Yük frekans kontrol sistemlerinde gürbüz kararlılık zaman gecikmesi paylarının belirlenmesi

Yıl 2024, Cilt: 13 Sayı: 2, 611 - 620, 15.04.2024

Kübra Nur Gül Şahin Sönmez Saffet Ayasun

https://doi.org/10.28948/ngumuh.1403702

Öz

Bu çalışma, zaman gecikmesi içeren Yük Frekans Kontrol (YFK) sistemlerinde parametrik belirsizliklerin olması durumunda sistemin gürbüz kararlılık gecikme payı değerlerini hesaplamayı amaçlamaktadır. YFK sistemlerinde frekans kararlılığının sürdürülmesi bakımından çeşitli elektrik verilerinin ölçülerek kontrol merkezine iletilmesi ve kontrol merkezinden frekans kontrol servisine katılım sağlayan santrallere kontrol sinyallerinin iletilmesi gerekmektedir. Bu süreçte, haberleşme ağlarında veri iletimi nedeniyle, zaman gecikmeleri kaçınılmaz hale gelmektedir ve sistemin dinamik performansı ve kararlılığı olumsuz etkilenmektedir. Ayrıca, YFK sisteminin modellenmesinden kaynaklı ve güç sisteminde oluşabilecek belirsizlikler nedeniyle sistem parametrelerinin belirsizlikleri dikkate alınarak haberleşme ağı tabanlı gözlemlenebilecek gecikme değerleri üzerinde böylesi belirsizliklerin etkisi incelenmelidir. Bu amaçla, YFK sisteminde üstel terimin yok edilmesi yöntemi ile Kharitonov Teoremi birlikte kullanılarak sistemin gürbüz kararlılığını sağlayabilen gürbüz zaman gecikme payı değerlerinin teorik olarak hesaplanması sağlanmıştır. Aynı zamanda Matlab/Simulink programı ve QPmR (Quasi Poliynomial Mapping Root Finder) algoritması kullanılarak elde edilen teorik sonuçların doğruluğu kanıtlanmıştır.

Anahtar Kelimeler

Yük frekans kontrol sistemi, Haberleşme zaman gecikmesi, Kharitonov teoremi, Üstel terimlerin yok edilmesi yöntemi

Determination of the robust stability delay margins for the load frequency control systems

Öz

This study computes the robust stability delay margins of the time delayed load frequency control (LFC) system towards parametric uncertainties. The LFC systems are extensively equipped with communication networks to maintain the system frequency stability and to transmit/receive the measurement and control signals between the control central and generation units. However, network induced time delays due to the extensive utilization of communication networks are inevitable in LFC systems. Such delays could negatively affect the LFC system stability and could degrade the dynamical performance of system. Moreover, the parametric uncertainties are significant challenges for robust stability of the LFC system. Therefore, the effect of parametric uncertainties on the communication delay values could be investigated. For this purpose, this study determines the robust stability delay margin of LFC system by cooperating the direct method and Kharitonov theorem. The accuracy of theoretical computations is verified by the time domain simulations and QPmR algorithm.

Anahtar Kelimeler

Load frequency control, Communication time delay, Kharitonov theorem, Direct method.

Kaynakça

• P. Kundur, Power System Stability and Control (1. Basım). McGraw-Hill Inc, New York, 1994.
• H. Saadat, Power System Analysis (1. Basım). McGraw-Hill Inc, New York, 1999.
• D. Muyizere, L. K. Letting, B. B. Muyazikwiye, Effects of communication signal delay on the power grid: a review. Electronics, 11, 874, 2022. https://doi.org/ 10.3390/electronics11060874.
• L. Jiang, W. Yao, J. Y. Wen, S. J. Cheng, and Q. H. Wu, Delaydependent stability for load frequency control with constant and time varying delay. IEEE Trans. Power Syst., 2012. https://doi.org/10.1109/ TPWRS.2011.2172821
• Ş. Sönmez, S. Ayasun, and C. O. Nwankpa, 2016. An exact method for computing delay margin for stability of load frequency control systems with constant communication delays. IEEE Transactions on Power Systems, 31(1), 370-377, 2016. https://doi.org/ 10.1109 /TPWRS.2015.2403865
• T. N. P. Janu, S. Nahavandi, L. V. Hien, H. Trinh and K. P. Wong,. Static output feedback frequency stabilization of time-delay power systems with coordinated electric vehicles state of charge control. IEEE Trans. Power Syst., 32(5), 3862–3874, 2017. https://doi.org/10.1109/TPWRS.2016.2633540.
• S. J. Zhou, H. B. Zeng, H. Q. Xia, Load frequency stability analysis of time-delayed multi-area power systems with evs aggregators based on bessel-legendre ınequality and model reduction technique. IEEE Access, 8, 99948-99955, 2020. https://doi.org/10.1109/ ACCESS.2020.2997002.
• A. Sarı, Ş. Sönmez, S. Ayasun, Y. Kabalcı, Delay-dependent stability analysis of multi-area LFC-EVs system. IEEE Transactions on Smart Grid, 14(3), 2178-2188, 2023. https://doi.org/ 10.1109/TSG.2022.32127 79.
• Ö Aydın, Ş. Sönmez and S. Ayasun, Stability delay margin computation of multi-area load frequency control system with electric vehicle using critical eigenvalue tracing method. Transactions of the Institute of Measurement and Control, 45(5), 874-885, 2023. https://doi.org/10.1177/01423312221122487.
• D. Katipoglu, 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. A. Pourmousavi and 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.
• D. Katipoglu, Ş. Sönmez, S. Ayasun, A. Naveed, Dinamik talep cevabı içeren zaman gecikmeli iki bölgeli yük frekans kontrol sistemlerinin kararlılık bölgelerinin hesaplanması. Gazi Üniversitesi Mühendislik ve Mimarlık Fakültesi, 39(1), 431-442, 2024. https://doi.org/10.17341/gazimmfd.951415.
• K. E. Walton and J. E. Marshall, Direct method for TDS stability analysis. IEEE Proceeding Part D, 134, 101-107, 1987. https://doi.org/10.1049/ip-d:19870018.
• J. Hongjie, Y. Xiaodan, A simple method for power system stability analysis with multiple time delays. IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy, Pittsburgh. USA, 2008. https://doi.org/10.1109/ PES.2008.4596157.
• J. Chen and H. A. Latchman, Frequency sweeping tests for stability independent of delay. IEEE Transactions on Automatic Control, 40 (9), 1640–1645, 1995. https://doi.org/10.1109/9.412637.
• Z. V. Rekasius, 1980. A stability test for systems with delays. Joint Automatic Control Conference, TP9-A, 1980. https://doi.org/10.1109/JACC.1980.4232120.
• N. Olgac and R. Sipahi, An exact method for the stability analysis of time-delayed linear time invariant (LTI) systems. IEEE Transactions on Automatic Control, 47(5), 793-797, 2002.https://doi.org/10.1109/ TAC.2002.1000275.
• L. Pekař, Q. Gao, Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results. IEEE Access, 6, 35457–35491,2018.https://doi.org/0.1109/ACCESS. 2018.2851453.
• A. Naveed, Ş. Sönmez, S. Ayasun, Impact of load sharing schemes on the stability delay margins computed by rekasius substitution method in load frequency control system with electric vehicles aggregator. International Transactions on Electrical Energy Systems, 31 (5), e12884, 2021. https://doi.org /10.1002/2050-7038.12884.
• A. Naveed, Ş. Sönmez, S. Ayasun, The ımpact of electric vehicles aggregator with communication time delay on stability regions and stability delay margins of load frequency control system. Journal of Modern Power Systems and Clean Energy, 9(3), 595-601, 2021.https://doi.org/10.35833/MPCE.2019.000244.
• Ş. Sonmez, S. Ayasun, Gain and phase margins-based delay margin computation of load frequency control systems using Rekasius substitution. Transactıons of the Instıtute of Measurement and Control, 41(12), 3385-3395, 2019. https://doi.org/10.1177/ 01423312 19826653.
• H. Gündüz, Ş. Sönmez and 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 and Distribution, 11(3), 719-729, 2017. https://doi.org/10.1049/iet-gtd.2016.0644.
• C. A. Macana, E. Mojica-Nava and N. Quijano, Time-delay effect on load frequency control for microgrids. IEEE International Conference on Networking, Sensing and Control (ICNSC), 544-549, 2013. https://doi.org/10.1109/ICNSC.2013.6548797.
• D. Katipoglu, Stability analysis using fractional-order pı controller in a time-delayed single-area load frequency control system with demand response. Advances in Electrical and Computer Engineering, 23 (2), 39-46, 2023. https://doi.org/10. 4316/AECE.2023. 02005.
• L. Jin,C. K. Zhang, Y. He, L. Jiang, M. Wu, Delay-dependent stability analysis of multi-area load frequency control with enhanced accuracy and computation efficiency. IEEE Transactions on Power Systems, 34 (5), 3687-3696, 2019. https://doi.org/ 10.1109/TPWRS.2019.2902373.
• C. Tunç, O. Tunç, Y. Wang and J. C. Yao, Qualitative analyses of differential systems with time-varying delays via Lyapunov–Krasovskiĭ approach. Mathematics, 9 (11), 1196, 2021. https://doi.org/10. 3390/math9111196.
• C. Hua, Y. Wang, Delay-dependent stability for load frequency control system via linear operator inequality. IEEE Transactions on Cybernetics, 52(7), 6984-6992. https://doi.org/10.1109/TCYB.2020.3037113.
• H. Bevrani, Robust power system frequency control. Springer-Verlag, New York, 2014. https://doi.org/ 10.1007/978-3-319-07278-4.
• M. R. Toulabi, M. Shiroei, A. M. Ranjbar, Robust Analysis and design of power system load frequency control using the Kharitonov’s Theorem. Int J Elect Power Energy Syst, 55, 51–58, 2014. https://doi.org/ 10.1016/j.ijepes.2013.08.014.
• S. Saxena, Y. V. Hote, Decentralized PID load frequency control for perturbed multi-area power systems. Int J Elect Power Energy Syst, 81, 405–415, 2016. https://doi.org/10.1016/j.ijepes.2016.02.041.
• J. Sharma, Y. V. Hote, R. Prasad, PID controller design for ınterval load frequency control system with communication time delay. Control Eng. Pract., 89, 154-168, 2019. https://doi.org/10.1016/j.conen gprac .2019.05.016.
• R. Lamba, S.K. Singla, S. Sondhi, Design of fractional order PID controller for load frequency control in perturbed two area ınterconnected system. Electr. Power Compon. Syst., 47 (11-12), 998–1011, 2019. https://doi.org/10.1080/15325008.2019.1660736.
• A. Naveed, Ş. Sönmez, S. Ayasun, S. Iqbal, H. Zeinoddini-Meymand, S. Kamel, Robust stability region analysis of time-delayed load frequency control systems with EVs aggregator using Kharitonov theorem”, IET Generation, Transmission and Distribution, 17 (19), 4386-4398, 2023. https://doi.org/ 10.1049/gtd2.12983.
• V. L. Kharitonov, Asymptotic stability of an equilibrium position of a family systems of linear differential equations. Differential’nye Uraveniya, 14, 1483-1485, 1978.
• T. Vyhlídal and P. Zítek, Mapping based algorithm for large-scale computation of quasi-polynomial zeros. IEEE Transactions Automatic Control, 2054 (1), 171-177, 2009. https://doi.org/10.1109/TAC.2008.2008345
• Matlab (R2019b), Natick, Massachusetts: The MathWorks Inc., 2019.