Một bộ điều khiển tối ưu mới $${\mathrm{PI}}^{{\uplambda }_{1}}{\mathrm{I}}^{{\uplambda }_{2}}{\mathrm{D}}^{{\upmu }_{1}}{\mathrm{D}}^{{\upmu }_{2}}$$ sử dụng thuật toán tối ưu bướm may cho hệ thống điều chỉnh điện áp tự động

Kundur P, Paserba J, Ajjarapu V, Andersson G, Bose A, Canizares C et al (2004) Definition and classification of power system stability. IEEE Trans Power Syst 19:1387–1401. https://doi.org/10.1109/TPWRS.2004.825981 Micev M, Ćalasan M, Oliva D (2020) Fractional order PID controller design for an AVR system using chaotic yellow saddle goatfish algorithm. Mathematics. https://doi.org/10.3390/math8071182 Kundur P, Balu N, Lauby M (1994) Power system stability and control, vol 7. McGraw-hill, New York Vahid-Pakdel MJ, Seyedi H, Mohammadi-Ivatloo B (2018) Enhancement of power system voltage stability in multi-carrier energy systems. Int J Electr Power Energy Syst 99:344–354. https://doi.org/10.1016/j.ijepes.2018.01.026 Vanfretti L, Arava VSN (2020) Decision tree-based classification of multiple operating conditions for power system voltage stability assessment. Int J Electr Power Energy Syst. https://doi.org/10.1016/j.ijepes.2020.106251 Sahib MA (2015) A novel optimal PID plus second order derivative controller for AVR system. Eng Sci Technol Int J 18:194–206. https://doi.org/10.1016/j.jestch.2014.11.006 El-Deen AT, Hakim Mahmoud AA, El-Sawi AR. (2015) Optimal PID tuning for DC motor speed controller based on genetic algorithm. Int Rev Automat Control 8:80–5. https://doi.org/10.15866/ireaco.v8i1.4839. Moschos I, Parisses C (2022) A novel optimal PIλDND2N2 controller using coyote optimization algorithm for an AVR system. Eng Sci Technol Int J. https://doi.org/10.1016/j.jestch.2021.04.010 Munagala VK, Jatoth RK (2022) Improved fractional PIλDμ controller for AVR system using Chaotic Black Widow algorithm. Comput Electr Eng. https://doi.org/10.1016/j.compeleceng.2021.107600 Dogruer T, Can MS (2022) Design and robustness analysis of fuzzy PID controller for automatic voltage regulator system using genetic algorithm. Trans Inst Meas Control. https://doi.org/10.1177/01423312211066758 Micev M, Ćalasan M, Ali ZM, Hasanien HM, Abdel Aleem SHE (2021) Optimal design of automatic voltage regulation controller using hybrid simulated annealing—Manta ray foraging optimization algorithm. Ain Shams Eng J 12:641–657. https://doi.org/10.1016/j.asej.2020.07.010 Altbawi SMA, Bin MAS, Jumani TA, Khan I, Hamadneh NN, Khan A (2021) Optimal design of fractional order PID controller based automatic voltage regulator system using gradient-based optimization algorithm. J King Saud Univ Eng Sci. https://doi.org/10.1016/j.jksues.2021.07.009 Tabak A (2021) Maiden application of fractional order PID plus second order derivative controller in automatic voltage regulator. Int Trans Electr Energy Syst. https://doi.org/10.1002/2050-7038.13211 Paliwal N, Srivastava L, Pandit M (2021) Equilibrium optimizer tuned novel FOPID-DN controller for automatic voltage regulator system. Int Trans Electr Energy Syst. https://doi.org/10.1002/2050-7038.12930 Tabak A (2021) A novel fractional order PID plus derivative (PIλDµDµ2) controller for AVR system using equilibrium optimizer. COMPEL Int J Comput Math Electr Electron Eng. https://doi.org/10.1108/COMPEL-02-2021-0044 Ayas MS, Sahin E (2021) FOPID controller with fractional filter for an automatic voltage regulator. Comput Electr Eng. https://doi.org/10.1016/j.compeleceng.2020.106895 Eltag K, Zhang B (2021) Design robust self-tuning FPIDF controller for AVR system. Int J Control Autom Syst 19:910–920. https://doi.org/10.1007/s12555-019-1071-8 Jumani TA, Mustafa MW, Hussain Z, Md. Rasid M, Saeed MS, Memon MM et al (2020) Jaya optimization algorithm for transient response and stability enhancement of a fractional-order PID based automatic voltage regulator system. Alexandria Eng J 59:2429–40. https://doi.org/10.1016/j.aej.2020.03.005 Sumpunsri S, Puangdownreong D. (2020) Multiobjective Lévy-flight firefly algorithm for optimal pida controller design. Int J Innovat Comput Inf Control 16:173–87. https://doi.org/10.24507/ijicic.16.01.173 Kose E (2020) Optimal control of AVR system with tree seed algorithm-based PID controller. IEEE Access 8:89457–89467. https://doi.org/10.1109/ACCESS.2020.2993628 Bhookya J, Jatoth RK (2020) Improved Jaya algorithm-based FOPID/PID for AVR system. COMPEL Int J Comput Math Electr Electron Eng 39:775–90. https://doi.org/10.1108/COMPEL-08-2019-0319 Bhullar AK, Kaur R, Sondhi S (2020) Enhanced crow search algorithm for AVR optimization. Soft Comput 24:11957–11987. https://doi.org/10.1007/s00500-019-04640-w Sikander A, Thakur P (2020) A new control design strategy for automatic voltage regulator in power system. ISA Trans 100:235–243. https://doi.org/10.1016/j.isatra.2019.11.031 Zhou G, Li J, Tang Z, Luo Q, Zhou Y (2020) An improved spotted hyena optimizer for PID parameters in an AVR system. Math Biosci Eng 17:3767–3783. https://doi.org/10.3934/MBE.2020211 Khan IA, Alghamdi AS, Jumani TA, Alamgir A, Awan AB, Khidrani A (2019) Salp Swarm optimization algorithm-based fractional order PID controller for dynamic response and stability enhancement of an automatic voltage regulator system. Electronics 8:1472. https://doi.org/10.3390/electronics8121472 Ekinci S, Hekimoglu B (2019) Improved kidney-inspired algorithm approach for tuning of PID controller in AVR system. IEEE Access 7:39935–39947. https://doi.org/10.1109/ACCESS.2019.2906980 Blondin MJ, Sicard P, Pardalos PM (2019) Controller tuning approach with robustness, stability and dynamic criteria for the original AVR System. Math Comput Simul 163:168–182. https://doi.org/10.1016/j.matcom.2019.02.019 Bingul Z, Karahan O (2018) A novel performance criterion approach to optimum design of PID controller using cuckoo search algorithm for AVR system. J Franklin Inst 355:5534–5559. https://doi.org/10.1016/j.jfranklin.2018.05.056 Mosaad AM, Attia MA, Abdelaziz AY (2018) Comparative performance analysis of AVR controllers using modern optimization techniques. Electr Power Compon Syst 46:2117–2130. https://doi.org/10.1080/15325008.2018.1532471 Li X, Wang Y, Li N, Han M, Tang Y, Liu F (2017) Optimal fractional order PID controller design for automatic voltage regulator system based on reference model using particle swarm optimization. Int J Mach Learn Cybern 8:1595–1605. https://doi.org/10.1007/s13042-016-0530-2 Güvenç U, Yiǧit T, Işik AH, Akkaya I (2016) Performance analysis of biogeography-based optimization for automatic voltage regulator system. Turk J Electr Eng Comput Sci 24:1150–1162. https://doi.org/10.3906/elk-1311-111 Zeng GQ, Chen J, Dai YX, Li LM, Zheng CW, Chen MR (2015) Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization. Neurocomputing 160:173–184. https://doi.org/10.1016/j.neucom.2015.02.051 Mohanty PK, Sahu BK, Panda S (2014) Tuning and assessment of proportional-integral-derivative controller for an automatic voltage regulator system employing local unimodal sampling algorithm. Electr Power Compon Syst 42:959–969. https://doi.org/10.1080/15325008.2014.903546 Ramezanian H, Balochian S, Zare A (2013) Design of optimal fractional-order PID controllers using particle swarm optimization algorithm for automatic voltage regulator (AVR) system. J Control Automat Electr Syst 24:601–611. https://doi.org/10.1007/s40313-013-0057-7 Panda S, Sahu BK, Mohanty PK (2012) Design and performance analysis of PID controller for an automatic voltage regulator system using simplified particle swarm optimization. J Franklin Inst 349:2609–2625. https://doi.org/10.1016/j.jfranklin.2012.06.008 Gozde H, Taplamacioglu MC (2011) Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system. J Franklin Inst 348:1927–1946. https://doi.org/10.1016/j.jfranklin.2011.05.012 Gozde H, Taplamacioglu MC, Kocaarslan I (2010) Applıcatıon of artıfıcıal bees colony algorıthm ın an automatıc voltage regulator (avr) system. Int J Tech Phys Problems Eng 4:88–92 Ghosh A, Ray AK, Nurujjaman M, Jamshidi M (2021) Voltage and frequency control in conventional and PV integrated power systems by a particle swarm optimized Ziegler-Nichols based PID controller. SN Appl Sci. https://doi.org/10.1007/s42452-021-04327-8 Potnuru D, Alice Mary K, Sai BC (2019) Experimental implementation of flower pollination algorithm for speed controller of a BLDC motor. Ain Shams Eng J 10:287–295. https://doi.org/10.1016/j.asej.2018.07.005 Li Y, Ang KH, Chong GCY (2006) PID control system analysis and design: problems, remedies, and future directions. IEEE Control Syst 26:32–41. https://doi.org/10.1109/MCS.2006.1580152 Forestiero A (2022) Heuristic recommendation technique in Internet of Things featuring swarm intelligence approach. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2021.115904 Dahou A, Abd Elaziz M, Chelloug SA, Awadallah MA, Al-Betar MA, Al-qaness MAA et al (2022) Intrusion detection system for IoT based on deep learning and modified reptile search algorithm. Comput Intell Neurosci 2022:1–15. https://doi.org/10.1155/2022/6473507 Naderi E, Pourakbari-Kasmaei M, Cerna FV, Lehtonen M (2021) A novel hybrid self-adaptive heuristic algorithm to handle single- and multi-objective optimal power flow problems. Int J Electr Power Energy Syst. https://doi.org/10.1016/j.ijepes.2020.106492 Abido MA (2002) Optimal power flow using particle swarm optimization. Int J Electr Power Energy Syst 24:563–571. https://doi.org/10.1016/S0142-0615(01)00067-9 Azizi M, Aickelin U, Khorshidi HA, Shishehgarkhaneh MB (2022) Shape and size optimization of truss structures by Chaos game optimization considering frequency constraints. J Adv Res 41:89–100. https://doi.org/10.1016/j.jare.2022.01.002 Awad R (2021) Sizing optimization of truss structures using the political optimizer (PO) algorithm. Structures 33:4871–4894. https://doi.org/10.1016/j.istruc.2021.07.027 Chen YQ, Petráš I, Xue D. (2009) Fractional order control a tutorial. In: Proceedings of the American control conference, 1397–411. https://doi.org/10.1109/ACC.2009.5160719 Fatoorehchi H, Rach R (2020) A method for inverting the Laplace transforms of two classes of rational transfer functions in control engineering. Alex Eng J 59:4879–4887. https://doi.org/10.1016/j.aej.2020.08.052 Podlubny I (1999) Fractional-order systems and PIλDμ-controllers. IEEE Trans Automat Contr 44:208–214. https://doi.org/10.1109/9.739144 Tepljakov A, Alagoz BB, Yeroglu C, Gonzalez E, HosseinNia SH, Petlenkov E (2018) FOPID controllers and their industrial applications: a survey of recent result. IFAC-PapersOnLine 51:25–30 Podlubny I (1994) Fractional-order systems and fractional-order controllers. Inst Exp Phys Slovak Academy Sci 12:1–18 Karimi-Ghartemani M, Zamani M, Sadati N, Parniani M. (2007) An Optimal Fractional Order Controller for an AVR System Using Particle Swarm Optimization Algorithm. In: 2007 large engineering systems conference on power engineering, IEEE; 244–9. https://doi.org/10.1109/LESCPE.2007.4437386. Zervoudakis K, Tsafarakis S (2020) A mayfly optimization algorithm. Comput Ind Eng. https://doi.org/10.1016/j.cie.2020.106559 Shayeghi H, Rahnama A, Alhelou HH (2021) Frequency control of fully-renewable interconnected microgrid using fuzzy cascade controller with demand response program considering. Energy Rep 7:6077–6094. https://doi.org/10.1016/j.egyr.2021.09.027 Ramasamy K, Ravichandran CS (2021) Optimal design of renewable sources of PV/wind/FC generation for power system reliability and cost using MA-RBFNN approach. Int J Energy Res 45:10946–10962. https://doi.org/10.1002/er.6578 Abdeen M, Sayyed M, Dominguez-Garcia JL, Kamel S (2022) Supplemental control for system frequency support of DFIG-based wind turbines. IEEE Access. https://doi.org/10.1109/ACCESS.2022.3185780 Zafar MH, Khan NM, Mirza AF, Mansoor M (2021) Bio-inspired optimization algorithms based maximum power point tracking technique for photovoltaic systems under partial shading and complex partial shading conditions. J Clean Prod. https://doi.org/10.1016/j.jclepro.2021.127279 Yousaf MZ, Raza A, Abbas G, Ullah N, Al-ahmadi AA, Yasin AR et al (2022) MTDC Grids: A Metaheuristic Solution for Nonlinear Control. Energies. https://doi.org/10.3390/en15124263 Shah P, Agashe S (2016) Review of fractional PID controller. Mechatronics 38:29–41. https://doi.org/10.1016/j.mechatronics.2016.06.005 Atangana A, Secer A (2013) A note on fractional order derivatives and table of fractional derivatives of some special functions. Abstract Appl Anal. https://doi.org/10.1155/2013/279681 Petráš I (2012) Tuning and implementation methods for fractional-order controllers. Fract Calc Appl Anal 15:282–303. https://doi.org/10.2478/s13540-012-0021-4 Cafagna D (2007) Past and present - fractional calculus: a mathematical tool from the past for present engineers. IEEE Ind Electron Mag 1:35–40. https://doi.org/10.1109/MIE.2007.901479 Oustaloup A, Levron F, Mathieu B, Nanot FM (2000) Frequency-band complex noninteger differentiator: characterization and synthesis. IEEE Trans Circ Syst I Fundam Theory Appl 47:25–39. https://doi.org/10.1109/81.817385 Wiora J, Wiora A (2020) Influence of methods approximating fractional-order differentiation on the output signal illustrated by three variants of oustaloup filter. Symmetry 12:1–19. https://doi.org/10.3390/sym12111898 Xue D, Zhao C, Chen YQ. (2006) A modified approximation method of fractional order system. In: IEEE ınternational conference on mechatronics and automation, ICMA 2006, 1043–1048. https://doi.org/10.1109/ICMA.2006.25776 Bingi K, Ibrahim R, Karsiti MN, Hassam SM, Harindran VR (2019) Frequency response based curve fitting approximation of fractional-order PID controllers. Int J Appl Math Comput Sci 29:311–326. https://doi.org/10.2478/amcs-2019-0023 Xue D, Chen Y, Atherton D (2007) Linear Feedback Control: Analysis and Design with MATLAB. Society for Industrial and Applied Mathematics, Philadelphia Gaing ZL (2004) A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 19:384–391. https://doi.org/10.1109/TEC.2003.821821 Sikander A, Thakur P, Bansal RC, Rajasekar S (2018) A novel technique to design cuckoo search based FOPID controller for AVR in power systems. Comput Electr Eng 70:261–274. https://doi.org/10.1016/j.compeleceng.2017.07.005 Gheisarnejad M (2018) An effective hybrid harmony search and cuckoo optimization algorithm based fuzzy PID controller for load frequency control. Appl Soft Comput J 65:121–138. https://doi.org/10.1016/j.asoc.2018.01.007 Jumani TA, Mustafa MW, Rasid MM, Memon ZA (2020) Dynamic response enhancement of grid-tied ac microgrid using salp swarm optimization algorithm. Int Trans Electr Energy Syst. https://doi.org/10.1002/2050-7038.12321 Sahu RK, Panda S, Padhan S (2014) Optimal gravitational search algorithm for automatic generation control of interconnected power systems. Ain Shams Eng J 5:721–733. https://doi.org/10.1016/j.asej.2014.02.004 Sahu RK, Panda S, Rout UK, Sahoo DK (2016) Teaching learning based optimization algorithm for automatic generation control of power system using 2-DOF PID controller. Int J Electr Power Energy Syst 77:287–301. https://doi.org/10.1016/j.ijepes.2015.11.082