.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "drive_examples/grid_connection/plot_2kw_im_diode_vhz.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_2kw_im_diode_vhz.py: 2.2-kW IM, diode bridge, V/Hz control ===================================== This example simulates pure open-loop V/Hz control of a 2.2-kW induction machine (IM) drive, fed from a six-pulse diode bridge. The diode bridge is supplied from a stiff grid through an AC choke. .. GENERATED FROM PYTHON SOURCE LINES 12-23 .. code-block:: Python from math import inf, pi, sqrt import matplotlib.pyplot as plt import motulator.drive.control.im as control from motulator.common.model import CompositeModel, DCBus, Simulation, ThreePhaseSource from motulator.common.utils import complex2abc from motulator.drive import model as drive_model from motulator.drive import utils as drive_utils from motulator.grid import model as grid_model .. GENERATED FROM PYTHON SOURCE LINES 24-25 Compute base values based on the nominal values. .. GENERATED FROM PYTHON SOURCE LINES 25-29 .. code-block:: Python nom = drive_utils.NominalValues(U=400, I=5, f=50, P=2.2e3, tau=14.6) base = drive_utils.BaseValues.from_nominal(nom, n_p=2) .. GENERATED FROM PYTHON SOURCE LINES 30-32 Configure the system model. The diode bridge and the inverter share the DC bus, and their models are combined into a composite model. .. GENERATED FROM PYTHON SOURCE LINES 32-54 .. code-block:: Python dc_bus = DCBus(C_dc=235e-6, u_dc=sqrt(2) * nom.U) grid_sys = grid_model.GridConverterSystem( grid_model.DiodeBridge(), grid_model.LFilter(L_f=1e-3), ThreePhaseSource(w_g=base.w, e_g=base.u), dc_bus=dc_bus, ) par = drive_model.InductionMachineInvGammaPars( n_p=2, R_s=3.7, R_R=2.1, L_sgm=0.021, L_M=0.224 ) machine = drive_model.InductionMachine(par) k = 1.1 * nom.tau / base.w_M**2 # Quadratic load torque profile mechanics = drive_model.MechanicalSystem(J=0.015, B_L=lambda w_M: k * abs(w_M)) converter = drive_model.VoltageSourceConverter( modulator=drive_model.CarrierComparison() ) drive_sys = drive_model.Drive(machine, mechanics, converter, dc_bus=dc_bus) mdl = CompositeModel({"grid": grid_sys, "drive": drive_sys}) .. GENERATED FROM PYTHON SOURCE LINES 55-56 Configure the control system as open-loop V/Hz control. .. GENERATED FROM PYTHON SOURCE LINES 56-64 .. 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 ) vhz_ctrl = control.ObserverBasedVHzController(est_par, cfg) ctrl = control.VHzControlSystem(vhz_ctrl, slew_rate=2 * pi * 60) .. GENERATED FROM PYTHON SOURCE LINES 65-66 Set the speed reference and the external load torque. .. GENERATED FROM PYTHON SOURCE LINES 66-70 .. code-block:: Python ctrl.set_speed_ref(lambda t: (t > 0.2) * base.w_M) mechanics.set_external_load_torque(lambda t: (t > 1) * 0.2 * nom.tau) .. GENERATED FROM PYTHON SOURCE LINES 71-73 Create the simulation object, with the control system of the drive by the model name, and simulate. Plot the drive results in per-unit values. .. GENERATED FROM PYTHON SOURCE LINES 73-81 .. code-block:: Python sim = Simulation(mdl, {"drive": ctrl}) res = sim.simulate(t_stop=1.4) res_drive = drive_model.SimulationResults(res.mdl.drive, res.ctrl.drive) # sphinx_gallery_thumbnail_number = 2 drive_utils.plot(res_drive, base) drive_utils.plot_stator_waveforms(res_drive, base, t_lims=(1.1, 1.125)) .. rst-class:: sphx-glr-horizontal * .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_001.png :alt: plot 2kw im diode vhz :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_001.png :class: sphx-glr-multi-img * .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_002.png :alt: plot 2kw im diode vhz :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_002.png :class: sphx-glr-multi-img .. GENERATED FROM PYTHON SOURCE LINES 82-86 Plot the grid-side waveforms: the phase-a voltages of the grid and the diode bridge, the DC-bus voltage, the phase-a current, and the DC currents of the diode bridge and the inverter. The diode bridge conducts in pulses, as the DC-bus voltage is close to the peak of the line-to-line grid voltage. .. GENERATED FROM PYTHON SOURCE LINES 86-103 .. code-block:: Python t, grid_ts = res.mdl.t, res.mdl.grid fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True) ax1.plot(t, complex2abc(grid_ts.ac_source.e_g_ab)[0] / base.u, label=r"$e_\mathrm{ga}$") ax1.plot(t, complex2abc(grid_ts.converter.u_c_ab)[0] / base.u, label=r"$u_\mathrm{ca}$") ax1.plot(t, grid_ts.dc_bus.u_dc / base.u, label=r"$u_\mathrm{dc}$") ax1.set_ylabel("Voltage (p.u.)") ax1.legend(loc="lower right") ax2.plot(t, complex2abc(grid_ts.ac_filter.i_g_ab)[0] / base.i, label=r"$i_\mathrm{ga}$") ax2.plot(t, -grid_ts.converter.i_dc_int / base.i, label=r"$i_\mathrm{r}$") ax2.plot(t, res.mdl.drive.converter.i_dc_int / base.i, label=r"$i_\mathrm{i}$") ax2.set_ylabel("Current (p.u.)") ax2.set_xlabel("Time (s)") ax2.set_xlim(1.1, 1.125) ax2.legend(loc="lower right") plt.show() .. image-sg:: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_003.png :alt: plot 2kw im diode vhz :srcset: /drive_examples/grid_connection/images/sphx_glr_plot_2kw_im_diode_vhz_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 104-119 .. note:: The DC link of this particular example is unstable at 1-p.u. speed at the rated load torque, since the inverter looks like a negative resistance to the DC link. After the speed has settled, an oscillation at about 150 Hz, half the frequency of the six-pulse ripple, grows in the DC-bus voltage. It is seen above as the unequal current pulses of the diode bridge. The oscillation does not grow without bound, but it settles into a limit cycle of about 77 V peak to peak at about 1.5 s. With twice the DC-bus capacitance, the oscillation does not occur, and only the six-pulse ripple remains. For analysis, see e.g., [#Hin2007]_. .. rubric:: References .. [#Hin2007] Hinkkanen, Harnefors, Luomi, "Control of induction motor drives equipped with small DC-Link capacitance," Proc. EPE, 2007, https://doi.org/10.1109/EPE.2007.4417763 .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 41.456 seconds) .. _sphx_glr_download_drive_examples_grid_connection_plot_2kw_im_diode_vhz.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_2kw_im_diode_vhz.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_2kw_im_diode_vhz.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_2kw_im_diode_vhz.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_