A general method to determine the characteristics and operating regions of distance relays in Z-plane

This paper studies a new and general method to determine the characteristics and operating regions of directional and distance relays in the complex plane (Z-plane). The derivation of the relay characteristics and operating regions uses the theory of functions of a complex variable Z; the straight-line equation (79) and circle equation (85) have not been used in the analysis of the performance of protective relays. The description of the new method, given in the Appendix, consists of a number of theorems and formulas which are easy to use and which simplify the work. The proof of the theorems is not given here. In this paper, the functions of a complex variable, f(z), are continuous functions with real values. Thus, the extension of the intermediate value theorem of a continuous function of one real variable [1] to the continuous functions of two real variables has been applied. The new method gives both the relay characteristic and the region where the relay will operate; for example, the relay will trip in the region where f(Z) > 0 and will restrain in the region where f(Z) < 0, or vice versa. The applications of the new method are given for both electromechanical and static distance relays.