REKASIUS YÖNTEMİ KULLANILARAK ZAMAN GECİKMELİ JENERATÖR UYARMA KONTROL SİSTEMİNİN MAKSİMUM ZAMAN GECİKMESİNİN HESAPLANMASI

Öz

   Bu çalışma, otomatik gerilim regülatörü (OGR) ve güç sistem dengeleyici (GSD) içeren zaman gecikmeli jeneratör uyarma kontrol sisteminin Rekasius yerine koyma yöntemi kullanılarak zaman gecikmesine bağlı kararlılığını incelemektedir. Sistemin kararlılığını kaybetmeden çalışabileceği zaman gecikmesi üst sınırının hesaplanması için Rekasius yönteminin farklı bir prosedürü kullanılmıştır. Önerilen yöntem, ilk olarak uyarma kontrol sisteminin karakteristik denkleminde bulunan üstel terimi herhangi bir yaklaşık içermeyen bir eşitlik yardımıyla elimine etmekte ve karakteristik denklemi sıradan bir polinoma dönüştürmekte ve daha sonra, sistemin sanal eksen üzerindeki köklerine karşılık gelen maksimum zaman gecikmesi değerlerini hesaplamaktadır. Jeneratör uyarma kontrol sisteminin kararlılık analizi için tek makineli sonsuz baralı (TMSB) bir güç sistemi seçilmiş ve GSD kazanç değerleri için sistemin zaman gecikmesi değerleri hesaplanmıştır. Elde edilen sonuçların doğruluğu, üstel terim içeren polinomların köklerini hesaplamak için geliştirilen QPmR (the quasi-polynomial mapping-based root finder) algoritması ve zaman düzleminde gerçekleştirilen benzetim çalışmaları ile gösterilmiştir.

Anahtar Kelimeler

• Haberleşme zaman gecikmesi,kararlılık,jeneratör uyarma kontrol sistemi,QPmR algoritması,Rekasius yöntemi

DELAY MARGIN COMPUTATION OF A TIME DELAYED GENERATOR EXCITATION CONTROL SYSTEM USING REKASIUS SUBSTITUON

Abstract

   This paper investigates the delay-dependent stability analysis of a time delayed generator excitation control system including an automatic voltage regulator and a power system stabilizer (PSS) using Rekasius substitution. A modified Rekasius substitution method is proposed to compute delay margin for which the system is marginally stable. The proposed method first eliminates transcendental terms in characteristic equation of the excitation control system without making any approximation and then, computes stability delay margins corresponding to purely imaginary roots with the crossing frequency. In this study, a single-machine-infinite-bus system is chosen as a test system. For a wide range of PSS gains, delay margins of the control system are computed. The accuracy of complex roots and delay margins are verified by using an independent algorithm, the quasi-polynomial mapping-based root finder (QPmR) and time-domain simulations, respectively.

Keywords

• Communication time delay,stability,generator excitation control system,QPmR Algorithm,Rekasius substitution

Kaynakça

1. SAADAT, H., Power System Analysis (2rd ed.), McGraw-Hill, New York, USA, 1999.
2. KUNDUR, P., Power System Stability and Control (1rd ed.), McGraw-Hill, New York, USA, 1994.
3. SAUER, P.W., PAI, M.A., Power System Dynamics and Stability (1rd ed.), Indian Reprint, Singapore, Asia, 2002.
4. NADUVATHUPARAMBIL, B., VALENTI, M.C., FELIACHI, A., “Communication delays in wide area measurement systems”, Proceedings of the 34th Southeastern Symposium on System Theory, 118-122. Alabama, USA, 2002.
5. XIA, X., XIN, Y., XIAO, J., WU, J., HAN, Y., “WAMS applications in Chinese power systems”, IEEE Power and Energy Magazine, 4, 54-63, 2006.
6. PHADKE, A.G., “Synchronized phasor measurements in power systems”, IEEE Computer Applications in Power, 6, 10-15, 1993.
7. WU, H., TSAKALIS, K., HEYDT, G.T., “Evaluation of time delay effects to wide-area power system stabilizer design”, IEEE Transactions on Power System, 19, 1935–1941, 2004.
8. LIU, M., YANG, L., GAN, D., WANG, D., GAO, F., CHEN, Y., “The stability of AGC systems with commensurate delays”, International Transactions on Electrical Energy Systems, 17, 615-627, 2007.

9. JIANG, L., YAO, W., WU, Q.H., WEN, J.Y., CHENG, S.J., “Delay-dependent stability for load frequency control with constant and time-varying delays”, IEEE Transactions on Power System, 27, 932-941, 2012.
10. YAO, W., JIANG, L., WU, Q.H., WEN, J.Y., CHENG, S.J., “Wide-area damping controller of FACTS devices for inter-area oscillations considering communication time delays”, IEEE Transactions on Power System, 29, 318-329, 2014.
11. AYASUN, S., GELEN, A., “Stability analysis of a generator excitation control system with time delays”, Electrical Engineering, 91, 347-355, 2010.
12. AYASUN, S., “Computation of time delay margin for power system small-signal stability”, International Transactions on Electrical Energy Systems, 19, 949-968, 2009.
13. CHEN, J., GU, G., NETT, C.N., “A new method for computing delay margins for stability of linear delay systems”, System and Control Letters, 26, 107-117, 1995.
14. WALTON, K.E., MARSHALL, J.E., “Direct method for TDS stability analysis”, IEE Proceeding Part D, 134: 101–107, 1987.
15. SÖNMEZ, Ş., AYASUN, S., NWANKPA, C.O., “An exact method for computing delay margin for stability of load frequency control systems with constant communication delays”, IEEE Transactions on Power Systems, 31, 370-377, 2016.
16. REKASIUS, Z.V., “A stability test for systems with delays”, Proceedings of the Joint Automatic Control Conference, TP9-A. San Francisco, USA, 1980.
17. OLGAÇ, N., SİPAHİ, R., “An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems”, IEEE Transactions on Automatic Control, 47, 793-797, 2002.
18. SİPAHİ, R., DELICE, I., “Advanced Clustering With Frequency Sweeping Methodology for the Stability Analysis of Multiple Time-Delay Systems”, IEEE Transactions on Automatic Control, 56, 467 – 472, 2011.
19. KHALIL, H., PENG, A.S., “An Accurate Method for Delay Margin Computation for Power System Stability”, Energies, 11, 3466, 2018.
20. KHALIL, H., PENG, A.S., “A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems”, Energies, 11, 3460, 2018.
21. SÖNMEZ, S., AYASUN, S., “Effect of load increase and power system stabilizer on stability delay margin of a generator excitation control system”, Turkish Journal of Electrical Engineering & Computer Sciences, 24, 5183 – 5194, 2016.
22. GÜNDÜZ, H., SÖNMEZ, S., AYASUN, S., “Comprehensive gain and phase margins based stability analysis of micro-grid frequency control system with constant communication time delays”, IET Generation, Transmission & Distribution, 11, 719 – 729, 2017.
23. SÖNMEZ, Ş., AYASUN, S., EMINOĞLU, U., “Computation of Time Delay Margins for Stability of a Single-Area Load Frequency Control System with Communication Delays”, WSEAS Transactions on Power Systems, 9, 67-76, 2014.
24. MACANA, C.A., MOJICA-NAVA, E., QUIJANO, N., “Time-delay effect on load frequency control for microgrids”, IEEE International Conference on Networking, Sensing and Control (ICNSC), 544-549. Evry, France, 2013.
25. GÜNDÜZ, H., AYASUN, S., SÖNMEZ, Ş., “Zaman gecikmeli mikro-şebeke sistemlerin Rekasius yerine koyma yöntemiyle kazanç ve faz payı tabanlı kararlılık analizi”, Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, Doi: 10.17341/gazimmfd.416515, 2018.
26. YAO, W., JIANG, L., WU, Q.H., WEN, J.Y., CHENG, S.J., “Delay-dependent stability analysis of the power system with a wide-area damping controller embedded“, IEEE Transactions on Power System, 26, 233–240, 2011.
27. HE, Y., WANG, Q.G., XIE, L.H., LIN, C., “Further improvement of free-weighting matrices technique for systems with time-varying delay”, IEEE Transactions on Automatic Control, 52, 293–299, 2007.
28. WU, M., HE, Y., SHE, J.H., LIU, G.P., “Delay-dependent criterion for robust stability of time-varying delay systems”, Automatica, 40, 1435–1439, 2004.
29. XU, S.Y., LAM, J., “On equivalence and efficiency of certain stability criteria for time-delay systems”, IEEE Transactions on Automatic Control, 52, 95–101, 2007.
30. VYHLIDAL, T., ZITEK, P., “Mapping based algorithm for large-scale computation of quasi-polynomial zeros”, IEEE Transactions on Automatic Control, 2054, 171-177, 2009.
31. SİMULINK, Model-Based and System-Based Design, Using Simulink, Natick, MathWorks, 2000.
32. VYHLIDAL, T., OLGAÇ, N., KUČERA, V., “Delayed resonator with acceleration feedback – Complete stability analysis by spectral methods and vibration absorber design” Journal of Sound and Vibration, 333, 6781– 6795, 2014.
33. KAMMER, A.S., OLGAÇ, N., “Delayed-feedback vibration absorbers to enhance energy harvesting”, Journal of Sound and Vibration, 363, 54–67, 2016.
34. SHAHGHOLIAN, G., FAIZ, J., “The effect of power system stabilizer on small-signal stability in single-machine-infinite-bus”, International Journal of Electrical and Power Engineering, 4, 45-53, 2010.