No-load voltage and damper winding loss and heat analysis of the pole shoe and damper winding centre line shifted structure of tubular hydro-generators

For the pole shoe and damper winding centre line shifted structure that has been gradually applied in hydro-generator in recent years, this let-ter selects one real integer and one fractional slot large tubular hydro- generator as examples. Then revealed the inﬂuence trends of different shift degrees on the no-load voltage waveform quality and the damper winding loss and heat under rated load conditions. Also, it compared these trends with those of the traditional stator skew 1 slot structure. The results show that for integer slot generator, this kind of shift structure can obtain high-quality no-load voltage waveform close to the tra- ditional stator skewed 1 slot scheme, and the damper winding loss and heatissigniﬁcantlysmallerthanthelatter.Forfractionalslotgenerators,thiskindofshiftstructurewillleadtothedeteriorationoftheno-load voltage waveform.

✉ Email: fanzhennan@126.com For the pole shoe and damper winding centre line shifted structure that has been gradually applied in hydro-generator in recent years, this letter selects one real integer and one fractional slot large tubular hydrogenerator as examples. Then revealed the influence trends of different shift degrees on the no-load voltage waveform quality and the damper winding loss and heat under rated load conditions. Also, it compared these trends with those of the traditional stator skew 1 slot structure. The results show that for integer slot generator, this kind of shift structure can obtain high-quality no-load voltage waveform close to the traditional stator skewed 1 slot scheme, and the damper winding loss and heat is significantly smaller than the latter. For fractional slot generators, this kind of shift structure will lead to the deterioration of the no-load voltage waveform.
Introduction: In recent years, the pole shoe and damper winding centre line shifted structure (as shown in Figure 1) has been applied to optimize the no-load voltage waveform of hydro-generator [1]. However, there is still a need to further explore the applicability of this structure, its influence on the loss and heat of damper winding, and whether it can be further promoted and applied. Therefore, it is necessary to implement indepth analysis of the influence of such a structure on the no-load voltage waveform and damper bar loss and heat.
However, it is unfortunate that, although some preliminary influence trends of damper bar pitch and stator slot skew degree on the no-load voltage waveform and the damper winding loss were revealed [2][3], for the pole shoe and damper winding centre line shifted structure, there have only been a few literatures concerning the no-load voltage optimization effect [4]. Based on this, specifically for this new structure, research work combining the no-load voltage waveform with the damper bar loss and heat was even less reported.
In view of this, in this letter, a real 34 MW integer slot and an 18 MW fractional slot large tubular hydro-generator were selected as examples, and their basic parameters are shown in Table 1. The structural design scheme is shown in Table 2. Then the influence trends of the pole shoe   It should be noted that, in this letter, t 1 is the stator tooth pitch, and it remains unchanged. The shift 0 scheme is the pole shoe and damper winding centre line with no shifted scheme.
Necessary explanation before the results discussion: As an important factor that affects the safe operation of generators and electric power communication, the quality of the no-load voltage waveform was defined using the following two parameters as per the Chinese national standard 1029-2005 GB/T [5].
The first parameter is the deviation of the actual waveform from the sinusoidal waveforms of the line voltage, which are defined by the harmonic distortion factor (HDF): The second parameter is the telephone harmonic factor (THF), which quantifies the disturbance of the voltage waveform harmonics in telecommunications:  where U is the actual line voltage, U i (i = 1, 2, 3 … n; n is the highest order considered) is the line voltage of the kth harmonic, and λ k is the weighted coefficient of the kth harmonic. For large generators, the 1029-2005 GB/T regulates HDF ≤ 5%, THF ≤ 1.5% [5].
In the damper winding loss and heat analysis of this letter, P is the total loss of the damper winding in the pair of the magnetic pole regions during the rated operation of the generator, and T max and T min are the maximum and minimum temperatures of the damper winding in the above region during the generator's rated operation, respectively.
Results and analysis of no-load voltage waveform: Some no-load voltage waveform calculation results are shown in Figures 2-4 and Table 3.
In general, regarding the integer slot generator SFWG34-44/6020 (q = 2), it can be seen from Figure 2 that with the increase in the shift degree of the pole shoe and damper winding centre line, the HDF and the THF show a trend of first decreasing then increasing, and then decreasing again. When the shift degree is near 0.2t 1 , the waveform quality is the best. As for the fractional slot generator SFWG18-68/5700 with q = 1 1 / 2 , the change in the above two parameters is the exact opposite. When the shift degree is near 0.2t 1 , the waveform quality is the worst.  Based on this, combined with Table 3, more specific situations can be observed.
1. For the integer slot generator SFWG34-44/6020 (q = 2), when the pole shoe and damper winding centre line were shifted by 0.2t 1 , the waveform quality was great, where its HDF and THF were only 17% and 44.6%, respectively, of the upper limit required by the Chinese national standard 1029-2005 GB/T. In this case, the waveform quality is not only significantly better than most of the other structural schemes, but it is also very close to the traditional stator skew 1 slot scheme, as shown in Figure 3. 2. For the fractional slot generator SFWG18-68/5700 with q = 1 1 / 2 , when the above shifted structure was adopted, the no-load waveform became worse. And when it was shifted by 0.2t 1 , the waveform quality was worst. The HDF and THF exceeded 161% and 263% of the upper limit required by Chinese national standard 1029-2005 GB/T, respectively. Also, the waveform quality was far inferior to the traditional stator skew 1 slot scheme, as shown in Figure 4.
Some calculation results of damper winding loss and heat underrated condition are shown in Figures 5-7 and Tables 4 and 5.
It can be seen from the above results that: 1. Whether for the integer slot generator SFWG34-44/6020 (q = 2) or for the fractional slot generator SFWG18-68/5700 (q = 1 1 / 2 ), when  the pole shoes and damper winding centre line shifted structure is adopted, although the damper winding loss and heat show a rising fluctuation trend with the increase in the shift degree (as shown in Figure 5), they are still significantly lower than those of the traditional stator skew 1 slot structure. 2. For the integer slot generator SFWG34-44/6020 (q = 2), when the pole shoe and damper winding centre line shifted 0.2t 1 structure is adopted, the total loss and the maximum temperature of the damper winding are reduced by 6.1% and 4.3%, respectively, in comparison with the traditional stator skew 1 slot structure. Also, the no-load voltage waveform is almost as good as the latter. As shown in Table 4 and Figure 6. 3. For the fractional slot generator SFWG18-68/5700 (q = 1 1 / 2 ), when this kind of structure is adopted, although the losses and the heat of the damper winding are lower than those of the traditional stator skew 1 slot structure, the no-load voltage waveform quality is far from the Chinese national standard 1029-2005 GB/T, which is neither acceptable to the generator design and manufacturing enterprises nor to the power sector (as shown in Table 5 and Figure 7).

Conclusion:
1. Whether it is an integer slot or a fractional slot tubular hydrogenerator, when the pole shoes and damper winding centre line shifted structure is adopted, the total loss of the damper winding and the maximum temperature show a rising fluctuation trend with the increase in the shift degree. However, it is worth noting that their value does not change much and that it is significantly smaller than that of the traditional stator skew 1 slot structure. 2. For the integer slot tubular hydro-generator, a better no-load voltage waveform can be realized when the pole shoe and damper winding centre line are reasonably shifted, where the voltage waveform quality almost reaches that of the stator skewed 1 slot structure. However, for the fractional slot tubular hydro-generator, this type of shifted structure can lead to deteriorating the no-load voltage waveform quality. Therefore, for fractional slot hydro-generator, it is still recommended to adopt a stator skewed slot scheme in design and manufacture.