.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "drive_examples/grid_connection/plot_6kw_im_deep_bars_dol.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_drive_examples_grid_connection_plot_6kw_im_deep_bars_dol.py: 5.6-kW deep-bar IM, direct-on-line start ======================================== This example simulates the direct-on-line start of a 5.6-kW induction machine (IM) with deep rotor bars. At high slip frequencies, the eddy currents in the bars increase the rotor resistance and decrease the rotor leakage inductance (deep-bar effect), which increases the starting torque. The deep-bar effect is modeled by means of the cage impedance [#Mol2020]_, and the main-flux saturation is also included. The parameters of the machine are given in [#Mol2021]_. .. GENERATED FROM PYTHON SOURCE LINES 15-23 .. code-block:: Python from math import pi import matplotlib.pyplot as plt import numpy as np from motulator.common.utils import set_style from motulator.drive import model, utils .. GENERATED FROM PYTHON SOURCE LINES 24-25 Compute base values based on the nominal values. The nominal speed is 1770 r/min. .. GENERATED FROM PYTHON SOURCE LINES 25-29 .. code-block:: Python nom = utils.NominalValues(U=460, I=9.5, f=60, P=5.6e3, tau=5.6e3 / (2 * pi * 1770 / 60)) base = utils.BaseValues.from_nominal(nom, n_p=2) .. GENERATED FROM PYTHON SOURCE LINES 30-32 The Γ model is used, with a constant leakage inductance and a stator inductance that saturates as a function of the stator flux linkage magnitude. .. GENERATED FROM PYTHON SOURCE LINES 32-39 .. code-block:: Python def L_s(psi, L_su=0.1857, c=1.4, S=6): """Stator inductance (H) as a function of the flux linkage magnitude (Vs).""" return L_su / (1 + (psi / c) ** S) .. GENERATED FROM PYTHON SOURCE LINES 40-43 The cage impedance is a ladder circuit of the first order, whose DC resistance is 0.64 Ω and DC inductance is 3.6 mH. Its resistance increases and its inductance decreases with the frequency of the rotor current, i.e., with the slip frequency. .. GENERATED FROM PYTHON SOURCE LINES 43-61 .. code-block:: Python cage = model.CageImpedance(R=[0.64, 2.1], L=[3.6e-3]) f = np.linspace(1, 100, 100) Z_c = cage.Z(2j * pi * f) set_style() fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True) ax1.plot(f, np.real(Z_c) / base.Z) ax1.set_ylabel("Resistance (p.u.)") ax1.set_ylim(0, 0.08) ax2.plot(f, np.imag(Z_c) / (2 * pi * f) / base.L) ax2.set_ylabel("Inductance (p.u.)") ax2.set_ylim(0, 0.06) ax2.set_xlabel("Frequency (Hz)") ax2.set_xlim(0, 100) plt.show() .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_001.png :alt: plot 6kw im deep bars dol :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 62-66 Configure the system model. For comparison, the machine can also be modeled without the deep-bar effect, in which case the rotor resistance is the DC resistance of the cage and the leakage inductance includes the DC inductance of the cage. The machine drives a fan, whose load torque is proportional to the square of the speed. .. GENERATED FROM PYTHON SOURCE LINES 66-82 .. code-block:: Python def create_model(deep_bars: bool) -> model.GridConnectedMachine: """Create the model of the grid-connected machine.""" if deep_bars: R_r, L_ell = cage, 12.4e-3 else: R_r, L_ell = 0.64, 12.4e-3 + 3.6e-3 par = model.InductionMachinePars(n_p=2, R_s=0.93, R_r=R_r, L_ell=L_ell, L_s=L_s) machine = model.InductionMachine(par) k = nom.tau / base.w_M**2 # Quadratic load torque profile mechanics = model.MechanicalSystem(J=0.1, B_L=lambda w_M: k * abs(w_M)) ac_source = model.ThreePhaseSource(w_g=base.w, e_g=base.u) return model.GridConnectedMachine(machine, mechanics, ac_source) .. GENERATED FROM PYTHON SOURCE LINES 83-85 Simulate the start with the deep-bar effect and plot the results in per-unit values. After the start, the machine operates close to its nominal operating point. .. GENERATED FROM PYTHON SOURCE LINES 85-90 .. code-block:: Python sim = model.Simulation(create_model(deep_bars=True)) res = sim.simulate(t_stop=1) utils.plot(res, base) .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_002.png :alt: plot 6kw im deep bars dol :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 91-94 Simulate the start without the deep-bar effect and compare the results. The deep-bar effect increases the torque during the start, while the operation at low slip frequencies is not affected. .. GENERATED FROM PYTHON SOURCE LINES 94-112 .. code-block:: Python sim = model.Simulation(create_model(deep_bars=False)) res_ref = sim.simulate(t_stop=1) fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True) for r, label in ((res, "Cage impedance"), (res_ref, "Rotor resistance")): ax1.plot(r.mdl.t, r.mdl.machine.w_M / base.w_M, label=label) ax2.plot(r.mdl.t, r.mdl.machine.tau_M / base.tau, label=label) ax1.set_ylabel("Speed (p.u.)") ax1.legend(loc="lower right") ax2.set_ylabel("Torque (p.u.)") ax2.legend(loc="upper right") ax2.set_xlabel("Time (s)") ax2.set_xlim(0, 1) plt.show() # sphinx_gallery_thumbnail_number = 3 .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_003.png :alt: plot 6kw im deep bars dol :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_6kw_im_deep_bars_dol_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 113-123 .. rubric:: References .. [#Mol2020] Mölsä, Saarakkala, Hinkkanen, Arkkio, Routimo, "A dynamic model for saturated induction machines with closed rotor slots and deep bars," IEEE Trans. Energy Convers., 2020, https://doi.org/10.1109/TEC.2019.2950810 .. [#Mol2021] Mölsä, Tiitinen, Saarakkala, Peretti, Hinkkanen, "Standstill identification of an induction motor model including deep-bar and saturation characteristics," IEEE Trans. Ind. Appl., 2021, https://doi.org/10.1109/TIA.2021.3089458 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.313 seconds) .. _sphx_glr_download_drive_examples_grid_connection_plot_6kw_im_deep_bars_dol.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_6kw_im_deep_bars_dol.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_6kw_im_deep_bars_dol.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_6kw_im_deep_bars_dol.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_