# Verification Methodology for Simulation Models of the Synchronous Generator on Transients Analysis
## 2 Modeling Methods for Transients Calculation
### Modeling of a Sudden Three-Phase Short-Circuit Using the FEM  
In order to conduct the FEM calculations, some preconditions needed to be introduced:  
* all of the coils in windings have equal numbers of conductors and therefore equal resistance; windings are placed symmetrically on poles, enabling the analysis of one repeating segment of the generator;
* the ratio of the core length and the end winding length of the generator is 3.2, and allows the 2D model to be applicable;
* the influence of the skin effect, which can appear in excitation or in armature winding conductors, is neglected;
* the stray current and the eddy current are excluded because the electric conductivity of iron can also be neglected;
* embedded materials are isotropic, the hysteresis loop is neglected, and the iron permeability depends on the magnetic field strength;
* the rotor speed variations throughout the transients, due to high inertia of mass, are also neglected; and
* the sources used to feed the windings are assumed to be perfect. These introduced assumptions significantly simplify the calculation. Therefore, although they have a certain influence on the obtained results, this calculation method gives the most accurate possible results because the original factory data on the dimensions, material properties, and other characteristics of all parts of the machine are used. Figure 1 shows a solid model of 8 poles of the hydro generator using the previously presented software [3]. As there are 306 slots on a 48-pole generator, the segment for the model is chosen so that the symmetry is repeated after each part. The model includes stator and rotor. Stator is made of non-skewed slots with three-phase winding conductors in a laminated core. Rotor poles are mounted on a steel hub and made of steel laminations. Excitation winding coils are placed around the poles, and they are comprised of copper wires. Five holes are in the pole shoes, where round copper bars are inserted, creating the damping winding. Damper winding slots are closed. The windings of armature are coupled in Star (Y) without grounding the neutral point. Resistance and inductance representing the end windings are connected into the series with each phase. Because the end windings are in the air, these parameters can be assumed to be constant. In the path between the neutral point and the beginning of the phase there  
Figure 1: A solid model of 8 poles of an analyzed hydro generator. is capacitance and resistance, which represents the capacitances of the windings to the ground. Into the series with capacitance a small resistance is connected (Figure 2). The excitation winding is connected to a current source, to which a diode is connected in parallel. The diode represents the branches of the rectifier bridge located on the output from the source that supplies the excitation winding and prevents overvoltage in the excitation circuit, allowing a positive current component to flow through it (Figure 3). Damper winding is short-circuited at the ends of the bars by copper segments of negligible resistance (Figure 4). Figure 4: Damper winding connection. Figure 3: Excitation winding connection. Figure 2: Armature windings connection. A 2D FEM solver that considers the motion of the rotor must be applied to calculate the sudden short-circuit. The field can be solved with the equations presented in (1):  
\[\oint\limits_{C}\vec{E}\cdot d\vec{l}=-\int\limits_{S}\frac{\partial\vec{B}}{ \partial t}\cdot\vec{n}\cdot dS=-\frac{d}{dt}\int\limits_{S}\vec{B}\cdot\vec{n} \cdot dS \tag{1}\]  
\[\oint\limits_{C}\vec{H}\cdot d\vec{l}=\int\limits_{S}\vec{J}\cdot\vec{n}\cdot dS \tag{2}\]  
\[\oint\limits_{S}\vec{B}\cdot\vec{n}\cdot dS=0 \tag{3}\]  
where  
\(\vec{E}\) is the electric field strength in the conductors,  
\(\vec{B}\) is the lux density,  
\(\vec{H}\) is the magnetic field strength,  
\(\vec{J}\) is the recurrent density,  
\(C\) is the curve bounding the surface \(S\),  
\(S\) is the plane in which the field is calculated, and  
\(\vec{n}\) is the unit vector normal to surface \(S\).