.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/power/plot_01_tesla_three_phase.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_electrical_engineering_power_plot_01_tesla_three_phase.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_electrical_engineering_power_plot_01_tesla_three_phase.py:


Tesla's polyphase system (1888)
===============================

In May 1888 Nikola Tesla presented "A new system of alternate current
motors and transformers" to the American Institute of Electrical
Engineers. Currents displaced in phase produce a rotating magnetic field,
which drives an induction motor with no commutator. Polyphase supply has a
second advantage that Mikhail Dolivo-Dobrovolsky exploited with three
phases in 1889-1891: a balanced three-phase load draws *constant*
instantaneous power, :math:`\sqrt3 V_L I_L \cos\phi`
(:func:`~engineeringkit.electrical_engineering.three_phase_power`), and the
three return currents cancel, so three wires do the work of six. This
example checks both, and draws the rotating field.

.. GENERATED FROM PYTHON SOURCE LINES 18-23

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.electrical_engineering import real_power, three_phase_power








.. GENERATED FROM PYTHON SOURCE LINES 24-26

Constant power from three pulsating phases
------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 26-41

.. code-block:: Python


    V_phase, I_line, phi, f = 230.0, 16.0, np.radians(30), 50.0
    w = 2 * np.pi * f
    t = np.linspace(0, 2 / f, 1000)
    shifts = np.array([0, -2 * np.pi / 3, 2 * np.pi / 3])
    v = np.sqrt(2) * V_phase * np.cos(w * t[:, None] + shifts)
    i = np.sqrt(2) * I_line * np.cos(w * t[:, None] + shifts - phi)
    p_phase = v * i
    p_total = p_phase.sum(axis=1)
    P = three_phase_power(np.sqrt(3) * V_phase, I_line, np.cos(phi))
    print(f"three-phase power {P / 1e3:.3f} kW; instantaneous total varies by {np.ptp(p_total):.1e} W")
    assert np.allclose(p_total, P)
    assert np.isclose(P, 3 * real_power(V_phase, I_line, np.cos(phi)))
    assert np.allclose(i.sum(axis=1), 0, atol=1e-9)  # no neutral current





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    three-phase power 9.561 kW; instantaneous total varies by 2.4e-11 W




.. GENERATED FROM PYTHON SOURCE LINES 42-47

The rotating field
------------------

Three coils 120 degrees apart, fed by the three currents, add up to a
field of constant magnitude turning at the supply frequency.

.. GENERATED FROM PYTHON SOURCE LINES 47-63

.. code-block:: Python


    coil_dirs = np.exp(1j * np.array([0, 2 * np.pi / 3, 4 * np.pi / 3]))
    field = (np.cos(w * t[:, None] + shifts) * coil_dirs).sum(axis=1)
    assert np.allclose(np.abs(field), 1.5)

    fig, axes = plt.subplots(1, 2, figsize=(10, 3.8))
    axes[0].plot(t * 1e3, p_phase / 1e3, lw=0.8)
    axes[0].plot(t * 1e3, p_total / 1e3, "k", label="sum of the three phases")
    axes[0].set(xlabel="time [ms]", ylabel="power [kW]", title="Instantaneous power")
    axes[0].legend()
    axes[1].plot(field.real, field.imag)
    axes[1].set_aspect("equal")
    axes[1].set(title="Tip of the rotating field", xlabel="x", ylabel="y")
    fig.tight_layout()

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/power/images/sphx_glr_plot_01_tesla_three_phase_001.png
   :alt: Instantaneous power, Tip of the rotating field
   :srcset: /api/gallery/electrical_engineering/power/images/sphx_glr_plot_01_tesla_three_phase_001.png
   :class: sphx-glr-single-img






.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.052 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_power_plot_01_tesla_three_phase.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../../lite/lab/index.html?path=api/gallery/electrical_engineering/power/plot_01_tesla_three_phase.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_01_tesla_three_phase.ipynb <plot_01_tesla_three_phase.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_01_tesla_three_phase.py <plot_01_tesla_three_phase.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_01_tesla_three_phase.zip <plot_01_tesla_three_phase.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_