Time Variation of Short-circuit Current

The short-circuit current from various sources is illustrated in figure 2-1. Since short-circuit current from rotating machines varies with time, it is convenient to express machine impedance (inductive reactance) as a variable value. This variable reactance will allow calculation of short-circuit current from a rotating machine at any instant in time. For the purpose of simplification, three values of reactance are assigned to rotating machines for the purpose of calculating short-circuit current at three specified times following the occurrence of a fault. These three  values are called sub=transient, transient, and synchronous reactances.

a. Sub-transient reactance (Xd”): Subtransient reactance is a value used to determine the short-circuit current during the first few cycles after a short-circuit occurs. This is the short-circuit current value to be used in all short-circuit studies.

b. Transient reactance (Xd’): Transient reactance is a value used to determine the short-circuit current from the first few cycles up to about 30 cycles after the short-circuit occurs (depending upon the design of the machine). This value is often used in voltage regulation studies.

• c. Synchronous reactance (Xd): Synchronous reactance is a value used to determine the short-circuit current when the steady state condition has been reached. Steady state is reached several seconds after the short-circuit occurs. This value is often used to determine the setting of generator backup overcurrent relays.