Question 3.AE.8: Based on results of the previous application example, explai......
Based on results of the previous application example, explain why low-frequency subharmonic voltages at the terminal of induction machines should be limited.
For subharmonic slip s_{0.1}=1.0 one obtains with Eq. E3.7-2 the fundamental slip s_1=1.0. Correspondingly for subharmonic slip s_{0.1}=0.82 one obtains s_1=0.982, and for subharmonic slip s_{0.1}=–0.82 one obtains s_1=0.818 (see Table E3.7.3).
s_1=(0.1)\left(s_{0.1}\right)+0.9=1.0 \text {. } (E3.7-2)
One notes that the subharmonic torque at 6 Hz (h=0.1) is relatively large in the generator region (T_{e0.1}=–4.61 Nm). If the worst case is considered as defined by Eq. 3-52 the corresponding low-frequency harmonic torque is even larger. This is the reason why the low-frequency harmonic voltages should be limited to less than a few percent (e.g., 2%) of rated voltage.
Table E3.7.3 Subharmonic Torque T_{e0.1} as a Function of Subharmonic Slip s_{0.1}.
\begin{array}{l|l|l|l|l|l|c} \hline S_{0.1}(-) & 1.0 & 0.9 & 0.82 & 0.8 & 0.7 & 0.6 \\ S_1(-) & 1.0 & 0.99 & 0.982 & 0.98 & 0.97 & 0.96 \\ T_{e 0.1}(\mathrm{Nm}) & 0.687 & 0.693 & 0.696 & 0.695 & 0.69 & 0.676 \\ S_{0.1}(-) & 0.5 & 0.4 & 0.3 & 0.2 & 0.1 & 0 \\ S_1(-) & 0.95 & 0.94 & 0.93 & 0.92 & 0.91 & 0.9 \\ T_{e 0.1}(\mathrm{Nm}) & 0.648 & 0.602 & 0.528 & 0.415 & 0.247 & 0 \\ S_{0.1}(-) & -0.1 & -0.2 & -0.3 & -0.4 & -0.5 & -0.6 \\ S_1(-) & 0.89 & 0.88 & 0.87 & 0.86 & 0.85 & 0.84 \\ T_{e 0.1}(\mathrm{Nm}) & -0.353 & -0.842 & -1.488 & -2.28 & -3.12 & -3.88 \\ S_{0.1}(-) & -0.7 & -0.8 & -0.82 & -0.9 & -1 & -1.1 \\ S_1(-) & 0.83 & 0.82 & 0.818 & 0.81 & 0.8 & 0.79 \\ T_{e 0.1}(\mathrm{Nm}) & -4.40 & -4.60 & -4.61 & -4.53 & -4.29 & -3.95 \\ S_{0.1}(-) & -1.2 & -1.3 & -1.4 & -1.5 & -1.6 & -1.7 \\ S_1(-) & 0.78 & 0.77 & 0.76 & 0.75 & 0.74 & 0.73 \\ T_{e 0.1}(\mathrm{Nm}) & -3.60 & -3.26 & -2.96 & -2.68 & -2.45 & -2.24 \\ S_{0.1}(-) & -2.0 & -3.0 & -4.0 & -5.0 & -6.0 & -7.0 \\ S_1(-) & 0.70 & 0.60 & 0.50 & 0.40 & 0.30 & 0.20 \\ T_{e 0.1}(\mathrm{Nm}) & -1.76 & -0.98 & -0.67 & -0.51 & -0.40 & -0.34 \\ S_{0.1}(-) & -8.0 & -9.0 & -10.0 & -11.0 & -12.0 & -13.0 \\ S_1(-) & 0.1 & 0 & -0.1 & -0.20 & -0.30 & -0.40 \\ T_{e 0.1}(\mathrm{Nm}) & -0.29 & -0.25 & -0.22 & -0.20 & -0.18 & -0.17 \\ \hline \end{array}