Effectiveness of dynamic equivalent models in predicting power system stability

Load flow and dynamic stability studies are routine procedures for a power utility in order to assure efficiency, safety, and stability of the electric power system. Due to the large size and the increasing number of interconnections of the modern power systems, the amount of information required to be included in the models representing these systems expands the complexity of various studies, especially the dynamic stability studies. In order to simplify dynamic stability studies, one may consider the local system in detail and represent the external systems by reduced order models, often referred to as dynamic equivalent models. Methods constructing dynamic equivalent models are frequently based on the coherency phenomenon of swinging machines, and involve the reduction of the differential equations describing the power system. A coherency-based equivalencing technique requires first the identification of coherent groups of generators, and second the aggregation of all generators belonging to the same coherent group. A new approach of constructing coherency-based reduced order models is introduced in this work. This approach is based on the network equations, and not the swing equations, giving, therefore, a physical interpretation of the mechanism of model reduction. The approach is closely compared to the well established Kron's network reduction technique. Two methods, the modal-coherent and the slow-coherent, are investigated to determine the effectiveness of dynamic equivalent models in predicting power system stability. The validity of the algorithms, used by these methods to identify coherent groups, is evaluated using the constituent matrices of the power system model. The inertial averaging aggregation method, associated with the modal-coherent technique, and the singular perturbation aggregation method, associated with the slow-coherent technique, are applied to the linear and nonlinear power system models in order to derive dynamic equivalent models. The analysis presented in this work shows that neither the modal-coherent nor the slow-coherent equivalent model is a conservative estimator of the stability of the unreduced power system. This result is unfortunate since the purpose of obtaining a dynamic equivalent model is to use the simplified representation of the power system to predict the behavior of the unreduced system.