Efficient Modeling and Simulation of Power Networks Using Model Order Reduction

Abstract

Electricity is distributed through a network of transmission and distribution lines to industrial, commercial and residential load. These networks cover a large geographical area making their analysis and monitoring a complex and expensive task. An alternate way is to use mathematical modeling and simulation of power distribution network where mathematical model involves differential equations and algebraic equations leading to a system of differential algebraic equations (DAEs). It is also known that simulation of such large complex systems is computationally expensive and takes a lot of time to simulate such large models for observing their behavior. To resolve this problem, the concept of Model Order Reduction (MOR) can be used in which a reduced order model is constructed from the original large scale model in a way that the behavior remains approximately same. Various MOR methodologies have been developed in the literature for linear systems such as Balanced Truncation, Moment Matching Methods, Krylov Projection techniques and Proper orthogonal decomposition. Most of these techniques are based on the transfer function of the system that are identified by the assumption that the initial condition is zero. This means that the performance of the MOR method may not be accurate when the initial condition is non-zero. In this research, some well-used model order reduction techniques have been applied including Balanced Truncation (BT), Iterative Rational Krylov Algorithm (IRKA), and their repeated implementation (BT-BT) to a model with non-zero initial condition. It is shown that the performance of the repeated implementation is better as compared to the direct reduction methods (BT and IRKA). A variant of the repeated MOR implementation (IRKA-IRKA) has been proposed and implemented on a comprehensive 100 km transmission line model. It is shown that the repeated use of IRKA improve the absolute error to 10−4 range for the specific transmission line model with 70% reduction in size. The convergence and accuracy of the results has been demonstrated specifically for BT-BT and IRKA-IRKA in terms of actual and reduced system responses, absolute error between actual and reduced system and computational time for simulation of actual and reduced system.