Stability Region of a Time-Delayed Single-Area Load Frequency Control System with Demand Response and Fractional-Order PI Controller

Öz

In this research, the parameter values of the fractional order proportional-integral (FOPI) controller, which ensure the stability of the system, were calculated in a time-delay single area load frequency control (LFC) system with dynamic demand response (DDR). An efficient and simple graphical method had been applied to calculate all FOPI controller gains. For a given time delay, the method calculated all the compensating proportional-integral (PI) controller gains in the (𝐾𝑃, 𝐾𝐼) plane, which creates a stability region in the parameter space of the FOPI controller. This was done by equating the real and imaginary parts of the characteristic equation of the system to zero. Finally, for time-delayed single area LFC-DDR system with FOPI controller, results obtained were verified by using the timedomain simulation studies in Matlab/Simulink.

Anahtar Kelimeler

• Communication delay
• load frequency control systems
• dynamic demand response
• fractional order PI control
• stability region

Kesir Dereceli PI Denetleyici ve Dinamik Talep Cevabı İçeren Zaman Gecikmeli Bir Bölgeli Yük Frekans Kontrol Sistemlerinin Kararlılık Bölgelerinin Belirlenmesi

Öz

Bu araştırmada, dinamik talep cevabı (DTC) içeren zaman gecikmeli bir bölgeli yük frekans kontrol (YFK) sisteminde kesir dereceli oransal - integral (FOPI) denetleyicinin sistemin kararlılığını garantileyen parametre değerleri hesaplanmıştır. Tüm FOPI kontrolör kazançlarını hesaplamak için etkili ve basit bir grafiksel yöntem uygulanmıştır. Belirli bir zaman gecikmesi için yöntem, FOPI denetleyicinin parametre uzayında bir kararlılık bölgesi oluşturan tüm dengeleyici orantılı-integral (PI) denetleyici kazançlarını (𝐾𝑃, 𝐾𝐼) düzleminde hesaplamaktadır. Bu işlem, sistemin karakteristik denkleminin reel ve sanal kısımları sıfıra eşitlenerek gerçekleştirilmiştir. Son olarak, Matlab/Simulink ortamında yapılan benzetim çalışmaları yardımıyla FOPI denetleyici içeren bir bölgeli YFK-DTC sistemi için elde edilen sonuçlar doğrulanmıştır.

Anahtar Kelimeler

• Haberleşme gecikmesi
• yük frekans kontrol sistemleri
• dinamik talep cevabı
• kesir dereceli PI denetleyici
• kararlılık bölgesi

Kaynakça

1. Alomoush MI, 2010. Load frequency control and automatic generation control using fractional-order controllers. Electrical Engineering, 91: 357- 368.
2. Beil I, Hiskens I, Backhaus S, 2016. Frequency regulation from commercial building HVAC demand response. Proceedings of the IEEE, 104(4): 745-757.
3. Chen X, Wang J, Xie J, Xu S, Yu K, Gan L, 2018. Demand response potential evaluation for residential air conditioning loads. IET Generation, Transmission and Distribution, 12(19): 4260-4268.
4. Chien F, Kamran HW, Albashar G, Iqbal W, 2021. Dynamic planning, conversion, and management strategy of different renewable energy sources: a sustainable solution for severe energy crises in emerging economies. International Journal of Hydrogen Energy, 46(11): 7745-7758.
5. Çelik V, Özdemir MT, Bayrak G, 2017. 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.
6. Çelik V, Özdemir MT, Lee KY, 2019. 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.
7. Gasca MV, Ibáñez F, Pozo D, 2022. Flexibility quantification of thermostatically controlled loads for demand response applications. Electric Power Systems Research, 202: 107592.
8. Hosseini SA, Toulabi M, Dobakhshari AS, Ashouri-Zadeh A, Ranjbar AM, 2019. Delay compensation of demand response and adaptive disturbance rejection applied to power system frequency control. IEEE Transactions on Power Systems, 35(3): 2037-2046.

9. Katipoğlu D, Sönmez Ş, Ayasun S, Naveed A, 2021. The effect of demand response control on stability delay margins of load frequency control systems with communication time-delays. Turkish Journal of Electrical Engineering and Computer Sciences, 29(3): 1383-1400.
10. Ko KS, Sung DK, 2017. 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.
11. Latif A, Das DC, Ranjan S, Hussain I, 2018. Integrated demand side management and generation control for frequency control of a microgrid using PSO and FA based controller. International Journal of Renewable Energy Research, 8(1): 188-199.
12. Mishra AK, Mishra P, Mathur HD, 2020. Load frequency control of a nonlinear power system via demand response control strategy based fractional order fuzzy controller. National Power Systems Conference: 1-6.
13. Özdemir MT, 2020. 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.
14. Panwar NL, Kaushik SC, Kothari S, 2011. Role of renewable energy sources in environmental protection: A review. Renewable and sustainable energy reviews, 15(3): 1513-1524.
15. Shayeghi H, Rahnama A, Alhelou HH, 2021. Frequency control of fully-renewable interconnected microgrid using fuzzy cascade controller with demand response program considering. Energy Reports, 7: 6077-6094.
16. Singh VP, Samuel P, Kishor N, 2017. Impact of demand response for frequency regulation in two‐area thermal power system. International Transactions on Electrical Energy Systems, 27(2): 2246.
17. Sondhi S, Hote YV, 2014. Fractional-order PID controller for load frequency control. Energy Conversion and Management, 85: 343-353.
18. Sönmez Ş, Ayasun S, 2016. Stability region in the parameter space of PI controller for a single-area load frequency control system with time delay. IEEE Transactions on Power Systems 31(1): 829–830.
19. Sönmez Ş, Ayasun S, 2018. 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.
20. Sönmez Ş, Ayasun S, 2019. Gain and phase margin based stability analysis of time delayed single area load frequency control system with fractional order PI controller. Journal of the Faculty of Engineering and Architecture of Gazi University, 34(2): 945-959.
21. Tan N, Kaya I, Yeroglu C, Atherton DP, 2006. Computation of stabilizing PI and PID controllers using the stability boundary locus. Energy Conversion and Management, 47:. 3045-3058.
22. Wang Q, Zhang C, Ding Y, Xydis G, Wang J, Qstergaard J, 2015. Review of real-time electricity markets for integrating distributed energy resources and demand response. Applied Energy, 138: 695-706.
23. Yildirim B, Gheisarnejad M, Khooban MH, 2021. A new parameter tuning technique for noninteger controllers in low-inertia modern power grids. IEEE Journal of Emerging and Selected Topics in Industrial Electronics, 3(2): 279-288.
24. Yildirim B, Gheisarnejad M, Khooban MH, 2021. A robust non-integer controller design for load frequency control in modern marine power grids. IEEE Transactions on Emerging Topics in Computational Intelligence.
25. Zheng S, Tang X, Song B, 2015. Graphical tuning method for non-linear fractional-order PID-type controllers free of analyticalmodel. Transactions of the Institute of Measurement and Control, 38(12): 1442-1459.
26. Zhu Q, Jiang L, Yao W, Zhang CK, Luo C, 2017. Robust load frequency control with dynamic demand response for deregulated power systems considering communication delays. Electric Power Components and Systems, 45(1): 75-87.