Performance Analysis of Static Network Reduction Methods Commonly Used in Power Systems Syed Mohammad Ashraf, Bhavna Rathore, and S. Chakrabarti, Senior Member, IEEE Department of Electrical Engineering, Indian Institute of Technology Kanpur, India smashraf@iitk.ac.in, bhavnar@iitk.ac.in, saikatc@iitk.ac.in Abstract— Network reduction techniques are useful means of analyzing large, interconnected power systems. The most desirable property of a reduced network is that it should represent the original network as accurately as possible. This paper explores some of the commonly used static network reduction techniques, such as Ward reduction, Kron reduction, Dimo’s method, and Zhukov’s method. The performances of the reduced networks are evaluated in terms of their ability to follow the bus voltages of the original network, with changes in operating conditions. The IEEE 14- bus and 118-bus systems are taken as the test beds. Keywords— Dimo’s method, Kron reduction, Ward reduction, Zhukov’s method. I. INTRODUCTION Modern power systems have become highly inter- connected to maintain acceptable levels of reliability and quality of the supply. These networks are now being operated under heavily loaded conditions in order to meet the ever-growing demand for electricity, with the limited generation, transmission, and distribution resources, and to maximize the economy. During the past few decades, the overall characteristics of the power system generations and loads have changed significantly due to increasing penetration of renewable energy sources, large-scale use of power-electronic converter interfaced sources and loads, and competitive electricity markets. Special attention, therefore, has to be given on the modelling of the power system for various types of analyses. It is a common practice for many of the power system analysis problems to use reduced model of the system in place of the complete detailed model. The reasons for using the reduced model can be many, some of which are as follows: (i) It may be required to monitor the system by using only a limited number of measurements from measuring instruments, such as phasor measurement units (PMUs); (ii) an interconnected power system typically consists of a number of areas owned by various utilities, each which are usually reluctant to share complete system information with others; (iii) practical limitations on the computational resources; and (iv) the fact that, as the electrical distance from the point of interest increases, the requirement for detailed modelling of the remote location also reduces. Modern power systems are mostly interconnected, with multiple areas connected with each other by tie lines. Usually, a utility’s own system called the internal subsystem or internal area. The rest of the system is called the external area for the internal subsystem under consideration. For running power system analysis functions in the internal area, the system is typically modelled in detail. The external areas are usually represented by simple models, referred to as the external equivalent system. At certain intervals, the interconnected utilities exchange detailed information regarding the network topology and operating conditions, based on which the external network equivalents are determined. However, the amount of such data exchange for a large interconnected system can be prohibitively large, requiring extensive investment in the communication infrastructure. From the computational point of view also, it requires significant resources to work with detailed models of all the external areas, for various power system studies. The usual practice is that the external network equivalents are updated for small changes in the operating conditions in the external network, usually by following some network parameter updation methodology. For major changes in the operating condition or topology in the external areas, the equivalents need to be computed afresh. Network reduction techniques can be broadly classified as static and dynamic, based on the representation of the model and its intended use [1-2]. Static reduction techniques are used for static analysis only, such as power flow calculations and system operation and planning studies. Whereas, for the analysis of system dynamics the reduced dynamic equivalents of the external areas are required. In this paper, the term ‘network reduction’ implies only the static reduction. This paper compares the performance of some of the commonly used network reduction methods, such as Ward reduction, Kron reduction, Dimo’s method, and Zhukov’s method. II. REDUCTION TECHNIQUES A. Ward Reduction The construction of this equivalents starts from the solved model of the entire interconnected system. The injected current () i i at each bus i is obtained from the bus’s known complex power () i s and voltage () i v . * * () () () i i i = i s v (1) Reduction of the network and the current vector is performed by using the Gaussian elimination technique. Let a power system be described by the following set of nodal equations, 978-1-4799-5141-3/14/$31.00 ©2014 IEEE