Computation of Delay-Dependent Stability Regions for Electric Power Systems with Time Delay

Öz

This work investigates delay-dependent stability analysis and stability regions in time delays space using eigenvalue tracing method for a time-delayed generator excitation control system including a power system stabilizer (PSS) and an automatic voltage regulator (AVR). Electrical power systems need to communication networks and measurement systems for keeping the voltage and frequency stability. However, the utilizing of communication networks and measurement systems causes inevitable time delays which deteriorate the system dynamical behavior. In the study, a simple method finding delay margin values and critical eigenvalues considering state-space equations of the excitation control system are used. Also, the stability regions using the obtained delay margin values are determined. For the stability analysis, a single-machine-infinite-bus (SMIB) system including AVR and PSS is assigned as a test system. The accuracy of the delay-dependent stability regions are verified by time-domain simulations and the quasi-polynomial mapping-based root finder (QPmR) algorithm which demonstrates the dominant roots of time-delayed systems in complex plane, respectively.

Anahtar Kelimeler

• Generator excitation control system
• communication time delay
• QPmR algorithm
• eigenvalue tracing method

Zaman Gecikmeli Elektrik Güç Sistemlerinin Gecikmeye Bağlı Kararlılık Bölgelerinin Hesaplanması

Öz

Bu çalışma, bir özdeğer izleme yöntemi kullanarak güç sistem dengeleyici (GSD) ve otomatik gerilim regülatörü (OGR) içeren zaman gecikmeli jeneratör uyarma kontrol sisteminin zaman gecikmeleri düzleminde kararlılık bölgesini elde etmeyi ve zaman gecikmesine bağlı kararlılık analizini incelemektedir. Elektrik güç sistemlerinde gerilim ve frekans kararlılığının sürdürülmesi bakımından haberleşme alt yapısına ve ölçme sistemlerine ihtiyaç duyulmaktadır. Ancak, haberleşme alt yapısı ve ölçme sistemlerinden dolayı sistemin dinamik davranışını ve kararlılığını olumsuz etkileyen zaman gecikmeleri meydana gelmektedir. Bu çalışmada, jeneratör uyarma kontrol sisteminin durum denklem modellerini kullanarak özdeğerlerini ve bu özdeğerlere karşılık gelen zaman gecikmesi değerlerini belirleyen bir yöntem kullanılmıştır. Ayrıca, bu gecikme değerleri kullanılarak gecikmeye bağlı bir kararlılık bölgesi elde edilmiştir. Kararlılık analizleri için, GSD ve OGR içeren tek makineli sonsuz baralı (TMSB) bir güç sistemi seçilmiştir. Gecikmeye bağlı kararlılık bölgelerinin doğruluğu, zaman düzleminde gerçekleştirilen benzetim çalışmaları ve zaman gecikmeli sistemlerin köklerini kompleks düzlemde hesaplayan QPmR (the quasi-polynomial mapping-based root finder) algoritması ile gösterilmiştir.

Anahtar Kelimeler

• Jeneratör uyarma kontrol sistemi
• Haberleşme zaman gecikmesi
• Özdeğer izleme yöntemi
• QPmR algoritması

Kaynakça

1. [1] Saadat H. “Power System Analysisˮ, McGraw-Hill Inc., New York, (1999).
2. [2] Kundur P. “Power System Stability and Controlˮ, McGraw-Hill Inc., New York, (1994).
3. [3] Sauer P.W. and Pai M.A., “Power System Dynamics and Stabilityˮ, 1st Indian Reprint, Singapore, (2002).
4. [4] Yao W., Jiang L., Wu Q.H., Wen J.Y. and Cheng S.J., “Delay-Dependent Stability Analysis of the Power System with a Wide-Area Damping Controller Embeddedˮ, IEEE Transactions on Power Systems, 26: 233- 240, (2011).
5. [5] Naduvathuparambil B., Valenti M.C. and Feliachi A., “Communication delays in wide area measurement systemsˮ, the 34th Southeastern Symposium on System Theory, Huntsville, Alabama, 118-122, (2002).
6. [6] Xia X., Xin Y., Xiao J., Wu J. and Han Y., “WAMS applications in Chinese power systemsˮ, IEEE Power and Energy Magazine, 4: 54-63, (2006).
7. [7] Phadke A.G., “Synchronized phasor measurements in power systems. IEEE Computer Applications in Power, 6: 10-15, (1993).
8. [8] Wu H., Tsakalis K. and Heydt G.T., “Evaluation of time delay effects to wide-area power system stabilizer designˮ, IEEE Transactions on Power Systems, 19: 1935–1941, (2004).

9. [9] Liu M., Yang L., Gan D., Wang D., Gao F. and Chen Y., “The stability of AGC systems with commensurate delaysˮ, European Transactions on Electrical Power, 17: 615-627, (2007).
10. [10] Jiang L., Yao W., Wu Q.H., Wen J.Y. and Cheng S.J., “Delay-dependent stability for load frequency control with constant and time-varying delaysˮ, IEEE Transactions on Power Systems, 27: 932-941, (2012).
11. [11] Yao W., Jiang L., Wu Q.H., Wen J.Y. and Cheng S.J., “Wide-area damping controller of FACTS devices for inter-area oscillations considering communication time delaysˮ, IEEE Transactions on Power Systems, 29: 318-329, (2014).
12. [12] Ayasun S., “Computation of time delay margin for power system small-signal stabilityˮ, European Transactions on Electrical Power, 19: 949-968, (2009).
13. [13] Liu M., Dassios I., Tzounas G. and Milano F., “Model-independent derivative control delay compensation methods for power systemsˮ, Energies, 13:342, (2020).
14. [14] Prakash T., Singh V.P. and Mohanty S.R., “A synchrophasor measurement based wide-area power system stabilizer design for inter-area oscillation damping considering variable time-delaysˮ, Electrical Power and Energy Systems, 105:131-141, (2019).
15. [15] Bento M.E.C., “Fixed Low-Order Wide-Area Damping Controller Considering Time Delays and Power System Operation Uncertaintiesˮ, IEEE Transactions on Power Systems, 35: 3918 - 3926, (2020).
16. [16] Qi J., Li Y. and Ou L., “PID damper design for wide-area power systems considering time delaysˮ, International Transactions on Electrical Energy Systems, 30: 1-18, (2020).
17. [17] Li C., Wu J., Duan C. and Du Z., “Development of an effective model for computing rightmost eigenvalues of power systems with inclusion of time delaysˮ, IEEE Transactions on Power Systems, 34: 4216-4227, (2019).
18. [18] Chen J., Gu G. and Nett C.N., “A new method for computing delay margins for stability of linear delay systemsˮ, System and Control Letters, 26: 107-117, (1995).
19. [19] Sönmez Ş., Ayasun S. and Nwankpa C.O., “An exact method for computing delay margin for stability of load frequency control systems with constant communication delaysˮ, IEEE Transactions on Power Systems, 31: 370-377, (2016).
20. [20] Rekasius Z.V., “A stability test for systems with delaysˮ, the Joint Automatic Control Conference, San Francisco, USA, TP9-A, (1980).
21. [21] Olgaç N. and Sipahi R., “An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systemsˮ, IEEE Transactions on Automatic Control, 47:793-797, (2002).
22. [22] Sönmez Ş. and Ayasun S., “Rekasius yöntemi kullanilarak zaman gecikmeli jeneratör uyarma kontrol sisteminin maksimum zaman gecikmesinin hesaplanmasi”, Niğde Ömer Halisdemir Üniversitesi Mühendislik Bilimleri Dergisi, 8: 783 – 795, (2019).
23. [23] Khalil A. and Peng A.S., “An Accurate Method for Delay Margin Computation for Power System Stabilityˮ, Energies, 11: 3466, (2018).
24. [24] Khalil A. and Peng A.S., “A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systemsˮ, Energies, 11: 3460, (2018).
25. [25] Jia H.J. and Yu X.D., “A Simple Method for Power System Stability Analysis with Multiple Time Delaysˮ, IEEE Power Engineering Society General Meeting, Pittsburgh, USA, 1-7, (2008).
26. [26] Sönmez Ş. and Ayasun S., “Effect of load increase and power system stabilizer on stability delay margin of a generator excitation control systemˮ, Turkish Journal of Electrical Engineering & Computer Sciences, 24: 5183 – 5194, (2016).
27. [27] Gündüz H., Sönmez Ş. and 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).
28. [28] Sönmez Ş. and Ayasun, S., “Gain and phase margins-based delay margin computation of load frequency control systems using Rekasius substitutionˮ, Transactions of the Institute of Measurement and Control, 41: 3385-3395, (2019).
29. [29] Naveed A., Sönmez Ş. and Ayasun S., “Impact of electric vehicle aggregator with communication time delay on stability regions and stability delay margins in load frequency control systemˮ, Accepted for publication in Journal of Modern Power Systems and Clean Energy, (2020). doi: 10.35833/MPCE.2019.000244
30. [30] Macana C.A., Mojica-Nava E. and Quijano N., “Time-delay effect on load frequency control for microgrids”, IEEE International Conference on Networking, Sensing and Control (ICNSC), Evry, France, 544-549, (2013).
31. [31] Gündüz, H., Ayasun, S. and Sönmez Ş., “Zaman gecikmeli mikro-şebeke sistemlerin Rekasius yerine koyma yöntemiyle kazanç ve faz payı tabanlı kararlılık analizi”, Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi, 34:553-568, (2019).
32. [32] Naveed A., Sönmez Ş. and Ayasun S. “Identification of stability delay margin for load frequency control system with electric vehicles aggregator using Rekasius substitutionˮ, IEEE 2019 Milan PowerTech, Milan, Italy, 1-6, (2019).
33. [33] Liu S., Wang X. and Liu P.X., “Impact of Communication Delays on Secondary Frequency Control in An Islanded Microgridˮ, IEEE Transactions on Industrial Electronics, 62: 2021-2031, (2015).
34. [34] Lou G., Gu V., Xu Y., Jin W. and Du X., “Stability Robustness for Secondary Voltage Control in Autonomous Microgrids With Consideration of Communication Delaysˮ, IEEE Transactions on Power Systems, 33: 4164-4178, (2018).
35. [35] Lou G., Gu W., Lu X., Xu Y. and Hong H., “Distributed Secondary Voltage Control in Islanded Microgrids With Consideration of Communication Network and Time Delaysˮ, IEEE Transactions on Smart Grid, 11: 3702 - 3715, (2020).
36. [36] Wu M., He Y., She J.H. and Liu G.P., “Delay-dependent criterion for robust stability of time-varying delay systemsˮ, Automatica, 40: 1435–1439, (2004).
37. [37] Xu S.Y. and Lam J., “On equivalence and efficiency of certain stability criteria for time-delay systemsˮ, IEEE Transactions on Automatic Control, 52: 95–101, (2007).
38. [38] Jin L., Zhang C.K., He Y., Jiang L. and Wu M., “Delay-dependent stability analysis of multi-area load frequency control with enhanced accuracy and computation efficiencyˮ, IEEE Transactions on Power Systems, 34: 3687-3696. (2019).
39. [39] Ko K.S. and Sung D.K., “The effect of EV aggregators with time-varying delays on the stability of a load frequency control systemˮ, IEEE Transactions on Power Systems, 33: 669–680, (2018).
40. [40] Simulink, “Model-Based and System-Based Designˮ, Natick: MathWorks, (2000).
41. [41] Vyhlídal, T. and Zítek, P., “Mapping based algorithm for large-scale computation of quasi-polynomial zerosˮ, IEEE Transactions on Automatic Control, 2054: 171-177, (2009).
42. [42] Vyhlídal, T., Olgaç, N. and Kučera, V., “Delayed resonator with acceleration feedback – Complete stability analysis by spectral methods and vibration absorber designˮ, Journal of Sound and Vibration, 333: 6781– 6795, (2014).
43. [43] Kammer, A.S. and Olgaç, N., “Delayed-feedback vibration absorbers to enhance energy harvestingˮ, Journal of Sound and Vibration, 363: 54–67, (2016).
44. [44] Shahgholian G. and Faiz J., “The effect of power system stabilizer on small-signal stability in single-machine-infinite-busˮ, International Journal of Electrical and Power Engineering, 4: 45-53, (2010).