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Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response

Year 2025, Volume: 14 Issue: 4, 1243 - 1252, 15.10.2025

Deniz Katipoğlu

Abstract

This research presents a load frequency control (LFC) system with demand response (DR) studied for robust stability analysis based on gain and phase margins (GPMs) utilizing a fractional-order proportional-integral (FOPI) controller. Electric power systems contain many parametric uncertainties. FOPI controller gains are adjustable parameters and can be designed to provide the desired frequency control and dynamic performance. Therefore, in this article, the robust stability regions containing a set of robust FOPI controller gains are designed for the range model of the load frequency control system using Kharitonov’s theorem, considering the uncertainties in the LFC-DR system parameters and the time delay. Further, the robust performance of the interval LFC-DR system in terms of design features, including GPMs, is investigated. Simulation studies indicate that GPM parameters provide a better dynamic performance in terms of fast damping of oscillations, less settling time, and overshoot time for the interval LFC-DR system.

Keywords

Gain margin Phase margins Demand response Fractional-order controller Robust stability region

References

  • C. Ghenai, T. Salameh, A. Merabet, Technico-economic analysis of off grid solar PV/Fuel cell energy system for residential community in desert region. International Journal of Hydrogen Energy, 45(20),11460-11470, 2020. https://doi.org/10.1016/j. ijhydene.2018.05.110.
  •    J. Li, G. Li, The utilization of renewable energy and the economic potential of offshore wind power supported by digital finance. Heliyon, 10(16), 2024. https://doi.org/10.1016/j.heliyon.2024.e35175.
  •    Al Hadi, C.A.S. Silva, E. Hossain, R. Challoo, Algorithm for demand response to maximize the penetration of renewable energy, IEEE Access 8, 55279-55288, 2020. https://doi.org/10.1109/ACCESS .2020.2981877.
  •    M. Ebeed, S. Ali, A.M. Kassem, M. Hashem, S. Kamel, A.G. Hussien, F. Jurado, E.A Mohamed, Solving stochastic optimal reactive power dispatch using an Adaptive Beluga Whale optimization considering uncertainties of renewable energy resources and the load growth. Ain Shams Engineering Journal, 102762, 2024. https://doi.org/10.1016/j.asej.2024.102762.
  •    S.A. Mansouri, A. Ahmarinejad, M. Ansarian, M.S. Javadi, J.P.S. Catalao, Stochastic planning and operation of energy hubs considering demand response programs using Benders decomposition approach. International Journal of Electrical Power Energy Systems, 120, 106030, 2020.https://doi.org/10. 1016/j.ijepes.2020.106030.
  •    R. Kaluthanthrige, A.D. Rajapakse, Demand response integrated day-ahead energy management strategy for remote off-grid hybrid renewable energy systems. International Journal of Electrical Power Energy Systems, 129, 106731, 2021. https://doi.org/10.1016/ j.ijepes.2020.106731.
  •    S.S Gul, D. Suchitra, A multistage coupon incentive-based demand response in energy market. Ain Shams Engineering Journal, 15(3), 102468, 2024. https:// doi.org/10.1016/j.asej.2023.102468.
  •    S. Nojavan, M.T. Hagh, K. Taghizad-Tavana, M. Ghanbari-Ghalehjoughi, Optimal demand response aggregation in wholesale electricity markets: Comparative analysis of polyhedral; ellipsoidal and box methods for modeling uncertainties. Heliyon 10(10), 2024. https://doi.org/10.1016/j.heliyon.2024. e31523.
  •    L. Liu, H. Matayoshi, M. E. Lotfy, M. Datta, T. Senjyu, Load frequency control using demand response and storage battery by considering renewable energy sources. Energies, 11(12), 3412, 2018. https://doi. org/10.3390/en11123412
  • A. S. Roberts, L. Meegahapola, A.Vahidnia, Frequency Control using Dynamic Demand Response and Grid-Scale Battery Energy Storage Systems: An Australian Case Study. In 2024 IEEE 34th Australasian Universities Power Engineering Conference (AUPEC) (pp. 1-6). IEEE, 2024. https://doi.org /10.1109/AUPEC 62273.2024.10807590
  • M. Hu, F. Xiao, Price-responsive model-based optimal demand response control of inverter air conditioners using genetic algorithm. Applied Energy, 219, 151-164, 2018. https://doi.org/10.1016/j.apenergy.2018. 03.036.
  • M. Afzalan, F. Jazizadeh, Residential loads flexibility potential for demand response using energy consumption patterns and user segments. Applied Energy, 254, 113693, 2019. https://doi.org/10.1016/ j.apenergy.2019.113693.
  • H. Golmohamadi, R. Keypour, B. Bak-Jensen, J.R. Pillai, A multi-agent based optimization of residential and industrial demand response aggregators. International Journal of Electrical Power Energy Systems, 107, 472-485, 2019. https://doi.org/10.1016/j. ijepes.2018.12.020.
  • S. Liu, P.X. Liu, X. Wang, Stability analysis and compensation of network-induced delays in communication-based power system control: A survey. ISA Transactions, 66, 143-153, 2017. https://doi.org /10.1016/j.isatra.2016.09.022.
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, A. Naveed, The effect of demand response control on stability delay margins of load frequency control systems with communication time-delays. The Turkish Journal of Electrical Engineering Computer Sciences, 29(3), 1383-1400, 2021. https://doi.org/10.3906/elk-2006-165.
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, A. Naveed, Impact of participation ratios on the stability delay margins computed by direct method for multiple-area load frequency control systems with demand response. Automatika, 63(1), 185-197, 2022. https://doi.org/10. 1080/00051144.2021.2020554.
  • S. Saxena, Y.V. Hote, Decentralized PID load frequency control for perturbed multi-area power systems. International Journal of Electrical Power & Energy Systems, 81, 405-415, 2016. https://doi.org/ 10.1016/j.ijepes.2016.02.041.
  • V.P. Singh, P. Samuel, N. Kishor, Impact of demand response for frequency regulation in two‐area thermal power system. International Transactions on Electrical Energy Systems, 27(2), e2246, 2017. https://doi.org/ 10.1002/etep.2246.
  • X. Wang, X. Zhang, H. Sun, Real-time incentive design under unknown demand response curves via a proportional-integral control framework, IEEE Tran. Smart Grid 14(5) (2023) 3654-3667, https://doi.org/10 .1109/TSG.2023.3245672.
  • V. Çelik, M.T. Özdemir, G. Bayrak, The effects on stability region of the fractional-order PI controller for one-area time-delayed load–frequency control systems. Transactions of the Institute of Measurement and Control, 39(10), 1509-1521, 2017. https://doi.org/10 .1177/0142331216642839.
  • V. Çelik, M.T. Özdemir, K.Y. Lee, Effects of fractional-order PI controller on delay margin in single-area delayed load frequency control systems. Journal of Modern Power Systems and Clean Energy, 7(2), 380-389, 2019. https://doi.org/10.1007/s40565-018-0458-5.
  • B. Yildirim, M. Gheisarnejad, M.H. Khooban, A robust non-integer controller design for load frequency control in modern marine power grids. IEEE Transactions on Emerging Topics in Computational Intelligence, 6(4), 852-862, 2021. https://doi.org/10.1109/TETCI.2021 .3114735.
  • A. Tabak, Fractional order frequency proportional-integral-derivative control of microgrid consisting of renewable energy sources based on multi-objective grasshopper optimization algorithm. Transactions of the Institute of Measurement and Control, 44(2), 378-392, 2022. https://doi.org/10.1177/014233122110346 60.
  • F. Asadi, N. Abut, Kharitonov’s theorem: A good starting point for robust control. The International Journal of Electrical Engineering & Education, 58(1), 57-82, 2021. https://doi.org/10.1177/0020720919829 708.
  • M. Ebrahimi, E. S. Alaviyan Shahri, A. Alfi, A graphical method-based Kharitonov theorem for robust stability analysis of incommensurate fractional-order uncertain systems. Computational and Applied Mathematics, 43(2), 101, 2024. https://doi.org/ 10.1007/s40314-024-02610-z
  • S.K. Pandey, J. Dey, S. Banerjee, Modified Kharitonov theorem based optimal PID controller design for MIMO systems. Journal of Electrical Engineering & Technology, 18(3), 2317-2334, 2023. https://doi .org/10.1007/s42835-022-01329-3
  • N. Tan, I. Kaya, C. Yeroglu, D.P. Atherton, Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47(18-19), 3045-3058, 2006. https://doi. org/10.1016/j.enconman.2006.03.022.
  • M.T. Söylemez, N. Munro, H. Baki, Fast calculation of stabilizing PID controllers. Automatica, 39(1), 121-126, 2003. https://doi.org/10.1016/S0005-1098(02)001 80-2.
  • O. Turksoy, S. Ayasun, Y. Hames, Ş. Sönmez, Computation of robust PI-based pitch controller parameters for large wind turbines. IEEE Canadian Journal of Electrical and Computer Engineering, 43(1), 57-63, 2019. https://doi.org/10.1109/CJECE.2019. 2923050.
  • Ş. Sönmez, S. Ayasun, Computation of PI controllers ensuring desired gain and phase margins for two-area load frequency control system with communication time delays. Electric Power Components and Systems, 46(8), 938-947, 2018. https://doi.org/10.1080/1532 5008.2018.1509914.
  • H. Gündüz, Ş. Sonmez, S. Ayasun, A comprehensive gain and phase margins-based stability analysis of micro-grid frequency control system with constant communication time delays. IET Generation, Transmission Distribution, 11(3), 719-729, 2017. https://doi.org/10.1049/iet-gtd.2016.0644.
  • M.T. Özdemir, The effects of the FOPI controller and time delay on stability region of the fuel cell microgrid. International Journal of Hydrogen Energy, 45(60), 35064-35072, 2020. https://doi.org/10.1016/j.ijhydene. 2020.05.211.
  • H. Gündüz, Ş. Sönmez, S. Ayasun, Identification of gain and phase margins based robust stability regions for a time-delayed micro-grid system including fractional-order controller in presenceof renewable power generation. The Turkish Journal of Electrical Engineering ComputerSciences, 30(3), 1097-1114, 2022. https://doi.org/10.55730/1300-0632.3829.
  • S. Sondhi, Y.V. Hote, Fractional order PID controller for perturbed load frequency control using Kharitonov’s theorem. International Journal of Electrical Power Energy Systems, 78, 884-896, 2016. https://doi.org/10.1016/j.ijepes.2015.11.103.
  • R. Lamba, S.K. Singla, S. Sondhi, Design of fractional order PID controller for load frequency control in perturbed two area interconnected system. Electric Power Components and Systems, 47(11-12), 998-1011, 2016. https://doi.org/10.1080/15325008.2019.16607 36.
  • C.H. Chang, K.W. Han, Gain margins and phase margins for control systems with adjustable parameters. Journal of Guidance, Control, and Dynamics, 13(3), 404–408, 1990. https://doi.org/10. 2514/3.25351.
  • Z.Y. Nie, Q.G. Wang, M. Wu, Y. He, Combined gain and phase margins. ISA Transactions, 48(4), 428-433, 2009. https://doi.org/10.1016/j.isatra.2009.07.004.
  • Simulink, Simulation and model-based design, Natick, MA, USA: MathWorks, 2019.
  • S.A. Pourmousavi, M.H. Nehrir, Introducing dynamic demand response in the LFC model. IEEE Transactions on Power Systems, 29(4), 1562-1572, 2014. https://doi.org/10.1109/TPWRS.2013.2296696.
  • J. Sharma, Y.V. Hote, R. Prasad, PID controller design for interval load frequency control system with communication time delay. Control Engineering Practice, 89, 154-168, 2019. https://doi.org/10.1016/ j.conengprac.2019.05.016.
  • A.J. Samy Jeya Veronica, N. Senthil Kumar, F. Gonzalez‐Longatt, Robust PI controller design for frequency stabilisation in a hybrid microgrid system considering parameter uncertainties and communication time delay. IET Generation, Transmission Distribution, 13(14), 3048-3056,2019. https://doi.org/10.1049/iet-gtd.2018.5240.
  • F.A. Hasan, A.T. Humod, L.J. Rashad, Robust decoupled controller of induction motor by combining PSO and Kharitonov’s theorem. Engineering Science and Technology, an International Journal, 23(6), 1415-1424, 2020. https://doi.org/10.1016/j.jestch.2020.04. 004.
  • K.S. Ko, D.K. Sung, The effect of EV aggregators with time-varying delays on the stability of a load frequency control system. IEEE Transactions on Power Systems, 33(1), 669-680, 2017. https://doi.org/10.1109/TPWRS. 2017.2690915.
  • D. Katipoğlu, Stability analysis using fractional-order PI controller in a time-delayed single-area load frequency control system with demand response. Advances in Electrical Computer Engineering, 23(2), 2023. https://doi.org/10.4316/AECE.2023.02005
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, Dinamik talep cevabı içeren zaman gecikmeli iki bölgeli yük frekans kontrol sistemlerinin kararlılık bölgelerinin hesaplanması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(1), 431-442, 2024. https://doi.org/ 10.17341/gazimmfd.951415
  • D. Katipoğlu, S. Soylu, Design of optimal FOPI controller for two-area time-delayed load frequency control system with demand response. Journal of Electrical Engineering & Technology, 19(7), 4073-4085, 2024. https://doi.org/10.1007/s42835-024-01900 -0

Talep yanıtı ile zaman gecikmeli bir bölgeli yük frekans kontrolü sistemi için istenen kazanç ve faz marjlarını sağlayan kesir dereceli PI denetleyicilerinin tanımlanması

Year 2025, Volume: 14 Issue: 4, 1243 - 1252, 15.10.2025

Deniz Katipoğlu

Abstract

Bu araştırma, kesir dereceli oransal-integral (KDOI) denetleyici kullanılarak, talep yanıtı (TY) ile yük frekans kontrolü (YFK) sisteminin gürbüzlük analizi için kazanç ve faz marjları (KFM'ler) temelinde incelendiği bir sistemi sunmaktadır. Elektrik güç sistemleri birçok parametre belirsizlik içermektedir. KDOI denetleyici kazançları ayarlanabilir parametrelerdir ve istenen frekans kontrolü ve dinamik performans sağlamak için tasarlanabilirler. Bu nedenle, bu makalede, YFK-TY sistem parametrelerindeki belirsizlikler ve zaman gecikmesi göz önünde bulundurularak, Kharitonov Teoremi kullanılarak yük frekans kontrol sisteminin aralık modelinin tasarımında gürbüz KDOI denetleyici kazançları içeren gürbüzlük bölgeleri tasarlanmıştır. Ayrıca, KFM'ler gibi tasarım özellikleri açısından aralık YFK-TY sisteminin güzbüz performansı incelenmiştir. Simülasyon çalışmaları, KFM parametrelerinin, aralık YFK-TY sistemi için salınımların hızlı bir şekilde sönümlenmesi, yerleşme zamanının ve aşım süresinin daha düşük olması açısından daha iyi bir dinamik performans sağladığını göstermektedir.

Keywords

Kazanç marjı Faz marjları Talep yanıtı Sağlamlık bölgesi Kesir dereceli denetleyici

References

  • C. Ghenai, T. Salameh, A. Merabet, Technico-economic analysis of off grid solar PV/Fuel cell energy system for residential community in desert region. International Journal of Hydrogen Energy, 45(20),11460-11470, 2020. https://doi.org/10.1016/j. ijhydene.2018.05.110.
  •    J. Li, G. Li, The utilization of renewable energy and the economic potential of offshore wind power supported by digital finance. Heliyon, 10(16), 2024. https://doi.org/10.1016/j.heliyon.2024.e35175.
  •    Al Hadi, C.A.S. Silva, E. Hossain, R. Challoo, Algorithm for demand response to maximize the penetration of renewable energy, IEEE Access 8, 55279-55288, 2020. https://doi.org/10.1109/ACCESS .2020.2981877.
  •    M. Ebeed, S. Ali, A.M. Kassem, M. Hashem, S. Kamel, A.G. Hussien, F. Jurado, E.A Mohamed, Solving stochastic optimal reactive power dispatch using an Adaptive Beluga Whale optimization considering uncertainties of renewable energy resources and the load growth. Ain Shams Engineering Journal, 102762, 2024. https://doi.org/10.1016/j.asej.2024.102762.
  •    S.A. Mansouri, A. Ahmarinejad, M. Ansarian, M.S. Javadi, J.P.S. Catalao, Stochastic planning and operation of energy hubs considering demand response programs using Benders decomposition approach. International Journal of Electrical Power Energy Systems, 120, 106030, 2020.https://doi.org/10. 1016/j.ijepes.2020.106030.
  •    R. Kaluthanthrige, A.D. Rajapakse, Demand response integrated day-ahead energy management strategy for remote off-grid hybrid renewable energy systems. International Journal of Electrical Power Energy Systems, 129, 106731, 2021. https://doi.org/10.1016/ j.ijepes.2020.106731.
  •    S.S Gul, D. Suchitra, A multistage coupon incentive-based demand response in energy market. Ain Shams Engineering Journal, 15(3), 102468, 2024. https:// doi.org/10.1016/j.asej.2023.102468.
  •    S. Nojavan, M.T. Hagh, K. Taghizad-Tavana, M. Ghanbari-Ghalehjoughi, Optimal demand response aggregation in wholesale electricity markets: Comparative analysis of polyhedral; ellipsoidal and box methods for modeling uncertainties. Heliyon 10(10), 2024. https://doi.org/10.1016/j.heliyon.2024. e31523.
  •    L. Liu, H. Matayoshi, M. E. Lotfy, M. Datta, T. Senjyu, Load frequency control using demand response and storage battery by considering renewable energy sources. Energies, 11(12), 3412, 2018. https://doi. org/10.3390/en11123412
  • A. S. Roberts, L. Meegahapola, A.Vahidnia, Frequency Control using Dynamic Demand Response and Grid-Scale Battery Energy Storage Systems: An Australian Case Study. In 2024 IEEE 34th Australasian Universities Power Engineering Conference (AUPEC) (pp. 1-6). IEEE, 2024. https://doi.org /10.1109/AUPEC 62273.2024.10807590
  • M. Hu, F. Xiao, Price-responsive model-based optimal demand response control of inverter air conditioners using genetic algorithm. Applied Energy, 219, 151-164, 2018. https://doi.org/10.1016/j.apenergy.2018. 03.036.
  • M. Afzalan, F. Jazizadeh, Residential loads flexibility potential for demand response using energy consumption patterns and user segments. Applied Energy, 254, 113693, 2019. https://doi.org/10.1016/ j.apenergy.2019.113693.
  • H. Golmohamadi, R. Keypour, B. Bak-Jensen, J.R. Pillai, A multi-agent based optimization of residential and industrial demand response aggregators. International Journal of Electrical Power Energy Systems, 107, 472-485, 2019. https://doi.org/10.1016/j. ijepes.2018.12.020.
  • S. Liu, P.X. Liu, X. Wang, Stability analysis and compensation of network-induced delays in communication-based power system control: A survey. ISA Transactions, 66, 143-153, 2017. https://doi.org /10.1016/j.isatra.2016.09.022.
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, A. Naveed, The effect of demand response control on stability delay margins of load frequency control systems with communication time-delays. The Turkish Journal of Electrical Engineering Computer Sciences, 29(3), 1383-1400, 2021. https://doi.org/10.3906/elk-2006-165.
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, A. Naveed, Impact of participation ratios on the stability delay margins computed by direct method for multiple-area load frequency control systems with demand response. Automatika, 63(1), 185-197, 2022. https://doi.org/10. 1080/00051144.2021.2020554.
  • S. Saxena, Y.V. Hote, Decentralized PID load frequency control for perturbed multi-area power systems. International Journal of Electrical Power & Energy Systems, 81, 405-415, 2016. https://doi.org/ 10.1016/j.ijepes.2016.02.041.
  • V.P. Singh, P. Samuel, N. Kishor, Impact of demand response for frequency regulation in two‐area thermal power system. International Transactions on Electrical Energy Systems, 27(2), e2246, 2017. https://doi.org/ 10.1002/etep.2246.
  • X. Wang, X. Zhang, H. Sun, Real-time incentive design under unknown demand response curves via a proportional-integral control framework, IEEE Tran. Smart Grid 14(5) (2023) 3654-3667, https://doi.org/10 .1109/TSG.2023.3245672.
  • V. Çelik, M.T. Özdemir, G. Bayrak, The effects on stability region of the fractional-order PI controller for one-area time-delayed load–frequency control systems. Transactions of the Institute of Measurement and Control, 39(10), 1509-1521, 2017. https://doi.org/10 .1177/0142331216642839.
  • V. Çelik, M.T. Özdemir, K.Y. Lee, Effects of fractional-order PI controller on delay margin in single-area delayed load frequency control systems. Journal of Modern Power Systems and Clean Energy, 7(2), 380-389, 2019. https://doi.org/10.1007/s40565-018-0458-5.
  • B. Yildirim, M. Gheisarnejad, M.H. Khooban, A robust non-integer controller design for load frequency control in modern marine power grids. IEEE Transactions on Emerging Topics in Computational Intelligence, 6(4), 852-862, 2021. https://doi.org/10.1109/TETCI.2021 .3114735.
  • A. Tabak, Fractional order frequency proportional-integral-derivative control of microgrid consisting of renewable energy sources based on multi-objective grasshopper optimization algorithm. Transactions of the Institute of Measurement and Control, 44(2), 378-392, 2022. https://doi.org/10.1177/014233122110346 60.
  • F. Asadi, N. Abut, Kharitonov’s theorem: A good starting point for robust control. The International Journal of Electrical Engineering & Education, 58(1), 57-82, 2021. https://doi.org/10.1177/0020720919829 708.
  • M. Ebrahimi, E. S. Alaviyan Shahri, A. Alfi, A graphical method-based Kharitonov theorem for robust stability analysis of incommensurate fractional-order uncertain systems. Computational and Applied Mathematics, 43(2), 101, 2024. https://doi.org/ 10.1007/s40314-024-02610-z
  • S.K. Pandey, J. Dey, S. Banerjee, Modified Kharitonov theorem based optimal PID controller design for MIMO systems. Journal of Electrical Engineering & Technology, 18(3), 2317-2334, 2023. https://doi .org/10.1007/s42835-022-01329-3
  • N. Tan, I. Kaya, C. Yeroglu, D.P. Atherton, Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47(18-19), 3045-3058, 2006. https://doi. org/10.1016/j.enconman.2006.03.022.
  • M.T. Söylemez, N. Munro, H. Baki, Fast calculation of stabilizing PID controllers. Automatica, 39(1), 121-126, 2003. https://doi.org/10.1016/S0005-1098(02)001 80-2.
  • O. Turksoy, S. Ayasun, Y. Hames, Ş. Sönmez, Computation of robust PI-based pitch controller parameters for large wind turbines. IEEE Canadian Journal of Electrical and Computer Engineering, 43(1), 57-63, 2019. https://doi.org/10.1109/CJECE.2019. 2923050.
  • Ş. Sönmez, S. Ayasun, Computation of PI controllers ensuring desired gain and phase margins for two-area load frequency control system with communication time delays. Electric Power Components and Systems, 46(8), 938-947, 2018. https://doi.org/10.1080/1532 5008.2018.1509914.
  • H. Gündüz, Ş. Sonmez, S. Ayasun, A comprehensive gain and phase margins-based stability analysis of micro-grid frequency control system with constant communication time delays. IET Generation, Transmission Distribution, 11(3), 719-729, 2017. https://doi.org/10.1049/iet-gtd.2016.0644.
  • M.T. Özdemir, The effects of the FOPI controller and time delay on stability region of the fuel cell microgrid. International Journal of Hydrogen Energy, 45(60), 35064-35072, 2020. https://doi.org/10.1016/j.ijhydene. 2020.05.211.
  • H. Gündüz, Ş. Sönmez, S. Ayasun, Identification of gain and phase margins based robust stability regions for a time-delayed micro-grid system including fractional-order controller in presenceof renewable power generation. The Turkish Journal of Electrical Engineering ComputerSciences, 30(3), 1097-1114, 2022. https://doi.org/10.55730/1300-0632.3829.
  • S. Sondhi, Y.V. Hote, Fractional order PID controller for perturbed load frequency control using Kharitonov’s theorem. International Journal of Electrical Power Energy Systems, 78, 884-896, 2016. https://doi.org/10.1016/j.ijepes.2015.11.103.
  • R. Lamba, S.K. Singla, S. Sondhi, Design of fractional order PID controller for load frequency control in perturbed two area interconnected system. Electric Power Components and Systems, 47(11-12), 998-1011, 2016. https://doi.org/10.1080/15325008.2019.16607 36.
  • C.H. Chang, K.W. Han, Gain margins and phase margins for control systems with adjustable parameters. Journal of Guidance, Control, and Dynamics, 13(3), 404–408, 1990. https://doi.org/10. 2514/3.25351.
  • Z.Y. Nie, Q.G. Wang, M. Wu, Y. He, Combined gain and phase margins. ISA Transactions, 48(4), 428-433, 2009. https://doi.org/10.1016/j.isatra.2009.07.004.
  • Simulink, Simulation and model-based design, Natick, MA, USA: MathWorks, 2019.
  • S.A. Pourmousavi, M.H. Nehrir, Introducing dynamic demand response in the LFC model. IEEE Transactions on Power Systems, 29(4), 1562-1572, 2014. https://doi.org/10.1109/TPWRS.2013.2296696.
  • J. Sharma, Y.V. Hote, R. Prasad, PID controller design for interval load frequency control system with communication time delay. Control Engineering Practice, 89, 154-168, 2019. https://doi.org/10.1016/ j.conengprac.2019.05.016.
  • A.J. Samy Jeya Veronica, N. Senthil Kumar, F. Gonzalez‐Longatt, Robust PI controller design for frequency stabilisation in a hybrid microgrid system considering parameter uncertainties and communication time delay. IET Generation, Transmission Distribution, 13(14), 3048-3056,2019. https://doi.org/10.1049/iet-gtd.2018.5240.
  • F.A. Hasan, A.T. Humod, L.J. Rashad, Robust decoupled controller of induction motor by combining PSO and Kharitonov’s theorem. Engineering Science and Technology, an International Journal, 23(6), 1415-1424, 2020. https://doi.org/10.1016/j.jestch.2020.04. 004.
  • K.S. Ko, D.K. Sung, The effect of EV aggregators with time-varying delays on the stability of a load frequency control system. IEEE Transactions on Power Systems, 33(1), 669-680, 2017. https://doi.org/10.1109/TPWRS. 2017.2690915.
  • D. Katipoğlu, Stability analysis using fractional-order PI controller in a time-delayed single-area load frequency control system with demand response. Advances in Electrical Computer Engineering, 23(2), 2023. https://doi.org/10.4316/AECE.2023.02005
  • D. Katipoğlu, Ş. Sönmez, S. Ayasun, Dinamik talep cevabı içeren zaman gecikmeli iki bölgeli yük frekans kontrol sistemlerinin kararlılık bölgelerinin hesaplanması. Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 39(1), 431-442, 2024. https://doi.org/ 10.17341/gazimmfd.951415
  • D. Katipoğlu, S. Soylu, Design of optimal FOPI controller for two-area time-delayed load frequency control system with demand response. Journal of Electrical Engineering & Technology, 19(7), 4073-4085, 2024. https://doi.org/10.1007/s42835-024-01900 -0
There are 46 citations in total.

Details

Primary Language English
Subjects Power Plants
Journal Section Research Articles
Authors

Deniz Katipoğlu 0000-0003-3082-3879

Early Pub Date September 17, 2025
Publication Date October 15, 2025
Submission Date January 2, 2025
Acceptance Date July 14, 2025
Published in Issue Year 2025 Volume: 14 Issue: 4

Cite

APA Katipoğlu, D. (2025). Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 14(4), 1243-1252. https://doi.org/10.28948/ngumuh.1612061
AMA Katipoğlu D. Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response. NOHU J. Eng. Sci. October 2025;14(4):1243-1252. doi:10.28948/ngumuh.1612061
Chicago Katipoğlu, Deniz. “Identification of Fractional Order PI Controllers Ensuring Desired Gain and Phase Margins for a Time-Delayed Single-Area Load Frequency Control System With Demand Response”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14, no. 4 (October 2025): 1243-52. https://doi.org/10.28948/ngumuh.1612061.
EndNote Katipoğlu D (October 1, 2025) Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14 4 1243–1252.
IEEE D. Katipoğlu, “Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response”, NOHU J. Eng. Sci., vol. 14, no. 4, pp. 1243–1252, 2025, doi: 10.28948/ngumuh.1612061.
ISNAD Katipoğlu, Deniz. “Identification of Fractional Order PI Controllers Ensuring Desired Gain and Phase Margins for a Time-Delayed Single-Area Load Frequency Control System With Demand Response”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi 14/4 (October2025), 1243-1252. https://doi.org/10.28948/ngumuh.1612061.
JAMA Katipoğlu D. Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response. NOHU J. Eng. Sci. 2025;14:1243–1252.
MLA Katipoğlu, Deniz. “Identification of Fractional Order PI Controllers Ensuring Desired Gain and Phase Margins for a Time-Delayed Single-Area Load Frequency Control System With Demand Response”. Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, vol. 14, no. 4, 2025, pp. 1243-52, doi:10.28948/ngumuh.1612061.
Vancouver Katipoğlu D. Identification of fractional order PI controllers ensuring desired gain and phase margins for a time-delayed single-area load frequency control system with demand response. NOHU J. Eng. Sci. 2025;14(4):1243-52.
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