Development of Methods for Element-Wise Assessment of Oscillatory Rotor Angle Stability

This thesis concerns the development of methods that can detect emerging stability issues related to undamped low frequency power oscillations. Power oscillations are caused by interactions of the dynamic system components and are an inherent property of interconnected electric power systems. As such the occurrence of these oscillations cannot be prevented but as long as they are well damped they do not affect the stability of the system. Certain operating conditions, however, can lead to oscillations of increasing magnitude, which in the worst case can lead to a complete system blackout. It is therefore of interest to develop a method which can predict the operating conditions under which the damping becomes critical and provide margins that can help the operator to counteract emerging stability problems in due time. The fundamental mechanisms that govern the characteristic of the oscillations were investigated. It was shown that the problem consists of two separate layers. The first layer concerns the dynamic properties of the system at the oscillatory frequency and the second is related to the steady state operating conditions that affect the dynamic performance of the system. In order to obtain a representative stability margin, the conditions that lead to instability of the dynamic system were determined. Furthermore, the interactions between the two layers were analyzed and a methodology, capable of identifying the steady state operating conditions which violate the
instability condition of the dynamic system, was developed. The stability boundary is determined by combining the sensitivity information of the steady state parameters at a given operating point with the derived sensitivities of the dynamic system. The relevant sensitivities are obtained as a result of the perturbation of the active power injection of a particular machine in the system. The resultant distance to the point of instability is therefore assessed on an element-wise basis providing an individual stability margin that is given as the maximum power a machine could inject into the system before instability occurs. To provide an informative measure of the distance to instability the maximum power that a machine could inject before the stability boundary is crossed is given as a percentage margin related to the loading of the machine. The assessment method was implemented in an algorithm that efficiently performs the required steps for carrying out the stability assessment. The algorithm takes snapshots of the current system state provided by phasor measurement units or state estimators as input and analyzes the stability of the given operating point. With further optimization the developed algorithm should be suited to perform a stability assessment of large power systems close to real time. The method was tested on a representation of the Nordic power system consisting of Norway, Sweden, Denmark and Finland. It was shown that the method was able to detect critical stability margins and relate the critical margin to specific system components and thereby already provides indicators for potential counter-measures. The method was capable of accurately predicting the distance to instability well away from the critical boundary and would therefore allow to apply suitable counter-measures in due time to prevent an emerging blackout.