Distributed Coordination of Grid-Forming and Grid-Following Inverters for Optimal Frequency Control in Power Systems
Open accessAbstract
The large-scale integration of inverter-interfaced renewable energy sources presents significant challenges to maintaining power balance and nominal frequency in modern power systems. This paper studies grid-level coordinated control of grid-forming (GFM) and grid-following (GFL) inverter-based resources (IBRs) for scalable and optimal frequency control. We propose a fully distributed optimal frequency control algorithm based on the projected primal-dual gradient method and by lever aging the structure of the underlying physical system dynamics. The proposed algorithm i) restores the nominal system frequency while minimizing total control cost and enforcing time-varying IBR power capacity limits and line thermal constraints, and ii) operates in a distributed manner that only needs local measurements and neighbor-to-neighbor communication. In particular, when the line thermal constraints are disregarded, the proposed algorithm admits a fully local implementation that requires no communication, while still ensuring optimality and satisfying IBR power capacity limits. We establish the global asymptotic stability of the algorithm using Lyapunov stability analysis. The effectiveness and optimality of the proposed algorithms are validated through high-fidelity, 100% inverter-based electromagnetic transient (EMT) simulations on the IEEE 39-bus system. The simulations further demonstrate the effective coordination between synchronous generators and IBRs under the proposed control algorithms, as well as the robustness to measurement noise, communication delays, and parameter uncertainties.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Optimization and Nonsmooth Analysis
Clarke, F. H. (1990) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9781611971309 · Cited by 10,435 · see citing works
Modeling, Analysis and Testing of Autonomous Operation of an Inverter-Based Microgrid
Pogaku, N., Prodanović, M., & Green, T. C. (2007) · IEEE Transactions on Power Electronics · doi:10.1109/tpel.2006.890003 · Cited by 3,025 · see citing works
Discontinuous dynamical systems
Cortés, J. (2008) · IEEE Control Systems · doi:10.1109/mcs.2008.919306 · Cited by 1,104 · see citing works
Secondary Frequency and Voltage Control of Islanded Microgrids via Distributed Averaging
Simpson-Porco, J. W., Shafiee, Q., Dörfler, F., Vasquez, J. C., Guerrero, J. M., & Bullo, F. (2015) · IEEE Transactions on Industrial Electronics · doi:10.1109/tie.2015.2436879 · Cited by 984 · see citing works
A Survey of Frequency and Voltage Control Ancillary Services—Part I: Technical Features
Rebours, Y. G., Kirschen, D. S., Trotignon, M., & Rossignol, S. (2007) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2006.888963 · Cited by 789 · see citing works
Yi, P., Hong, Y., & Liu, F. (2016) · Automatica · doi:10.1016/j.automatica.2016.08.007 · Cited by 489 · see citing works
Design and Stability of Load-Side Primary Frequency Control in Power Systems
Zhao, C., Topcu, U., Li, N., & Low, S. H. (2014) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2014.2298140 · Cited by 460 · see citing works
On the Secondary Control Architectures of AC Microgrids: An Overview
Khayat, Y., Shafiee, Q., Heydari, R., Naderi, M., Dragičević, T., Simpson-Porco, J. W., Dörfler, F., Fathi, M., Blaabjerg, F., Guerrero, J. M., et al. (2019) · IEEE Transactions on Power Electronics · doi:10.1109/tpel.2019.2951694 · Cited by 385 · see citing works
Understanding Small-Signal Stability of Low-Inertia Systems
Markovic, U., Stanojev, O., Aristidou, P., Vrettos, E., Callaway, D. S., & Hug, G. (2021) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2021.3061434 · Cited by 376 · see citing works
Stability of primal–dual gradient dynamics and applications to network optimization
Feijer, D., & Paganini, F. (2010) · Automatica · doi:10.1016/j.automatica.2010.08.011 · Cited by 349 · see citing works
Du, W., Tuffner, F., Schneider, K. P., Lasseter, R. H., Xie, J., Chen, Z., & Bhattarai, B. P. (2020) · IEEE Transactions on Power Delivery · doi:10.1109/tpwrd.2020.3018647 · Cited by 347 · see citing works
Connecting Automatic Generation Control and Economic Dispatch From an Optimization View
Li, N., Zhao, C., & Chen, L. (2015) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2015.2459451 · Cited by 301 · see citing works
Cherukuri, A., & Cortés, J. (2016) · Automatica · doi:10.1016/j.automatica.2016.07.003 · Cited by 259 · see citing works
Optimal Load-Side Control for Frequency Regulation in Smart Grids
Mallada, E., Zhao, C., & Low, S. H. (2014) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton.2014.7028527 · Cited by 248 · see citing works
Aggregate Power Flexibility in Unbalanced Distribution Systems
Chen, X., Dall’Anese, E., Zhao, C., & Li, N. (2019) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2019.2920991 · Cited by 242 · see citing works
Self-citationOn the Stability of Globally Projected Dynamical Systems
Xia, Y. S., & Wang, J. (2000) · Journal of Optimization Theory and Applications · doi:10.1023/a:1004611224835 · Cited by 201 · see citing works
Asymptotic convergence of constrained primal–dual dynamics
Cherukuri, A. K., Mallada, E., & Cortés, J. (2015) · Systems & Control Letters · doi:10.1016/j.sysconle.2015.10.006 · Cited by 189 · see citing works
On the Exponential Stability of Primal-Dual Gradient Dynamics
Qu, G., & Li, N. (2018) · IEEE Control Systems Letters · doi:10.1109/lcsys.2018.2851375 · Cited by 154 · see citing works
Chen, X., Wu, W., & Zhang, B. (2017) · IEEE Transactions on Sustainable Energy · doi:10.1109/tste.2017.2754421 · Cited by 142 · see citing works
Self-citationDecentralized Optimal Frequency Control in Autonomous Microgrids
Khayat, Y., Naderi, M., Shafiee, Q., Batmani, Y., Fathi, M., Guerrero, J. M., & Bevrani, H. (2018) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2018.2889671 · Cited by 120 · see citing works
Ruszczyński, A. (2011) · Princeton University Press eBooks · doi:10.2307/j.ctvcm4hcj · Cited by 120 · see citing works
Exponential stability of globally projected dynamic systems
Gao, X. (2003) · IEEE Transactions on Neural Networks · doi:10.1109/tnn.2003.809409 · Cited by 119 · see citing works
Robust Decentralized Secondary Frequency Control in Power Systems: Merits and Tradeoffs
Weitenberg, E., Jiang, Y. H., Zhao, C., Mallada, E., Persis, C. D., & Dörfler, F. (2018) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2018.2884650 · Cited by 101 · see citing works
Reinforcement Learning for Optimal Primary Frequency Control: A Lyapunov Approach
Cui, W., Jiang, Y. H., & Zhang, B. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3176525 · Cited by 81 · see citing works
Evans, L. C. (1981) · SIAM Review · doi:10.1137/1023111 · Cited by 58 · see citing works
Li, Z., Cheng, Z., Liang, J., & Si, J. (2022) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2022.3218583 · Cited by 57 · see citing works
Distributed Optimization for Integrated Frequency Regulation and Economic Dispatch in Microgrids
Xu, Y., Dong, Z., Li, Z., Liu, Y., & Ding, Z. (2021) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2021.3089421 · Cited by 54 · see citing works
Distributed Automatic Load Frequency Control With Optimality in Power Systems
Chen, X., Zhao, C., & Li, N. (2020) · IEEE Transactions on Control of Network Systems · doi:10.1109/tcns.2020.3024489 · Cited by 51 · see citing works
Self-citationDistributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model
Wang, Z., Liu, F., Pang, J. Z. F., Low, S. H., & Mei, S. (2018) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2018.2861941 · Cited by 40 · see citing works
Tang, Y., Qu, G., & Li, N. (2020) · Systems & Control Letters · doi:10.1016/j.sysconle.2020.104754 · Cited by 34 · see citing works
Johnson, B., Roberts, T. G., Ajala, O., Domínguez-García, A. D., Dhople, S. V., Ramasubramanian, D., Tuohy, A., Divan, D. M., & Kroposki, B. (2022) · Hawaii International Conference on System Sciences (HICSS) · doi:10.24251/hicss.2022.416 · Cited by 26 · see citing works
Stochastic Model Predictive Control Based Fast-Slow Coordination Automatic Generation Control
Shen, Y., Wu, W., & Sun, S. (2023) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2023.3321847 · Cited by 26 · see citing works
Liu, J., Song, H., Chen, C., Guerrero, J. M., Liu, M., & Qu, Y. (2023) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2023.3274235 · Cited by 25 · see citing works
An Extension of Pseudolinear Functions and Variational Inequality Problems
Bianchi, M., & Schaible, S. (2000) · Journal of Optimization Theory and Applications · doi:10.1023/a:1004672604998 · Cited by 22 · see citing works
Lyu, C., Wang, W., Wang, J., Bai, Y., Song, Z., Wang, W., & Meng, J. (2024) · Applied Energy · doi:10.1016/j.apenergy.2024.124131 · Cited by 21 · see citing works
Safe Data-Driven Secondary Control of Distributed Energy Resources
Zholbaryssov, M., & Domínguez-García, A. D. (2021) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2021.3084440 · Cited by 16 · see citing works
Distributed optimal load frequency control considering nonsmooth cost functions
Wang, Z., Liu, F., Zhao, C., Ma, Z., & Wei, W. (2020) · Systems & Control Letters · doi:10.1016/j.sysconle.2019.104607 · Cited by 13 · see citing works
Jiang, Y. H., Cui, W., Zhang, B., & Cortés, J. (2022) · IEEE Open Journal of Control Systems · doi:10.1109/ojcsys.2022.3202202 · Cited by 13 · see citing works
Zhao, Y., Liu, T., & Hill, D. J. (2024) · IEEE Transactions on Power Systems · doi:10.1109/tpwrs.2024.3469132 · Cited by 11 · see citing works
A Data-Driven Centralized Secondary Control Design Methodology for Microgrids
dos Santos, L. E., Huaman, J. F., Peña, J. C. U., Queiroz, E. D., & Dotta, D. (2025) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2025.3558108 · Cited by 9 · see citing works
Chen, X., Poveda, J. I., & Li, N. (2025) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2025.3537956 · Cited by 6 · see citing works
Self-citationWang, X., & Chen, X. (2025) · IEEE Power Engineering Society General Meeting · doi:10.1109/pesgm52009.2025.11225381 · Cited by 3 · see citing works
Self-citationWang, Y., Liu, S., Cao, X., & Chow, M. (2024) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2024.3384341 · Cited by 3 · see citing works
Source-Load Collaborative Frequency Control With Real-Time Optimality in Power Networks
Wu, C., Wu, Z. S., Gu, W., Yi, Z., Chen, X., & Shi, Z. (2024) · IEEE Transactions on Smart Grid · doi:10.1109/tsg.2024.3446792 · Cited by 2 · see citing works
Self-citation
Flagged first, then by citations
Cited by
Sorted by citations
COORDINATED FREQUENCY SUPPORT OF GRID FORMING AND GRID FOLLOWING CONVERTER CLUSTERS
Tong, Z., Yue, S., Zhong, Z., Su, X., Liang, K., & Yang, L. (2026) · World Journal of Engineering Research · doi:10.61784/wjer3128
- Authors
- Wang, X., & Chen, X.
- Affiliations
- Texas A&M University (US)
- Venue
- IEEE Transactions on Power Systems
- Published
- 2026-09
- Volume
- 41
- Issue
- 5
- Pages
- 3831-3846
- ISSN
- 0885-8950 (ISSN-L)
- 1558-0679
- OpenAlex
- W7154631809
- Cited by
- 0
- References
- 45
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- IEEE Transactions on Power Systems (publishedVersion)
- arXiv (Cornell University) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- NSF AMPS (2523934)
- NSF CAREER (2541998)
- Consortium on AI and Large Flexible Load at Texas A&M University (TPWRS-01308-2025)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Frequency Control in Power Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Microgrid Control and Optimization
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Keywords
- grid-forming inverters, grid-following inverters, inverter-based resources, distributed coordination, Lyapunov stability, communication delay, measurement noise robustness
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review