4.2 Total Harmonic Distortion
THD is given by the following equation:
where
k is an integer and refers to the harmonic order (
k = 2, 3, 4…),
Vk is the amplitude of
kth order harmonic, and
V1 is the fundamental frequency component. The improvement in THD for the 2/3 pitch configuration is clearly seen, and this is because of the elimination of the third harmonic component that is present in the 5/6 pitch configuration (see
Figure 7).
Table 4,
Table 5 and
Table 6 show a comparison between the THD values of the induced phase voltage under different conditions. Simulations were carried out for three different frequencies of flux pump excitation (60 Hz, 120 Hz and 240 Hz). Under “no load” conditions, it was observed that the THD values with G10 stator were lower than those with the steel stator (
Table 4). This reduction in THD can be attributed to higher fringing effects and sharper transition of the fields in the case of steel yoke stator for the hexagonal design of the rotor without pole shoes. The change in the winding pitch resulted in a decrease in the induced voltage levels, but improved the harmonic performance. The voltage levels were compensated by increasing the number of stator conductors, as mentioned in
Section 3.
As discussed in
Section 3, since the winding pitch is a critical factor in tuning the harmonic performance [
33,
34,
35,
36], results are analysed for two different pitches. The THD for the 2/3 pitch configuration is significantly reduced when compared to the 5/6 pitch configuration for both steel and G10 stator yokes. The reason for this improvement is the successful elimination of the third harmonic component (
Figure 7). Based on these results, for further simulations, the stator yoke material was selected to be G10, and the winding pitch was selected to be 2/3.
Simulations for different loaded conditions (rated load, 1/2 rated and 1/4 rated loads) were carried out for two different configurations. Balanced resistive loads were coupled to the ANSYS Maxwell model using ANSYS Maxwell Circuit Editor for these simulations. With S-S configuration, the THD of the induced phase voltage (V
ph) is ~3.3% lower than with the “no load” THD values (see
Table 4 and
Table 5).
On further investigation, it was observed that the field current profiles for the “no load” condition are affected by the pulsating nature of the flux pump excitation, whereas the pulsating effect does not have much of an effect under loaded conditions (see
Figure 8). However, the field current is increasing in both of the cases; the field current oscillations in the case of the loaded condition have a higher sinusoidal variation than the field currents with the “no load” condition. For further simulations, Star-Delta (S-D) was selected as the load configuration. The THD values at different levels (Rated, 1/2 and 1/4 loads) are as tabulated in
Table 6. Minimum THD is observed at rated load.
It is also observed that the THD values for the S-D configuration are slightly lower than the S-S configuration. This is most likely due to the lower armature reaction in the case of the S-D configuration. Studies on armature reaction and analyses of direct axis reactance (Xd) and quadrature axis reactance of the machine (Xq) of the machine are likely to give a better understanding of the ongoing phenomenon from magnetic field interaction. The THD limit as specified in IEEE STD 519-2014 is 5% for a bus voltage <69 kV at the point of common coupling, and the permitted limit is 8% for lower voltage generation <1 kV. Hence, the proof of concept generator to be tested in field and designed for 400 V meets prescribed standards.
The final commercial product based on this proof of concept generator will be a flux pump-integrated MW class wind turbine HTS generator, and the generated voltage levels for this generator are expected to be >1 kV and <69 kV. For this class of generation, the maximum limit of THD is 8%, as per the prescribed standard.
The observed THD limits are well within this limit, and with this design, a tolerance offset of ~3% can be considered for the additional harmonics introduced due to control circuitry and the power electronic switching circuitry, which will be integrated at different points of the generation and transmission. The overall variation trend of THD against various design parameters is shown in the bar graphs of
Figure 9. It is seen that the S-D configuration with a pitch of 2/3 at rated load gives the least THD. The results are in consistence with the results observed for similar ironless machines [
37].
As discussed in
Section 3, the stator made of FRP epoxy (G-10) is better suited in cryogenic applications. In the absence of a ferromagnetic yoke, the field distribution is less concentrated and the drop in the field is higher, with a small increase in the distance from the centre of the field coil. To improvise the THD performance, design modifications were carried out on the stator geometry, and are discussed in the following sections.