motulator_multiphase.utils#

Utilities for multi-three-phase machine drives.

The machine has n three-phase winding sets. The phase a of the set k is located at the angle theta_sets[k] with respect to the stationary α axis. The space vector of the set k in its own coordinates is abc2complex(x_abc_k), and in the common stationary coordinates exp(1j*theta_sets[k])*abc2complex(x_abc_k).

The decoupled multi-stator (DMS) transformation maps the space vectors of the sets in the common stationary coordinates to the common mode (CM) and n - 1 differential modes (DMs), see dms_matrix(). For two sets, x_cm = (x_1 + x_2)/2 and x_dm = (x_1 - x_2)/2. Including the set angles, the modes are D @ x_sets, where D = T*exp(1j*theta_sets) and x_sets are the set vectors in their own coordinates, and the inverse is n*D.conj().T.

The plotting function and the base values of motulator are re-exported for convenience.

Functions#

`default_set_angles`(n_sets)	Angles of the winding sets of an asymmetrical multi-three-phase machine.
`dms_matrix`(n_sets)	Decoupled multi-stator (DMS) transformation matrix.
`plot_sets`(res[, t_lims, latex, save_path])	Plot the set and differential-mode currents.
`to_parallel`(par, n_sets)	Parameters of the equivalent machine with the sets connected in parallel.

Module Contents#

motulator_multiphase.utils.default_set_angles(n_sets)[source]#

Angles of the winding sets of an asymmetrical multi-three-phase machine.

The sets are displaced by pi/(3*n_sets), e.g., 30° for a dual-three-phase machine and 15° for a quadruple-three-phase machine.

Parameters:: n_sets (int) – Number of three-phase sets.
Returns:: Angles (rad) of the phases a of the sets.
Return type:: ndarray, shape (n_sets,)

Examples

>>> from motulator_multiphase.utils import default_set_angles
>>> np.degrees(default_set_angles(2))
array([ 0., 30.])

motulator_multiphase.utils.dms_matrix(n_sets)[source]#

Decoupled multi-stator (DMS) transformation matrix.

The transformation maps the space vectors of the sets in common coordinates to the common mode and the differential modes [1]. The first row gives the common mode as the mean of the sets. The other rows give the differential modes, x_dm_u ∝ (n - u)*x_u - sum(x_{u+1}, …, x_n). The rows are orthogonal and scaled such that the inverse is n_sets*T.T.

Parameters:: n_sets (int) – Number of three-phase sets.
Returns:: Transformation matrix.
Return type:: ndarray, shape (n_sets, n_sets)

References

Examples

>>> from motulator_multiphase.utils import dms_matrix
>>> dms_matrix(2)
array([[ 0.5,  0.5],
       [ 0.5, -0.5]])
>>> T = dms_matrix(4)
>>> bool(np.allclose(4 * T.T @ T, np.eye(4)))
True

motulator_multiphase.utils.plot_sets(res, t_lims=None, latex=False, save_path=None, **savefig_kwargs)[source]#

Plot the set and differential-mode currents.

The first subplot shows the current magnitudes of the sets. The second subplot shows the DM currents in the controller coordinates (d solid, q dash-dotted) and their references (black dashed).

Parameters:

res (SimulationResults) – Simulation results of a multi-three-phase drive.
t_lims (tuple[float, float], optional) – Time axis limits. If None, uses full time range.
latex (bool, optional) – Use LaTeX fonts for the labels, defaults to False.
save_path (str | Path, optional) – Path to save the figure. If None, the figure is not saved.
**savefig_kwargs – Additional keyword arguments passed to plt.savefig().

Return type:

None

motulator_multiphase.utils.to_parallel(par, n_sets)[source]#

Parameters of the equivalent machine with the sets connected in parallel.

The given parameters describe one three-phase set, when all sets carry equal currents (i.e., the common mode only). When the sets are connected in parallel, the voltages and the flux linkages remain unchanged, while the currents are multiplied by n_sets. Hence, the resistances and inductances are divided by n_sets, and the core-loss conductance is multiplied by it. The equivalent machine produces the total torque of the machine. The maps of saturated machines are scaled accordingly, keeping their analytic Jacobians (e.g., of GradNet flux maps).

Parameters:

par (MachinePars) – Parameters of one set (balanced operation of all sets).
n_sets (int) – Number of three-phase sets.

Returns:

Parameters of the equivalent three-phase machine, of the same type as par.

Return type:

MachinePars

Examples

>>> from motulator_multiphase import model, utils
>>> par = model.SynchronousMachinePars(
...     n_p=3, R_s=3.6, L_d=0.036, L_q=0.051, psi_f=0.545
... )
>>> utils.to_parallel(par, 2)
SynchronousMachinePars(n_p=3, R_s=1.8, L_d=0.018, L_q=0.0255, psi_f=0.545, G_c=0.0)