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Add a simple transformer effficiency model to pvlib (#2053)
* wrote a simple transformer efficiency model * edited documentation to include latex, unsure if it will compile correctly in docs. * removed "if __main__" * removed "if __main__" * changed whatsnew rst * updated to be in compliance with Flake8 * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * + added transformer to index.rst + added transformer.rst to pvlib/docs/source/sphinx/reference * Update docs/sphinx/source/reference/transformer.rst Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * updated names of loss values and changed to [unitless] * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * forgot to update arguments in test function * updated formatting of docstring * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * adding space between equations in docstring * fixing flake8 linting * removing whitespace * Update docs/sphinx/source/reference/transformer.rst Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Cliff Hansen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update docs/sphinx/source/whatsnew/v0.11.0.rst Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/tests/test_transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Kevin Anderson <[email protected]> * Update pvlib/transformer.py Co-authored-by: Kevin Anderson <[email protected]> * Update docs/sphinx/source/whatsnew/v0.11.0.rst Co-authored-by: Adam R. Jensen <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * Update pvlib/transformer.py Co-authored-by: Echedey Luis <[email protected]> * clean up derivation and docstring * change code calculations to match docstring * test recovery of no-load and full-load values * bit more cleanup * typo * Apply suggestions from code review Co-authored-by: Cliff Hansen <[email protected]> * Apply suggestions from code review --------- Co-authored-by: Cliff Hansen <[email protected]> Co-authored-by: Echedey Luis <[email protected]> Co-authored-by: Kevin Anderson <[email protected]> Co-authored-by: Adam R. Jensen <[email protected]>
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‎docs/sphinx/source/reference/index.rst

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@@ -20,3 +20,4 @@ API reference
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bifacial
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scaling
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location
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transformer

‎docs/sphinx/source/reference/transformer.rst

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.. currentmodule:: pvlib
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Transformer losses
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==================
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Methods to account for losses in transformers
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.. autosummary::
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:toctree: generated/
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transformer.simple_efficiency

‎docs/sphinx/source/whatsnew/v0.11.0.rst

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Enhancements
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~~~~~~~~~~~~
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* Add a simple transformer efficiency model :py:func:`pvlib.transformer.simple_efficiency`.
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(:issue:`1269`, :pull:`2053`)
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* Add function :py:func:`pvlib.shading.shaded_fraction1d`, to calculate the
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shade perpendicular to ``axis_azimuth``. The function is applicable to both
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fixed-tilt and one-axis tracking systems.
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Contributors
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~~~~~~~~~~~~
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* Cliff Hansen (:ghuser:`cwhanse`)
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* Kurt Rhee (:ghuser:`kurt-rhee`)
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* Mark Mikofski (:ghuser:`mikofski`)
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* Siddharth Kaul (:ghuser:`k10blogger`)
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* Ioannis Sifnaios (:ghuser:`IoannisSifnaios`)

‎pvlib/tests/test_transformer.py

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import pandas as pd
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from numpy.testing import assert_allclose
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from pvlib import transformer
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def test_simple_efficiency():
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# define test inputs
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input_power = pd.Series([
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-800.0,
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436016.609823837,
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1511820.16603752,
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1580687.44677249,
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1616441.79660171
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])
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no_load_loss = 0.002
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load_loss = 0.007
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transformer_rating = 2750000
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# define expected test results
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expected_output_power = pd.Series([
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-6300.10103234071,
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430045.854892526,
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1500588.39919874,
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1568921.77089526,
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1604389.62839879
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])
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# run test function with test inputs
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calculated_output_power = transformer.simple_efficiency(
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input_power=input_power,
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no_load_loss=no_load_loss,
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load_loss=load_loss,
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transformer_rating=transformer_rating
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)
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# determine if expected results are obtained
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assert_allclose(calculated_output_power, expected_output_power)
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def test_simple_efficiency_known_values():
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no_load_loss = 0.005
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load_loss = 0.01
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rating = 1000
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args = (no_load_loss, load_loss, rating)
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# verify correct behavior at no-load condition
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assert_allclose(
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transformer.simple_efficiency(no_load_loss*rating, *args),
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0.0
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)
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# verify correct behavior at rated condition
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assert_allclose(
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transformer.simple_efficiency(rating*(1 + no_load_loss + load_loss),
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*args),
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rating,
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)

‎pvlib/transformer.py

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"""
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This module contains functions for transformer modeling.
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Transformer models calculate AC power output and losses at a given input power.
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"""
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def simple_efficiency(
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input_power, no_load_loss, load_loss, transformer_rating
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):
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r'''
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Calculate the power at the output terminal of the transformer
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after taking into account efficiency using a simple calculation.
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The equation used in this function can be derived from [1]_.
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For a zero input power, the output power will be negative.
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This means the transformer will consume energy from the grid at night if
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it stays connected (due to the parallel impedance in the equivalent
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circuit).
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If the input power is negative, the output power will be even more
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negative; so the model can be used bidirectionally when drawing
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energy from the grid.
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Parameters
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----------
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input_power : numeric
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The real AC power input to the transformer. [W]
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no_load_loss : numeric
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The constant losses experienced by a transformer, even
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when the transformer is not under load. Fraction of transformer rating,
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value from 0 to 1. [unitless]
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load_loss: numeric
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The load dependent losses experienced by the transformer.
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Fraction of transformer rating, value from 0 to 1. [unitless]
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transformer_rating: numeric
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The nominal output power of the transformer. [VA]
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Returns
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-------
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output_power : numeric
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Real AC power output. [W]
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Notes
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-------
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First, assume that the load loss :math:`L_{load}` (as a fraction of rated power
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:math:`P_{nom}`) is proportional to the square of output power:
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.. math::
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L_{load}(P_{out}) &= L_{load}(P_{rated}) \times (P_{out} / P_{nom})^2
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&= L_{full, load} \times (P_{out} / P_{nom})^2
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Total loss is the constant no-load loss plus the variable load loss:
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.. math::
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L_{total}(P_{out}) &= L_{no, load} + L_{load}(P_{out})
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&= L_{no, load} + L_{full, load} \times (P_{out} / P_{nom})^2
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By conservation of energy, total loss is the difference between input and
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output power:
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.. math::
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\frac{P_{in}}{P_{nom}} &= \frac{P_{out}}{P_{nom}} + L_{total}(P_{out})
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&= \frac{P_{out}}{P_{nom}} + L_{no, load} + L_{full, load} \times (P_{out} / P_{nom})^2
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Now use the quadratic formula to solve for :math:`P_{out}` as a function of
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:math:`P_{in}`.
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.. math::
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\frac{P_{out}}{P_{nom}} &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
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a &= L_{full, load}
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b &= 1
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c &= L_{no, load} - P_{in} / P_{nom}
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Therefore:
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.. math::
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P_{out} = P_{nom} \frac{-1 \pm \sqrt{1 - 4 L_{full, load}
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\times (L_{no, load} - P_{in}/P_{nom})}}{2 L_{full, load}}
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The positive root should be chosen, so that the output power is
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positive.
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References
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----------
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.. [1] Central Station Engineers of the Westinghouse Electric Corporation,
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"Electrical Transmission and Distribution Reference Book" 4th Edition.
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pg. 101.
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''' # noqa: E501
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input_power_normalized = input_power / transformer_rating
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a = load_loss
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b = 1
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c = no_load_loss - input_power_normalized
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output_power_normalized = (-b + (b**2 - 4*a*c)**0.5) / (2 * a)
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output_power = output_power_normalized * transformer_rating
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return output_power

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