Question 3.AE.9: Terminal currents of a three-phase induction motor contain a......
Terminal currents of a three-phase induction motor contain a forward-rotating subharmonic of 6 Hz at an amplitude I_{0.1}=5% of the fundamental I_1=1.73 A. The parameters of a three-phase induction machine are as follows:
3A/1.73A, Δ/Y connected, f = 60Hz,
n_{rat} = 1773rpm, p = 4 poles, (E3.9-1)
R_s = 7.0Ω, ω_1L_{sL} = 5Ω, ω_1L_m = 110Ω,
R_r^{\prime}=5 \Omega, \quad \omega_1 L_{r \ell}^{\prime}=4 \OmegaCompute the fundamental torque (T_{e1}) as a function of the fundamental slip (s_1) and subharmonic torque (T_{e0.1}) as a function of the subharmonic slip (s_{0.1}).
The parameters of Eqs. 3-53 and 3-54 and the corresponding fundamental and subharmonic torques are listed in Tables E3.9.1 through E3.9.3 as a function of the fundamental h=1 and the subharmonic h=0.1.
One notes that the low-frequency harmonic torques at 6 Hz and 5% harmonic current amplitudes are very small (about 0.0063 Nm).
Table E3.9.1 Maximum Torques for Fundamental and Subharmonic Currents, where the Fundamental Current is 1.73 A and the Subharmonic Current is 5% of the Fundamental Current
\begin{array}{l|c|l|l|l|l} \hline \boldsymbol{h} & \left.\left|\tilde{\boldsymbol{V}}_{\text {sh }}\right|(\mathbf{V})\right] & {\begin{array}{l} \pm \boldsymbol{S}_{\text {hmax }} \\ (-) \end{array}} & \begin{array}{l} \boldsymbol{\omega}_{\text {msh }} \\ (\mathrm{rad} / \mathrm{s}) \end{array} & \begin{array}{l} T_{\text {ehmax }}^{\text {mot }} \\ (\mathrm{Nm}) \end{array} & \begin{array}{l} T_{\text {ehmmax }}^{\text {gen }} \\ (\mathbf{N m}) \end{array} \\ \hline 1 & 190.3 & 0.044 & 188.49 & 2.53 & -2.35 \\ 0.1 & 0.952 & 0.439 & 18.849 & 0.0063 & -0.0063 \\ \hline \end{array}
Table E3.9.2 Torque as a Function of Slip s_1 for Fundamental (h=1) Currents
\begin{array}{l|l|l|l|l|l} \hline S_1(-) & 1.0 & 0.9 & 0.8 & 0.7 & 0.6 \\ T_{e 1}(\mathrm{Nm}) & 0.221 & 0.246 & 0.276 & 0.316 & 0.368 \\ S_1(-) & 0.5 & 0.4 & 0.3 & 0.2 & 0.1 \\ T_{e 1}(\mathrm{Nm}) & 0.440 & 0.548 & 0.724 & 1.058 & 1.860 \\ \hline \end{array}
Table E3.9.3 Torque as a Function of Slip s_{0.1} for Subharmonic (h=0.1) Currents of 5% of the Fundamental Current
\begin{array}{l|l|l|l|l|l} \hline S_{0.1}(-) & 1.0 & 0.9 & 0.8 & 0.7 & 0.6 \\ T_{e 0.1}(\mathrm{Nm}) & 0.0047 & 0.0050 & 0.0053 & 0.0057 & 0.0060 \\ S_{0.1}(-) & 0.5 & 0.4 & 0.3 & 0.2 & 0.1 \\ T_{e 0.1}(\mathrm{Nm}) & 0.0063 & 0.0063 & 0.0059 & 0.0048 & 0.0027 \\ \hline \end{array}