When a generator is operating at no load, that is, with the generator breaker open, the only flux produced in the machine is a result of the DC current in the field windings on the rotor. This rotor flux bridges the air gap between the rotor and the stator and travels around the perimeter of the stator at rotor speed. As it sweeps across the stator, it passes through the A, B, and C phase stator windings, inducing a voltage in each stator coil.
The instantaneous flux in the “A” phase stator winding is a function of the air gap flux magnitude and the angle a between the rotor and the center of the A phase coil. This angle varies with time. From the perspective of a point on the rotor, the field flux appears as a DC flux. When viewed from a point on the stator, the flux appears sinusoidal. Since the phase windings are physically spaced 120 electrical degrees apart around the stator, the flux in each phase is displaced by that same amount. The voltage induced in a stator winding is defined by Faraday’s law, which states that the voltage induced in a coil is a function of the rate of change of the flux and the number of turns, N.
Under load, the vector summation of rotor and stator flux forms the air gap flux. The air gap flux in turn defines the internal voltages used in calculating the generator fault current. The transient behavior of the fault current is governed by the interaction of the air gap flux and the magnetic circuits within the generator. The generator has two distinct magnetic circuits. The first is aligned with the field pole and is referred to as the “direct” or “d-axis.” It contains the rotor field winding and is characterized by a small air gap. The other magnetic circuit path, known as the “quadrature” or “q-axis,” lies between the field poles. This path has a larger air gap and is electrically 90˚ from the direct axis. Stabilizing windings, called amortisseur windings, or structures that act as stabilizing windings may also be found in one or both axes. Each path, because of the differences in air gap length and because of different windings located in the path, has unique steady-state and transient behavior.
Generator behavior is predicted by determining the response of each axis individually, then combining the d and q components to define the air gap reresponse. The variations of the air gap flux determine the transient characteristic of the short-circuit current. Flux linkages between the various windings cannot change instantaneously. When a fault occurs, the initial current is determined by the flux linkages “stamped” into each axis by the prefault load condition.
For fault analysis, the d- and q-axes magnetic paths are represented as equivalent electrical circuits. The d-axis contains the field winding and the q-axis does not; thus, different equivalent circuits apply for each axis. When a fault occurs at the generator, it has the effect of simultaneously closing the switches in each equivalent circuit. The d- and q-axes circuits have multiple loop current paths; each path has a unique time constant and initial driving voltage. The driving voltages are representative of the initial flux linkages. This multiloop configuration gives rise to the multi-exponent (subtransient, transient) decay characteristic of the generator fault current.