I have a three phase squirrel cage induction motor with given parameters (stator winding connected in delta)
- nominal power: \$P_n = 22.4\,\mathrm{kW}\$
- nominal stator voltage: \$V_{sn} = 230\,\mathrm{V}\$
- nominal stator current: \$I_{sn} = 39.5\,\mathrm{A}\$
- nominal stator frequency: \$f_{sn} = 60\,\mathrm{Hz}\$
- nominal speed: \$n_n = 1168\,\mathrm{min}^{-1}\$
- number of pole pairs: 3
- stator resistance per phase (T equivalent circuit): \$R_s = 0.294\,\Omega\$
- stator leakage inductance per phase (T equivalent circuit): \$L_{sl} = 0.00139\,\mathrm{H}\$
- rotor resistance per phase (T equivalent circuit): \$R_r = 0.156\,\Omega\$
- rotor leakage inductance per phase (T equivalent circuit): \$L_{rl} = 0.0007401\,\mathrm{H}\$
- magnetizing inductance per phase (T equivalent circuit): \$L_{m} = 0.041\,\mathrm{H}\$
I have been struggling with calculation of the nominal value of the rotor flux.
My idea was that I will use the T equivalent circuit for that purpose
and I will use nominal values of the motor quantities i.e. I set the motor
operating point into the nominal operation point (nominal slip, nominal stator voltage etc.). Then I calculate phasor of the stator current (\$\hat{I}_s\$) and phasor of the rotor current (\$\hat{I}_r\$) according to the below given set of equations
$$
\begin{bmatrix}
\hat{V}_s \\
0
\end{bmatrix}
=
\begin{bmatrix}
R_s + j\cdot(X_{sl} + X_m) & j\cdot X_m \\
j\cdot X_m & \frac{R_r}{s} + j\cdot(X_{rl} + X_m)
\end{bmatrix}
\cdot
\begin{bmatrix}
\hat{I}_s \\
\hat{I}_r
\end{bmatrix}
$$
For the motor parameters mentioned above the Scilab command linsolve gave me
$$
\hat{I}_s = – 34.946619 + 17.574273j
$$
$$
\hat{I}_r = 35.797115 – 3.954462j
$$
Based on the known phasors of the stator and rotor current I used the below given equation for calculation of the phasor of the rotor flux
$$
\hat{\lambda}_r = (L_{rl} + L_m)\cdot\hat{I}_r + L_m\cdot\hat{I}_s
$$
which gives \$\lambda_r = 0.5554856 – 0.0613638j\$ i.e. \$|\lambda_r|=0.5588647\,\mathrm{V}\cdot\mathrm{s}\$.
This value seems to me to be too low. So I have doubts regarding the way I have used for its calculation. Unfortunatelly I don't know any other way for its calculation which I can use for verification. Can anybody tell me whether the applied procedure is correct or not? I would also appreciate any idea how to verify my results. Thanks in advance.
Best Answer