# Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis
## 4 Results and Discussion
### The Results of the FEM Calculation Method  
The calculation was performed in the time from 0 to 0.1 s, i.e., which corresponds to five periods of the fundamental harmonic. The rotor speed was constant and equal to the nominal value. Figure 9 shows the magnetic field as the result of the FEM at the beginning of the transient, and in Figure 10 the magnetic field is shown after half of the period, when the current at one phase reaches its maximum.  
Figure 8: Three-phase short-circuit at the generator terminals.  
Figure 11 shows the steady state magnetic field. In the moment of the half period after the start of a short-circuit, the magnetic field of the stator is the same as at no load but does not penetrate the rotor. In addition, the magnetic field of the rotor is the same as at the initial moment. In the steady state, the magnetic field is much smaller, but its distribution is similar to that at no load. The magnetic field penetrates the rotor. The results are as expected and in accordance with well-known theory.  
Figure 11: Steady state magnetic field.  
Figure 9: No load magnetic field.  
The magnetic induction absolute value at each point in the model can be read in the legend in the upper right corner of each Figure.  
The current densities in the phase windings and damper winding bars, half the time after the beginning of the short-circuit, are shown in Figure 12. The current densities are of different amounts and their absolute value is visible in the logarithmic scale located in the upper right corner of Figure 12. The current density in an individual bar depends on its position on the pole shoe, and on the current position of the pole relative to the stator. The current densities are higher in the bars placed at the ends of the pole, while the current density decreases in the bars placed closer to the middle of the pole. The reason for that difference is that the current loop formed by the end bars has the largest surface through which the magnetic flux passes. The symmetry in damper bar currents is repeated for each generator segment.  
The currents in the damping bars affect the saturation of the core above the slot. Figure 13 shows that the highest saturation is just above the slots where the current density is highest. The peak value of the sudden short-circuit current depends on the magnetic flux component that closes just above the slot. In addition, harmonics in the phase currents may also occur.  
Figure 14 shows the results for phase currents obtained by the FEM calculation. The current in phase \"w\" reaches a maximum of 27.8 kA, as the initial moment is selected when the voltage in that phase is equal to zero.  
In all the currents, a distortion of sinusoidal shape is present because of calculations with materials that have a nonlinear magnetization characteristic. The material used for the poles and the stator core is dynamo sheet M330-50A. It is known that the short-circuit current is mostly affected by the initial reactances, and that they depend on the shape of the damper winding slot. In the case of this generator, these slots are closed, and the reactance is dependent on the current flowing through the damper bars. The saturation of the magnetic paths above the damping winding, and thus the phase current of the generator, depends on the current through the damper bars. This impact can only be seen by the FEM in the time domain calculation.  
In addition to the harmonics in the phase currents, DC components are disclosed, which decrease with the subtransient and transient time constants.  
Figure 12: Presentation of current density in windings at half a period after short-circuit.