Investigation and visualization of the stability boundary for stressed power systems
Present interconnected power systems are being pushed to their limits due to heavier loading of the transmission network and delay in facility construction. The resultant vulnerability in withstanding system disturbances requires a more accurate understanding of system stability behavior. This dissertation presents the use of real normal form of vector fields, a comparatively new analysis tool in the area of power systems, combined with the use of XGobi, an effective graphic package for multi-dimensional visualization, to investigate and visualize the stability boundary of the stressed system. It also depicts the structural characteristics for the stressed power system corresponding to specific fault scenarios by computing the participation factors and the nonlinear indices along the actual fault trajectory which is obtained from time simulation of the equations governing system dynamics. The objective of this research is to analyze and explain the nonlinear phenomena in stressed power systems and characterize the stability boundary of the power system when subjected to large disturbances. The structural information provided by the method of normal forms will also be utilized in explaining the mechanism of instability near the stability boundary and will be used to determine the critical interactions involved;The main idea of this dissertation is to characterize the stability boundary of the stressed power system by obtaining the nonlinear structural information through the visualization of the stability boundary in multiple dimensions, and by utilizing the analytical measures of nonlinear interaction indices and nonlinear participation factors obtained using the method of normal forms;The proposed approach has been tested on the IEEE 4-generator system and 11-generator system. The stability boundary of the system is approximated by a second order stable manifold of the controlling unstable equilibrium point. The stable manifold is constructed by spanning all stable directions. The effective graphic tool XGobi is used to visualize the approximated stability boundary in all dimensions of the system, which helps to obtain a global structural information of the system. The shape and curvature of the stability boundary are detected. An extended approach to deal with large sized power systems is studied, which provide an effective method to study large sized power systems. The computation of linear and nonlinear participation factors, together with the nonlinear indices of the fault trajectory obtained by the time simulation provides the basis to study the structural characteristics of the system. The structural information helps the tuning of control action, which is valuable for maintaining the stability of practical power systems.