy management in microgrid and multi-microgrid. IET Renewable Power Gen. 2023;18(15):3480-3508. https://www.doi.org/10.1049/rpg2.12816
- Chen R, Xu H, Zhou L, et al. Underfrequency Load Shedding Strategy With an Adaptive Variation Capability for Multi-Microgrids. IEEE Access. 2023;11:17294-17304. https://www.doi.org/10.1109/ACCESS.2023.3246088
- Rodriguez-Martinez OF, Andrade F, Vega-Penagos CA, et al. A Review of Distributed Secondary Control Architectures in Islanded-Inverter-Based Microgrids. Energies. 2023;16(2):878. https://www.doi.org/10.3390/en16020878
- Hezzi A, Elbouchikhi E, Bouzid A, et al. Active Disturbance Rejection Control for Distributed Energy Resources in Microgrids. Machines. 2024;12(1):67. https://www.doi.org/10.3390/machines12010067
- Akinwola AB, Alkuhayli Walrus Optimization-Based Adaptive Virtual Inertia Control for Frequency Regulation in Islanded Microgrids. Electronics. 2025;14(20):3980. https://www.doi.org/10.3390/electronics14203980
- Elkasem Ahmed HA, Kamel S, Hassan MH, et al. An Eagle Strategy Arithmetic Optimization Algorithm for Frequency Stability Enhancement Considering High Renewable Power Penetration and Time-Varying Load. Mathematics. 2022;10(6):854. https://www.doi.org/10.3390/math10060854
- Rosso R, Wang X, Liserre M, et Grid-Forming Converters: Control Approaches, Grid-Synchronization, and Future Trends—A Re-view. IEEE Open J Ind Applicat. 2021;2:93-109. https://www.doi.org/10.1109/OJIA.2021.3074028
- Chen WH, Yang J, Guo L, et al. Disturbance-Observer-Based Control and Related Methods—An Overview. IEEE Trans Ind Electron. 2016;63(2):1083-1095. https://www.doi.org/10.1109/TIE.2015.2478397
- Sufyan A, Jamil M, Ghafoor S, et al. A Robust Nonlinear Sliding Mode Controller for a Three-Phase Grid-Connected Inverter with an LCL Fil-ter. Energies. 2022;15(24):9428. https://www.doi.org/10.3390/en15249428
- Huang GB, Zhu QY, Siew CK. Extreme learning machine: Theory and applications. Neurocomputing. 2006;70(1-3):489-501. https://www.doi.org/10.1016/j.neucom.2005.126
- Esp´ın-Sarzosa D, Palma-Behnke R, Can˜izares CA, et al. Microgrid Modeling for Stability Anal-ysis. IEEE Trans Smart Grid. 2024;15(3):2459- https://www.doi.org/10.1109/TSG.2023.3326063
- Paspatis AG, Konstantopoulos GC, Dedeoglu S. Control design and small-Signal stability analysis of inverter-Based microgrids with inherent current limitation under extreme load conditions. Electric Power Systems Research. 2021;193:106929. https://www.doi.org/10.1016/j.epsr.2020.106929
- Rogalla S, Ernst P, Lens H, et al. Grid-forming converters in interconnected power systems: Requirements, testing aspects, and system im-pact. IET Renewable Power Gen. 2024;18(15): 3053-3066. https://www.doi.org/10.1049/rpg2.12967
- Baeckeland N, Chatterjee D, Lu M, et al. Overcur-rent Limiting in Grid-Forming Inverters: A Com-prehensive Review and Discussion. IEEE Trans Power Electron. 2024;39(11):14493-14517. https://www.doi.org/10.1109/TPEL.2024.3430316
