.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "_autogenerated_examples/300_module_efficiency/module_efficiency_demo.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download__autogenerated_examples_300_module_efficiency_module_efficiency_demo.py>`
        to download the full example code.

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

.. _sphx_glr__autogenerated_examples_300_module_efficiency_module_efficiency_demo.py:


Module efficiency models
========================

Fit seven models to sample measurements and find the best one.

.. GENERATED FROM PYTHON SOURCE LINES 7-39

.. code-block:: Python


    from pvpltools.module_efficiency import (
        adr,
        heydenreich,
        motherpv,
        pvgis,
        mpm5,
        mpm6,
        bilinear,
    )
    from pvpltools.module_efficiency import fit_efficiency_model, fit_bilinear

    import numpy as np
    import pandas as pd
    import matplotlib
    import matplotlib.pyplot as plt

    from pathlib import Path
    import os

    # different current working directories for Sphinx-gallery / normal interpreter
    try:
        cwd = os.path.dirname(__file__)
    except NameError:
        cwd = os.getcwd()
    cwd = Path(cwd)

    matplotlib.style.use("classic")
    matplotlib.rcParams["figure.facecolor"] = "w"
    matplotlib.rcParams["axes.grid"] = True
    matplotlib.rcParams["lines.linewidth"] = 2








.. GENERATED FROM PYTHON SOURCE LINES 40-43

Now get some efficiency measurements to work with. A file containing
module matrix measurements can be downloaded from
the PVPMC website at https://pvpmc.sandia.gov/download/7701/.

.. GENERATED FROM PYTHON SOURCE LINES 43-73

.. code-block:: Python


    # this is the filename of the data file under "examples/data"
    measurements_file = cwd.parent.joinpath(
        "data", "Sandia_PV_Module_P-Matrix-and-TempCo-Data_2019.xlsx"
    )

    # The first sheet is for the Panasonic HIT module
    TYPE = "Panasonic HIT"

    matrix = pd.read_excel(
        measurements_file,
        sheet_name=0,
        usecols="B,C,H",
        header=None,
        skiprows=5,
        nrows=27,
    )
    matrix.columns = ["temperature", "irradiance", "p_mp"]

    # calculate efficiency from power
    matrix = matrix.eval("eta = p_mp / irradiance")
    eta_stc = matrix.query("irradiance == 1000 and temperature == 25").eta
    matrix.eta /= eta_stc.values

    # just keep the columns that are needed
    matrix = matrix[["irradiance", "temperature", "eta"]]

    matrix







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>irradiance</th>
          <th>temperature</th>
          <th>eta</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>100</td>
          <td>15</td>
          <td>0.935730</td>
        </tr>
        <tr>
          <th>1</th>
          <td>200</td>
          <td>15</td>
          <td>0.978227</td>
        </tr>
        <tr>
          <th>2</th>
          <td>400</td>
          <td>15</td>
          <td>1.007194</td>
        </tr>
        <tr>
          <th>3</th>
          <td>600</td>
          <td>15</td>
          <td>1.022552</td>
        </tr>
        <tr>
          <th>4</th>
          <td>800</td>
          <td>15</td>
          <td>1.027077</td>
        </tr>
        <tr>
          <th>5</th>
          <td>1000</td>
          <td>15</td>
          <td>1.026549</td>
        </tr>
        <tr>
          <th>6</th>
          <td>100</td>
          <td>25</td>
          <td>0.907523</td>
        </tr>
        <tr>
          <th>7</th>
          <td>200</td>
          <td>25</td>
          <td>0.948437</td>
        </tr>
        <tr>
          <th>8</th>
          <td>400</td>
          <td>25</td>
          <td>0.980789</td>
        </tr>
        <tr>
          <th>9</th>
          <td>600</td>
          <td>25</td>
          <td>0.994289</td>
        </tr>
        <tr>
          <th>10</th>
          <td>800</td>
          <td>25</td>
          <td>0.998903</td>
        </tr>
        <tr>
          <th>11</th>
          <td>1000</td>
          <td>25</td>
          <td>1.000000</td>
        </tr>
        <tr>
          <th>12</th>
          <td>1100</td>
          <td>25</td>
          <td>0.998982</td>
        </tr>
        <tr>
          <th>13</th>
          <td>100</td>
          <td>50</td>
          <td>0.833199</td>
        </tr>
        <tr>
          <th>14</th>
          <td>200</td>
          <td>50</td>
          <td>0.879565</td>
        </tr>
        <tr>
          <th>15</th>
          <td>400</td>
          <td>50</td>
          <td>0.908011</td>
        </tr>
        <tr>
          <th>16</th>
          <td>600</td>
          <td>50</td>
          <td>0.920241</td>
        </tr>
        <tr>
          <th>17</th>
          <td>800</td>
          <td>50</td>
          <td>0.925466</td>
        </tr>
        <tr>
          <th>18</th>
          <td>1000</td>
          <td>50</td>
          <td>0.927551</td>
        </tr>
        <tr>
          <th>19</th>
          <td>1100</td>
          <td>50</td>
          <td>0.926319</td>
        </tr>
        <tr>
          <th>20</th>
          <td>100</td>
          <td>75</td>
          <td>0.746943</td>
        </tr>
        <tr>
          <th>21</th>
          <td>200</td>
          <td>75</td>
          <td>0.792776</td>
        </tr>
        <tr>
          <th>22</th>
          <td>400</td>
          <td>75</td>
          <td>0.826435</td>
        </tr>
        <tr>
          <th>23</th>
          <td>600</td>
          <td>75</td>
          <td>0.842713</td>
        </tr>
        <tr>
          <th>24</th>
          <td>800</td>
          <td>75</td>
          <td>0.847741</td>
        </tr>
        <tr>
          <th>25</th>
          <td>1000</td>
          <td>75</td>
          <td>0.849045</td>
        </tr>
        <tr>
          <th>26</th>
          <td>1100</td>
          <td>75</td>
          <td>0.849035</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 74-76

it really is matrix data
this becomes more obvious when you pivot it

.. GENERATED FROM PYTHON SOURCE LINES 76-82

.. code-block:: Python


    grid = matrix.pivot(index="irradiance", columns="temperature", values="eta")

    grid







.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th>temperature</th>
          <th>15</th>
          <th>25</th>
          <th>50</th>
          <th>75</th>
        </tr>
        <tr>
          <th>irradiance</th>
          <th></th>
          <th></th>
          <th></th>
          <th></th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>100</th>
          <td>0.935730</td>
          <td>0.907523</td>
          <td>0.833199</td>
          <td>0.746943</td>
        </tr>
        <tr>
          <th>200</th>
          <td>0.978227</td>
          <td>0.948437</td>
          <td>0.879565</td>
          <td>0.792776</td>
        </tr>
        <tr>
          <th>400</th>
          <td>1.007194</td>
          <td>0.980789</td>
          <td>0.908011</td>
          <td>0.826435</td>
        </tr>
        <tr>
          <th>600</th>
          <td>1.022552</td>
          <td>0.994289</td>
          <td>0.920241</td>
          <td>0.842713</td>
        </tr>
        <tr>
          <th>800</th>
          <td>1.027077</td>
          <td>0.998903</td>
          <td>0.925466</td>
          <td>0.847741</td>
        </tr>
        <tr>
          <th>1000</th>
          <td>1.026549</td>
          <td>1.000000</td>
          <td>0.927551</td>
          <td>0.849045</td>
        </tr>
        <tr>
          <th>1100</th>
          <td>NaN</td>
          <td>0.998982</td>
          <td>0.926319</td>
          <td>0.849035</td>
        </tr>
      </tbody>
    </table>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 83-84

now fit my favorite model

.. GENERATED FROM PYTHON SOURCE LINES 84-94

.. code-block:: Python


    popt, pcov = fit_efficiency_model(
        matrix.irradiance,
        matrix.temperature,
        matrix.eta,
        adr,
    )
    popt






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

 .. code-block:: none


    array([ 0.99879112, -5.85209308,  0.01939665,  0.0696307 ,  0.21036569])



.. GENERATED FROM PYTHON SOURCE LINES 95-96

wait, it can't be that easy!

.. GENERATED FROM PYTHON SOURCE LINES 96-100

.. code-block:: Python


    adr(600, 15, *popt)






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

 .. code-block:: none


    np.float64(1.022515949060066)



.. GENERATED FROM PYTHON SOURCE LINES 101-102

yes it can

.. GENERATED FROM PYTHON SOURCE LINES 105-106

define some ranges for plotting

.. GENERATED FROM PYTHON SOURCE LINES 106-111

.. code-block:: Python


    ggg = np.logspace(-0.1, 3.1, 51)
    tt = np.array([0, 15, 25, 50, 75, 90])









.. GENERATED FROM PYTHON SOURCE LINES 112-113

Plot the results

.. GENERATED FROM PYTHON SOURCE LINES 113-124

.. code-block:: Python


    plt.figure()

    for t in tt:
        plt.plot(ggg, adr(ggg, t, *popt))

    plt.plot(grid, "ko")

    plt.title("Nice fit for model %s on module %s" % ("ADR", TYPE))





.. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_001.png
   :alt: Nice fit for model ADR on module Panasonic HIT
   :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    Text(0.5, 1.0, 'Nice fit for model ADR on module Panasonic HIT')



.. GENERATED FROM PYTHON SOURCE LINES 125-126

Gather plotting commands into a convenient function

.. GENERATED FROM PYTHON SOURCE LINES 126-154

.. code-block:: Python



    def plot_model(model, params):

        ggg = np.logspace(-0.1, 3.1, 51)
        tt = np.array([0, 15, 25, 50, 75, 90])

        plt.figure()
        plt.gca().set_prop_cycle(
            "color", plt.cm.rainbow(np.linspace(0, 1, len(tt)))
        )

        for t in tt:
            plt.plot(ggg, model(ggg, t, *params))

        plt.xlim(-50, 1350)
        plt.ylim(0.45, 1.15)
        plt.xlabel("Irradiance [W/m²]")
        plt.ylabel("Relative efficiency")
        plt.legend(tt, title="Temperature", ncol=2, loc="best")
        plt.title(model.__name__.upper())
        return plt.gca()


    ax = plot_model(adr, popt)
    ax.plot(grid, "ko")





.. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_002.png
   :alt: ADR
   :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_002.png
   :class: sphx-glr-single-img


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

 .. code-block:: none


    [<matplotlib.lines.Line2D object at 0x7fa8c2bc1f40>, <matplotlib.lines.Line2D object at 0x7fa8c2cba900>, <matplotlib.lines.Line2D object at 0x7fa8c2bc1dc0>, <matplotlib.lines.Line2D object at 0x7fa8c2c9ee40>]



.. GENERATED FROM PYTHON SOURCE LINES 155-156

now run and plot all the available models

.. GENERATED FROM PYTHON SOURCE LINES 156-170

.. code-block:: Python


    models = [bilinear, heydenreich, motherpv, pvgis, mpm5, mpm6, adr]

    for model in models:

        if model is bilinear:
            interpolator = fit_bilinear(**matrix)
            popt = [interpolator]
        else:
            popt, pcov = fit_efficiency_model(**matrix, model=model)
        plot_model(model, popt)
        plt.plot(grid, "ko")





.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_003.png
         :alt: BILINEAR
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_003.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_004.png
         :alt: HEYDENREICH
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_004.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_005.png
         :alt: MOTHERPV
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_005.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_006.png
         :alt: PVGIS
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_006.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_007.png
         :alt: MPM5
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_007.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_008.png
         :alt: MPM6
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_008.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_009.png
         :alt: ADR
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_009.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 171-172

make a function to calculate rms error

.. GENERATED FROM PYTHON SOURCE LINES 172-190

.. code-block:: Python



    def efficiency_model_rmse(irradiance, temperature, eta, model, p):

        from numpy import sqrt as root, mean, square

        eta_hat = model(irradiance, temperature, *p)

        return root(mean(square(eta_hat - eta)))


    rmse = efficiency_model_rmse(
        matrix.irradiance, matrix.temperature, matrix.eta, model, popt
    )

    print(TYPE, model.__name__.upper(), rmse)






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

 .. code-block:: none

    Panasonic HIT ADR 0.002028199009144769




.. GENERATED FROM PYTHON SOURCE LINES 191-192

compare the models

.. GENERATED FROM PYTHON SOURCE LINES 192-206

.. code-block:: Python


    for model in models:

        if model is bilinear:
            interpolator = fit_bilinear(**matrix)
            popt = [interpolator]
        else:
            popt, pcov = fit_efficiency_model(**matrix, model=model)

        rmse = efficiency_model_rmse(**matrix, model=model, p=popt)

        print("%20s, %-20s %.5f" % (TYPE, model.__name__.upper(), rmse))






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

 .. code-block:: none

           Panasonic HIT, BILINEAR             2.30300
           Panasonic HIT, HEYDENREICH          0.00605
           Panasonic HIT, MOTHERPV             0.00249
           Panasonic HIT, PVGIS                0.00158
           Panasonic HIT, MPM5                 0.00291
           Panasonic HIT, MPM6                 0.00279
           Panasonic HIT, ADR                  0.00203




.. GENERATED FROM PYTHON SOURCE LINES 207-208

now run one of the harder tests: extrapolating to the low irradiance values

.. GENERATED FROM PYTHON SOURCE LINES 208-225

.. code-block:: Python


    subset_fit = matrix.query("irradiance >  200")
    subset_err = matrix.query("irradiance <= 200")

    for model in models:

        if model is bilinear:
            interpolator = fit_bilinear(**subset_fit)
            popt = [interpolator]
        else:
            popt, pcov = fit_efficiency_model(**subset_fit, model=model)

        rmse = efficiency_model_rmse(**subset_err, model=model, p=popt)

        print("%20s, %-20s %.5f" % (TYPE, model.__name__.upper(), rmse))






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

 .. code-block:: none

           Panasonic HIT, BILINEAR             0.40747
           Panasonic HIT, HEYDENREICH          0.02965
           Panasonic HIT, MOTHERPV             0.15097
           Panasonic HIT, PVGIS                0.02889
           Panasonic HIT, MPM5                 0.00490
           Panasonic HIT, MPM6                 0.08156
           Panasonic HIT, ADR                  0.00401




.. GENERATED FROM PYTHON SOURCE LINES 226-227

the graphs make these differences more striking

.. GENERATED FROM PYTHON SOURCE LINES 227-239

.. code-block:: Python


    for model in models:

        if model is bilinear:
            interpolator = fit_bilinear(**subset_fit)
            popt = [interpolator]
        else:
            popt, pcov = fit_efficiency_model(**subset_fit, model=model)
        plot_model(model, popt)
        plt.plot(grid, "ko")





.. rst-class:: sphx-glr-horizontal


    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_010.png
         :alt: BILINEAR
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_010.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_011.png
         :alt: HEYDENREICH
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_011.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_012.png
         :alt: MOTHERPV
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_012.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_013.png
         :alt: PVGIS
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_013.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_014.png
         :alt: MPM5
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_014.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_015.png
         :alt: MPM6
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_015.png
         :class: sphx-glr-multi-img

    *

      .. image-sg:: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_016.png
         :alt: ADR
         :srcset: /_autogenerated_examples/300_module_efficiency/images/sphx_glr_module_efficiency_demo_016.png
         :class: sphx-glr-multi-img





.. GENERATED FROM PYTHON SOURCE LINES 240-243

just one small detail missing:
the last parameter of MPM6 should not be larger than zero
so bounds need to be defined for all its parameters

.. GENERATED FROM PYTHON SOURCE LINES 243-266

.. code-block:: Python


    MPM6_BOUNDS = (
        [
            -np.inf,
            -np.inf,
            -np.inf,
            -np.inf,
            -np.inf,
        ],
        [+np.inf, +np.inf, +np.inf, +np.inf, 0.0],
    )

    model = mpm6

    popt, pcov = fit_efficiency_model(
        **subset_fit, model=model, bounds=MPM6_BOUNDS
    )
    rmse = efficiency_model_rmse(**subset_err, model=model, p=popt)

    print("%-20s %-20s RMSE = %.5f" % (TYPE, model.__name__.upper(), rmse))
    print("popt =", popt)






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

 .. code-block:: none

    Panasonic HIT        MPM6                 RMSE = 0.08156
    popt = [ 1.03574966 -0.00299249 -0.04758015 -0.00717004 -0.0290341 ]




.. GENERATED FROM PYTHON SOURCE LINES 267-268

in this case the bounds did not influence the result


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

   **Total running time of the script:** (0 minutes 1.846 seconds)


.. _sphx_glr_download__autogenerated_examples_300_module_efficiency_module_efficiency_demo.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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