.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/electrical_engineering/ac_circuits/plot_01_stanley_transformer.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_ac_circuits_plot_01_stanley_transformer.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_ac_circuits_plot_01_stanley_transformer.py:


Stanley's transformer (1886)
============================

In March 1886 William Stanley, working for George Westinghouse, lit the
shops of Great Barrington, Massachusetts, from a 500 V alternator through
transformers that stepped the voltage down to 100 V at each building. His
design, refined from the Gaulard-Gibbs secondary generator and the
Hungarian ZBD transformer of 1885, had a closed iron core and windings in
parallel across the line. An ideal transformer scales voltage by the turns
ratio, :math:`V_2 = V_1 N_2/N_1`
(:func:`~engineeringkit.electrical_engineering.transformer_secondary`),
current by its inverse and impedance by its square. This example shows why
that made AC distribution win: stepping up the voltage cuts line losses by
the square of the ratio.

.. GENERATED FROM PYTHON SOURCE LINES 19-24

.. code-block:: Python

    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.electrical_engineering import transformer_secondary








.. GENERATED FROM PYTHON SOURCE LINES 25-27

Voltage, current and impedance
------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 27-38

.. code-block:: Python


    N1, N2 = 500, 100
    V1 = 500.0
    V2 = transformer_secondary(V1, N1, N2)
    R_load = 10.0
    I2 = V2 / R_load
    I1 = I2 * N2 / N1
    print(f"V2 = {V2:.0f} V, I2 = {I2:.1f} A, I1 = {I1:.1f} A")
    assert np.isclose(V1 * I1, V2 * I2)  # an ideal transformer is lossless
    assert np.isclose(V1 / I1, R_load * (N1 / N2) ** 2)  # load reflected by the turns ratio squared





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

 .. code-block:: none

    V2 = 100 V, I2 = 10.0 A, I1 = 2.0 A




.. GENERATED FROM PYTHON SOURCE LINES 39-44

Why step up?
------------

Deliver 100 kW over a line of 2 ohm total resistance, stepping a 1 kV
generator up to different voltages.

.. GENERATED FROM PYTHON SOURCE LINES 44-58

.. code-block:: Python


    P, R_line, V_gen = 100e3, 2.0, 1e3
    ratios = np.array([1, 2, 5, 10, 20, 50])
    V_line = transformer_secondary(V_gen, 1, ratios)
    loss = (P / V_line) ** 2 * R_line
    for r, vl, lo in zip(ratios, V_line, loss):
        print(f"1:{r:<3d} {vl / 1e3:5.0f} kV line, loss {lo / P:7.3%} of the power")
    assert np.allclose(loss[0] / loss, ratios**2)

    fig, ax = plt.subplots()
    ax.loglog(V_line / 1e3, loss / P * 100, "o-")
    ax.set(xlabel="transmission voltage [kV]", ylabel="line loss [% of delivered power]", title="Loss falls as 1/V²")

    plt.show()



.. image-sg:: /api/gallery/electrical_engineering/ac_circuits/images/sphx_glr_plot_01_stanley_transformer_001.png
   :alt: Loss falls as 1/V²
   :srcset: /api/gallery/electrical_engineering/ac_circuits/images/sphx_glr_plot_01_stanley_transformer_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    1:1       1 kV line, loss 20.000% of the power
    1:2       2 kV line, loss  5.000% of the power
    1:5       5 kV line, loss  0.800% of the power
    1:10     10 kV line, loss  0.200% of the power
    1:20     20 kV line, loss  0.050% of the power
    1:50     50 kV line, loss  0.008% of the power





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

   **Total running time of the script:** (0 minutes 0.034 seconds)


.. _sphx_glr_download_api_gallery_electrical_engineering_ac_circuits_plot_01_stanley_transformer.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/ac_circuits/plot_01_stanley_transformer.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_01_stanley_transformer.ipynb <plot_01_stanley_transformer.ipynb>`

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

      :download:`Download Python source code: plot_01_stanley_transformer.py <plot_01_stanley_transformer.py>`

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

      :download:`Download zipped: plot_01_stanley_transformer.zip <plot_01_stanley_transformer.zip>`


.. only:: html

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

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