motulator-multiphase

Multi-three-phase machine drives for motulator

Documentation: https://aalto-electric-drives.github.io/motulator-multiphase/

This package extends motulator with models and control of machines having n three-phase winding sets (e.g., dual-three-phase machines), each set supplied by its own converter. The models and the control are based on the decoupled multi-stator (DMS) transformation [1], which maps the sets to the common mode (CM) and n − 1 differential modes (DMs). The CM is equivalent to a three-phase machine whose sets are connected in parallel, so the machine models and vector controllers of motulator (synchronous and induction machines, flux-vector and current-vector control, sensored and sensorless) are reused for it. The DMs are resistive-inductive circuits, controlled by complex-vector PI current controllers, and the current sharing between the sets can be changed during operation.

Installation

Install the package in a virtual environment (motulator is installed as a dependency). On Linux and macOS:

python3 -m venv .venv
source .venv/bin/activate
pip install motulator-multiphase

On Windows, the environment is created and activated with py -m venv .venv and .venv\Scripts\activate.

For development, clone the repository and install the package with pip install -e ".[dev]".

Usage

A sensorless flux-vector-controlled dual-three-phase IPMSM drive, whose sets are displaced by 30°:

from math import pi

import motulator.drive.control.sm as sm_control
from motulator_multiphase import control, model, utils

# System model: the parameters describe one three-phase set, when both sets carry
# equal currents, and L_ls is the leakage inductance not coupled to the other set
par = model.SynchronousMachinePars(n_p=3, R_s=3.6, L_d=0.036, L_q=0.051, psi_f=0.545)
machine = model.MultiThreePhaseMachine(par, L_ls=0.005, n_sets=2)
converter = model.MultiThreePhaseConverter(u_dc=540, n_sets=2)
mdl = model.MultiThreePhaseDrive(machine, model.MechanicalSystem(J=0.03), converter)

# Control system: the flux-vector controller of motulator for the CM, parametrized
# with the parallel-connected equivalent machine, and a current controller for the DM
est_par = utils.to_parallel(par, 2)
cfg = sm_control.FluxVectorControllerCfg(i_s_max=18, sensorless=True)
vector_ctrl = sm_control.FluxVectorController(est_par, cfg)
dm_ctrl = control.DifferentialModeController(L_ls=0.005, n_sets=2)
speed_ctrl = sm_control.SpeedController(J=0.03, alpha_s=2 * pi * 4)
ctrl = control.MultiThreePhaseControlSystem(vector_ctrl, dm_ctrl, speed_ctrl)

# Speed reference, load torque, and current sharing (75% in the first set at the end)
ctrl.set_speed_ref(lambda t: (t > 0.2) * 150)
mdl.mechanics.set_external_load_torque(lambda t: (t > 0.8) * 28)
ctrl.set_current_sharing(lambda t: [1.5, 0.5] if t > 1.2 else [1.0, 1.0])

res = model.Simulation(mdl, ctrl).simulate(t_stop=1.6)
utils.plot(res)  # CM quantities, the current being the sum of the set currents
utils.plot_sets(res)  # Set currents and DM currents

The sets are displaced by 60°/n by default (30° for a dual-three-phase machine); other arrangements are given with theta_sets. Complete examples are in the example gallery.

Scope

• Identical sets, any number n ≥ 1; a drive with one set equals the three-phase drive of motulator.
• The saturated machine models and GradNet flux maps of motulator can be used for the CM, see utils.to_parallel.
• Each DM is a resistive-inductive circuit of the stator resistance and the leakage inductance of a set; it is not saturated and produces no torque.
• Gate blocking (standby control) is not supported.

References

1. Rubino, Dordevic, Armando, Bojoi, Levi, "A novel matrix transformation for decoupled control of modular multiphase PMSM drives," IEEE Trans. Power Electron., 2021, https://doi.org/10.1109/TPEL.2020.3043083

Contributors

Sandro Rubino 🤔 🔬

Marko Hinkkanen 💻 💡