A 3D electromagnetic model of the end region of a 1550 MW nuclear generator is set up. The electromagnetic forces on the involute and nose parts of the end winding under a rated operation are obtained through the 3D time-step finite element method. The electromagnetic forces on different coils in the same phase are analyzed. By changing the rotor’s relative length and stator coil’s linear length in the 3D electromagnetic model, the electromagnetic force distributions on the end winding are obtained. The influence of each structure change on the electromagnetic force in different directions is studied in detail. Conclusions that can be helpful in decreasing the electromagnetic forces on the end winding through optimizing the end region design are presented.
Vibrations caused by electromagnetic forces can severely damage end-winding insulations [
The accurate calculation of electromagnetic field in the end region and electromagnetic force on end winding is the basis of studies on electromagnetic force. Many studies focus on calculation.
In the early years, analytical methods were used to calculate the electromagnetic field in the end region. Methods based on the Biot-Savart law are the most popular among them [
Relatively few studies focus on the electromagnetic force on end winding. Simplifying the end coil as straight line inductors, Richard et al. [
In this paper, a 3D FE model of the end region of a 1550 MW nuclear generator is set up. The electromagnetic force on the end winding at rated operation is obtained by the FE method. The rotor relative length and the stator coil linear length are set to different values in the FE model. The radial, tangential, and axial force density distributions in different parts of the end winding are presented. The influence of the two parameters on the electromagnetic force on end winding is analyzed. Conclusions that can help in decreasing the electromagnetic forces on end winding through optimal design are presented.
The end region of a half-speed nuclear generator is quite complex. The end part of cores and windings is 3D in structure. The end region contains three end components: copper shield, press plate, and press finger. The structure of the end region is shown in Figure
End region of a half-speed nuclear generator.
To improve computational efficiency, the following are assumed: The distribution of current in the stator and rotor windings is uniform. The high-order harmonics of current and displacement current are ignored. The hysteresis effect is ignored. The core material is isotropic [ The cross section of the solution domain of the magnetic field calculation is shown in Figure
Cross section of the solution domain.
The solution domain is shown in Figure
The axial flux is very small in
The stator current cannot be calculated from the above model because the solution domain only contains the end region. Thus, an additional 2D model of the generator is required. The solution domain of the 2D model is shown in Figure
Solution domain of the 2D model.
The mathematical model can be described as follows:
Besides,
With the magnetic field in the end region, the electromagnetic force density can be calculated as
A 1550 MW nuclear generator is adopted because the electromagnetic force in a large generator is large. The basic parameters of the generator are shown in Table
Parameters of the 1550 MW nuclear generator.
Parameters | Values |
---|---|
Power | 1550 MW |
Voltage | 27 kV |
Frequency | 50 Hz |
Number of poles | 4 |
Current | 36926.9 A |
Power factor | 0.9 (lagging) |
JMAG 12.1 is used to build the model and perform the calculation. A 3D FE model of the end region is established per the actual design of the proposed generator. The meshing of the FE model is shown in Figure
FE model mesh of the proposed generator end region. (a) Stator. (b) Rotor.
A 2D FE model of the generator is set up with ANSYS Maxwell 16.1. The stator and rotor currents are obtained by iteration at a rated condition. The result is shown in Table
Iteration result of stator and rotor currents.
Parameters | Values |
---|---|
Rotor current | 6668 A |
|
−246° |
The experiment is performed on an 1150 MW nuclear generator because the 1550 MW nuclear generator is not available for the experiment. The FE model of the 1150 MW generator is built on the same principles, and the structure of the 1150 MW nuclear generator is almost the same as but smaller than that of the 1550 MW generator. Therefore, the relative errors of the two FE models have a similar order. Three probes are set as shown in Figure
Comparison between the calculated and measured value of magnetic density.
Probes | Calculated result | Measured result | Relative error |
---|---|---|---|
A | 0.25 T | 0.27 T | −7.41% |
B | 0.70 T | 0.76 T | −7.89% |
C | 0.77 T | 0.79 T | −2.53% |
Distribution of the test points.
We should analyze only the electromagnetic force on one winding phase because the generator and the electromagnetic force on each winding phase are symmetric. The electromagnetic forces on phase A are analyzed in this paper. In the proposed generator, a winding phase has eight coils. The eight coils are numbered as shown in Figure
Numbering of phase A coils.
Definition of the parts of the end coil.
The magnetic fields on different coils in the same phase are different. Therefore, the electromagnetic forces on different coils are also different, as shown in Figure
Electromagnetic forces on different coils of phase A.
Although the force on the nose part is smaller than that on the involute part, the vibration on the nose part is even larger than that on the involute part because of the weak constraint [
Rotor relative length (
Definition of rotor relative length.
The electromagnetic force distribution on the involute part at 0.039 s is shown in Figure
Electromagnetic force density distribution on the involute part at 0.039 s, when
Figure
Electromagnetic forces on the involute part with different rotor relative lengths.
The electromagnetic force distribution on the nose part is shown in Figure
Electromagnetic force density magnitude distribution on the nose part at 0.039 s, when
The maximum electromagnetic forces on the nose part with different rotor relative lengths are shown in Figure
Electromagnetic forces on the nose part with different rotor relative lengths.
For large generators, the radial vibration of end winding is the most serious [
The stator coil linear length (
Definition of stator coil linear length.
The electromagnetic force density distributions on the involute part at 0.039 s with different stator coil linear lengths are shown in Figure
Electromagnetic force density distribution on the involute part at 0.039 s, when
Figure
Electromagnetic forces on the involute part with different stator coil linear length.
The distribution of the electromagnetic force density magnitude on the nose part with different
Electromagnetic force density magnitude distribution on the nose part at 0.039 s, when
Figure
Electromagnetic forces on the nose part with different stator coil linear lengths.
To reduce the radial vibration on end winding, a relatively large stator coil linear length can be adopted. Consequently, the radial force on the involute and nose parts and the axial force on the nose part will decrease. In contrast, the tangential and axial forces on the involute part increase.
In this paper, a 3D FE model of the end region of a 1550 MW nuclear generator is set up. The electromagnetic force on the stator end winding at a rated operation is calculated. The electromagnetic forces on different coils in the same phase are presented. By changing the rotor relative length and stator coil linear length in the FE model, the influence of these parameters on electromagnetic force is analyzed in detail. The following conclusions are drawn: The electromagnetic force on the involute part varies in different coils at the same phase and the upper involute part of the last coil in the rotation direction suffers the largest force. The electromagnetic force on the nose part is smaller than that on the involute part and changes slightly in different coils. Decreasing the rotor relative length decreases the radial forces on the involute and nose parts. However, decreasing the rotor relative length increases the tangential and axial forces on the involute parts. The stator coil linear length can be increased to decrease the radial forces on the end winding. The radial force on the involute and nose parts decreases significantly but the tangential and axial forces on the involute parts simultaneously increase.
The authors declare that they have no conflicts of interest.
The work is financially supported by the project supported by the National Natural Science Foundation of China (Grant no. 51477015).