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docs/_downloads/01a31468f0628d249938535bd3e8e129/plot_flux_vector_pmsyrm_5kw.py

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5.5-kW PM-SyRM, saturated
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=========================
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This example simulates sensorless stator-flux-vector control of a 5.5-kW
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PM-SyRM (Baldor ECS101M0H7EF4) drive. The machine model is parametrized using
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the algebraic saturation model from [#Lel2024]_, fitted to the flux linkage
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maps measured using the constant-speed test. For comparison, the measured data
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is plotted together with the model predictions. Notice that the control system
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used in this example does not consider the saturation, only the system model
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This example simulates sensorless stator-flux-vector control of a 5.5-kW
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PM-SyRM (Baldor ECS101M0H7EF4) drive. The machine model is parametrized using
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the algebraic saturation model from [#Lel2024]_, fitted to the flux linkage
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maps measured using the constant-speed test. For comparison, the measured data
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is plotted together with the model predictions. Notice that the control system
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used in this example does not consider the saturation, only the system model
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does.
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"""
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def i_s(psi_s):
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"""
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Saturation model for a 5.5-kW PM-SyRM.
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This model takes into account the bridge saturation in addition to the
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regular self- and cross-saturation effects of the d- and q-axis. The bridge
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saturation model is based on a nonlinear reluctance element in parallel
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with the Norton-equivalent PM model.
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This model takes into account the bridge saturation in addition to the
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regular self- and cross-saturation effects of the d- and q-axis. The bridge
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saturation model is based on a nonlinear reluctance element in parallel
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with the Norton-equivalent PM model.
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Parameters
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----------
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Notes
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-----
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For simplicity, the saturation model parameters are hard-coded in the
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function below. This model can also be used for other PM-SyRMs by changing
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the model parameters.
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For simplicity, the saturation model parameters are hard-coded in the
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function below. This model can also be used for other PM-SyRMs by changing
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the model parameters.
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"""
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# d-axis self-saturation

docs/_downloads/04c5141a67584a6524f8c198ae23ef35/plot_flux_vector_syrm_7kw.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# 6.7-kW SyRM, saturated, disturbance estimation\n\nThis example simulates sensorless stator-flux-vector control of a saturated\n6.7-kW synchronous reluctance motor drive. The saturation is not taken into\naccount in the control method (only in the system model). Even if the machine \nhas no magnets, the PM-flux disturbance estimation is enabled [#Tuo2018]_. In \nthis case, this PM-flux estimate lumps the effects of inductance errors. \nNaturally, the PM-flux estimation can be used in PM machine drives as well. \n"
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"\n# 6.7-kW SyRM, saturated, disturbance estimation\n\nThis example simulates sensorless stator-flux-vector control of a saturated\n6.7-kW synchronous reluctance motor drive. The saturation is not taken into\naccount in the control method (only in the system model). Even if the machine\nhas no magnets, the PM-flux disturbance estimation is enabled [#Tuo2018]_. In\nthis case, this PM-flux estimate lumps the effects of inductance errors.\nNaturally, the PM-flux estimation can be used in PM machine drives as well.\n"
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]
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},
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{

docs/_downloads/063cf0c7a6cd6584d8b416190228666c/plot_gfl_lcl_10kva.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# 10-kVA converter, LCL filter\n \nThis example simulates a grid-following-controlled converter connected to a\nstrong grid through an LCL filter. The control system includes a phase-locked\nloop (PLL) to synchronize with the grid, a current reference generator, and a\nPI-type current controller. The dynamics of the LCL filter are not taken into\naccount in the control system.\n"
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"\n# 10-kVA converter, LCL filter\n\nThis example simulates a grid-following-controlled converter connected to a\nstrong grid through an LCL filter. The control system includes a phase-locked\nloop (PLL) to synchronize with the grid, a current reference generator, and a\nPI-type current controller. The dynamics of the LCL filter are not taken into\naccount in the control system.\n"
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]
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},
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{

docs/_downloads/0e8207fbfefb0b923d7f22208bd3cd83/plot_obs_vhz_ctrl_pmsm_2kw_two_mass.py

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This example simulates observer-based V/Hz control of a 2.2-kW PMSM drive. The
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mechanical subsystem is modeled as a two-mass system. The resonance frequency
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of the mechanics is around 85 Hz. The mechanical parameters correspond to
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[#Saa2015]_, except that the torsional damping is set to a smaller value in
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of the mechanics is around 85 Hz. The mechanical parameters correspond to
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[#Saa2015]_, except that the torsional damping is set to a smaller value in
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this example.
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"""

docs/_downloads/11388a34fc999c2467fbd17556f5ee11/plot_gfm_rfpsc_13kva.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# 12.5-kVA converter, RFPSC\n \nThis example simulates reference-feedforward power-synchronization control \n(RFPSC) of a converter connected to a weak grid. \n"
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"\n# 12.5-kVA converter, RFPSC\n\nThis example simulates reference-feedforward power-synchronization control\n(RFPSC) of a converter connected to a weak grid.\n"
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]
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},
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{

docs/_downloads/16706dd8bc863891161047a58b1fa773/plot_gfl_dc_bus_10kva.py

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"""
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10-kVA converter, DC-bus voltage
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================================
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This example simulates a grid-following-controlled converter connected to a
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strong grid and regulating the DC-bus voltage. The control system includes a
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DC-bus voltage controller, a phase-locked loop (PLL) to synchronize with the
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strong grid and regulating the DC-bus voltage. The control system includes a
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DC-bus voltage controller, a phase-locked loop (PLL) to synchronize with the
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grid, a current reference generator, and a PI-type current controller.
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"""
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docs/_downloads/1901236edeea2d2b57c3aeb0455fdb6c/plot_vhz_ctrl_im_2kw.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# 2.2-kW induction motor, diode bridge\n\nA diode bridge, stiff three-phase grid, and a DC link is modeled. The default\nparameters in this example yield open-loop V/Hz control. \n"
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"\n# 2.2-kW induction motor, diode bridge\n\nA diode bridge, stiff three-phase grid, and a DC link is modeled. The default\nparameters in this example yield open-loop V/Hz control.\n"
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]
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},
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{
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docs/_downloads/1a774b5e6ea2682176bf1201b07c962e/plot_obs_vhz_ctrl_syrm_7kw.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"\n# 6.7-kW SyRM, saturated\n\nThis example simulates observer-based V/Hz control of a saturated 6.7-kW\nsynchronous reluctance motor drive. The saturation is not taken into account in \nthe control method (only in the system model).\n"
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"\n# 6.7-kW SyRM, saturated\n\nThis example simulates observer-based V/Hz control of a saturated 6.7-kW\nsynchronous reluctance motor drive. The saturation is not taken into account in\nthe control method (only in the system model).\n"
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]
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},
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{
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},
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"outputs": [],
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"source": [
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"def i_s(psi_s):\n \"\"\"\n Magnetic model for a 6.7-kW synchronous reluctance motor.\n\n Parameters\n ----------\n psi_s : complex\n Stator flux linkage (Vs).\n\n Returns\n -------\n complex\n Stator current (A).\n\n Notes\n -----\n For nonzero `i_f`, the initial value of the stator flux linkage `psi_s0` \n needs to be solved, e.g., as follows::\n\n from scipy.optimize import minimize_scalar\n res = minimize_scalar(\n lambda psi_d: np.abs(\n (a_d0 + a_dd*np.abs(psi_d)**S)*psi_d - i_f))\n psi_s0 = complex(res.x)\n\n \"\"\"\n # Parameters\n a_d0, a_dd, S = 17.4, 373., 5 # d-axis self-saturation\n a_q0, a_qq, T = 52.1, 658., 1 # q-axis self-saturation\n a_dq, U, V = 1120., 1, 0 # Cross-saturation\n i_f = 0 # MMF of PMs\n # Inverse inductance functions\n G_d = a_d0 + a_dd*np.abs(psi_s.real)**S + (\n a_dq/(V + 2)*np.abs(psi_s.real)**U*np.abs(psi_s.imag)**(V + 2))\n G_q = a_q0 + a_qq*np.abs(psi_s.imag)**T + (\n a_dq/(U + 2)*np.abs(psi_s.real)**(U + 2)*np.abs(psi_s.imag)**V)\n # Stator current\n return G_d*psi_s.real - i_f + 1j*G_q*psi_s.imag"
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"def i_s(psi_s):\n \"\"\"\n Magnetic model for a 6.7-kW synchronous reluctance motor.\n\n Parameters\n ----------\n psi_s : complex\n Stator flux linkage (Vs).\n\n Returns\n -------\n complex\n Stator current (A).\n\n Notes\n -----\n For nonzero `i_f`, the initial value of the stator flux linkage `psi_s0`\n needs to be solved, e.g., as follows::\n\n from scipy.optimize import minimize_scalar\n res = minimize_scalar(\n lambda psi_d: np.abs(\n (a_d0 + a_dd*np.abs(psi_d)**S)*psi_d - i_f))\n psi_s0 = complex(res.x)\n\n \"\"\"\n # Parameters\n a_d0, a_dd, S = 17.4, 373., 5 # d-axis self-saturation\n a_q0, a_qq, T = 52.1, 658., 1 # q-axis self-saturation\n a_dq, U, V = 1120., 1, 0 # Cross-saturation\n i_f = 0 # MMF of PMs\n # Inverse inductance functions\n G_d = a_d0 + a_dd*np.abs(psi_s.real)**S + (\n a_dq/(V + 2)*np.abs(psi_s.real)**U*np.abs(psi_s.imag)**(V + 2))\n G_q = a_q0 + a_qq*np.abs(psi_s.imag)**T + (\n a_dq/(U + 2)*np.abs(psi_s.real)**(U + 2)*np.abs(psi_s.imag)**V)\n # Stator current\n return G_d*psi_s.real - i_f + 1j*G_q*psi_s.imag"
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]
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},
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{

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