Bu çalışmada, Senkronaltı Rezonans (SSR) oluşan bir elektrik güç sistemindeki Hopf çatallanmaları incelenmekte ve kararsız burulma salınımlarının sönümlendirilmesi için tasarlanan bir kontrolör sunulmaktadır. SSR araştırmaları için geliştirilen IEEE İkinci Gösterge Modelinin birinci sistemi kullanılmıştır. Senkron makinenin amortisör sargıları doğrusal olmayan modele dahil edilmiştir. Seri kompanzasyon kapasitörü tesis edilmiş olan enerji iletim hatlarına bağlı senkron makineler, potansiyel olarak senkronaltı elektrik modunun, türbin-generatör şaft sisteminin burulma salınım modları ile etkileşimine maruz kalabilirler. Modellenen elektrik güç sisteminde meydana gelen Hopf çatallanmalarının hangi tip olduğu, birinci Lyapunov katsayılarının analitik olarak hesaplanması ile belirlenmiştir. Sabit ikaz uygulanan modelde kritik-altı Hopf çatallanması meydana gelmektedir. Diğer yandan, Otomatik Gerilim Düzenleyicisinin (AVR) eklenmesi ile modelde kritik-üstü Hopf çatallanması oluşmaktadır. Ayrıca, SSR sonucu ortaya çıkan kararsız burulma salınımlarının sönümlendirilmesi için, zaman gecikmeli geri besleme kontrol teorisine dayanan bir kontrolör tasarlanmıştır. Kontrol girdisi olarak sadece senkron makine rotorunun açısal hızını kullanan kontrolörün zaman gecikme ve kazanç parametreleri için uygun değerler, sistemin dinamik cevabını değerlendiren bir performans endeksi hesaplanarak belirlenmiştir. Tasarlanan kontrolörün etkili sonuçlar verdiği benzetimler yardımı ile gösterilmiştir. Kontrolör etkinliği değerlendirilirken, AVR ve kontrolör çıkış sınırlayıcıları da modele dahil edilmiş ve seri kapasitör kompanzasyonunun pratik işletme değerleri için kontrolörün etkili olduğu görülmüştür.

Series capacitor compensation of AC transmission lines as a means of increasing load carrying capacity and enhancing transient stability has a widespread use in power systems, particularly in the North America. On the other hand, potential danger of interaction between torsional oscillation modes of the turbine generator shaft system and the subsynchronous electrical mode may arise in electric power systems consisting of turbine-generators connected to transmission lines with series compensation capacitors. This phenomenon is called Subsynchronous Resonance (SSR). Unless adequate measures are implemented, unstable torsional mode oscillations due to SSR can lead to catastrophic turbine- generator shaft failures, as occured at Mohave power plant in 1970 and 1971. Since then, considerable effort to the analysis of SSR phenomenon has been devoted by researchers and industry professionals. In this study, Hopf bifurcations in a power system susceptible to SSR is investigted and a novel controller based on the delayed feedback control theory to stabilize unstable torsional oscillations caused by SSR is presented. Bifurcation theory is employed for the analysis of torsional oscillations in a power system which consists of a synchronous generator connected to an infinite busbar through two parallel transmission lines one of which is equipped with a series compensation capacitor. The first system of the IEEE Second Benchmark Model for Subsynchronous Resonance studies has been used. Damper windings of the synchronous generator are included in the nonlinear model. The state equations representing the dynamics of the electrical system, mechanical system and the excitation system are obtained separately and then combined into one set of ordinary differential equations. Occurrence of Hopf bifurcations in the model at certain values of the series compensation factor has been verified by tracing the eigenvalues of the Jacobian matrix evaluated at equilibrium. Loss of stability occurs in the first and second torsional oscillation modes through Hopf bifurcation due to SSR. Instead of using the Floquet multipliers method, the first Lyapunov coefficient has been computed analytically to determine the type of Hopf bifurcations (supercritical or subcritical), thereby stability condition of the limit cycles emanating from the Hopf bifurcation points. It is found that subcritical Hopf bifurcation occurs in the model without an Automatic Voltage Regulator (AVR). On the other hand, in the model with AVR, supercritical Hopf bifurcation occurs. Time domain simulations in MATLABSimulink are presented to demonstrate the validity of analytic findings. The proposed controller is based on the delayed feedback control theory. The Time Delay Auto- Synchronization (TDAS) controller requires the measurement of the synchronous generator rotor angular speed as the only input. The difference between the value of the controller input signal in τ- time unit in the past and its current value is multiplied by a gain to obtain an output signal which is combined into the AVR as the stabilizing signal. The effective performance of the controller in providing sufficient damping for the unstable torsional oscillations depends on the correct setting of time delay and gain parameters of the controller. For this purpose, an optimization performance index (OPI), which evaluates damping performance of the controller in time-domain dynamic responses of the model, has been defined. Time-domain simulations in MATLAB-Simulink were carried out to evaluate the effectiveness of the TDAS controller in providing additional damping for the unstable torsional oscillations at various series compensation levels, provided that the time delay and gain parameters are correctly set. Performance of the TDAS controller has been investigated in the presence of AVR limiters in order to obtain a realistic assessment. The TDAS controller output limiter is also included so that the impact on the AVR’s voltage regulating performance remains limited. Time domain simulations are presented to demonstrate the effectiveness of the proposed controller even in the presence of the limiters within the practical operating ranges of series capacitor compensation.