Bifurcation and chaotic analysis of the line conditioners for voltage stability

Keywords : Power Flow Continuation, Voltage Stability, FACTS, Bifurcation Analysis, Chaotic Oscillations It is becoming increasingly important for power system planning and operating engineers to be capable of performing comprehensive voltage stability analyses of the systems. This need is largely due to the recent trends towards operating systems under stressed conditions as a result of increasing system loads without sufficient transmission and generation enhancements. There have been many failures, due to voltage instability in power systems around the world. In recent years voltage stability and voltage collapse phenomena have become more and more important issues in power system analysis and control. Researchers have suggested techniques for voltage stability analysis considering both static and dynamic aspects. The bifurcation theory is one of the most common theory which is used to analysis the problems such as angular and voltage stability in power systems. Bifurcation theory allows us to develop practical methods especially in analysis of dynamic events such as small-signal stability and bifurcation of balance nodes oscillate instabilities and voltage collapse. Power systems are consist of Saddle-Node and Hopf bifurcations which as a result of load increasing. Saddle node bifurcation is known as voltage collapse node in power systems and on this mode one of the eigenvalues of the system jacobian matrix is on the origin. The system has two eigenvalues on the imaginary axis and these eigenvalues cause oscillative instabilities. Both of these bifurcation events explain the instability mechanism that is in the nonlinear work zone of the power system and enable us to establish the loading intervals that will be turn into chaotic building. These parametric values can be used in stability and control studies of the system. In this thesis, voltage stability analysis is dealing with both static and dynamic approaches. Bifurcation and chaotic analysis have been done by using the static and dynamic models of the devices that improve the voltage stability, such as tap changer transformers (LTC), phase shifting transformers (PST), Static var Compensators (SVC) known as Flexible Alternatif Current Transmission Systems (FACTS) devices and Thyristor Controlled Series Capacitors (TCSC) in power systems that work on the nonlinear zones. The power system models that has been obtained. Furthermore the improving performances of these devices have been compared. In this study, firstly a two bus power system has been taken up, then by generalizing this, it has been indicated that it can be applied to N bus system.