Model Order Reduction of non-linear power system using Projections Technique

Abstract

Stable and reliable operations of power systems are based on continuous or frequent monitoring and control of the systems by collecting and analyzing real-time data and optimizing its working. Multiple measurement devices are often deployed across various nodes of the power network to monitor the behavior. This framework of physically monitoring large-scale power network is significantly time consuming and inefficient in terms of human efforts and resources. An alternative method involves determining the mathematical model of the power system, simulating it, and analyzing the system’s behavior to observe the desired outcomes. These mathematical models associated with large scale power systems involve differential as well as algebraic equations (DAE) and their simulation can be computationally cumbersome. Furthermore the dynamics of the system are often nonlinear which further adds to its complexity. Awremedywto this problemwis model order reduction, where the dynamics of original system are reduced such that its behaviour remain the same. In this thesis,wwe consider the problem of modelworder reduction for nonlinear power system models by constructing a reduced bilinear model from the original large-scale model with approximately the same behavior as the original model. Two specific approaches, bilinear balanced truncation (BBT)wand bilinear iterative rationalwKrylov algorithm (BIRKA) has been utilized and compared. It is observed that the performance of the two approaches is almost comparable and they offerwtrade-off between accuracy and the size of the reducedworder model. Two examples of bilinear power networks has been utilized from the literature for their comparison and analysis. Numerical resultswshow that the reducedworder models from the two approaches are highly accurate, stable, and significantly faster to simulate as compared to the original VII List of Figures model. The BIRKA method is more useful than the BBT method in the sense that it canbe easily extended to very large-scale settings as it involves only matrix-vector multiplications. offerwtrade-off between accuracy and the size of the reducedworder model. Two examples of bilinear power networks has been utilized from the literature for their comparison and analysis. Numerical resultswshow that the reducedworder models from the two approaches are highly accurate, stable, and significantly faster to simulate as compared to the original model. The BIRKA method is more useful than the BBT method in the sense that it canwbe easily extended to large-scale settings as it involves only matrix-vector multiplications.