Document Type : Research Articles
Authors
Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran
Abstract
The consensus of Cyber-Physical Power Systems (CPPSs), where generators agree on common desired rotor angles and speeds, is vital for maintaining system stability and efficiency. This study explores this consensus using fractional-order multi-agent systems, offering advantages over traditional methods. CPPSs often encounter issues like faults, uncertainties, disturbances, and cyber-attacks. To address these, a new Adaptive Fractional-Order Sliding Mode Controller (AFOSMC) is proposed, designed to achieve consensus despite unknown nonlinear functional upper bounds characterizing system perturbations. The AFOSMC uses stable adaptive laws to determine these unknown coefficients, ensuring robust performance even under adverse conditions. It outperforms conventional Integer-Order counterparts by reducing chattering and enabling faster convergence during the initial phase of CPPS operations. The AFOSMC also ensures finite-time convergence to the sliding surface, enhancing system responsiveness and stability. The controller's stability is rigorously proven using Lyapunov's theorem. Finally, extensive simulations demonstrate the practical benefits of the AFOSMC, and comparisons with recent research highlight its superior performance in robustness and efficiency.
Keywords
- Cyber-Physical Power Systems (CPPSs)
- Fractional-order multi agent systems
- Sliding-mode control
- Adaptive control
- uncertainty and disturbance
Main Subjects
[1] P. A. Oyewole and D. Jayaweera, "Power System Security with Cyber-Physical Power System Operation," in IEEE Access, vol. 8, pp. 179970-179982, 2020.
[2] M. Abdelmalak, V. Venkataramanan and R. Macwan, "A Survey of Cyber-Physical Power System Modeling Methods for Future Energy Systems," in IEEE Access, vol. 10, pp. 99875-99896, 2022.
[3] Z. Dong, M. Tian and L. Ding, "A Framework for Modeling and Structural Vulnerability Analysis of Spatial CyberPhysical Power Systems from an Attack–Defense Perspective," in IEEE Systems Journal, vol. 15, no. 1, pp. 1369-1380, March 2021.
[4] Y. He, Q. Feng, Z. Chen, X. Yang and C. Wu, "Research and simulation of freight vehicle cooperative adaptive cruise formation control model," 6th International Conference on Transportation Information and Safety (ICTIS), Wuhan, China, pp. 1327-1331, 2021.
[5] J. B. Hu, F. Li, J. Wu et al, “Research on aviation electric power cyber physical systems,” Adv Mater Res, pp. 846-847:126–133, 2013.
[6] S. Mokred, Y. Wang, T. Chen, “Modern voltage stability index for prediction of voltage collapse and estimation of maximum load-ability for weak buses and critical lines identification,” International Journal of Electrical Power & Energy Systems, Vol. 145, pp. 108596, 2023.
[7] T. Kim, T. K. Oh, K. S. Kook, Y. H. Moon, “Bifurcation Control Application to-Voltage Collapse in a Model Power System,” IFAC Proceedings Volumes, vol. 36, no. 20, pp. 815-819, 2003.
[8] K. Khan, F. Hassan, J. Koo, M. A. Mohammed, Y. Hasan, Shamsheela, D. Muhammad, B. S. Chowdhry, N. M. Faseeh Qureshi, “Blockchain-based applications and energy effective electric vehicle charging – A systematic literature review, challenges, comparative analysis and opportunities,” Computers and Electrical Engineering, vol. 112, pp. 108959, 2023,
[9] P. Wu, H. Sun, W. Zhong, H. Chang, D. Huang and Y. Jiang, "Rotor Angle Stability with Different Penetration Levels of Wind Generation in the Sending Grid," 2020 IEEE Sustainable Power and Energy Conference (iSPEC), Chengdu, China, pp. 948-954, 2020,
[10] [10] Pan K, Yang F, Feng Z, Pan Q. Attack estimation–based resilient control for cyber-physical power systems. Transactions of the Institute of Measurement and Control, 45(5), pp. 886-898, 2023.
[11] Y. Li, T. Yong, J. Cao J et al, “A consensus control strategy for dynamic power system look-ahead scheduling,” Neurocomputing, vol. 168, pp.1085–1093, 2015.
[12] M. J. Morshed and A. Fekih, "A Coordinated Controller Design for DFIG-Based Multi-Machine Power Systems," in IEEE Systems Journal, vol. 13, no. 3, pp. 3211-3222, Sept. 2019.
[13] A. Pisano and E. Usai, “Sliding mode control: A survey with applications in math,” Mathematics and Computers in Simulation, vol. 81(5), pp. 954-979, 2011.
[14] [14] M. H. Zarif and E. Abbaszadeh, Fractional-Order Variable Structure Equations In Robust Control, International Journal of Industrial Electronics, Control and Optimization (IECO), 6(2), pp. 101-111, 2023.
[15] Q. H. Zhang, J. G. Lu, “Robust stability of fractional-order systems with mixed uncertainties: The 0<α<1 case,” Communications in Nonlinear Science and Numerical Simulation, vol. 126, pp. 107511, 2023.
[16] A. Djari, T. Bouden, A. Boulkroune, “Design of Fractionalorder Sliding Mode Controller (FSMC) for a class of Fractional-order Non-linear Commensurate Systems using a Particle Swarm Optimization (PSO) Algorithm,” CEAI, Vol.16, No.3 pp. 46-55, 2014.
[17] L. Chen, R. Wu, Y. He, Y. Chai, “Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances,” Nonlinear Dyn, 2014.
[18] A. Nemati, M. Peimani, S. Mobayen and S. J. Sayyedfattahi, Adaptive terminal sliding mode controller design for cyber-physical systems under external disturbance and actuator cyber-attack, Int J Adapt Control Signal Process, 37(6), pp. 1369-1388, 2023.
[19] Yanmei Xue, Wen Ren, Bo-Chao Zheng, Jinke Han, Event-triggered adaptive sliding mode control of cyberphysical systems under false data injection attack, Applied Mathematics and Computation, 433, 127403, 2022.
[20] A. Razzaghian, R. K. Moghaddam and N. Pariz,Adaptive fuzzy fractional-order fast terminal sliding mode control for a class of uncertain nonlinear systems, International Journal of Industrial Electronics, Control and Optimization (IECO), 5(1), pp. 77-87, 2022.
[21] T. Zhan, X. Liu, S. Ma, “A new singular system approach to output feedback sliding mode control for fractional order nonlinear systems,” Journal of the Franklin Institute, 2018.
[22] J. l. Zhou, S. Q. Zhang, Y. B. He, “Existence and stability of solution for a nonlinear fractional differential equation,” Journal of Mathematical Analysis and Applications, vol. 498, no. 1, pp. 124921, 2021,
[23] M. A. Zahedi Tajrishi, A. Akbarzadeh Kalat, “Fast finite time fractional-order robust-adaptive sliding mode control of nonlinear systems with unknown dynamics,” Journal of Computational and Applied Mathematics, Vol. 438, pp. 115554, 2024.
[24] N. Djeghali, M. Bettayeb, S. Djennoune, “Sliding mode active disturbance rejection control for uncertain nonlinear fractional-order systems,” European Journal of Control, vol. 57, pp. 54-67, 2021.
[25] K. Mathiyalagan and G. Sangeetha, Second-order sliding mode control for nonlinear fractional-order systems, Applied Mathematics and Computation, 383, 125264, 2020.
[26] Yajie Jiang, Yun Yang, Siew-Chong Tan, and Shu Yuen Hui, Distributed Sliding Mode Observer-Based Secondary Control for DC Microgrids Under Cyber-Attacks, ieee journal on emerging and selected topics in circuits and systems, vol. 11, no. 1, march 2021.
[27] H. Liu, H. Wang, J. Cao, A. Alsaedi and T. Hayat, Composite learning adaptive sliding mode control of fractional-order nonlinear systems with actuator faults, Journal of the Franklin Institute, 356(16), pp. 9580-9599, 2019.
[28] Tuglie E, Iannone S, Torelli F, A coherency-based method to increase dynamic security in power systems. Electronic Power System Res 78(8):1425–1436, 2008.
[29] Godsil, C. and G. Royle (2000). Algebraic graph theory. Springer.
[30] Huang, Ch., Ch. Feng and J. Cao. Consensus of cyberphysical power systems based on multi-agent systems with communication constraints, , 2019.
[31] Soorki, M., & Tavazoei, M. Fractional-order linear time invariant swarm systems: asymptotic swarm stability and time response analysis. Open Physics, 11(6), 845-854, 2013.
[32] Caponetto, R., G. Dongola, L. Fortuna and I. Petras. Fractional-order Systems: Modeling and Control Applications. World Scientific, 2010.
[33] Naderi Soorki, M., & Saleh Tavazoei, M. Adaptive consensus tracking for fractional-order linear time invariant swarm systems. Journal of Computational and Nonlinear Dynamics, 9(3), 031012, 2014.
[34] Soorki, M. N., & Tavazoei, M. S. Adaptive robust control of fractional‐order swarm systems in the presence of model uncertainties and external disturbances. IET control theory & applications, 12(7), 961-969, 2018.
[35] Wang, Zh., X. Huang and H. Shen. Control of an uncertain fractional order economic system via adaptive sliding mode. Neurocomputing, 83, pp. 83–88, 2012.
[36] Diethelm, K., N. J. Ford and A. D. Freed. A predictorcorrector approach for the numerical solution of fractional differential equations. Nonlinear Dynamics, 29(1-4), pp. 3-22, 2002.
)