Abstract：Distributed secondary frequency regulation in virtual synchronous generator (VSG)-based islanded microgrids usually relies on consensus algorithms to achieve frequency restoration and active-power allocation. However, such methods strongly depend on communication links among distributed generation (DG) converters. Denial-of-service (DoS) attacks can block information transmission, while deception attacks can tamper with communication data. The combined action of these two types of attacks may cause more severe damage to microgrids. Existing studies on microgrid secondary control under hybrid attacks mainly focus on direct-current microgrids or droop-controlled alternating-current microgrids, and are difficult to directly apply to VSG-based alternating-current islanded microgrids. Conventional periodic communication mechanisms impose high communication bandwidth overhead and computational burden, while static event-triggered mechanisms may still be frequently triggered by small errors during the steady-state stage. Although dynamic event-triggered mechanisms have been introduced in existing studies, they are all established under the premise of reliable communication links. Under an event-triggered communication mechanism, the attack occurrence interval cannot be directly regarded as the actual affected interval of the microgrid, making the coordinated design of the converter secondary frequency regulation controller and the triggering mechanism more complex. To address these problems, this paper develops a distributed dynamic event-triggered secondary frequency regulation strategy for VSG-based islanded microgrids under hybrid communication attacks. First, a distributed sequential hybrid attack model is established by considering the relationship between attack intervals and event-triggered instants. Effective attack intervals and actual affected intervals are defined according to the triggering instants of each DG converter. A binary attack indication variable is introduced to describe whether each DG is attacked at a triggering instant, and a scaling factor is adopted to uniformly describe DoS attacks and multiplicative deception attacks. In this way, the model can uniformly characterize distributed attack scenarios in which different communication links are subjected to different attack strategies, as well as global attack scenarios. On this basis, a distributed consensus-based secondary frequency regulation controller against hybrid attacks is designed by incorporating the VSG primary frequency regulation dynamics and active-power coordination requirements. The frequency reference and active-power reference are regulated through local information exchange. A dynamic event-triggered mechanism is further introduced, in which the triggering threshold is adjusted online according to the local consensus error and measurement error, thereby reducing unnecessary communication updates during the steady-state stage. Finally, the effects of hybrid attack constraints and the maximum triggering interval are simultaneously considered in the Lyapunov analysis. Sufficient conditions for the asymptotic convergence of the system are derived, and the tuning principles of triggering parameters for practical applications are investigated. A case study is built in Matlab/Simulink for an islanded microgrid system containing six VSG converters operating in parallel. In the communication topology, only DG2 and DG6 can directly obtain the virtual leader frequency information, while the remaining DGs complete distributed secondary frequency regulation through a sparse communication network. Under load disturbances, the system exhibits steady-state frequency deviations when only VSG primary frequency regulation is used. After the secondary frequency regulation controller is activated, the frequencies of all DGs recover to values close to the rated value, and the active-power outputs of DG1~DG6 satisfy the preset active-power allocation relationship. In the distributed hybrid attack scenario, the maximum DoS attack duty cycle on the communication links reaches 53.73%, and the maximum deception attack duty cycle reaches 45.28%, representing a relatively severe attack scenario within the theoretical stability boundary. Without the attack mitigation strategy, the frequency regulation performance of the system deteriorates significantly. After the designed attack mitigation strategy is introduced, periodic triggering, static event triggering, and dynamic event triggering can all achieve frequency restoration and active-power coordination. Compared with periodic communication, the dynamic event-triggered mechanism slightly increases the transient adjustment time but significantly reduces the communication burden. When the periodic communication interval is 0.1 ms, the average number of communication triggering events for each converter within 8 s is approximately 67.3×103 under DoS attacks. After the dynamic event-triggered mechanism is adopted, DG5 has the largest average number of triggering events, with only 529 events, reducing the number of communication triggering events by approximately 99%. Compared with the static event-triggered mechanism, the dynamic event-triggered mechanism further reduces the average number of triggering events by 49.61% while maintaining similar frequency regulation performance. The proposed strategy is further verified under global hybrid attacks, communication delays, parameter variations, and complex communication conditions. In the global hybrid attack scenario, the DoS attack and deception attack duty cycles are set to 21.62% and 14.55%, respectively, and four operating conditions are verified: pure DoS attack, amplification attack, attenuation attack, and scaling hybrid attack. All four types of attacks increase the average frequency deviation of the system and prolong the recovery process. Nevertheless, the proposed strategy can still restore the system frequency to the rated value, and it shows better control performance under the global amplification attack. Under 10~100 ms constant communication delays and time-varying communication delays, the system frequency can still be restored to the rated value. The extended case with eight DGs and the backup communication link reconfiguration case show that when the communication topology remains connected and at least one converter can obtain the leader frequency information, the designed strategy can still achieve frequency restoration and active-power allocation. When the attack intensity exceeds the theoretical tolerance range, the attacked link needs to be isolated and the connected topology should be reconstructed through a backup communication link to restore accurate active-power allocation.
[1] 刘思佳, 刘海涛, 张隽, 等. 基于等效阻抗的虚拟同步机电压支撑影响因素分析与改进控制策略研究[J]. 电工技术学报, 2025, 40(9): 2738-2751. Liu Sijia, Liu Haitao, Zhang Jun, et al.Research on the analysis of virtual synchronous generator voltage support influence factors and improvement control strategies based on equivalent impedance[J]. Transactions of China Electrotechnical Society, 2025, 40(9): 2738-2751. [2] 徐菘, 杨博, 刘浩, 等. 一种提高虚拟同步机电流质量的电压-电流级联闭环控制方案[J]. 电工技术学报, 2024, 39(6): 1871-1885. Xu Song, Yang Bo, Liu Hao, et al.A cascaded harmonic voltage and current closed-loop control method to improve the current quality of virtual synchronous generators[J]. Transactions of China Electrotechnical Society, 2024, 39(6): 1871-1885. [3] Liu Jia, Miura Y, Ise T.Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter-based distributed generators[J]. IEEE Transactions on Power Electronics, 2016, 31(5): 3600-3611. [4] Jiang Kun, Su Hongsheng, Lin Hongjian, et al.A practical secondary frequency control strategy for virtual synchronous generator[J]. IEEE Transactions on Smart Grid, 2020, 11(3): 2734-2736. [5] 周晖, 王跃, 李明烜, 等. 孤岛并联虚拟同步发电机暂态功率分配机理分析与优化控制[J]. 电工技术学报, 2019, 34(增刊2): 654-663. Zhou Hui, Wang Yue, Li Mingxuan, et al.Analysis and optimal control of transient active power sharing between islanded parallel virtual synchronous generators[J]. Transactions of China Electrotechnical Society, 2019, 34(S2): 654-663. [6] 刘伟, 刘欣悦. 基于能量函数和改进虚拟同步控制的低频振荡抑制策略[J]. 电气技术, 2024, 25(9): 1-8. Liu Wei, Liu Xinyue.Low-frequency oscillation suppression strategy based on the energy function and improved virtual synchronization control[J]. Electrical Engineering, 2024, 25(9): 1-8. [7] 朱振山, 翁凯亮, 欧阳海涛. 基于动态参与因子和自适应模型预测控制的电池储能二次调频控制策略[J]. 电工技术学报, 2026, 41(1): 343-358. Zhu Zhenshan, Weng Kailiang, Ouyang Haitao.Secondary frequency modulation control strategy for battery energy storage based on dynamic participation factor and adaptive model predictive control[J]. Transactions of China Electrotechnical Society, 2026, 41(1): 343-358. [8] 杨珺, 侯俊浩, 刘亚威, 等. 分布式协同控制方法及在电力系统中的应用综述[J]. 电工技术学报, 2021, 36(19): 4035-4049. Yang Jun, Hou Junhao, Liu Yawei, et al.Distributed cooperative control method and application in power system[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 4035-4049. [9] 孙伟, 方昭, 杨建平, 等. 考虑随机时变延时的孤岛微电网分布式二次控制[J]. 中国电机工程学报, 2022, 42(3): 864-876. Sun Wei, Fang Zhao, Yang Jianping, et al.Distributed secondary control of islanded microgrid with stochastic time-varying delay[J]. Proceedings of the CSEE, 2022, 42(3): 864-876. [10] Khayat Y, Shafiee Q, Heydari R, et al.On the secondary control architectures of AC microgrids: an overview[J]. IEEE Transactions on Power Electronics, 2020, 35(6): 6482-6500. [11] Bidram A, Davoudi A, Lewis F L, et al.Distributed cooperative secondary control of microgrids using feedback linearization[J]. IEEE Transactions on Power Systems, 2013, 28(3): 3462-3470. [12] 许振宇, 陈殷, 石梦璇, 等. 基于一致性算法的并联虚拟同步机系统小信号模型分析[J]. 中国电机工程学报, 2022, 42(7): 2427-2437. Xu Zhenyu, Chen Yin, Shi Mengxuan, et al.Small-signal analysis of consensus-algorithm-based parallel virtual synchronization generators system[J]. Proceedings of the CSEE, 2022, 42(7): 2427-2437. [13] Liu Yonghui, Wang Yue, Xu Hefan, et al.Modeling and parameter analysis for consensus based secondary control of parallel Virtual Synchronous Generators[J]. Energy Reports, 2020, 6: 1462-1475. [14] Yang Shaohua, Lao Kengweng, Hui Hongxun, et al.Secure distributed control for demand response in power systems against deception cyber-attacks with arbitrary patterns[J]. IEEE Transactions on Power Systems, 2024, 39(6): 7277-7290. [15] Peng Chen, Li Jicai, Fei Minrui.Resilient event-triggering H∞ load frequency control for multi-area power systems with energy-limited DoS attacks[J]. IEEE Transactions on Power Systems, 2017, 32(5): 4110-4118. [16] Yang Hanqing, Li Tieshan, Long Yue, et al.Event-triggered distributed secondary control with model-free predictive compensation in AC/DC networked microgrids under DoS attacks[J]. IEEE Transactions on Cybernetics, 2024, 54(1): 298-307. [17] Chen Yulin, Qi Donglian, Dong Hangning, et al.A FDI attack-resilient distributed secondary control strategy for islanded microgrids[J]. IEEE Transactions on Smart Grid, 2021, 12(3): 1929-1938. [18] Sahoo S, Mishra S, Peng J C, et al.A stealth cyber-attack detection strategy for DC microgrids[J]. IEEE Transactions on Power Electronics, 2019, 34(8): 8162-8174. [19] Zhang Jianwen, Fan Sha, Deng Chao, et al.Resilient distributed secondary control for bidirectional interlinking converters in hybrid AC/DC microgrids against FDI attacks[J]. IEEE Transactions on Industrial Electronics, 2025, 72(3): 3028-3038. [20] Li Shifen, Liang Kun, He Wangli.Fully distributed event-triggered secure consensus of general linear multi-agent systems under sequential scaling attacks[J]. ISA Transactions, 2022, 127: 146-155. [21] Liu Xiaokang, Wen Changyun, Xu Qianwen, et al.Resilient control and analysis for DC microgrid system under DoS and impulsive FDI attacks[J]. IEEE Transactions on Smart Grid, 2021, 12(5): 3742-3754. [22] Wang Yu, Deng Chao, Liu Yun, et al.A cyber-resilient control approach for islanded microgrids under hybrid attacks[J]. International Journal of Electrical Power & Energy Systems, 2023, 147: 108889. [23] Lin Pengfeng, Deng Chao, Yang Yongheng, et al.Resilience-oriented control for cyber-physical hybrid energy storage systems using a semiconsensus scheme: design and practice[J]. IEEE Transactions on Industrial Electronics, 2023, 70(3): 2508-2519. [24] Liu Chuang, Wang Xinsheng, Ren Yu, et al.A novel distributed secondary control of heterogeneous virtual synchronous generators via event-triggered communication[J]. IEEE Transactions on Smart Grid, 2022, 13(6): 4174-4189. [25] Lu Linyu, Chu C C.Consensus-based droop control of isolated micro-grids by ADMM implementations[J]. IEEE Transactions on Smart Grid, 2018, 9(5): 5101-5112. [26] Shao Yingying, Zhang Zhenzhen, Chen Hao, et al.Bandwidth awareness related event triggered robust control on power system with VSG-LFC scheme under unreliable network[J]. IEEE Transactions on Automation Science and Engineering, 2025, 22: 12383-12394. [27] Yang Chao, Yao Wei, Fang Jiakun, et al.Dynamic event-triggered robust secondary frequency control for islanded AC microgrid[J]. Applied Energy, 2019, 242: 821-836. [28] Huang Boyang, Xiao Yong, Jin Xin, et al.A novel dynamic event-triggered mechanism for distributed secondary control in islanded AC microgrids[J]. Energies, 2022, 15(19): 6883. [29] Biswas P P, Tan Hengchuan, Zhu Qingbo, et al.A synthesized dataset for cybersecurity study of IEC 61850 based substation[C]//2019 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), Beijing, China, 2019: 1-7. [30] Wagner E, Bader L, Wolsing K, et al.Sherlock: a dataset for process-aware intrusion detection research on power grid networks: dataset paper[C]// Proceedings of the Fifteenth ACM Conference on Data and Application Security and Privacy, Pittsburgh, USA, 2025: 419-424. [31] Senejohnny D, Tesi P, De Persis C.A jamming-resilient algorithm for self-triggered network coordination[J]. IEEE Transactions on Control of Network Systems, 2018, 5(3): 981-990. [32] He Wangli, Li Shifen, Ge Xiaohua, et al.Secure fully distributed event-triggered consensus of multi-agent systems against distributed sequential scaling attacks[J]. IEEE Transactions on Industrial Informatics, 2024, 20(2): 1764-1775. [33] He Wangli, Qian Feng, Han Qinglong, et al.Almost sure stability of nonlinear systems under random and impulsive sequential attacks[J]. IEEE Transactions on Automatic Control, 2020, 65(9): 3879-3886. [34] Xu Yong.Resilient secure control of networked systems over unreliable communication networks[J]. IEEE Transactions on Industrial Informatics, 2022, 18(6): 4069-4077. [35] Cheng Zihao, Hu Songlin, Yue Dong, et al.Resilient distributed coordination control of multiarea power systems under hybrid attacks[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2022, 52(1): 7-18. [36] Wen Guanghui, Wang Peijun, Huang Tingwen, et al.Distributed consensus of layered multi-agent systems subject to attacks on edges[J]. IEEE Transactions on Circuits and Systems I: Regular Papers, 2020, 67(9): 3152-3162. [37] Wang Xin, Park J H, Liu Zongcheng, et al.Dynamic event-triggered control for GSES of memristive neural networks under multiple cyber-attacks[J]. IEEE Transactions on Neural Networks and Learning Systems, 2024, 35(6): 7602-7611. [38] Gallo A J, Turan M S, Boem F, et al.A distributed cyber-attack detection scheme with application to DC microgrids[J]. IEEE Transactions on Automatic Control, 2020, 65(9): 3800-3815. [39] Guo Fanghong, Wen Changyun, Mao Jianfeng, et al.Distributed secondary voltage and frequency restoration control of droop-controlled inverter-based microgrids[J]. IEEE Transactions on Industrial Electronics, 2015, 62(7): 4355-4364.
2026, Vol. 41 
