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Merged
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Aug 14, 2020
Merged

Add function to fit Sandia inverter model #1011

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7de7a77
WIP: fitting inverter model
cwhanse Jun 22, 2020
31f0407
correct calculated data, improve test
cwhanse Jun 25, 2020
4426306
Merge branch 'master' of https://github.com/pvlib/pvlib-python into i…
cwhanse Jul 24, 2020
0391eb0
move code to pvlib modules, rename data file
cwhanse Jul 24, 2020
e7c1594
fix test, stickler
cwhanse Jul 24, 2020
c38679f
sort out np.polyfit vs. np.polynomial.polynomial.polyfit
cwhanse Jul 24, 2020
b67766d
correct file name
cwhanse Jul 24, 2020
c0f96dd
api, whatsnew
cwhanse Jul 24, 2020
3b37893
docstring improvements
cwhanse Jul 24, 2020
ae4380f
revisions from review
cwhanse Aug 4, 2020
ecce111
correct use of np.roots
cwhanse Aug 4, 2020
303ab1c
use pytest.approx instead of converting dicts to np.array
cwhanse Aug 4, 2020
768d39d
correct kwarg for pytest.approx
cwhanse Aug 5, 2020
e8662fb
back to solve_quad instead of np.roots, lint
cwhanse Aug 5, 2020
a9bd4bf
Merge branch 'master' of https://github.com/pvlib/pvlib-python into i…
cwhanse Aug 9, 2020
de6916c
change to Series inputs
cwhanse Aug 13, 2020
3d38e6c
correct test, Series to array_like
cwhanse Aug 14, 2020
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29 changes: 19 additions & 10 deletions docs/sphinx/source/api.rst
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Expand Up @@ -265,6 +265,15 @@ Low-level functions for solving the single diode equation.
singlediode.bishop88_v_from_i
singlediode.bishop88_mpp

Functions for fitting diode models

.. autosummary::
:toctree: generated/

ivtools.fit_sde_sandia
ivtools.fit_sdm_cec_sam
ivtools.fit_sdm_desoto

Inverter models (DC to AC conversion)
-------------------------------------

Expand All @@ -275,6 +284,16 @@ Inverter models (DC to AC conversion)
inverter.adr
inverter.pvwatts

Functions for fitting inverter models

.. autosummary::
:toctree: generated/

inverter.fit_sandia

Functions for fitting inverter models


PV System Models
----------------

Expand Down Expand Up @@ -311,16 +330,6 @@ PVWatts model
inverter.pvwatts
pvsystem.pvwatts_losses

Functions for fitting diode models
----------------------------------

.. autosummary::
:toctree: generated/

ivtools.fit_sde_sandia
ivtools.fit_sdm_cec_sam
ivtools.fit_sdm_desoto

Other
-----

Expand Down
2 changes: 2 additions & 0 deletions docs/sphinx/source/whatsnew/v0.8.0.rst
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Expand Up @@ -38,6 +38,8 @@ Enhancements
* Add :py:func:`pvlib.iam.marion_diffuse` and
:py:func:`pvlib.iam.marion_integrate` to calculate IAM values for
diffuse irradiance. (:pull:`984`)
* Add :py:func:`pvlib.inverter.fit_sandia` that fits the Sandia inverter model
to a set of inverter efficiency curves. (:pull:`1011`)

Bug fixes
~~~~~~~~~
Expand Down
127 changes: 127 additions & 0 deletions pvlib/data/inverter_fit_snl_meas.csv
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@@ -0,0 +1,127 @@
fraction_of_rated_power,dc_voltage_level,ac_power,dc_voltage,efficiency
0.1,Vmin,32800,660.5,0.95814
0.2,Vmin,73000,660.9,0.9755
0.3,Vmin,107500,660.73,0.97787
0.5,Vmin,168100,660.1,0.97998
0.75,Vmin,235467,660.27,0.97785
1,Vmin,318067,660.03,0.97258
0.1,Vnom,32800,740.1,0.95441
0.2,Vnom,72900,740.2,0.96985
0.3,Vnom,107600,740.13,0.97611
0.5,Vnom,167500,740.57,0.97554
0.75,Vnom,234967,741.87,0.97429
1,Vnom,317267,737.7,0.97261
0.1,Vmax,32800,959.07,0.94165
0.2,Vmax,71600,959.43,0.95979
0.3,Vmax,107300,959.1,0.96551
0.5,Vmax,166700,959.5,0.96787
0.75,Vmax,234767,958.8,0.96612
1,Vmax,317467,957,0.96358
0.1,Vmin,32800,660.77,0.95721
0.2,Vmin,73000,660.77,0.97247
0.3,Vmin,107500,660.47,0.97668
0.5,Vmin,168100,660.23,0.98018
0.75,Vmin,235333.3333,660.3,0.97716
1,Vmin,317466.6667,659.8,0.97184
0.1,Vnom,32800,740.27,0.95534
0.2,Vnom,72900,740.27,0.97071
0.3,Vnom,107600,740.2,0.97523
0.5,Vnom,167500,740.8,0.97592
0.75,Vnom,234966.6667,741.67,0.97429
1,Vnom,317300,737.97,0.97252
0.1,Vmax,32800,959.23,0.93718
0.2,Vmax,71600,959.4,0.96107
0.3,Vmax,107300,959.27,0.96638
0.5,Vmax,166700,959.57,0.96825
0.75,Vmax,234733.3333,959.17,0.96731
1,Vmax,317466.6667,957.07,0.96241
0.1,Vmin,32800,660.57,0.95814
0.2,Vmin,73000,660.67,0.97333
0.3,Vmin,107500,660.5,0.97609
0.5,Vmin,168100,660.1,0.97884
0.75,Vmin,235066.6667,660.3,0.97781
1,Vmin,316900,659.27,0.97209
0.1,Vnom,32800,740.17,0.95441
0.2,Vnom,72900,740.27,0.97028
0.3,Vnom,107600,740.23,0.97464
0.5,Vnom,167500,740.3,0.97573
0.75,Vnom,235133.3333,742.13,0.97417
1,Vnom,317300,737.9,0.97252
0.1,Vmax,32800,959.2,0.93626
0.2,Vmax,71600,959.43,0.95979
0.3,Vmax,107300,959.2,0.96493
0.5,Vmax,166700,959.5,0.96806
0.75,Vmax,234833.3333,958.97,0.96573
1,Vmax,317400,956.87,0.96279
0.1,Vmin,32800,660.63,0.95627
0.2,Vmin,73000,660.9,0.97377
0.3,Vmin,107500,661.07,0.97846
0.5,Vmin,168100,660.13,0.97827
0.75,Vmin,235200,660.43,0.97701
1,Vmin,316933.3333,660.07,0.97308
0.1,Vnom,32800,740.27,0.95441
0.2,Vnom,72900,740.37,0.96985
0.3,Vnom,107600,740.27,0.97464
0.5,Vnom,167500,740.53,0.97592
0.75,Vnom,234800,742.13,0.97374
1,Vnom,317300,737.73,0.97202
0.1,Vmax,32800,959.2,0.93271
0.2,Vmax,71600,959.27,0.95594
0.3,Vmax,107300,959.2,0.96783
0.5,Vmax,166700,959.47,0.96806
0.75,Vmax,234700,958.67,0.96505
1,Vmax,317433.3333,956.8,0.96299
0.1,Vmin,32800,660.67,0.95534
0.2,Vmin,73000,660.8,0.9755
0.3,Vmin,107500,661.23,0.97905
0.5,Vmin,168100,660.33,0.97941
0.75,Vmin,236566.6667,660.43,0.97741
1,Vmin,317866.6667,659.53,0.97366
0.1,Vnom,32800,740.13,0.95627
0.2,Vnom,72900,740.37,0.97071
0.3,Vnom,107600,740.4,0.97523
0.5,Vnom,167500,740.57,0.97649
0.75,Vnom,234733.3333,741.83,0.97413
1,Vnom,317333.3333,737.77,0.97222
0.1,Vmax,32800,959.03,0.9336
0.2,Vmax,71600,959.33,0.96108
0.3,Vmax,107300,959.2,0.96464
0.5,Vmax,166700,959.57,0.96975
0.75,Vmax,234700,958.83,0.96584
1,Vmax,317400,956.7,0.96338
0.1,Vmin,32800,660.43,0.95349
0.2,Vmin,73000,660.83,0.97247
0.3,Vmin,107500,660.47,0.97668
0.5,Vmin,168100,660.27,0.97941
0.75,Vmin,236167,660.57,0.97657
1,Vmin,317833,660.47,0.97177
0.1,Vnom,32800,740.2,0.95534
0.2,Vnom,72900,740.3,0.96985
0.3,Vnom,107600,740.33,0.97434
0.5,Vnom,167500,740.53,0.9763
0.75,Vnom,234833,741.93,0.97468
1,Vnom,317333,737.73,0.97242
0.1,Vmax,32800,959.03,0.93626
0.2,Vmax,71600,959.37,0.95936
0.3,Vmax,107300,959.23,0.96464
0.5,Vmax,166700,959.5,0.96731
0.75,Vmax,235267,958.67,0.96592
1,Vmax,317400,957.07,0.96269
0.1,Vmin,32800,660.73,0.95627
0.2,Vmin,73000,660.57,0.97204
0.3,Vmin,107500,660.97,0.97787
0.5,Vmin,168100,660,0.97865
0.75,Vmin,236200,659.77,0.97778
1,Vmin,317200,659.2,0.97221
0.1,Vnom,32800,740.2,0.95257
0.2,Vnom,72900,740.33,0.97071
0.3,Vnom,107600,740.43,0.97464
0.5,Vnom,167500,740.63,0.97592
0.75,Vnom,235100,741.87,0.97458
1,Vnom,317333.3333,737.83,0.97232
0.1,Vmax,32800,959,0.93182
0.2,Vmax,71600,959.4,0.9585
0.3,Vmax,107300,959.07,0.96783
0.5,Vmax,166700,959.7,0.96806
0.75,Vmax,235466.6667,958.77,0.96569
1,Vmax,317400,956.6,0.96308
19 changes: 19 additions & 0 deletions pvlib/data/inverter_fit_snl_sim.csv
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fraction_of_rated_power,efficiency,dc_voltage_level,dc_voltage,dc_power,ac_power,efficiency
0.1,0.892146066,Vmin,220,112.0892685,100,0.892146067
0.1,0.876414009,Vnom,240,114.1013254,100,0.876414009
0.1,0.861227164,Vmax,260,116.1133835,100,0.861227164
0.2,0.925255801,Vmin,220,216.15644,200,0.925255801
0.2,0.916673906,Vnom,240,218.1800951,200,0.916673906
0.2,0.908249736,Vmax,260,220.2037524,200,0.908249736
0.3,0.936909957,Vmin,220,320.2015283,300,0.936909957
0.3,0.93099374,Vnom,240,322.2363236,300,0.93099374
0.3,0.925151763,Vmax,260,324.2711217,300,0.925151763
0.5,0.946565413,Vmin,220,528.2255121,500,0.946565413
0.5,0.94289593,Vnom,240,530.2812159,500,0.94289593
0.5,0.939254781,Vmax,260,532.336923,500,0.939254781
0.75,0.951617818,Vmin,220,788.1315225,750,0.951617818
0.75,0.949113828,Vnom,240,790.2108027,750,0.949113828
0.75,0.946622992,Vmax,260,792.2900736,750,0.946622992
1,0.954289529,Vmin,220,1047.900002,1000,0.95428953
1,0.952380952,Vnom,240,1050,1000,0.952380952
1,0.950479992,Vmax,260,1052.1,1000,0.950479992
133 changes: 131 additions & 2 deletions pvlib/inverter.py
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@@ -1,12 +1,21 @@
# -*- coding: utf-8 -*-
"""
This module contains functions for inverter modeling, primarily conversion of
DC to AC power.
This module contains functions for inverter modeling and for fitting inverter
models to data.

Inverter models calculate AC power output from DC input. Model parameters
should be passed as a single dict.

Functions for estimating parameters for inverter models should follow the
naming pattern 'fit_<model name>', e.g., fit_sandia.

"""

import numpy as np
import pandas as pd

from numpy.polynomial.polynomial import polyfit # different than np.polyfit


def sandia(v_dc, p_dc, inverter):
r'''
Expand Down Expand Up @@ -306,3 +315,123 @@ def pvwatts(pdc, pdc0, eta_inv_nom=0.96, eta_inv_ref=0.9637):
power_ac = np.maximum(0, power_ac) # GH 541

return power_ac


def fit_sandia(curves, p_ac_0, p_nt):
r'''
Determine parameters for the Sandia inverter model from efficiency
curves.

Parameters
----------
curves : DataFrame
Columns must be ``'fraction_of_rated_power'``, ``'dc_voltage_level'``,
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Is fraction_of_rated_power actually required? I don't see it getting used anywhere.

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@cwhanse cwhanse Aug 4, 2020 •
edited
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The values are not used explicitly, but I think it would be confusing to describe the needed input without fraction_of_rated_power. If working from a datasheet, efficiency in usually given in terms of fraction_of_rated_power rather than ac_power.

``'dc_voltage'``, ``'ac_power'``, ``'efficiency'``. See notes for the
definition and unit for each column.
p_ac_0 : numeric
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Is it intentional that p_ac_0 and p_nt are spelled differently here than in inverter.sandia? Seems like these two functions would benefit from a consistent interface.

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I agree, which would you prefer? p_ac_0 is more appealing than Pac0 as a program variable. The inertia is with Pac0, which is the column key for this parameter read from the SAM files.

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It's not clear to me where the balance should be struck between (1) presenting a consistent interface across functions or (2) maintaining as clear a connection as possible to the original model definitions. I think I would lean towards p_ac_0 over Pac0 with the hope that existing Pac0s would be changed to match.

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That is my preference as well. The function returns a dict ready for pvlib.inverter.sandia so at least in one direction the two are compatible.

Rated AC power of the inverter [W].
p_nt : numeric
Night tare, i.e., power consumed while inverter is not delivering
AC power. [W]

Returns
-------
dict with parameters for the Sandia inverter model. See
:py:func:`snl_inverter` for a description of entries in the returned dict.

See Also
--------
snlinverter

Notes
-----
An inverter efficiency curve comprises a series of pairs
('fraction_of_rated_power', 'efficiency'), e.g. (0.1, 0.5), (0.2, 0.7),
etc. at a specified DC voltage level and AC power level. The DataFrame
`curves` must contain at least one efficiency curve for each combination
of DC voltage level and AC power level. Columns in `curves` must be the
following:

================ ========================================
Column name Description
================ ========================================
'fraction_of_rated_power' Fraction of rated AC power `p_ac_0`. The
CEC inverter test protocol specifies values
of 0.1, 0.2, 0.3, 0.5, 0.75 and 1.0. [unitless]
'dc_voltage_level' Must be 'Vmin', 'Vnom', or 'Vmax'. Curves must
be provided for all three voltage levels. At
least one curve must be provided for each
combination of fraction_of_rated_power and
dc_voltage_level.
'dc_voltage' DC input voltage. [V]
'ac_power' Output AC power. [W]
'efficiency' Ratio of AC output power to DC input power.
[unitless]

For each curve, DC input power is calculated from AC power and efficiency.

References
----------
.. [1] SAND2007-5036, "Performance Model for Grid-Connected
Photovoltaic Inverters by D. King, S. Gonzalez, G. Galbraith, W.
Boyson
.. [2] Sandia Inverter Model page, PV Performance Modeling Collaborative
https://pvpmc.sandia.gov/modeling-steps/dc-to-ac-conversion/sandia-inverter-model/ # noqa: E501
'''

voltage_levels = ['Vmin', 'Vnom', 'Vmax']

# average dc input voltage at each voltage level
v_d = np.array(
[curves['dc_voltage'][curves['dc_voltage_level'] == 'Vmin'].mean(),
curves['dc_voltage'][curves['dc_voltage_level'] == 'Vnom'].mean(),
curves['dc_voltage'][curves['dc_voltage_level'] == 'Vmax'].mean()])
v_nom = v_d[1] # model parameter
# independent variable for regressions, x_d
x_d = v_d - v_nom

curves['dc_power'] = curves['ac_power'] / curves['efficiency']
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Doesn't this modify the input DataFrame?


# empty dataframe to contain intermediate variables
coeffs = pd.DataFrame(index=voltage_levels,
columns=['a', 'b', 'c', 'p_dc', 'p_s0'], data=np.nan)

def solve_quad(a, b, c):
return (-b + (b**2 - 4 * a * c)**.5) / (2 * a)

# [2] STEP 3E, fit a line to (DC voltage, model_coefficient)
def extract_c(x_d, add):
test = polyfit(x_d, add, 1)
beta0, beta1 = test
c = beta1 / beta0
return beta0, beta1, c

for d in voltage_levels:
x = curves['dc_power'][curves['dc_voltage_level'] == d]
y = curves['ac_power'][curves['dc_voltage_level'] == d]
# [2] STEP 3B
# fit a quadratic to (DC power, AC power)
c, b, a = polyfit(x, y, 2)

# [2] STEP 3D, solve for p_dc and p_s0
p_dc = solve_quad(a, b, (c - p_ac_0))
p_s0 = solve_quad(a, b, c)

# Add values to dataframe at index d
coeffs['a'][d] = a
coeffs['b'][d] = b
coeffs['c'][d] = c
coeffs['p_dc'][d] = p_dc
coeffs['p_s0'][d] = p_s0

b_dc0, b_dc1, c1 = extract_c(x_d, coeffs['p_dc'])
b_s0, b_s1, c2 = extract_c(x_d, coeffs['p_s0'])
b_c0, b_c1, c3 = extract_c(x_d, coeffs['a'])

p_dc0 = b_dc0
p_s0 = b_s0
c0 = b_c0

# prepare dict and return
return {'Paco': p_ac_0, 'Pdco': p_dc0, 'Vdco': v_nom, 'Pso': p_s0,
'C0': c0, 'C1': c1, 'C2': c2, 'C3': c3, 'Pnt': p_nt}
26 changes: 25 additions & 1 deletion pvlib/tests/test_inverter.py
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Expand Up @@ -6,8 +6,10 @@
from pandas.testing import assert_series_equal
from numpy.testing import assert_allclose

from conftest import needs_numpy_1_10, DATA_DIR
import pytest

from pvlib import inverter
from conftest import needs_numpy_1_10


def test_adr(adr_inverter_parameters):
Expand Down Expand Up @@ -131,3 +133,25 @@ def test_pvwatts_series():
expected = pd.Series(np.array([np.nan, 0., 47.608436, 95.]))
out = inverter.pvwatts(pdc, pdc0, 0.95)
assert_series_equal(expected, out)


INVERTER_TEST_MEAS = DATA_DIR / 'inverter_fit_snl_meas.csv'
INVERTER_TEST_SIM = DATA_DIR / 'inverter_fit_snl_sim.csv'


@pytest.mark.parametrize('infilen, expected', [
(INVERTER_TEST_MEAS, {'Paco': 333000., 'Pdco': 343251., 'Vdco': 740.,
'Pso': 1427.746, 'C0': -5.768e-08, 'C1': 3.596e-05,
'C2': 1.038e-03, 'C3': 2.978e-05, 'Pnt': 1.}),
(INVERTER_TEST_SIM, {'Paco': 1000., 'Pdco': 1050., 'Vdco': 240.,
'Pso': 10., 'C0': 1e-6, 'C1': 1e-4, 'C2': 1e-2,
'C3': 1e-3, 'Pnt': 1.}),
])
def test_fit_sandia(infilen, expected):
curves = pd.read_csv(infilen)
result_dict = inverter.fit_sandia(curves, expected['Paco'],
expected['Pnt'])
keys = ['Paco', 'Pdco', 'Vdco', 'Pso', 'C0', 'C1', 'C2', 'C3', 'Pnt']
exp = np.array([expected[k] for k in keys])
result = np.array([result_dict[k] for k in keys])
assert_allclose(exp, result, rtol=1e-3)