Thermal equivalent short-time currents in three-phase balanced short circuits

This letter presents the analytical calculation of the thermal equivalent currents occurring in three-phase balanced near-to-generator short circuits and having decaying ac components. The thermal equivalent currents are the squared root of the integral of the squared armature currents, whose equations are calculated considering a sudden symmetrical short circuit of an unloaded synchronous generator rotating at fixed speed. The relative differential equations have been simplified by omitting the terms containing the squared armature resistance and neglecting the resistances of the field and of the dampers windings. These expressions used for the currents depend on the angle λ between the axis of the phase A and the direct-axis in the instant of the short circuit and are valid also for salient pole generators, which have quadrature-axis and direct-axis subtransient reactances with different values.