def fixed_nrel(power_or_irradiance,
daytime,
r2_min=0.94,
min_hours=5,
peak_min=None):
"""Flag days that match the profile of a fixed PV system on a sunny day.
This algorithm relies on the observation that the power profile of a
fixed tilt PV system often resembles a quadratic polynomial on a
sunny day, with a single peak when the sun is near the system azimuth.
A day is marked True when the :math:`r^2` for a quadratic fit to the
power data is greater than `r2_min`.
Parameters
----------
power_or_irradiance : Series
Timezone localized series of power or irradiance measurements.
daytime : Series
Boolean series with True for times that are during the
day. For best results this mask should exclude early morning
and evening as well as night. Data at these times may have
problems with shadows that interfere with curve fitting.
r2_min : float, default 0.94
Minimum :math:`r^2` of a quadratic fit for a day to be marked True.
min_hours : float, default 5.0
Minimum number of hours with data to attempt a fit on a day.
peak_min : float, default None
The maximum `power_or_irradiance` value for a day must be
greater than `peak_min` for a fit to be attempted. If the
maximum for a day is less than `peak_min` then the day will be
marked False.
Returns
-------
Series
True for values on days where `power_or_irradiance` matches
the expected parabolic profile for a fixed PV system on a sunny day.
Notes
-----
This algorithm is based on the PVFleets QA Analysis
project. Copyright (c) 2020 Alliance for Sustainable Energy, LLC.
"""
freq = pd.infer_freq(power_or_irradiance.index)
daily_data = _group.by_day(power_or_irradiance[daytime])
minutes = pd.Series(power_or_irradiance.index.hour * 60 +
power_or_irradiance.index.minute,
index=power_or_irradiance.index)
fixed_days = daily_data.apply(_conditional_fit,
fitfunc=_fit.quadratic_r2,
minutes=minutes,
freq=freq,
min_hours=min_hours,
peak_min=peak_min)
return (fixed_days > r2_min).reindex(power_or_irradiance.index,
method='pad',
fill_value=False)
def _peak_times(data):
minute_of_day = pd.Series(data.index.hour * 60 + data.index.minute,
index=data.index)
peak_minutes = _group.by_day(data).apply(
lambda day: pd.Timedelta(minutes=round(
_fit.quadratic_vertex(
x=minute_of_day[day.index],
y=day,
))))
return pd.DatetimeIndex(np.unique(data.index.date),
tz=data.index.tz) + peak_minutes
def tracking_nrel(power_or_irradiance, daytime, r2_min=0.915,
r2_fixed_max=0.96, min_hours=5, peak_min=None,
quadratic_mask=None):
"""Flag days that match the profile of a single-axis tracking PV system
on a sunny day.
This algorithm relies on the observation that the power profile of
a single-axis tracking PV system tends to resemble a quartic
polynomial on a sunny day, I.e., two peaks are observed, one
before and one after the sun crosses the tracker azimuth. By
contrast, the power profile for a fixed tilt PV system often
resembles a quadratic polynomial on a sunny day, with a single
peak when the sun is near the system azimuth.
The algorithm fits both a quartic and a quadratic polynomial to
each day's data. A day is marked True if the quartic fit has a
sufficiently high :math:`r^2` and the quadratic fit has a
sufficiently low :math:`r^2`. Specifically, a day is marked True
when three conditions are met:
1. a restricted quartic [#]_ must fit the data with :math:`r^2`
greater than `r2_min`
2. the :math:`r^2` for the restricted quartic fit must be greater
than the :math:`r^2` for a quadratic fit
3. the :math:`r^2` for a quadratic fit must be less than
`r2_fixed_max`
Values on days where any one of these conditions is not met are
marked False.
.. [#] The specific quartic used for this fit is centered within
70 minutes of 12:00, the y-value at the center must be within
15% of the median for the day, and it must open downwards.
Parameters
----------
power_or_irradiance : Series
Timezone localized series of power or irradiance measurements.
daytime : Series
Boolean series with True for times that are during the
day. For best results this mask should exclude early morning
and late afternoon as well as night. Data at these times may have
problems with shadows that interfere with curve fitting.
r2_min : float, default 0.915
Minimum :math:`r^2` of a quartic fit for a day to be marked True.
r2_fixed_max : float, default 0.96
If the :math:`r^2` of a quadratic fit exceeds
`r2_fixed_max`, then tracking/fixed cannot be distinguished
and the day is marked False.
min_hours : float, default 5.0
Minimum number of hours with data to attempt a fit on a day.
peak_min : float, default None
The maximum `power_or_irradiance` value for a day must be
greater than `peak_min` for a fit to be attempted. If the
maximum for a day is less than `peak_min` then the day will be
marked False.
quadratic_mask : Series, default None
If None then `daytime` is used. This Series is used to remove
morning and afternoon times from the data before applying a
quadratic fit. The mask should
typically exclude more data than `daytime` in order to
eliminate long tails in the morning or afternoon that can
appear if a tracker is stuck in a West or East orientation.
Returns
-------
Series
Boolean series with True for every value on a day that has a
tracking profile (see criteria above).
Notes
-----
This algorithm is based on the PVFleets QA Analysis
project. Copyright (c) 2020 Alliance for Sustainable Energy, LLC.
"""
if quadratic_mask is None:
quadratic_mask = daytime
freq = pd.infer_freq(power_or_irradiance.index)
minutes = pd.Series(
power_or_irradiance.index.hour * 60 + power_or_irradiance.index.minute,
index=power_or_irradiance.index
)
daily_data = _group.by_day(power_or_irradiance[daytime])
tracking_days = daily_data.apply(
_conditional_fit,
fitfunc=_fit.quartic_restricted_r2,
minutes=minutes,
freq=freq,
min_hours=min_hours,
peak_min=peak_min
)
fixed_days = _group.by_day(power_or_irradiance[quadratic_mask]).apply(
_conditional_fit,
fitfunc=_fit.quadratic_r2,
minutes=minutes,
freq=freq,
min_hours=min_hours,
peak_min=peak_min
)
return (
(tracking_days > r2_min)
& (tracking_days > fixed_days)
& (fixed_days < r2_fixed_max)
).reindex(power_or_irradiance.index, method='pad', fill_value=False)
def infer_orientation_daily_peak(power_or_poa, sunny, tilts,
azimuths, solar_azimuth,
solar_zenith, ghi, dhi, dni):
"""Determine system azimuth and tilt from power or POA using solar
azimuth at the daily peak.
The time of the daily peak is estimated by fitting a quadratic to
to the data for each day in `power_or_poa` and finding the vertex
of the fit. A brute force search is performed on clearsky POA
irradiance for all pairs of candidate azimuths and tilts
(`azimuths` and `tilts`) to find the pair that results in the
closest azimuth to the azimuths calculated at the peak times from
the curve fitting step. Closest is determined by minimizing the
sum of squared difference between the solar azimuth at the peak
time in `power_or_poa` and the solar azimuth at maximum clearsky
POA irradiance.
The accuracy of the tilt and azimuth returned by this function will
vary with the time-resolution of the clearsky and solar position
data. For the best accuracy pass `solar_azimuth`, `solar_zenith`,
and the clearsky data (`ghi`, `dhi`, and `dni`) with one-minute
timestamp spacing. If `solar_azimuth` has timestamp spacing less
than one minute it will be resampled and interpolated to estimate
azimuth at each minute of the day. Regardless of the timestamp
spacing these parameters must cover the same days as
`power_or_poa`.
Parameters
----------
power_or_poa : Series
Timezone localized series of power or POA irradiance
measurements.
sunny : Series
Boolean series with True for values during clearsky
conditions.
tilts : array-like
Candidate tilts in degrees.
azimuths : array-like
Candidate azimuths in degrees.
solar_azimuth : Series
Time series of solar azimuth.
solar_zenith : Series
Time series of solar zenith.
ghi : Series
Clear sky GHI.
dhi : Series
Clear sky DHI.
dni : Series
Clear sky DNI.
Returns
-------
azimuth : float
tilt : float
Notes
-----
Based on PVFleets QA project.
"""
peak_times = _peak_times(power_or_poa[sunny])
azimuth_by_minute = solar_azimuth.resample('T').interpolate(
method='linear'
)
modeled_azimuth = azimuth_by_minute[peak_times]
best_azimuth = None
best_tilt = None
smallest_sse = None
for azimuth in azimuths:
for tilt in tilts:
poa = pvlib.irradiance.get_total_irradiance(
tilt,
azimuth,
solar_zenith,
solar_azimuth,
ghi=ghi,
dhi=dhi,
dni=dni
).poa_global
poa_azimuths = azimuth_by_minute[
_group.by_day(poa).idxmax()
]
filtered_azimuths = poa_azimuths[np.isin(
poa_azimuths.index.date,
modeled_azimuth.index.date
)]
sum_of_squares = sum(
(filtered_azimuths.values - modeled_azimuth.values)**2
)
if (smallest_sse is None) or (smallest_sse > sum_of_squares):
smallest_sse = sum_of_squares
best_azimuth = azimuth
best_tilt = tilt
return best_azimuth, best_tilt
