.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples/drive/plot_45kw_im_vhz_mechanical_impedance.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_examples_drive_plot_45kw_im_vhz_mechanical_impedance.py: 45-kW IM, V/Hz control, mechanical impedance ============================================ This example measures the mechanical impedance of a 45-kW induction machine (IM) drive under open-loop V/Hz control and under observer-based V/Hz (O-V/Hz) control. The machine parameters correspond to [#Har2023]_. .. GENERATED FROM PYTHON SOURCE LINES 12-21 .. code-block:: Python from math import inf import matplotlib.pyplot as plt import motulator.drive.control.im as control import numpy as np from motulator.drive import model, utils from motulator_impedance import drive .. GENERATED FROM PYTHON SOURCE LINES 22-23 Compute base values based on the nominal values. .. GENERATED FROM PYTHON SOURCE LINES 23-27 .. code-block:: Python nom = utils.NominalValues(U=400, I=81, f=50, P=45e3, tau=291) base = utils.BaseValues.from_nominal(nom, n_p=2) .. GENERATED FROM PYTHON SOURCE LINES 28-29 Configure the measurement. .. GENERATED FROM PYTHON SOURCE LINES 29-34 .. code-block:: Python meas_cfg = drive.MeasurementCfg( abs_w_e=0.002 * base.w_M, freqs=np.geomspace(1, 500, 50) ) .. GENERATED FROM PYTHON SOURCE LINES 35-37 Configure the system model. The rotor speed is imposed, i.e., no mechanical system is used. The operating-point speed is 0.25 p.u. .. GENERATED FROM PYTHON SOURCE LINES 37-47 .. code-block:: Python w_M0 = 0.25 * base.w_M par = model.InductionMachineInvGammaPars( n_p=2, R_s=60e-3, R_R=30e-3, L_sgm=2.2e-3, L_M=24.5e-3 ) mechanics = model.ExternalRotorSpeed() mechanics.set_external_rotor_speed(w_M0) converter = model.VoltageSourceConverter(u_dc=540) mdl = model.Drive(model.InductionMachine(par), mechanics, converter) .. GENERATED FROM PYTHON SOURCE LINES 48-50 Configure open-loop V/Hz control without stator resistance compensation and slip compensation. .. GENERATED FROM PYTHON SOURCE LINES 50-59 .. code-block:: Python est_par = control.InductionMachineInvGammaPars(n_p=2, R_s=0, R_R=0, L_sgm=0, L_M=inf) cfg = control.ObserverBasedVHzControllerCfg( psi_s_nom=base.psi, i_s_max=inf, alpha_f=0, alpha_tau=0, alpha_psi=0 ) open_loop_ctrl = control.VHzControlSystem( control.ObserverBasedVHzController(est_par, cfg) ) .. GENERATED FROM PYTHON SOURCE LINES 60-61 Configure O-V/Hz control. .. GENERATED FROM PYTHON SOURCE LINES 61-66 .. code-block:: Python cfg = control.ObserverBasedVHzControllerCfg(psi_s_nom=base.psi, i_s_max=1.5 * base.i) ovhz_ctrl = control.VHzControlSystem(control.ObserverBasedVHzController(par, cfg)) ctrls = {"Open-loop V/Hz": open_loop_ctrl, "O-V/Hz": ovhz_ctrl} .. GENERATED FROM PYTHON SOURCE LINES 67-69 Measure the mechanical impedance at no load, i.e., the speed reference equals the rotor speed, and plot the results. .. GENERATED FROM PYTHON SOURCE LINES 69-77 .. code-block:: Python if __name__ == "__main__": results = {} for label, ctrl in ctrls.items(): ctrl.set_speed_ref(w_M0) results[label] = drive.measure_mechanical_impedance(mdl, ctrl, meas_cfg) drive.plot_mechanical_impedance(results) .. image-sg:: /examples/drive/images/sphx_glr_plot_45kw_im_vhz_mechanical_impedance_001.png :alt: plot 45kw im vhz mechanical impedance :srcset: /examples/drive/images/sphx_glr_plot_45kw_im_vhz_mechanical_impedance_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 78-85 The phase of the mechanical impedance under open-loop V/Hz control is below -90° around 10 Hz, i.e., the impedance is non-passive. Instead of damping torsional vibrations, the drive may amplify them. Under O-V/Hz control, the impedance is passive in the measured frequency range. Simulate the acceleration to the operating point with rigid mechanics. Under open-loop V/Hz control, the drive becomes unstable, while it is stable under O-V/Hz control. .. GENERATED FROM PYTHON SOURCE LINES 85-108 .. code-block:: Python if __name__ == "__main__": times = np.array([0, 0.5, 1.5, 3]) values = np.array([0, 0, 1, 1]) * w_M0 _, (ax1, ax2) = plt.subplots(2, 1, sharex=True) for label, ctrl in ctrls.items(): mdl = model.Drive( model.InductionMachine(par), model.MechanicalSystem(J=0.49), model.VoltageSourceConverter(u_dc=540), ) ctrl.set_speed_ref(utils.SequenceGenerator(times, values)) res = model.Simulation(mdl, ctrl).simulate(t_stop=3) ax1.plot(res.mdl.t, res.mdl.mechanics.w_M / base.w_M, label=label) ax2.plot(res.mdl.t, res.mdl.machine.tau_M / base.tau, label=label) ax1.set_ylabel(r"$\omega_\mathrm{m}$ (p.u.)") ax2.set_ylabel(r"$\tau_\mathrm{m}$ (p.u.)") ax2.set_xlabel("Time (s)") ax2.set_xlim(0, 3) ax1.legend(loc="upper left") ax2.legend(loc="upper left") plt.show() .. image-sg:: /examples/drive/images/sphx_glr_plot_45kw_im_vhz_mechanical_impedance_002.png :alt: plot 45kw im vhz mechanical impedance :srcset: /examples/drive/images/sphx_glr_plot_45kw_im_vhz_mechanical_impedance_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 109-114 .. rubric:: References .. [#Har2023] Hartikainen, Tiitinen, Laine, Hinkkanen, "Identification of mechanical impedance of an electric machine drive for drivetrain design," Proc. IEEE IEMDC, 2023, https://doi.org/10.1109/IEMDC55163.2023.10238992 .. rst-class:: sphx-glr-timing **Total running time of the script:** (2 minutes 28.009 seconds) .. _sphx_glr_download_examples_drive_plot_45kw_im_vhz_mechanical_impedance.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_45kw_im_vhz_mechanical_impedance.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_45kw_im_vhz_mechanical_impedance.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_45kw_im_vhz_mechanical_impedance.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_