A tutorial on calculating source impedance ratios for determining line length

Classifying the length of a line is an important step in determining the transmission line protection philosophy and relay settings. The length of a line can be defined by physical distance, impedance, or its source impedance ratio (SIR). The SIR is the ratio of the source impedance, Z_S, to the line impedance, Z_L. The SIR is well established in the industry as the preferred method for classifying the electrical length of a line for the purpose of setting protective relays. Many references discuss setting criteria and performance specifications relative to the SIR. However, very few references define the proper method for calculating the source impedance to use in the ratio. The transmission system is a complex network with many sources and branches, and the topology of the network can have a major effect on the results, depending on the method used. This paper analyzes several methods in common usage and presents a simple method that provides a better result. The effect of the SIR on line relay settings and examples of various transmission network topologies are discussed.