pvsystem.py

"""
The ``pvsystem`` module contains functions for modeling the output and
performance of PV modules and inverters.
"""

from collections import OrderedDict
import functools
import io
import itertools
from pathlib import Path
import inspect
from urllib.request import urlopen
import numpy as np
from scipy import constants
import pandas as pd
from dataclasses import dataclass
from abc import ABC, abstractmethod
from typing import Optional, Union
from pvlib._deprecation import renamed_kwarg_warning
import pvlib  # used to avoid albedo name collision in the Array class
from pvlib import (atmosphere, iam, inverter, irradiance,
                   singlediode as _singlediode, spectrum, temperature)
from pvlib.tools import _build_kwargs, _build_args
import pvlib.tools as tools


# a dict of required parameter names for each DC power model
_DC_MODEL_PARAMS = {
    'sapm': {
        # i_x and i_xx params (IXO, IXXO, C4-C7) not required
        'C0', 'C1', 'C2', 'C3',
        'Isco', 'Impo', 'Voco', 'Vmpo', 'Aisc', 'Aimp', 'Bvoco',
        'Mbvoc', 'Bvmpo', 'Mbvmp', 'N', 'Cells_in_Series'},
    'desoto': {
        'alpha_sc', 'a_ref', 'I_L_ref', 'I_o_ref',
        'R_sh_ref', 'R_s'},
    'cec': {
        'alpha_sc', 'a_ref', 'I_L_ref', 'I_o_ref',
        'R_sh_ref', 'R_s', 'Adjust'},
    'pvsyst': {
        'gamma_ref', 'mu_gamma', 'I_L_ref', 'I_o_ref',
        'R_sh_ref', 'R_sh_0', 'R_s', 'alpha_sc', 'EgRef',
        'cells_in_series'},
    'singlediode': {
        'alpha_sc', 'a_ref', 'I_L_ref', 'I_o_ref',
        'R_sh_ref', 'R_s'},
    'pvwatts': {'pdc0', 'gamma_pdc'}
}


def _unwrap_single_value(func):
    """Decorator for functions that return iterables.

    If the length of the iterable returned by `func` is 1, then
    the single member of the iterable is returned. If the length is
    greater than 1, then entire iterable is returned.

    Adds 'unwrap' as a keyword argument that can be set to False
    to force the return value to be a tuple, regardless of its length.
    """
    @functools.wraps(func)
    def f(*args, **kwargs):
        unwrap = kwargs.pop('unwrap', True)
        x = func(*args, **kwargs)
        if unwrap and len(x) == 1:
            return x[0]
        return x
    return f


# not sure if this belongs in the pvsystem module.
# maybe something more like core.py? It may eventually grow to
# import a lot more functionality from other modules.
class PVSystem:
    """
    The PVSystem class defines a standard set of PV system attributes
    and modeling functions. This class describes the collection and
    interactions of PV system components rather than an installed system
    on the ground. It is typically used in combination with
    :py:class:`~pvlib.location.Location` and
    :py:class:`~pvlib.modelchain.ModelChain`
    objects.

    The class supports basic system topologies consisting of:

        * `N` total modules arranged in series
          (`modules_per_string=N`, `strings_per_inverter=1`).
        * `M` total modules arranged in parallel
          (`modules_per_string=1`, `strings_per_inverter=M`).
        * `NxM` total modules arranged in `M` strings of `N` modules each
          (`modules_per_string=N`, `strings_per_inverter=M`).

    The class is complementary to the module-level functions.

    The attributes should generally be things that don't change about
    the system, such the type of module and the inverter. The instance
    methods accept arguments for things that do change, such as
    irradiance and temperature.

    Parameters
    ----------
    arrays : Array or iterable of Array, optional
        An Array or list of arrays that are part of the system. If not
        specified, a single array is created from the other parameters (e.g.
        `surface_tilt`, `surface_azimuth`). If specified as a list, the list
        must contain at least one Array;
        if length of arrays is 0 a ValueError is raised. If `arrays` is
        specified the following PVSystem parameters are ignored:

        - ``surface_tilt``
        - ``surface_azimuth``
        - ``albedo``
        - ``surface_type``
        - ``module``
        - ``module_type``
        - ``module_parameters``
        - ``temperature_model_parameters``
        - ``modules_per_string``
        - ``strings_per_inverter``

    surface_tilt: float or array-like, default 0
        Surface tilt angles in decimal degrees.
        The tilt angle is defined as degrees from horizontal
        (e.g. surface facing up = 0, surface facing horizon = 90)

    surface_azimuth: float or array-like, default 180
        Azimuth angle of the module surface in decimal degrees.
        North=0, East=90, South=180, West=270.

    albedo : float, optional
        Ground surface albedo. If not supplied, then ``surface_type`` is used
        to look up a value in  :py:const:`pvlib.albedo.SURFACE_ALBEDOS`.
        If ``surface_type`` is also not supplied then a ground surface albedo
        of 0.25 is used.

    surface_type : string, optional
        The ground surface type. See  :py:const:`pvlib.albedo.SURFACE_ALBEDOS`
        for valid values.

    module : string, optional
        The model name of the modules.

    module_type : string, default 'glass_polymer'
         Describes the module's construction. Valid strings are 'glass_polymer'
         and 'glass_glass'. Used for cell and module temperature calculations.

    module_parameters : dict or Series, optional
        Module parameters as defined by the SAPM, CEC, or other.

    temperature_model_parameters : dict or Series, optional
        Temperature model parameters as required by one of the models in
        :py:mod:`pvlib.temperature` (excluding ``poa_global``, ``temp_air`` and
        ``wind_speed``).

    modules_per_string: int or float, default 1
        See system topology discussion above.

    strings_per_inverter: int or float, default 1
        See system topology discussion above.

    inverter : string, optional
        The model name of the inverters.

    inverter_parameters : dict or Series, optional
        Inverter parameters as defined by the SAPM, CEC, or other.

    racking_model : string, optional
        Valid strings are ``'open_rack'``, ``'close_mount'``,
        ``'insulated_back'``, ``'freestanding'`` and ``'insulated'``.
        Used to identify a parameter set for the SAPM or PVsyst cell
        temperature model.
        See :py:func:`~pvlib.temperature.sapm_module` and
        :py:func:`~pvlib.temperature.pvsyst_cell` for definitions.

    losses_parameters : dict or Series, optional
        Losses parameters as defined by PVWatts or other.

    name : string, optional

    **kwargs
        Arbitrary keyword arguments.
        Included for compatibility, but not used.

    Raises
    ------
    ValueError
        If ``arrays`` is not None and has length 0.

    See also
    --------
    pvlib.location.Location
    """

    def __init__(self,
                 arrays=None,
                 surface_tilt=0, surface_azimuth=180,
                 albedo=None, surface_type=None,
                 module=None, module_type=None,
                 module_parameters=None,
                 temperature_model_parameters=None,
                 modules_per_string=1, strings_per_inverter=1,
                 inverter=None, inverter_parameters=None,
                 racking_model=None, losses_parameters=None, name=None):

        if arrays is None:
            if losses_parameters is None:
                array_losses_parameters = {}
            else:
                array_losses_parameters = _build_kwargs(['dc_ohmic_percent'],
                                                        losses_parameters)
            self.arrays = (Array(
                FixedMount(surface_tilt, surface_azimuth, racking_model),
                albedo,
                surface_type,
                module,
                module_type,
                module_parameters,
                temperature_model_parameters,
                modules_per_string,
                strings_per_inverter,
                array_losses_parameters,
            ),)
        elif isinstance(arrays, Array):
            self.arrays = (arrays,)
        elif len(arrays) == 0:
            raise ValueError("PVSystem must have at least one Array. "
                             "If you want to create a PVSystem instance "
                             "with a single Array pass `arrays=None` and pass "
                             "values directly to PVSystem attributes, e.g., "
                             "`surface_tilt=30`")
        else:
            self.arrays = tuple(arrays)

        self.inverter = inverter
        if inverter_parameters is None:
            self.inverter_parameters = {}
        else:
            self.inverter_parameters = inverter_parameters

        if losses_parameters is None:
            self.losses_parameters = {}
        else:
            self.losses_parameters = losses_parameters

        self.name = name

    def __repr__(self):
        repr = f'PVSystem:\n  name: {self.name}\n  '
        for array in self.arrays:
            repr += '\n  '.join(array.__repr__().split('\n'))
            repr += '\n  '
        repr += f'inverter: {self.inverter}'
        return repr

    def _validate_per_array(self, values, system_wide=False):
        """Check that `values` is a tuple of the same length as
        `self.arrays`.

        If `values` is not a tuple it is packed in to a length-1 tuple before
        the check. If the lengths are not the same a ValueError is raised,
        otherwise the tuple `values` is returned.

        When `system_wide` is True and `values` is not a tuple, `values`
        is replicated to a tuple of the same length as `self.arrays` and that
        tuple is returned.
        """
        if system_wide and not isinstance(values, tuple):
            return (values,) * self.num_arrays
        if not isinstance(values, tuple):
            values = (values,)
        if len(values) != len(self.arrays):
            raise ValueError("Length mismatch for per-array parameter")
        return values

    @_unwrap_single_value
    def _infer_cell_type(self):
        """
        Examines module_parameters and maps the Technology key for the CEC
        database and the Material key for the Sandia database to a common
        list of strings for cell type.

        Returns
        -------
        cell_type: str
        """
        return tuple(array._infer_cell_type() for array in self.arrays)

    @_unwrap_single_value
    def get_aoi(self, solar_zenith, solar_azimuth):
        """Get the angle of incidence on the Array(s) in the system.

        Parameters
        ----------
        solar_zenith : float or Series.
            Solar zenith angle.
        solar_azimuth : float or Series.
            Solar azimuth angle.

        Returns
        -------
        aoi : Series or tuple of Series
            The angle of incidence
        """

        return tuple(array.get_aoi(solar_zenith, solar_azimuth)
                     for array in self.arrays)

    @_unwrap_single_value
    def get_irradiance(self, solar_zenith, solar_azimuth, dni, ghi, dhi,
                       dni_extra=None, airmass=None, albedo=None,
                       model='haydavies', **kwargs):
        """
        Uses :py:func:`pvlib.irradiance.get_total_irradiance` to
        calculate the plane of array irradiance components on the tilted
        surfaces defined by each array's ``surface_tilt`` and
        ``surface_azimuth``.

        Parameters
        ----------
        solar_zenith : float or Series
            Solar zenith angle.
        solar_azimuth : float or Series
            Solar azimuth angle.
        dni : float, Series, or tuple of float or Series
            Direct Normal Irradiance. [W/m2]
        ghi : float, Series, or tuple of float or Series
            Global horizontal irradiance. [W/m2]
        dhi : float, Series, or tuple of float or Series
            Diffuse horizontal irradiance. [W/m2]
        dni_extra : float, Series or tuple of float or Series, optional
            Extraterrestrial direct normal irradiance. [W/m2]
        airmass : float or Series, optional
            Airmass. [unitless]
        albedo : float or Series, optional
            Ground surface albedo. [unitless]
        model : String, default 'haydavies'
            Irradiance model.

        kwargs
            Extra parameters passed to
            :py:func:`pvlib.irradiance.get_total_irradiance`.

        Notes
        -----
        Each of ``dni``, ``ghi``, and ``dni`` may be passed as a float, Series,
        or tuple of float or Series. If passed as a float or Series, these
        values are used for all Arrays. If passed as a tuple, the tuple length
        must be the same as the number of Arrays. The first tuple element is
        used for the first Array, the second tuple element for the second
        Array, and so forth.

        Some sky irradiance models require ``dni_extra``. For these models,
        if ``dni_extra`` is not provided and ``solar_zenith`` has a
        ``DatetimeIndex``, then ``dni_extra`` is calculated.
        Otherwise, ``dni_extra=1367`` is assumed.

        Returns
        -------
        poa_irradiance : DataFrame or tuple of DataFrame
            Column names are: ``'poa_global', 'poa_direct', 'poa_diffuse',
            'poa_sky_diffuse', 'poa_ground_diffuse'``.

        See also
        --------
        pvlib.irradiance.get_total_irradiance
        """
        dni = self._validate_per_array(dni, system_wide=True)
        ghi = self._validate_per_array(ghi, system_wide=True)
        dhi = self._validate_per_array(dhi, system_wide=True)

        albedo = self._validate_per_array(albedo, system_wide=True)

        return tuple(
            array.get_irradiance(solar_zenith, solar_azimuth,
                                 dni, ghi, dhi,
                                 dni_extra=dni_extra, airmass=airmass,
                                 albedo=albedo, model=model, **kwargs)
            for array, dni, ghi, dhi, albedo in zip(
                self.arrays, dni, ghi, dhi, albedo
            )
        )

    @_unwrap_single_value
    def get_iam(self, aoi, iam_model='physical'):
        """
        Determine the incidence angle modifier using the method specified by
        ``iam_model``.

        Parameters for the selected IAM model are expected to be in
        ``PVSystem.module_parameters``. Default parameters are available for
        the 'physical', 'ashrae' and 'martin_ruiz' models.

        Parameters
        ----------
        aoi : numeric or tuple of numeric
            The angle of incidence in degrees.

        aoi_model : string, default 'physical'
            The IAM model to be used. Valid strings are 'physical', 'ashrae',
            'martin_ruiz', 'sapm' and 'interp'.
        Returns
        -------
        iam : numeric or tuple of numeric
            The AOI modifier.

        Raises
        ------
        ValueError
            if `iam_model` is not a valid model name.
        """
        aoi = self._validate_per_array(aoi)
        return tuple(array.get_iam(aoi, iam_model)
                     for array, aoi in zip(self.arrays, aoi))

    @_unwrap_single_value
    def get_cell_temperature(self, poa_global, temp_air, wind_speed, model,
                             effective_irradiance=None):
        """
        Determine cell temperature using the method specified by ``model``.

        Parameters
        ----------
        poa_global : numeric or tuple of numeric
            Total incident irradiance in W/m^2.

        temp_air : numeric or tuple of numeric
            Ambient dry bulb temperature in degrees C.

        wind_speed : numeric or tuple of numeric
            Wind speed in m/s.

        model : str
            Supported models include ``'sapm'``, ``'pvsyst'``,
            ``'faiman'``, ``'fuentes'``, and ``'noct_sam'``

        effective_irradiance : numeric or tuple of numeric, optional
            The irradiance that is converted to photocurrent in W/m^2.
            Only used for some models.

        Returns
        -------
        numeric or tuple of numeric
            Values in degrees C.

        See Also
        --------
        Array.get_cell_temperature

        Notes
        -----
        The `temp_air` and `wind_speed` parameters may be passed as tuples
        to provide different values for each Array in the system. If passed as
        a tuple the length must be the same as the number of Arrays. If not
        passed as a tuple then the same value is used for each Array.
        """
        poa_global = self._validate_per_array(poa_global)
        temp_air = self._validate_per_array(temp_air, system_wide=True)
        wind_speed = self._validate_per_array(wind_speed, system_wide=True)
        # Not used for all models, but Array.get_cell_temperature handles it
        effective_irradiance = self._validate_per_array(effective_irradiance,
                                                        system_wide=True)

        return tuple(
            array.get_cell_temperature(poa_global, temp_air, wind_speed,
                                       model, effective_irradiance)
            for array, poa_global, temp_air, wind_speed, effective_irradiance
            in zip(
                self.arrays, poa_global, temp_air, wind_speed,
                effective_irradiance
            )
        )

    @_unwrap_single_value
    def calcparams_desoto(self, effective_irradiance, temp_cell):
        """
        Use the :py:func:`calcparams_desoto` function, the input
        parameters and ``self.module_parameters`` to calculate the
        module currents and resistances.

        Parameters
        ----------
        effective_irradiance : numeric or tuple of numeric
            The irradiance (W/m2) that is converted to photocurrent.

        temp_cell : float or Series or tuple of float or Series
            The average cell temperature of cells within a module in C.

        Returns
        -------
        See pvsystem.calcparams_desoto for details
        """
        effective_irradiance = self._validate_per_array(effective_irradiance)
        temp_cell = self._validate_per_array(temp_cell)

        build_kwargs = functools.partial(
            _build_kwargs,
            ['a_ref', 'I_L_ref', 'I_o_ref', 'R_sh_ref',
             'R_s', 'alpha_sc', 'EgRef', 'dEgdT',
             'irrad_ref', 'temp_ref']
        )

        return tuple(
            calcparams_desoto(
                effective_irradiance, temp_cell,
                **build_kwargs(array.module_parameters)
            )
            for array, effective_irradiance, temp_cell
            in zip(self.arrays, effective_irradiance, temp_cell)
        )

    @_unwrap_single_value
    def calcparams_cec(self, effective_irradiance, temp_cell):
        """
        Use the :py:func:`calcparams_cec` function, the input
        parameters and ``self.module_parameters`` to calculate the
        module currents and resistances.

        Parameters
        ----------
        effective_irradiance : numeric or tuple of numeric
            The irradiance (W/m2) that is converted to photocurrent.

        temp_cell : float or Series or tuple of float or Series
            The average cell temperature of cells within a module in C.

        Returns
        -------
        See pvsystem.calcparams_cec for details
        """
        effective_irradiance = self._validate_per_array(effective_irradiance)
        temp_cell = self._validate_per_array(temp_cell)

        build_kwargs = functools.partial(
            _build_kwargs,
            ['a_ref', 'I_L_ref', 'I_o_ref', 'R_sh_ref',
             'R_s', 'alpha_sc', 'Adjust', 'EgRef', 'dEgdT',
             'irrad_ref', 'temp_ref']
        )

        return tuple(
            calcparams_cec(
                effective_irradiance, temp_cell,
                **build_kwargs(array.module_parameters)
            )
            for array, effective_irradiance, temp_cell
            in zip(self.arrays, effective_irradiance, temp_cell)
        )

    @_unwrap_single_value
    def calcparams_pvsyst(self, effective_irradiance, temp_cell):
        """
        Use the :py:func:`calcparams_pvsyst` function, the input
        parameters and ``self.module_parameters`` to calculate the
        module currents and resistances.

        Parameters
        ----------
        effective_irradiance : numeric or tuple of numeric
            The irradiance (W/m2) that is converted to photocurrent.

        temp_cell : float or Series or tuple of float or Series
            The average cell temperature of cells within a module in C.

        Returns
        -------
        See pvsystem.calcparams_pvsyst for details
        """
        effective_irradiance = self._validate_per_array(effective_irradiance)
        temp_cell = self._validate_per_array(temp_cell)

        build_kwargs = functools.partial(
            _build_kwargs,
            ['gamma_ref', 'mu_gamma', 'I_L_ref', 'I_o_ref',
             'R_sh_ref', 'R_sh_0', 'R_sh_exp',
             'R_s', 'alpha_sc', 'EgRef',
             'irrad_ref', 'temp_ref',
             'cells_in_series']
        )

        return tuple(
            calcparams_pvsyst(
                effective_irradiance, temp_cell,
                **build_kwargs(array.module_parameters)
            )
            for array, effective_irradiance, temp_cell
            in zip(self.arrays, effective_irradiance, temp_cell)
        )

    @_unwrap_single_value
    def sapm(self, effective_irradiance, temp_cell):
        """
        Use the :py:func:`sapm` function, the input parameters,
        and ``self.module_parameters`` to calculate
        Voc, Isc, Ix, Ixx, Vmp, and Imp.

        Parameters
        ----------
        effective_irradiance : numeric or tuple of numeric
            The irradiance (W/m2) that is converted to photocurrent.

        temp_cell : float or Series or tuple of float or Series
            The average cell temperature of cells within a module in C.

        Returns
        -------
        See pvsystem.sapm for details
        """
        effective_irradiance = self._validate_per_array(effective_irradiance)
        temp_cell = self._validate_per_array(temp_cell)

        return tuple(
            sapm(effective_irradiance, temp_cell, array.module_parameters)
            for array, effective_irradiance, temp_cell
            in zip(self.arrays, effective_irradiance, temp_cell)
        )

    @_unwrap_single_value
    def sapm_spectral_loss(self, airmass_absolute):
        """
        Use the :py:func:`pvlib.spectrum.spectral_factor_sapm` function,
        the input parameters, and ``self.module_parameters`` to calculate F1.

        Parameters
        ----------
        airmass_absolute : numeric
            Absolute airmass.

        Returns
        -------
        F1 : numeric or tuple of numeric
            The SAPM spectral loss coefficient.
        """
        return tuple(
            spectrum.spectral_factor_sapm(airmass_absolute,
                                          array.module_parameters)
            for array in self.arrays
        )

    @_unwrap_single_value
    def sapm_effective_irradiance(self, poa_direct, poa_diffuse,
                                  airmass_absolute, aoi,
                                  reference_irradiance=1000):
        """
        Use the :py:func:`sapm_effective_irradiance` function, the input
        parameters, and ``self.module_parameters`` to calculate
        effective irradiance.

        Parameters
        ----------
        poa_direct : numeric or tuple of numeric
            The direct irradiance incident upon the module.  [W/m2]

        poa_diffuse : numeric or tuple of numeric
            The diffuse irradiance incident on module.  [W/m2]

        airmass_absolute : numeric
            Absolute airmass. [unitless]

        aoi : numeric or tuple of numeric
            Angle of incidence. [degrees]

        Returns
        -------
        effective_irradiance : numeric or tuple of numeric
            The SAPM effective irradiance. [W/m2]
        """
        poa_direct = self._validate_per_array(poa_direct)
        poa_diffuse = self._validate_per_array(poa_diffuse)
        aoi = self._validate_per_array(aoi)
        return tuple(
            sapm_effective_irradiance(
                poa_direct, poa_diffuse, airmass_absolute, aoi,
                array.module_parameters)
            for array, poa_direct, poa_diffuse, aoi
            in zip(self.arrays, poa_direct, poa_diffuse, aoi)
        )

    @_unwrap_single_value
    def first_solar_spectral_loss(self, pw, airmass_absolute):
        """
        Use :py:func:`pvlib.spectrum.spectral_factor_firstsolar` to
        calculate the spectral loss modifier. The model coefficients are
        specific to the module's cell type, and are determined by searching
        for one of the following keys in self.module_parameters (in order):

        - 'first_solar_spectral_coefficients' (user-supplied coefficients)
        - 'Technology' - a string describing the cell type, can be read from
          the CEC module parameter database
        - 'Material' - a string describing the cell type, can be read from
          the Sandia module database.

        Parameters
        ----------
        pw : array-like
            atmospheric precipitable water (cm).

        airmass_absolute : array-like
            absolute (pressure corrected) airmass.

        Returns
        -------
        modifier: array-like or tuple of array-like
            spectral mismatch factor (unitless) which can be multiplied
            with broadband irradiance reaching a module's cells to estimate
            effective irradiance, i.e., the irradiance that is converted to
            electrical current.
        """
        pw = self._validate_per_array(pw, system_wide=True)

        def _spectral_correction(array, pw):
            if 'first_solar_spectral_coefficients' in \
                    array.module_parameters.keys():
                coefficients = \
                    array.module_parameters[
                        'first_solar_spectral_coefficients'
                    ]
                module_type = None
            else:
                module_type = array._infer_cell_type()
                coefficients = None

            return spectrum.spectral_factor_firstsolar(
                pw, airmass_absolute, module_type, coefficients
            )
        return tuple(
            itertools.starmap(_spectral_correction, zip(self.arrays, pw))
        )

    def singlediode(self, photocurrent, saturation_current,
                    resistance_series, resistance_shunt, nNsVth):
        """Wrapper around the :py:func:`pvlib.pvsystem.singlediode` function.

        See :py:func:`pvsystem.singlediode` for details
        """
        return singlediode(photocurrent, saturation_current,
                           resistance_series, resistance_shunt, nNsVth)

    def i_from_v(self, voltage, photocurrent, saturation_current,
                 resistance_series, resistance_shunt, nNsVth):
        """Wrapper around the :py:func:`pvlib.pvsystem.i_from_v` function.

        See :py:func:`pvlib.pvsystem.i_from_v` for details.

        .. versionchanged:: 0.10.0
           The function's arguments have been reordered.
        """
        return i_from_v(voltage, photocurrent, saturation_current,
                        resistance_series, resistance_shunt, nNsVth)

    def get_ac(self, model, p_dc, v_dc=None):
        r"""Calculates AC power from p_dc using the inverter model indicated
        by model and self.inverter_parameters.

        Parameters
        ----------
        model : str
            Must be one of 'sandia', 'adr', or 'pvwatts'.
        p_dc : numeric, or tuple, list or array of numeric
            DC power on each MPPT input of the inverter. Use tuple, list or
            array for inverters with multiple MPPT inputs. If type is array,
            p_dc must be 2d with axis 0 being the MPPT inputs. [W]
        v_dc : numeric, or tuple, list or array of numeric
            DC voltage on each MPPT input of the inverter. Required when
            model='sandia' or model='adr'. Use tuple, list or
            array for inverters with multiple MPPT inputs. If type is array,
            v_dc must be 2d with axis 0 being the MPPT inputs. [V]

        Returns
        -------
        power_ac : numeric
            AC power output for the inverter. [W]

        Raises
        ------
        ValueError
            If model is not one of 'sandia', 'adr' or 'pvwatts'.
        ValueError
            If model='adr' and the PVSystem has more than one array.

        See also
        --------
        pvlib.inverter.sandia
        pvlib.inverter.sandia_multi
        pvlib.inverter.adr
        pvlib.inverter.pvwatts
        pvlib.inverter.pvwatts_multi
        """
        model = model.lower()
        multiple_arrays = self.num_arrays > 1
        if model == 'sandia':
            p_dc = self._validate_per_array(p_dc)
            v_dc = self._validate_per_array(v_dc)
            if multiple_arrays:
                return inverter.sandia_multi(
                    v_dc, p_dc, self.inverter_parameters)
            return inverter.sandia(v_dc[0], p_dc[0], self.inverter_parameters)
        elif model == 'pvwatts':
            kwargs = _build_kwargs(['eta_inv_nom', 'eta_inv_ref'],
                                   self.inverter_parameters)
            p_dc = self._validate_per_array(p_dc)
            if multiple_arrays:
                return inverter.pvwatts_multi(
                    p_dc, self.inverter_parameters['pdc0'], **kwargs)
            return inverter.pvwatts(
                p_dc[0], self.inverter_parameters['pdc0'], **kwargs)
        elif model == 'adr':
            if multiple_arrays:
                raise ValueError(
                    'The adr inverter function cannot be used for an inverter',
                    ' with multiple MPPT inputs')
            # While this is only used for single-array systems, calling
            # _validate_per_arry lets us pass in singleton tuples.
            p_dc = self._validate_per_array(p_dc)
            v_dc = self._validate_per_array(v_dc)
            return inverter.adr(v_dc[0], p_dc[0], self.inverter_parameters)
        else:
            raise ValueError(
                model + ' is not a valid AC power model.',
                ' model must be one of "sandia", "adr" or "pvwatts"')

    @_unwrap_single_value
    def scale_voltage_current_power(self, data):
        """
        Scales the voltage, current, and power of the `data` DataFrame
        by `self.modules_per_string` and `self.strings_per_inverter`.

        Parameters
        ----------
        data: DataFrame or tuple of DataFrame
            May contain columns `'v_mp', 'v_oc', 'i_mp' ,'i_x', 'i_xx',
            'i_sc', 'p_mp'`.

        Returns
        -------
        scaled_data: DataFrame or tuple of DataFrame
            A scaled copy of the input data.
        """
        data = self._validate_per_array(data)
        return tuple(
            scale_voltage_current_power(data,
                                        voltage=array.modules_per_string,
                                        current=array.strings)
            for array, data in zip(self.arrays, data)
        )

    @renamed_kwarg_warning(
        "0.13.0", "g_poa_effective", "effective_irradiance")
    @_unwrap_single_value
    def pvwatts_dc(self, effective_irradiance, temp_cell):
        """
        Calculates DC power according to the PVWatts model using
        :py:func:`pvlib.pvsystem.pvwatts_dc`, `self.module_parameters['pdc0']`,
        and `self.module_parameters['gamma_pdc']`.

        See :py:func:`pvlib.pvsystem.pvwatts_dc` for details.
        """
        effective_irradiance = self._validate_per_array(effective_irradiance)
        temp_cell = self._validate_per_array(temp_cell)
        return tuple(
            pvwatts_dc(effective_irradiance, temp_cell,
                       array.module_parameters['pdc0'],
                       array.module_parameters['gamma_pdc'],
                       **_build_kwargs(['temp_ref'], array.module_parameters))
            for array, effective_irradiance, temp_cell
            in zip(self.arrays, effective_irradiance, temp_cell)
        )

    def pvwatts_losses(self):
        """
        Calculates DC power losses according the PVwatts model using
        :py:func:`pvlib.pvsystem.pvwatts_losses` and
        ``self.losses_parameters``.

        See :py:func:`pvlib.pvsystem.pvwatts_losses` for details.
        """
        kwargs = _build_kwargs(['soiling', 'shading', 'snow', 'mismatch',
                                'wiring', 'connections', 'lid',
                                'nameplate_rating', 'age', 'availability'],
                               self.losses_parameters)
        return pvwatts_losses(**kwargs)

    @_unwrap_single_value
    def dc_ohms_from_percent(self):
        """
        Calculates the equivalent resistance of the wires for each array using
        :py:func:`pvlib.pvsystem.dc_ohms_from_percent`

        See :py:func:`pvlib.pvsystem.dc_ohms_from_percent` for details.
        """

        return tuple(array.dc_ohms_from_percent() for array in self.arrays)

    @property
    def num_arrays(self):
        """The number of Arrays in the system."""
        return len(self.arrays)


class Array:
    """
    An Array is a set of modules at the same orientation.

    Specifically, an array is defined by its mount, the
    module parameters, the number of parallel strings of modules
    and the number of modules on each string.

    Parameters
    ----------
    mount: FixedMount, SingleAxisTrackerMount, or other
        Mounting for the array, either on fixed-tilt racking or horizontal
        single axis tracker. Mounting is used to determine module orientation.
        If not provided, a FixedMount with zero tilt is used.

    albedo : float, optional
        Ground surface albedo. If not supplied, then ``surface_type`` is used
        to look up a value in  :py:const:`pvlib.albedo.SURFACE_ALBEDOS`.
        If ``surface_type`` is also not supplied then a ground surface albedo
        of 0.25 is used.

    surface_type : string, optional
        The ground surface type. See  :py:const:`pvlib.albedo.SURFACE_ALBEDOS`
        for valid values.

    module : string, optional
        The model name of the modules.
        May be used to look up the module_parameters dictionary
        via some other method.

    module_type : string, optional
         Describes the module's construction. Valid strings are 'glass_polymer'
         and 'glass_glass'. Used for cell and module temperature calculations.

    module_parameters : dict or Series, optional
        Parameters for the module model, e.g., SAPM, CEC, or other.

    temperature_model_parameters : dict or Series, optional
        Parameters for the module temperature model, e.g., SAPM, Pvsyst, or
        other.

    modules_per_string: int, default 1
        Number of modules per string in the array.

    strings: int, default 1
        Number of parallel strings in the array.

    array_losses_parameters : dict or Series, optional
        Supported keys are 'dc_ohmic_percent'.

    name : str, optional
        Name of Array instance.
    """

    def __init__(self, mount,
                 albedo=None, surface_type=None,
                 module=None, module_type=None,
                 module_parameters=None,
                 temperature_model_parameters=None,
                 modules_per_string=1, strings=1,
                 array_losses_parameters=None,
                 name=None):
        self.mount = mount

        self.surface_type = surface_type
        if albedo is None:
            self.albedo = pvlib.albedo.SURFACE_ALBEDOS.get(surface_type, 0.25)
        else:
            self.albedo = albedo

        self.module = module
        if module_parameters is None:
            self.module_parameters = {}
        else:
            self.module_parameters = module_parameters

        self.module_type = module_type

        self.strings = strings
        self.modules_per_string = modules_per_string

        if temperature_model_parameters is None:
            self.temperature_model_parameters = \
                self._infer_temperature_model_params()
        else:
            self.temperature_model_parameters = temperature_model_parameters

        if array_losses_parameters is None:
            self.array_losses_parameters = {}
        else:
            self.array_losses_parameters = array_losses_parameters

        self.name = name

    def __repr__(self):
        attrs = ['name', 'mount', 'module',
                 'albedo', 'module_type',
                 'temperature_model_parameters',
                 'strings', 'modules_per_string']

        return 'Array:\n  ' + '\n  '.join(
            f'{attr}: {getattr(self, attr)}' for attr in attrs
        )

    def _infer_temperature_model_params(self):
        # try to infer temperature model parameters from racking_model
        # and module_type
        param_set = f'{self.mount.racking_model}_{self.module_type}'
        if param_set in temperature.TEMPERATURE_MODEL_PARAMETERS['sapm']:
            return temperature._temperature_model_params('sapm', param_set)
        elif 'freestanding' in param_set:
            return temperature._temperature_model_params('pvsyst',
                                                         'freestanding')
        elif 'insulated' in param_set:  # after SAPM to avoid confusing keys
            return temperature._temperature_model_params('pvsyst',
                                                         'insulated')
        elif 'semi_integrated' in param_set:
            return temperature._temperature_model_params('pvsyst',
                                                         'semi_integrated')
        else:
            return {}

    def _infer_cell_type(self):
        """
        Examines module_parameters and maps the Technology key for the CEC
        database and the Material key for the Sandia database to a common
        list of strings for cell type.

        Returns
        -------
        cell_type: str

        """

        _cell_type_dict = {'Multi-c-Si': 'multisi',
                           'Mono-c-Si': 'monosi',
                           'Thin Film': 'cigs',
                           'a-Si/nc': 'asi',
                           'CIS': 'cigs',
                           'CIGS': 'cigs',
                           '1-a-Si': 'asi',
                           'CdTe': 'cdte',
                           'a-Si': 'asi',
                           '2-a-Si': None,
                           '3-a-Si': None,
                           'HIT-Si': 'monosi',
                           'mc-Si': 'multisi',
                           'c-Si': 'multisi',
                           'Si-Film': 'asi',
                           'EFG mc-Si': 'multisi',
                           'GaAs': None,
                           'a-Si / mono-Si': 'monosi'}

        if 'Technology' in self.module_parameters.keys():
            # CEC module parameter set
            cell_type = _cell_type_dict[self.module_parameters['Technology']]
        elif 'Material' in self.module_parameters.keys():
            # Sandia module parameter set
            cell_type = _cell_type_dict[self.module_parameters['Material']]
        else:
            cell_type = None

        return cell_type

    def get_aoi(self, solar_zenith, solar_azimuth):
        """
        Get the angle of incidence on the array.

        Parameters
        ----------
        solar_zenith : float or Series
            Solar zenith angle.
        solar_azimuth : float or Series
            Solar azimuth angle

        Returns
        -------
        aoi : Series
            Then angle of incidence.
        """
        orientation = self.mount.get_orientation(solar_zenith, solar_azimuth)
        return irradiance.aoi(orientation['surface_tilt'],
                              orientation['surface_azimuth'],
                              solar_zenith, solar_azimuth)

    def get_irradiance(self, solar_zenith, solar_azimuth, dni, ghi, dhi,
                       dni_extra=None, airmass=None, albedo=None,
                       model='haydavies', **kwargs):
        """
        Get plane of array irradiance components.

        Uses :py:func:`pvlib.irradiance.get_total_irradiance` to
        calculate the plane of array irradiance components for a surface
        defined by ``self.surface_tilt`` and ``self.surface_azimuth``.

        Parameters
        ----------
        solar_zenith : float or Series.
            Solar zenith angle.
        solar_azimuth : float or Series.
            Solar azimuth angle.
        dni : float or Series
            Direct normal irradiance. [W/m2]
        ghi : float or Series. [W/m2]
            Global horizontal irradiance
        dhi : float or Series
            Diffuse horizontal irradiance. [W/m2]
        dni_extra : float or Series, optional
            Extraterrestrial direct normal irradiance. [W/m2]
        airmass : float or Series, optional
            Airmass. [unitless]
        albedo : float or Series, optional
            Ground surface albedo. [unitless]
        model : String, default 'haydavies'
            Irradiance model.

        kwargs
            Extra parameters passed to
            :py:func:`pvlib.irradiance.get_total_irradiance`.

        Returns
        -------
        poa_irradiance : DataFrame
            Column names are: ``'poa_global', 'poa_direct', 'poa_diffuse',
            'poa_sky_diffuse', 'poa_ground_diffuse'``.

        Notes
        -----
        Some sky irradiance models require ``dni_extra``. For these models,
        if ``dni_extra`` is not provided and ``solar_zenith`` has a
        ``DatetimeIndex``, then ``dni_extra`` is calculated.
        Otherwise, ``dni_extra=1367`` is assumed.

        See also
        --------
        :py:func:`pvlib.irradiance.get_total_irradiance`
        """
        if albedo is None:
            albedo = self.albedo

        # dni_extra is not needed for all models, but this is easier
        if dni_extra is None:
            if (hasattr(solar_zenith, 'index') and
                    isinstance(solar_zenith.index, pd.DatetimeIndex)):
                # calculate extraterrestrial irradiance
                dni_extra = irradiance.get_extra_radiation(
                    solar_zenith.index)
            else:
                # use the solar constant
                dni_extra = 1367.0

        if airmass is None:
            airmass = atmosphere.get_relative_airmass(solar_zenith)

        orientation = self.mount.get_orientation(solar_zenith, solar_azimuth)
        return irradiance.get_total_irradiance(orientation['surface_tilt'],
                                               orientation['surface_azimuth'],
                                               solar_zenith, solar_azimuth,
                                               dni, ghi, dhi,
                                               dni_extra=dni_extra,
                                               airmass=airmass,
                                               albedo=albedo,
                                               model=model,
                                               **kwargs)

    def get_iam(self, aoi, iam_model='physical'):
        """
        Determine the incidence angle modifier using the method specified by
        ``iam_model``.

        Parameters for the selected IAM model are expected to be in
        ``Array.module_parameters``. Default parameters are available for
        the 'physical', 'ashrae' and 'martin_ruiz' models.

        Parameters
        ----------
        aoi : numeric
            The angle of incidence in degrees.

        aoi_model : string, default 'physical'
            The IAM model to be used. Valid strings are 'physical', 'ashrae',
            'martin_ruiz', 'sapm' and 'interp'.

        Returns
        -------
        iam : numeric
            The AOI modifier.

        Raises
        ------
        ValueError
            if `iam_model` is not a valid model name.
        """
        model = iam_model.lower()
        if model in ['ashrae', 'physical', 'martin_ruiz', 'interp']:
            func = getattr(iam, model)  # get function at pvlib.iam
            # get all parameters from function signature to retrieve them from
            # module_parameters if present
            params = set(inspect.signature(func).parameters.keys())
            params.discard('aoi')  # exclude aoi so it can't be repeated
            kwargs = _build_kwargs(params, self.module_parameters)
            return func(aoi, **kwargs)
        elif model == 'sapm':
            return iam.sapm(aoi, self.module_parameters)
        else:
            raise ValueError(model + ' is not a valid IAM model')

    def get_cell_temperature(self, poa_global, temp_air, wind_speed, model,
                             effective_irradiance=None):
        """
        Determine cell temperature using the method specified by ``model``.

        Parameters
        ----------
        poa_global : numeric
            Total incident irradiance [W/m^2]

        temp_air : numeric
            Ambient dry bulb temperature [C]

        wind_speed : numeric
            Wind speed [m/s]

        model : str
            Supported models include ``'sapm'``, ``'pvsyst'``,
            ``'faiman'``, ``'fuentes'``, and ``'noct_sam'``

        effective_irradiance : numeric, optional
            The irradiance that is converted to photocurrent in W/m^2.
            Only used for some models.

        Returns
        -------
        numeric
            Values in degrees C.

        See Also
        --------
        pvlib.temperature.sapm_cell, pvlib.temperature.pvsyst_cell,
        pvlib.temperature.faiman, pvlib.temperature.fuentes,
        pvlib.temperature.noct_sam

        Notes
        -----
        Some temperature models have requirements for the input types;
        see the documentation of the underlying model function for details.
        """
        # convenience wrapper to avoid passing args 2 and 3 every call
        _build_tcell_args = functools.partial(
            _build_args, input_dict=self.temperature_model_parameters,
            dict_name='temperature_model_parameters')

        if model == 'sapm':
            func = temperature.sapm_cell
            required = _build_tcell_args(['a', 'b', 'deltaT'])
            optional = _build_kwargs(['irrad_ref'],
                                     self.temperature_model_parameters)
        elif model == 'pvsyst':
            func = temperature.pvsyst_cell
            required = tuple()
            optional = {
                **_build_kwargs(['module_efficiency', 'alpha_absorption'],
                                self.module_parameters),
                **_build_kwargs(['u_c', 'u_v'],
                                self.temperature_model_parameters)
            }
        elif model == 'faiman':
            func = temperature.faiman
            required = tuple()
            optional = _build_kwargs(['u0', 'u1'],
                                     self.temperature_model_parameters)
        elif model == 'fuentes':
            func = temperature.fuentes
            required = _build_tcell_args(['noct_installed'])
            optional = _build_kwargs([
                'wind_height', 'emissivity', 'absorption',
                'surface_tilt', 'module_width', 'module_length'],
                self.temperature_model_parameters)
            if self.mount.module_height is not None:
                optional['module_height'] = self.mount.module_height
        elif model == 'noct_sam':
            func = functools.partial(temperature.noct_sam,
                                     effective_irradiance=effective_irradiance)
            required = _build_tcell_args(['noct', 'module_efficiency'])
            optional = _build_kwargs(['transmittance_absorptance',
                                      'array_height', 'mount_standoff'],
                                     self.temperature_model_parameters)
        else:
            raise ValueError(f'{model} is not a valid cell temperature model')

        temperature_cell = func(poa_global, temp_air, wind_speed,
                                *required, **optional)
        return temperature_cell

    def dc_ohms_from_percent(self):
        """
        Calculates the equivalent resistance of the wires using
        :py:func:`pvlib.pvsystem.dc_ohms_from_percent`

        Makes use of array module parameters according to the
        following DC models:

        CEC:

            * `self.module_parameters["V_mp_ref"]`
            * `self.module_parameters["I_mp_ref"]`

        SAPM:

            * `self.module_parameters["Vmpo"]`
            * `self.module_parameters["Impo"]`

        PVsyst-like or other:

            * `self.module_parameters["Vmpp"]`
            * `self.module_parameters["Impp"]`

        Other array parameters that are used are:
        `self.losses_parameters["dc_ohmic_percent"]`,
        `self.modules_per_string`, and
        `self.strings`.

        See :py:func:`pvlib.pvsystem.dc_ohms_from_percent` for more details.
        """

        # get relevent Vmp and Imp parameters from CEC parameters
        if all(elem in self.module_parameters
               for elem in ['V_mp_ref', 'I_mp_ref']):
            vmp_ref = self.module_parameters['V_mp_ref']
            imp_ref = self.module_parameters['I_mp_ref']

        # get relevant Vmp and Imp parameters from SAPM parameters
        elif all(elem in self.module_parameters for elem in ['Vmpo', 'Impo']):
            vmp_ref = self.module_parameters['Vmpo']
            imp_ref = self.module_parameters['Impo']

        # get relevant Vmp and Imp parameters if they are PVsyst-like
        elif all(elem in self.module_parameters for elem in ['Vmpp', 'Impp']):
            vmp_ref = self.module_parameters['Vmpp']
            imp_ref = self.module_parameters['Impp']

        # raise error if relevant Vmp and Imp parameters are not found
        else:
            raise ValueError('Parameters for Vmp and Imp could not be found '
                             'in the array module parameters. Module '
                             'parameters must include one set of '
                             '{"V_mp_ref", "I_mp_Ref"}, '
                             '{"Vmpo", "Impo"}, or '
                             '{"Vmpp", "Impp"}.'
                             )

        return dc_ohms_from_percent(
            vmp_ref,
            imp_ref,
            self.array_losses_parameters['dc_ohmic_percent'],
            self.modules_per_string,
            self.strings)


@dataclass
class AbstractMount(ABC):
    """
    A base class for Mount classes to extend. It is not intended to be
    instantiated directly.
    """

    @abstractmethod
    def get_orientation(self, solar_zenith, solar_azimuth):
        """
        Determine module orientation.

        Parameters
        ----------
        solar_zenith : numeric
            Solar apparent zenith angle [degrees]
        solar_azimuth : numeric
            Solar azimuth angle [degrees]

        Returns
        -------
        orientation : dict-like
            A dict-like object with keys `'surface_tilt', 'surface_azimuth'`
            (typically a dict or pandas.DataFrame)
        """


@dataclass
class FixedMount(AbstractMount):
    """
    Racking at fixed (static) orientation.

    Parameters
    ----------
    surface_tilt : float, default 0
        Surface tilt angle. The tilt angle is defined as angle from horizontal
        (e.g. surface facing up = 0, surface facing horizon = 90) [degrees]

    surface_azimuth : float, default 180
        Azimuth angle of the module surface. North=0, East=90, South=180,
        West=270. [degrees]

    racking_model : str, optional
        Valid strings are ``'open_rack'``, ``'close_mount'``,
        ``'insulated_back'``, ``'freestanding'``, ``'insulated'``, and
        ``'semi_integrated'``.
        Used to identify a parameter set for the SAPM or PVsyst cell
        temperature model.
        See :py:func:`~pvlib.temperature.sapm_module` and
        :py:func:`~pvlib.temperature.pvsyst_cell` for definitions.

    module_height : float, optional
       The height above ground of the center of the module [m]. Used for
       the Fuentes cell temperature model.
    """

    surface_tilt: float = 0.0
    surface_azimuth: float = 180.0
    racking_model: Optional[str] = None
    module_height: Optional[float] = None

    def get_orientation(self, solar_zenith, solar_azimuth):
        # note -- docstring is automatically inherited from AbstractMount
        return {
            'surface_tilt': self.surface_tilt,
            'surface_azimuth': self.surface_azimuth,
        }


@dataclass
class SingleAxisTrackerMount(AbstractMount):
    """
    Single-axis tracker racking for dynamic solar tracking.

    Parameters
    ----------
    axis_tilt : float, default 0
        The tilt of the axis of rotation (i.e, the y-axis defined by
        axis_azimuth) with respect to horizontal. [degrees]

    axis_azimuth : float, default 180
        A value denoting the compass direction along which the axis of
        rotation lies, measured east of north. [degrees]

    max_angle : float or tuple, default 90
        A value denoting the maximum rotation angle, in decimal degrees,
        of the one-axis tracker from its horizontal position (horizontal
        if axis_tilt = 0). If a float is provided, it represents the maximum
        rotation angle, and the minimum rotation angle is assumed to be the
        opposite of the maximum angle. If a tuple of (min_angle, max_angle) is
        provided, it represents both the minimum and maximum rotation angles.

        A rotation to 'max_angle' is a counter-clockwise rotation about the
        y-axis of the tracker coordinate system. For example, for a tracker
        with 'axis_azimuth' oriented to the south, a rotation to 'max_angle'
        is towards the west, and a rotation toward 'min_angle' is in the
        opposite direction, toward the east. Hence a max_angle of 180 degrees
        (equivalent to max_angle = (-180, 180)) allows the tracker to achieve
        its full rotation capability.

    backtrack : bool, default True
        Controls whether the tracker has the capability to "backtrack"
        to avoid row-to-row shading. False denotes no backtrack
        capability. True denotes backtrack capability.

    gcr : float, default 2.0/7.0
        A value denoting the ground coverage ratio of a tracker system
        which utilizes backtracking; i.e. the ratio between the PV array
        surface area to total ground area. A tracker system with modules
        2 meters wide, centered on the tracking axis, with 6 meters
        between the tracking axes has a gcr of 2/6=0.333. If gcr is not
        provided, a gcr of 2/7 is default. gcr must be <=1. [unitless]

    cross_axis_tilt : float, default 0.0
        The angle, relative to horizontal, of the line formed by the
        intersection between the slope containing the tracker axes and a plane
        perpendicular to the tracker axes. Cross-axis tilt should be specified
        using a right-handed convention. For example, trackers with axis
        azimuth of 180 degrees (heading south) will have a negative cross-axis
        tilt if the tracker axes plane slopes down to the east and positive
        cross-axis tilt if the tracker axes plane slopes up to the east. Use
        :func:`~pvlib.tracking.calc_cross_axis_tilt` to calculate
        `cross_axis_tilt`. [degrees]

    racking_model : str, optional
        Valid strings are ``'open_rack'``, ``'close_mount'``,
        ``'insulated_back'``, ``'freestanding'``, ``'insulated'``, and
        ``'semi_integrated'``.
        Used to identify a parameter set for the SAPM or PVsyst cell
        temperature model. ``'open_rack'`` or ``'freestanding'`` should
        be used for systems with single-axis trackers.
        See :py:func:`~pvlib.temperature.sapm_module` and
        :py:func:`~pvlib.temperature.pvsyst_cell` for definitions.

    module_height : float, optional
       The height above ground of the center of the module [m]. Used for
       the Fuentes cell temperature model.
    """
    axis_tilt: float = 0.0
    axis_azimuth: float = 0.0
    max_angle: Union[float, tuple] = 90.0
    backtrack: bool = True
    gcr: float = 2.0/7.0
    cross_axis_tilt: float = 0.0
    racking_model: Optional[str] = None
    module_height: Optional[float] = None

    def get_orientation(self, solar_zenith, solar_azimuth):
        # note -- docstring is automatically inherited from AbstractMount
        from pvlib import tracking  # avoid circular import issue
        tracking_data = tracking.singleaxis(
            solar_zenith, solar_azimuth,
            self.axis_tilt, self.axis_azimuth,
            self.max_angle, self.backtrack,
            self.gcr, self.cross_axis_tilt
        )
        return tracking_data


def calcparams_desoto(effective_irradiance, temp_cell,
                      alpha_sc, a_ref, I_L_ref, I_o_ref, R_sh_ref, R_s,
                      EgRef=1.121, dEgdT=-0.0002677,
                      irrad_ref=1000, temp_ref=25):
    '''
    Calculates five parameter values for the single diode equation at
    effective irradiance and cell temperature using the De Soto et al.
    model. The five values returned by ``calcparams_desoto`` can be used by
    singlediode to calculate an IV curve.

    The model is described in [1]_.

    Parameters
    ----------
    effective_irradiance : numeric
        The irradiance (W/m2) that is converted to photocurrent.

    temp_cell : numeric
        The average cell temperature of cells within a module in C.

    alpha_sc : float
        The short-circuit current temperature coefficient of the
        module in units of A/C.

    a_ref : float
        The product of the usual diode ideality factor (n, unitless),
        number of cells in series (Ns), and cell thermal voltage at reference
        conditions, in units of V.

    I_L_ref : float
        The light-generated current (or photocurrent) at reference conditions,
        in amperes.

    I_o_ref : float
        The dark or diode reverse saturation current at reference conditions,
        in amperes.

    R_sh_ref : float
        The shunt resistance at reference conditions, in ohms.

    R_s : float
        The series resistance at reference conditions, in ohms.

    EgRef : float
        The energy bandgap at reference temperature in units of eV.
        1.121 eV for crystalline silicon. EgRef must be >0.  For parameters
        from the SAM CEC module database, EgRef=1.121 is implicit for all
        cell types in the parameter estimation algorithm used by NREL.

    dEgdT : float
        The temperature dependence of the energy bandgap at reference
        conditions in units of 1/K. May be either a scalar value
        (e.g. -0.0002677 as in [1]_) or a DataFrame (this may be useful if
        dEgdT is a modeled as a function of temperature). For parameters from
        the SAM CEC module database, dEgdT=-0.0002677 is implicit for all cell
        types in the parameter estimation algorithm used by NREL.

    irrad_ref : float, default 1000
        Reference irradiance in W/m^2.

    temp_ref : float, default 25
        Reference cell temperature in C.

    Returns
    -------
    Tuple of the following results:

    photocurrent : numeric
        Light-generated current in amperes

    saturation_current : numeric
        Diode saturation current in amperes

    resistance_series : numeric
        Series resistance in ohms

    resistance_shunt : numeric
        Shunt resistance in ohms

    nNsVth : numeric
        The product of the usual diode ideality factor (n, unitless),
        number of cells in series (Ns), and cell thermal voltage at
        specified effective irradiance and cell temperature.

    References
    ----------
    .. [1] W. De Soto et al., "Improvement and validation of a model for
       photovoltaic array performance", Solar Energy, vol 80, pp. 78-88,
       2006.

    .. [2] System Advisor Model web page. https://sam.nrel.gov.

    .. [3] A. Dobos, "An Improved Coefficient Calculator for the California
       Energy Commission 6 Parameter Photovoltaic Module Model", Journal of
       Solar Energy Engineering, vol 134, 2012.

    .. [4] O. Madelung, "Semiconductors: Data Handbook, 3rd ed." ISBN
       3-540-40488-0

    See Also
    --------
    singlediode
    retrieve_sam

    Notes
    -----
    If the reference parameters in the ModuleParameters struct are read
    from a database or library of parameters (e.g. System Advisor
    Model), it is important to use the same EgRef and dEgdT values that
    were used to generate the reference parameters, regardless of the
    actual bandgap characteristics of the semiconductor. For example, in
    the case of the System Advisor Model library, created as described
    in [3], EgRef and dEgdT for all modules were 1.121 and -0.0002677,
    respectively.

    This table of reference bandgap energies (EgRef), bandgap energy
    temperature dependence (dEgdT), and "typical" airmass response (M)
    is provided purely as reference to those who may generate their own
    reference module parameters (a_ref, IL_ref, I0_ref, etc.) based upon
    the various PV semiconductors. Again, we stress the importance of
    using identical EgRef and dEgdT when generation reference parameters
    and modifying the reference parameters (for irradiance, temperature,
    and airmass) per DeSoto's equations.

     Crystalline Silicon (Si):
         * EgRef = 1.121
         * dEgdT = -0.0002677

         >>> M = np.polyval([-1.26E-4, 2.816E-3, -0.024459, 0.086257, 0.9181],
         ...                AMa) # doctest: +SKIP

         Source: [1]

     Cadmium Telluride (CdTe):
         * EgRef = 1.475
         * dEgdT = -0.0003

         >>> M = np.polyval([-2.46E-5, 9.607E-4, -0.0134, 0.0716, 0.9196],
         ...                AMa) # doctest: +SKIP

         Source: [4]

     Copper Indium diSelenide (CIS):
         * EgRef = 1.010
         * dEgdT = -0.00011

         >>> M = np.polyval([-3.74E-5, 0.00125, -0.01462, 0.0718, 0.9210],
         ...                AMa) # doctest: +SKIP

         Source: [4]

     Copper Indium Gallium diSelenide (CIGS):
         * EgRef = 1.15
         * dEgdT = ????

         >>> M = np.polyval([-9.07E-5, 0.0022, -0.0202, 0.0652, 0.9417],
         ...                AMa) # doctest: +SKIP

         Source: Wikipedia

     Gallium Arsenide (GaAs):
         * EgRef = 1.424
         * dEgdT = -0.000433
         * M = unknown

         Source: [4]
    '''

    # Boltzmann constant in eV/K, 8.617332478e-05
    k = constants.value('Boltzmann constant in eV/K')

    # reference temperature
    Tref_K = temp_ref + 273.15
    Tcell_K = temp_cell + 273.15

    E_g = EgRef * (1 + dEgdT*(Tcell_K - Tref_K))

    nNsVth = a_ref * (Tcell_K / Tref_K)

    # In the equation for IL, the single factor effective_irradiance is
    # used, in place of the product S*M in [1]. effective_irradiance is
    # equivalent to the product of S (irradiance reaching a module's cells) *
    # M (spectral adjustment factor) as described in [1].
    IL = effective_irradiance / irrad_ref * \
        (I_L_ref + alpha_sc * (Tcell_K - Tref_K))
    I0 = (I_o_ref * ((Tcell_K / Tref_K) ** 3) *
          (np.exp(EgRef / (k*(Tref_K)) - (E_g / (k*(Tcell_K))))))
    # Note that the equation for Rsh differs from [1]. In [1] Rsh is given as
    # Rsh = Rsh_ref * (S_ref / S) where S is broadband irradiance reaching
    # the module's cells. If desired this model behavior can be duplicated
    # by applying reflection and soiling losses to broadband plane of array
    # irradiance and not applying a spectral loss modifier, i.e.,
    # spectral_modifier = 1.0.
    # use errstate to silence divide by warning
    with np.errstate(divide='ignore'):
        Rsh = R_sh_ref * (irrad_ref / effective_irradiance)

    Rs = R_s

    numeric_args = (effective_irradiance, temp_cell)
    # IL: photocurrent, I0: saturation_current, Rs: resistance_series,
    # Rsh: resistance_shunt
    out = (IL, I0, Rs, Rsh, nNsVth)

    if all(map(np.isscalar, numeric_args)):
        return out

    index = tools.get_pandas_index(*numeric_args)

    if index is None:
        return np.broadcast_arrays(*out)

    return tuple(pd.Series(a, index=index).rename(None) for a in out)


def calcparams_cec(effective_irradiance, temp_cell,
                   alpha_sc, a_ref, I_L_ref, I_o_ref, R_sh_ref, R_s,
                   Adjust, EgRef=1.121, dEgdT=-0.0002677,
                   irrad_ref=1000, temp_ref=25):
    '''
    Calculates five parameter values for the single diode equation at
    effective irradiance and cell temperature using the CEC
    model. The CEC model [1]_ differs from the De soto et al.
    model [3]_ by the parameter Adjust. The five values returned by
    calcparams_cec can be used by singlediode to calculate an IV curve.

    Parameters
    ----------
    effective_irradiance : numeric
        The irradiance (W/m2) that is converted to photocurrent.

    temp_cell : numeric
        The average cell temperature of cells within a module in C.

    alpha_sc : float
        The short-circuit current temperature coefficient of the
        module in units of A/C.

    a_ref : float
        The product of the usual diode ideality factor (n, unitless),
        number of cells in series (Ns), and cell thermal voltage at reference
        conditions, in units of V.

    I_L_ref : float
        The light-generated current (or photocurrent) at reference conditions,
        in amperes.

    I_o_ref : float
        The dark or diode reverse saturation current at reference conditions,
        in amperes.

    R_sh_ref : float
        The shunt resistance at reference conditions, in ohms.

    R_s : float
        The series resistance at reference conditions, in ohms.

    Adjust : float
        The adjustment to the temperature coefficient for short circuit
        current, in percent

    EgRef : float
        The energy bandgap at reference temperature in units of eV.
        1.121 eV for crystalline silicon. EgRef must be >0.  For parameters
        from the SAM CEC module database, EgRef=1.121 is implicit for all
        cell types in the parameter estimation algorithm used by NREL.

    dEgdT : float
        The temperature dependence of the energy bandgap at reference
        conditions in units of 1/K. May be either a scalar value
        (e.g. -0.0002677 as in [3]) or a DataFrame (this may be useful if
        dEgdT is a modeled as a function of temperature). For parameters from
        the SAM CEC module database, dEgdT=-0.0002677 is implicit for all cell
        types in the parameter estimation algorithm used by NREL.

    irrad_ref : float, default 1000
        Reference irradiance in W/m^2.

    temp_ref : float, default 25
        Reference cell temperature in C.

    Returns
    -------
    Tuple of the following results:

    photocurrent : numeric
        Light-generated current in amperes

    saturation_current : numeric
        Diode saturation curent in amperes

    resistance_series : numeric
        Series resistance in ohms

    resistance_shunt : numeric
        Shunt resistance in ohms

    nNsVth : numeric
        The product of the usual diode ideality factor (n, unitless),
        number of cells in series (Ns), and cell thermal voltage at
        specified effective irradiance and cell temperature.

    References
    ----------
    .. [1] A. Dobos, "An Improved Coefficient Calculator for the California
       Energy Commission 6 Parameter Photovoltaic Module Model", Journal of
       Solar Energy Engineering, vol 134, 2012.

    .. [2] System Advisor Model web page. https://sam.nrel.gov.

    .. [3] W. De Soto et al., "Improvement and validation of a model for
       photovoltaic array performance", Solar Energy, vol 80, pp. 78-88,
       2006.

    See Also
    --------
    calcparams_desoto
    singlediode
    retrieve_sam

    '''

    # pass adjusted temperature coefficient to desoto
    return calcparams_desoto(effective_irradiance, temp_cell,
                             alpha_sc*(1.0 - Adjust/100),
                             a_ref, I_L_ref, I_o_ref,
                             R_sh_ref, R_s,
                             EgRef=EgRef, dEgdT=dEgdT,
                             irrad_ref=irrad_ref, temp_ref=temp_ref)


def calcparams_pvsyst(effective_irradiance, temp_cell,
                      alpha_sc, gamma_ref, mu_gamma,
                      I_L_ref, I_o_ref,
                      R_sh_ref, R_sh_0, R_s,
                      cells_in_series,
                      R_sh_exp=5.5,
                      EgRef=1.121,
                      irrad_ref=1000, temp_ref=25):
    '''
    Calculates five parameter values for the single diode equation at
    effective irradiance and cell temperature using the PVsyst v6
    model.  The PVsyst v6 model is described in [1]_, [2]_, [3]_.
    The five values returned by calcparams_pvsyst can be used by singlediode
    to calculate an IV curve.

    Parameters
    ----------
    effective_irradiance : numeric
        The irradiance (W/m2) that is converted to photocurrent.

    temp_cell : numeric
        The average cell temperature of cells within a module in C.

    alpha_sc : float
        The short-circuit current temperature coefficient of the
        module in units of A/C.

    gamma_ref : float
        The diode ideality factor

    mu_gamma : float
        The temperature coefficient for the diode ideality factor, 1/K

    I_L_ref : float
        The light-generated current (or photocurrent) at reference conditions,
        in amperes.

    I_o_ref : float
        The dark or diode reverse saturation current at reference conditions,
        in amperes.

    R_sh_ref : float
        The shunt resistance at reference conditions, in ohms.

    R_sh_0 : float
        The shunt resistance at zero irradiance conditions, in ohms.

    R_s : float
        The series resistance at reference conditions, in ohms.

    cells_in_series : integer
        The number of cells connected in series.

    R_sh_exp : float
        The exponent in the equation for shunt resistance, unitless. Defaults
        to 5.5.

    EgRef : float
        The energy bandgap at reference temperature in units of eV.
        1.121 eV for crystalline silicon. EgRef must be >0.

    irrad_ref : float, default 1000
        Reference irradiance in W/m^2.

    temp_ref : float, default 25
        Reference cell temperature in C.

    Returns
    -------
    Tuple of the following results:

    photocurrent : numeric
        Light-generated current in amperes

    saturation_current : numeric
        Diode saturation current in amperes

    resistance_series : numeric
        Series resistance in ohms

    resistance_shunt : numeric
        Shunt resistance in ohms

    nNsVth : numeric
        The product of the usual diode ideality factor (n, unitless),
        number of cells in series (Ns), and cell thermal voltage at
        specified effective irradiance and cell temperature.

    References
    ----------
    .. [1] K. Sauer, T. Roessler, C. W. Hansen, Modeling the Irradiance and
       Temperature Dependence of Photovoltaic Modules in PVsyst,
       IEEE Journal of Photovoltaics v5(1), January 2015.

    .. [2] A. Mermoud, PV modules modelling, Presentation at the 2nd PV
       Performance Modeling Workshop, Santa Clara, CA, May 2013

    .. [3] A. Mermoud, T. Lejeune, Performance Assessment of a Simulation Model
       for PV modules of any available technology, 25th European Photovoltaic
       Solar Energy Conference, Valencia, Spain, Sept. 2010

    See Also
    --------
    calcparams_desoto
    singlediode

    '''

    gamma = _pvsyst_gamma(temp_cell, gamma_ref, mu_gamma, temp_ref)

    nNsVth = _pvsyst_nNsVth(temp_cell, gamma, cells_in_series)

    IL = _pvsyst_IL(effective_irradiance, temp_cell, I_L_ref, alpha_sc,
                    irrad_ref, temp_ref)

    I0 = _pvsyst_Io(temp_cell, gamma, I_o_ref, EgRef, temp_ref)

    Rsh = _pvsyst_Rsh(effective_irradiance, R_sh_ref, R_sh_0, R_sh_exp,
                      irrad_ref)

    Rs = R_s

    numeric_args = (effective_irradiance, temp_cell)
    # IL: photocurrent, I0: saturation_current, Rs: resistance_series,
    # Rsh: resistance_shunt
    out = (IL, I0, Rs, Rsh, nNsVth)

    if all(map(np.isscalar, numeric_args)):
        return out

    index = tools.get_pandas_index(*numeric_args)

    if index is None:
        return np.broadcast_arrays(*out)

    return tuple(pd.Series(a, index=index).rename(None) for a in out)


def _pvsyst_Rsh(effective_irradiance, R_sh_ref, R_sh_0, R_sh_exp=5.5,
                irrad_ref=1000):
    Rsh_tmp = \
        (R_sh_ref - R_sh_0 * np.exp(-R_sh_exp)) / (1.0 - np.exp(-R_sh_exp))
    Rsh_base = np.maximum(0.0, Rsh_tmp)

    Rsh = Rsh_base + (R_sh_0 - Rsh_base) * \
        np.exp(-R_sh_exp * effective_irradiance / irrad_ref)

    return Rsh


def _pvsyst_IL(effective_irradiance, temp_cell, I_L_ref, alpha_sc,
               irrad_ref=1000, temp_ref=25):
    Tref_K = temp_ref + 273.15
    Tcell_K = temp_cell + 273.15
    IL = effective_irradiance / irrad_ref * \
        (I_L_ref + alpha_sc * (Tcell_K - Tref_K))
    return IL


def _pvsyst_Io(temp_cell, gamma, I_o_ref, EgRef, temp_ref=25):
    k = constants.k  # Boltzmann constant in J/K
    q = constants.e  # elementary charge in coulomb

    Tref_K = temp_ref + 273.15
    Tcell_K = temp_cell + 273.15

    Io = I_o_ref * ((Tcell_K / Tref_K) ** 3) * \
        (np.exp((q * EgRef) / (k * gamma) * (1 / Tref_K - 1 / Tcell_K)))

    return Io


def _pvsyst_gamma(temp_cell, gamma_ref, mu_gamma, temp_ref=25):
    gamma = gamma_ref + mu_gamma * (temp_cell - temp_ref)
    return gamma


def _pvsyst_nNsVth(temp_cell, gamma, cells_in_series):
    k = constants.k  # Boltzmann constant in J/K
    q = constants.e  # elementary charge in coulomb
    Tcell_K = temp_cell + 273.15

    nNsVth = gamma * k / q * cells_in_series * Tcell_K
    return nNsVth


def retrieve_sam(name=None, path=None):
    """
    Retrieve latest module and inverter info from a file bundled with pvlib,
    a path or an URL (like SAM's website).

    This function will retrieve either:

    * CEC module database
    * Sandia Module database
    * CEC Inverter database
    * Anton Driesse Inverter database

    and return it as a pandas DataFrame.

    .. note::
        Only provide one of ``name`` or ``path``.

    Parameters
    ----------
    name : string, optional
        Use one of the following strings to retrieve a database bundled with
        pvlib:

        * ``'CECMod'`` - returns the CEC module database
        * ``'CECInverter'`` - returns the CEC Inverter database
        * ``'SandiaInverter'`` - returns the CEC Inverter database
          (CEC is only current inverter db available; tag kept for
          backwards compatibility)
        * ``'SandiaMod'`` - returns the Sandia Module database
        * ``'ADRInverter'`` - returns the ADR Inverter database

    path : string, optional
        Path to a CSV file or a URL.

    Returns
    -------
    DataFrame
        A DataFrame containing all the elements of the desired database.
        Each column represents a module or inverter, and a specific
        dataset can be retrieved by the command

    Raises
    ------
    ValueError
        If no ``name`` or ``path`` is provided.
    ValueError
        If both ``name`` and ``path`` are provided.
    KeyError
        If the provided ``name`` is not a valid database name.

    Notes
    -----
    Files available at
        https://github.com/NREL/SAM/tree/develop/deploy/libraries

    Examples
    --------
    Using a database bundled with pvlib:

    >>> from pvlib import pvsystem
    >>> invdb = pvsystem.retrieve_sam(name='CECInverter')
    >>> inverter = invdb.AE_Solar_Energy__AE6_0__277V_
    >>> inverter
    Vac                          277
    Pso                    36.197575
    Paco                      6000.0
    Pdco                 6158.746094
    Vdco                       360.0
    C0                     -0.000002
    C1                     -0.000026
    C2                     -0.001253
    C3                       0.00021
    Pnt                          1.8
    Vdcmax                     450.0
    Idcmax                 17.107628
    Mppt_low                   100.0
    Mppt_high                  450.0
    CEC_Date                     NaN
    CEC_Type     Utility Interactive
    Name: AE_Solar_Energy__AE6_0__277V_, dtype: object

    Using a remote database, via URL:

    >>> url = "https://raw.githubusercontent.com/NREL/SAM/refs/heads/develop/deploy/libraries/CEC%20Inverters.csv"
    >>> inv_db = pvsystem.retrieve_sam(path=url)
    >>> inv_db.keys()
    Index(['ABB__PVI_3_0_OUTD_S_US_A__208V_', 'ABB__PVI_3_0_OUTD_S_US_A__240V_', ...],
          dtype='object', length=...)
    """  # noqa: E501
    # error: path was previously silently ignored if name was given GH#2018
    if name is not None and path is not None:
        raise ValueError("Please provide either 'name' or 'path', not both.")
    elif name is None and path is None:
        raise ValueError("Please provide either 'name' or 'path'.")
    elif name is not None:
        internal_dbs = {
            "cecmod": "sam-library-cec-modules-2019-03-05.csv",
            "sandiamod": "sam-library-sandia-modules-2015-6-30.csv",
            "adrinverter": "adr-library-cec-inverters-2019-03-05.csv",
            # Both 'cecinverter' and 'sandiainverter', point to same database
            # to provide for old code, while aligning with current expectations
            "cecinverter": "sam-library-cec-inverters-2019-03-05.csv",
            "sandiainverter": "sam-library-cec-inverters-2019-03-05.csv",
        }
        try:
            csvdata_path = Path(__file__).parent.joinpath(
                "data", internal_dbs[name.lower()]
            )
        except KeyError:
            raise KeyError(
                f"Invalid name {name}. "
                + f"Provide one of {list(internal_dbs.keys())}."
            ) from None
    else:  # path is not None
        if path.lower().startswith("http"):  # URL check is not case-sensitive
            response = urlopen(path)  # URL is case-sensitive
            csvdata_path = io.StringIO(response.read().decode(errors="ignore"))
        else:
            csvdata_path = path
    return _parse_raw_sam_df(csvdata_path)


def _normalize_sam_product_names(names):
    '''
    Replace special characters within the product names to make them more
    suitable for use as Dataframe column names.
    '''
    # Contributed by Anton Driesse (@adriesse), PV Performance Labs. July, 2019

    import warnings

    BAD_CHARS = ' -.()[]:+/",'
    GOOD_CHARS = '____________'

    mapping = str.maketrans(BAD_CHARS, GOOD_CHARS)
    names = pd.Series(data=names)
    norm_names = names.str.translate(mapping)

    n_duplicates = names.duplicated().sum()
    if n_duplicates > 0:
        warnings.warn('Original names contain %d duplicate(s).' % n_duplicates)

    n_duplicates = norm_names.duplicated().sum()
    if n_duplicates > 0:
        warnings.warn(
            'Normalized names contain %d duplicate(s).' % n_duplicates)

    return norm_names.values


def _parse_raw_sam_df(csvdata):

    df = pd.read_csv(csvdata, index_col=0, skiprows=[1, 2])

    df.columns = df.columns.str.replace(' ', '_')
    df.index = _normalize_sam_product_names(df.index)
    df = df.transpose()

    if 'ADRCoefficients' in df.index:
        ad_ce = 'ADRCoefficients'
        # for each inverter, parses a string of coefficients like
        # ' 1.33, 2.11, 3.12' into a list containing floats:
        # [1.33, 2.11, 3.12]
        df.loc[ad_ce] = df.loc[ad_ce].map(lambda x: list(
            map(float, x.strip(' []').split())))

    return df


def sapm(effective_irradiance, temp_cell, module, *, temperature_ref=25,
         irradiance_ref=1000):
    '''
    The Sandia PV Array Performance Model (SAPM) generates 5 points on a
    PV module's I-V curve (Voc, Isc, Ix, Ixx, Vmp/Imp) according to
    SAND2004-3535. Assumes a reference cell temperature of 25°C.

    Parameters
    ----------
    effective_irradiance : numeric
        Irradiance reaching the module's cells, after reflections and
        adjustment for spectrum. [Wm⁻²]

    temp_cell : numeric
        Cell temperature [°C].

    module : dict-like
        A dict or Series defining the SAPM parameters. See the notes section
        for more details.

    temperature_ref : numeric, optional
        Reference temperature [°C]

    irradiance_ref : numeric, optional
        Reference irradiance [Wm⁻²]

    Returns
    -------
    A DataFrame with the columns:

        * i_sc : Short-circuit current (A)
        * i_mp : Current at the maximum-power point (A)
        * v_oc : Open-circuit voltage (V)
        * v_mp : Voltage at maximum-power point (V)
        * p_mp : Power at maximum-power point (W)
        * i_x : Current at module V = 0.5Voc, defines 4th point on I-V
          curve for modeling curve shape.  Omitted if ``IXO``, ``C4``, and
          ``C5`` parameters are not supplied.
        * i_xx : Current at module V = 0.5(Voc+Vmp), defines 5th point on
          I-V curve for modeling curve shape.  Omitted if ``IXXO``, ``C6``,
          and ``C7`` parameters are not supplied.

    Notes
    -----
    The Sandia module database contains parameter values for a limited set
    of modules. The CEC module database does not contain these parameters.
    Both databases can be accessed using :py:func:`retrieve_sam`. The full list
    of SAPM parameters is presented in the table below. Those that are required
    in the ``module`` parameter to run this model are as follows:

    * ``C0``, ``C1``, ``C2``, ``C3``
    * ``Isco``
    * ``Impo``
    * ``Voco``
    * ``Vmpo``
    * ``Aisc``
    * ``Aimp``
    * ``Bvoco``
    * ``Mbvoc``
    * ``Bvmpo``
    * ``Mbvmp``
    * ``N``
    * ``Cells_in_series``

    ================   ========================================================
    Key                Description
    ================   ========================================================
    A0-A4              The airmass coefficients used in calculating
                       effective irradiance
    B0-B5              The angle of incidence coefficients used in calculating
                       effective irradiance
    C0-C7              The empirically determined coefficients relating
                       Imp, Vmp, Ix, and Ixx to effective irradiance
    Isco               Short circuit current at reference condition (amps)
    Impo               Maximum power current at reference condition (amps)
    Voco               Open circuit voltage at reference condition (amps)
    Vmpo               Maximum power voltage at reference condition (amps)
    Aisc               Short circuit current temperature coefficient at
                       reference condition (1/°C)
    Aimp               Maximum power current temperature coefficient at
                       reference condition (1/°C)
    Bvoco              Open circuit voltage temperature coefficient at
                       reference condition (V/°C)
    Mbvoc              Coefficient providing the irradiance dependence for the
                       BetaVoc temperature coefficient at reference irradiance
                       (V/°C)
    Bvmpo              Maximum power voltage temperature coefficient at
                       reference condition
    Mbvmp              Coefficient providing the irradiance dependence for the
                       BetaVmp temperature coefficient at reference irradiance
                       (V/°C)
    N                  Empirically determined "diode factor" (dimensionless)
    Cells_in_Series    Number of cells in series in a module's cell string(s)
    IXO                Ix at reference conditions
    IXXO               Ixx at reference conditions
    FD                 Fraction of diffuse irradiance used by module
    ================   ========================================================

    References
    ----------
    .. [1] King, D. et al, 2004, "Sandia Photovoltaic Array Performance
       Model", SAND Report 3535, Sandia National Laboratories, Albuquerque,
       NM.

    See Also
    --------
    retrieve_sam
    pvlib.temperature.sapm_cell
    pvlib.temperature.sapm_module
    '''

    q = constants.e  # Elementary charge in units of coulombs
    kb = constants.k  # Boltzmann's constant in units of J/K

    # avoid problem with integer input
    Ee = np.array(effective_irradiance, dtype='float64') / irradiance_ref

    # set up masking for 0, positive, and nan inputs
    Ee_gt_0 = np.full_like(Ee, False, dtype='bool')
    Ee_eq_0 = np.full_like(Ee, False, dtype='bool')
    notnan = ~np.isnan(Ee)
    np.greater(Ee, 0, where=notnan, out=Ee_gt_0)
    np.equal(Ee, 0, where=notnan, out=Ee_eq_0)

    Bvmpo = module['Bvmpo'] + module['Mbvmp']*(1 - Ee)
    Bvoco = module['Bvoco'] + module['Mbvoc']*(1 - Ee)
    delta = module['N'] * kb * (temp_cell + 273.15) / q

    # avoid repeated computation
    logEe = np.full_like(Ee, np.nan)
    np.log(Ee, where=Ee_gt_0, out=logEe)
    logEe = np.where(Ee_eq_0, -np.inf, logEe)
    # avoid repeated __getitem__
    cells_in_series = module['Cells_in_Series']

    out = OrderedDict()

    out['i_sc'] = (
        module['Isco'] * Ee * (1 + module['Aisc']*(temp_cell -
                                                   temperature_ref)))

    out['i_mp'] = (
        module['Impo'] * (module['C0']*Ee + module['C1']*(Ee**2)) *
        (1 + module['Aimp']*(temp_cell - temperature_ref)))

    out['v_oc'] = np.maximum(0, (
        module['Voco'] + cells_in_series * delta * logEe +
        Bvoco*(temp_cell - temperature_ref)))

    out['v_mp'] = np.maximum(0, (
        module['Vmpo'] +
        module['C2'] * cells_in_series * delta * logEe +
        module['C3'] * cells_in_series * ((delta * logEe) ** 2) +
        Bvmpo*(temp_cell - temperature_ref)))

    out['p_mp'] = out['i_mp'] * out['v_mp']

    if 'IXO' in module and 'C4' in module and 'C5' in module:
        out['i_x'] = (
            module['IXO'] * (module['C4']*Ee + module['C5']*(Ee**2)) *
            (1 + module['Aisc']*(temp_cell - temperature_ref)))

    if 'IXXO' in module and 'C6' in module and 'C7' in module:
        out['i_xx'] = (
            module['IXXO'] * (module['C6']*Ee + module['C7']*(Ee**2)) *
            (1 + module['Aimp']*(temp_cell - temperature_ref)))

    if isinstance(out['i_sc'], pd.Series):
        out = pd.DataFrame(out)

    return out


def sapm_effective_irradiance(poa_direct, poa_diffuse, airmass_absolute, aoi,
                              module):
    r"""
    Calculates the SAPM effective irradiance using the SAPM spectral
    loss and SAPM angle of incidence loss functions.

    Parameters
    ----------
    poa_direct : numeric
        The direct irradiance incident upon the module. [W/m2]

    poa_diffuse : numeric
        The diffuse irradiance incident on module.  [W/m2]

    airmass_absolute : numeric
        Absolute airmass. [unitless]

    aoi : numeric
        Angle of incidence. [degrees]

    module : dict-like
        A dict, Series, or DataFrame defining the SAPM performance
        parameters. See the :py:func:`sapm` notes section for more
        details.

    Returns
    -------
    effective_irradiance : numeric
        Effective irradiance accounting for reflections and spectral content.
        [W/m2]

    Notes
    -----
    The SAPM model for effective irradiance [1]_ translates broadband direct
    and diffuse irradiance on the plane of array to the irradiance absorbed by
    a module's cells.

    The model is

    .. math::

        Ee = f_1(AM_a) (E_b f_2(AOI) + f_d E_d)

    where :math:`Ee` is effective irradiance (W/m2), :math:`f_1` is a fourth
    degree polynomial in air mass :math:`AM_a`, :math:`E_b` is beam (direct)
    irradiance on the plane of array, :math:`E_d` is diffuse irradiance on the
    plane of array, :math:`f_2` is a fifth degree polynomial in the angle of
    incidence :math:`AOI`, and :math:`f_d` is the fraction of diffuse
    irradiance on the plane of array that is not reflected away.

    References
    ----------
    .. [1] D. King et al, "Sandia Photovoltaic Array Performance Model",
       SAND2004-3535, Sandia National Laboratories, Albuquerque, NM

    See also
    --------
    pvlib.iam.sapm
    pvlib.spectrum.spectral_factor_sapm
    pvlib.pvsystem.sapm
    """

    F1 = spectrum.spectral_factor_sapm(airmass_absolute, module)
    F2 = iam.sapm(aoi, module)

    Ee = F1 * (poa_direct * F2 + module['FD'] * poa_diffuse)

    return Ee


def singlediode(photocurrent, saturation_current, resistance_series,
                resistance_shunt, nNsVth, method='lambertw'):
    r"""
    Solve the single diode equation to obtain a photovoltaic IV curve.

    Solves the single diode equation [1]_

    .. math::

        I = I_L -
            I_0 \left[
                \exp \left(\frac{V+I R_s}{n N_s V_{th}} \right)-1
            \right] -
            \frac{V + I R_s}{R_{sh}}

    for :math:`I` and :math:`V` when given :math:`I_L, I_0, R_s, R_{sh},` and
    :math:`n N_s V_{th}` which are described later. The five points on the I-V
    curve specified in [3]_ are returned. If :math:`I_L, I_0, R_s, R_{sh},` and
    :math:`n N_s V_{th}` are all scalars, a single curve is returned. If any
    are array-like (of the same length), multiple IV curves are calculated.

    The input parameters can be calculated from meteorological data using a
    function for a single diode model, e.g.,
    :py:func:`~pvlib.pvsystem.calcparams_desoto`.

    Parameters
    ----------
    photocurrent : numeric
        Light-generated current :math:`I_L` (photocurrent)
        ``0 <= photocurrent``. [A]

    saturation_current : numeric
        Diode saturation :math:`I_0` current under desired IV curve
        conditions. ``0 < saturation_current``. [A]

    resistance_series : numeric
        Series resistance :math:`R_s` under desired IV curve conditions.
        ``0 <= resistance_series < numpy.inf``.  [ohm]

    resistance_shunt : numeric
        Shunt resistance :math:`R_{sh}` under desired IV curve conditions.
        ``0 < resistance_shunt <= numpy.inf``.  [ohm]

    nNsVth : numeric
        The product of three components: 1) the usual diode ideality factor
        :math:`n`, 2) the number of cells in series :math:`N_s`, and 3)
        the cell thermal voltage
        :math:`V_{th}`. The thermal voltage of the cell (in volts) may be
        calculated as :math:`k_B T_c / q`, where :math:`k_B` is
        Boltzmann's constant (J/K), :math:`T_c` is the temperature of the p-n
        junction in Kelvin, and :math:`q` is the charge of an electron
        (coulombs). ``0 < nNsVth``.  [V]

    method : str, default 'lambertw'
        Determines the method used to calculate points on the IV curve. The
        options are ``'lambertw'``, ``'newton'``, ``'brentq'``, or
        ``'chandrupatla'``.

        .. note::
           ``'chandrupatla'`` requires scipy 1.15 or greater.

    Returns
    -------
    dict or pandas.DataFrame
        The returned dict-like object always contains the keys/columns:

        * i_sc - short circuit current in amperes.
        * v_oc - open circuit voltage in volts.
        * i_mp - current at maximum power point in amperes.
        * v_mp - voltage at maximum power point in volts.
        * p_mp - power at maximum power point in watts.
        * i_x - current, in amperes, at ``v = 0.5*v_oc``.
        * i_xx - current, in amperes, at ``v = 0.5*(v_oc+v_mp)``.

        A dict is returned when the input parameters are scalars.

    See also
    --------
    calcparams_desoto
    calcparams_cec
    calcparams_pvsyst
    sapm
    pvlib.singlediode.bishop88

    Notes
    -----
    If the method is ``'lambertw'`` then the solution employed to solve the
    implicit diode equation utilizes the Lambert W function to obtain an
    explicit function of :math:`V=f(I)` and :math:`I=f(V)` as shown in [2]_.

    If the method is ``'newton'`` then the root-finding Newton-Raphson method
    is used. It should be safe for well behaved IV-curves, but the ``'brentq'``
    method is recommended for reliability.

    If the method is ``'brentq'`` then Brent's bisection search method is used
    that guarantees convergence by bounding the voltage between zero and
    open-circuit.

    References
    ----------
    .. [1] S.R. Wenham, M.A. Green, M.E. Watt, "Applied Photovoltaics" ISBN
       0 86758 909 4

    .. [2] A. Jain, A. Kapoor, "Exact analytical solutions of the
       parameters of real solar cells using Lambert W-function", Solar
       Energy Materials and Solar Cells, 81 (2004) 269-277.

    .. [3] D. King et al, "Sandia Photovoltaic Array Performance Model",
       SAND2004-3535, Sandia National Laboratories, Albuquerque, NM

    .. [4] "Computer simulation of the effects of electrical mismatches in
       photovoltaic cell interconnection circuits" JW Bishop, Solar Cell (1988)
       https://doi.org/10.1016/0379-6787(88)90059-2
    """
    args = (photocurrent, saturation_current, resistance_series,
            resistance_shunt, nNsVth)  # collect args
    # Calculate points on the IV curve using the LambertW solution to the
    # single diode equation
    if method.lower() == 'lambertw':
        out = _singlediode._lambertw(*args)
        points = out[:7]
    else:
        # Calculate points on the IV curve using either 'newton' or 'brentq'
        # methods. Voltages are determined by first solving the single diode
        # equation for the diode voltage V_d then backing out voltage
        v_oc = _singlediode.bishop88_v_from_i(
            0.0, *args, method=method.lower()
        )
        i_mp, v_mp, p_mp = _singlediode.bishop88_mpp(
            *args, method=method.lower()
        )
        i_sc = _singlediode.bishop88_i_from_v(
            0.0, *args, method=method.lower()
        )
        i_x = _singlediode.bishop88_i_from_v(
            v_oc / 2.0, *args, method=method.lower()
        )
        i_xx = _singlediode.bishop88_i_from_v(
            (v_oc + v_mp) / 2.0, *args, method=method.lower()
        )
        points = i_sc, v_oc, i_mp, v_mp, p_mp, i_x, i_xx

    columns = ('i_sc', 'v_oc', 'i_mp', 'v_mp', 'p_mp', 'i_x', 'i_xx')

    if all(map(np.isscalar, args)):
        out = {c: p for c, p in zip(columns, points)}
        return out

    points = np.atleast_1d(*points)  # convert scalars to 1d-arrays
    points = np.vstack(points).T  # collect rows into DataFrame columns

    # save the first available pd.Series index, otherwise set to None
    index = next((a.index for a in args if isinstance(a, pd.Series)), None)

    out = pd.DataFrame(points, columns=columns, index=index)

    return out


def max_power_point(photocurrent, saturation_current, resistance_series,
                    resistance_shunt, nNsVth, d2mutau=0, NsVbi=np.inf,
                    method='brentq'):
    """
    Given the single diode equation coefficients, calculates the maximum power
    point (MPP).

    Parameters
    ----------
    photocurrent : numeric
        photo-generated current [A]
    saturation_current : numeric
        diode reverse saturation current [A]
    resistance_series : numeric
        series resitance [ohms]
    resistance_shunt : numeric
        shunt resitance [ohms]
    nNsVth : numeric
        product of thermal voltage ``Vth`` [V], diode ideality factor ``n``,
        and number of serices cells ``Ns``
    d2mutau : numeric, default 0
        PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon
        (a-Si) modules that accounts for recombination current in the
        intrinsic layer. The value is the ratio of intrinsic layer thickness
        squared :math:`d^2` to the diffusion length of charge carriers
        :math:`\\mu \\tau`. [V]
    NsVbi : numeric, default np.inf
        PVsyst parameter for cadmium-telluride (CdTe) and amorphous-silicon
        (a-Si) modules that is the product of the PV module number of series
        cells ``Ns`` and the builtin voltage ``Vbi`` of the intrinsic layer.
        [V].
    method : str
        either ``'newton'``, ``'brentq'``, or ``'chandrupatla'``.

        .. note::
           ``'chandrupatla'`` requires scipy 1.15 or greater.


    Returns
    -------
    OrderedDict or pandas.DataFrame
        ``(i_mp, v_mp, p_mp)``

    Notes
    -----
    Use this function when you only want to find the maximum power point. Use
    :func:`singlediode` when you need to find additional points on the IV
    curve. This function uses Brent's method by default because it is
    guaranteed to converge.
    """
    i_mp, v_mp, p_mp = _singlediode.bishop88_mpp(
        photocurrent, saturation_current, resistance_series,
        resistance_shunt, nNsVth, d2mutau, NsVbi, method=method.lower()
    )
    if isinstance(photocurrent, pd.Series):
        ivp = {'i_mp': i_mp, 'v_mp': v_mp, 'p_mp': p_mp}
        out = pd.DataFrame(ivp, index=photocurrent.index)
    else:
        out = OrderedDict()
        out['i_mp'] = i_mp
        out['v_mp'] = v_mp
        out['p_mp'] = p_mp
    return out


def v_from_i(current, photocurrent, saturation_current, resistance_series,
             resistance_shunt, nNsVth, method='lambertw'):
    '''
    Device voltage at the given device current for the single diode model.

    Uses the single diode model (SDM) as described in, e.g.,
    Jain and Kapoor 2004 [1]_.
    The solution is per Eq 3 of [1]_ except when resistance_shunt=numpy.inf,
    in which case the explict solution for voltage is used.
    Ideal device parameters are specified by resistance_shunt=np.inf and
    resistance_series=0.
    Inputs to this function can include scalars and pandas.Series, but it is
    the caller's responsibility to ensure that the arguments are all float64
    and within the proper ranges.

    .. versionchanged:: 0.10.0
       The function's arguments have been reordered.

    Parameters
    ----------
    current : numeric
        The current in amperes under desired IV curve conditions.

    photocurrent : numeric
        Light-generated current (photocurrent) in amperes under desired
        IV curve conditions. Often abbreviated ``I_L``.
        0 <= photocurrent

    saturation_current : numeric
        Diode saturation current in amperes under desired IV curve
        conditions. Often abbreviated ``I_0``.
        0 < saturation_current

    resistance_series : numeric
        Series resistance in ohms under desired IV curve conditions.
        Often abbreviated ``Rs``.
        0 <= resistance_series < numpy.inf

    resistance_shunt : numeric
        Shunt resistance in ohms under desired IV curve conditions.
        Often abbreviated ``Rsh``.
        0 < resistance_shunt <= numpy.inf

    nNsVth : numeric
        The product of three components. 1) The usual diode ideal factor
        (n), 2) the number of cells in series (Ns), and 3) the cell
        thermal voltage under the desired IV curve conditions (Vth). The
        thermal voltage of the cell (in volts) may be calculated as
        ``k*temp_cell/q``, where k is Boltzmann's constant (J/K),
        temp_cell is the temperature of the p-n junction in Kelvin, and
        q is the charge of an electron (coulombs).
        0 < nNsVth

    method : str
        Method to use: ``'lambertw'``, ``'newton'``, ``'brentq'``, or
        ``'chandrupatla'``. *Note*: ``'brentq'`` is limited to
        non-negative current.

        .. note::
           ``'chandrupatla'`` requires scipy 1.15 or greater.


    Returns
    -------
    current : np.ndarray or scalar

    References
    ----------
    .. [1] A. Jain, A. Kapoor, "Exact analytical solutions of the
       parameters of real solar cells using Lambert W-function", Solar
       Energy Materials and Solar Cells, 81 (2004) 269-277.
    '''
    args = (current, photocurrent, saturation_current,
            resistance_series, resistance_shunt, nNsVth)
    if method.lower() == 'lambertw':
        return _singlediode._lambertw_v_from_i(*args)
    else:
        # Calculate points on the IV curve using either 'newton' or 'brentq'
        # methods. Voltages are determined by first solving the single diode
        # equation for the diode voltage V_d then backing out voltage
        V = _singlediode.bishop88_v_from_i(*args, method=method.lower())
        if all(map(np.isscalar, args)):
            return V
        shape = _singlediode._shape_of_max_size(*args)
        return np.broadcast_to(V, shape)


def i_from_v(voltage, photocurrent, saturation_current, resistance_series,
             resistance_shunt, nNsVth, method='lambertw'):
    '''
    Device current at the given device voltage for the single diode model.

    Uses the single diode model (SDM) as described in, e.g.,
    Jain and Kapoor 2004 [1]_.
    The solution is per Eq 2 of [1] except when resistance_series=0,
    in which case the explict solution for current is used.
    Ideal device parameters are specified by resistance_shunt=np.inf and
    resistance_series=0.
    Inputs to this function can include scalars and pandas.Series, but it is
    the caller's responsibility to ensure that the arguments are all float64
    and within the proper ranges.

    .. versionchanged:: 0.10.0
       The function's arguments have been reordered.

    Parameters
    ----------
    voltage : numeric
        The voltage in Volts under desired IV curve conditions.

    photocurrent : numeric
        Light-generated current (photocurrent) in amperes under desired
        IV curve conditions. Often abbreviated ``I_L``.
        0 <= photocurrent

    saturation_current : numeric
        Diode saturation current in amperes under desired IV curve
        conditions. Often abbreviated ``I_0``.
        0 < saturation_current

    resistance_series : numeric
        Series resistance in ohms under desired IV curve conditions.
        Often abbreviated ``Rs``.
        0 <= resistance_series < numpy.inf

    resistance_shunt : numeric
        Shunt resistance in ohms under desired IV curve conditions.
        Often abbreviated ``Rsh``.
        0 < resistance_shunt <= numpy.inf

    nNsVth : numeric
        The product of three components. 1) The usual diode ideal factor
        (n), 2) the number of cells in series (Ns), and 3) the cell
        thermal voltage under the desired IV curve conditions (Vth). The
        thermal voltage of the cell (in volts) may be calculated as
        ``k*temp_cell/q``, where k is Boltzmann's constant (J/K),
        temp_cell is the temperature of the p-n junction in Kelvin, and
        q is the charge of an electron (coulombs).
        0 < nNsVth

    method : str
        Method to use: ``'lambertw'``, ``'newton'``, ``'brentq'``, or
        ``'chandrupatla'``. *Note*: ``'brentq'`` is limited to
        non-negative current.

        .. note::
           ``'chandrupatla'`` requires scipy 1.15 or greater.


    Returns
    -------
    current : np.ndarray or scalar

    References
    ----------
    .. [1] A. Jain, A. Kapoor, "Exact analytical solutions of the
       parameters of real solar cells using Lambert W-function", Solar
       Energy Materials and Solar Cells, 81 (2004) 269-277.
    '''
    args = (voltage, photocurrent, saturation_current,
            resistance_series, resistance_shunt, nNsVth)
    if method.lower() == 'lambertw':
        return _singlediode._lambertw_i_from_v(*args)
    else:
        # Calculate points on the IV curve using either 'newton' or 'brentq'
        # methods. Voltages are determined by first solving the single diode
        # equation for the diode voltage V_d then backing out voltage
        current = _singlediode.bishop88_i_from_v(*args, method=method.lower())
        if all(map(np.isscalar, args)):
            return current
        shape = _singlediode._shape_of_max_size(*args)
        return np.broadcast_to(current, shape)


def scale_voltage_current_power(data, voltage=1, current=1):
    """
    Scales the voltage, current, and power in data by the voltage
    and current factors.

    Parameters
    ----------
    data: DataFrame
        May contain columns `'v_mp', 'v_oc', 'i_mp' ,'i_x', 'i_xx',
        'i_sc', 'p_mp'`.
    voltage: numeric, default 1
        The amount by which to multiply the voltages.
    current: numeric, default 1
        The amount by which to multiply the currents.

    Returns
    -------
    scaled_data: DataFrame
        A scaled copy of the input data.
        `'p_mp'` is scaled by `voltage * current`.
    """

    # as written, only works with a DataFrame
    # could make it work with a dict, but it would be more verbose
    voltage_keys = ['v_mp', 'v_oc']
    current_keys = ['i_mp', 'i_x', 'i_xx', 'i_sc']
    power_keys = ['p_mp']
    voltage_df = data.filter(voltage_keys, axis=1) * voltage
    current_df = data.filter(current_keys, axis=1) * current
    power_df = data.filter(power_keys, axis=1) * voltage * current
    df = pd.concat([voltage_df, current_df, power_df], axis=1)
    df_sorted = df[data.columns]  # retain original column order
    return df_sorted


@renamed_kwarg_warning(
    "0.13.0", "g_poa_effective", "effective_irradiance")
def pvwatts_dc(effective_irradiance, temp_cell, pdc0, gamma_pdc, temp_ref=25.,
               k=None, cap_adjustment=False):
    r"""
    Implement NREL's PVWatts (Version 5) DC power model.

    Parameters
    ----------
    effective_irradiance: numeric
        Irradiance transmitted to the PV cells. To be
        fully consistent with PVWatts, the user must have already
        applied angle of incidence losses, but not soiling, spectral,
        etc. [Wm⁻²]
    temp_cell: numeric
        Cell temperature [C].
    pdc0: numeric
        Power of the modules at 1000 Wm⁻² and cell reference temperature. [W]
    gamma_pdc: numeric
        The temperature coefficient of power. Typically -0.002 to
        -0.005 per degree C. [1/°C]
    temp_ref: numeric, default 25.0
        Cell reference temperature. PVWatts defines it to be 25 °C and
        is included here for flexibility. [°C]
    k: numeric, optional
        Irradiance correction factor, defined in [2]_. Typically positive.
        [unitless]
    cap_adjustment: Boolean, default False
        If True, apply the optional adjustment at and below 1000 Wm⁻²

    Returns
    -------
    pdc: numeric
        DC power. [W]

    Notes
    -----
    The PVWatts Version 5 DC model [1]_ is:

    .. math::

        P_{dc} = \frac{G_{poa eff}}{1000} P_{dc0} ( 1 + \gamma_{pdc} (T_{cell} - T_{ref}))

    This model has also been referred to as the power temperature coefficient
    model.

    This function accepts an optional irradiance adjustment factor, `k`, based
    on [2]_. This applies a piece-wise adjustment to power based on irradiance,
    where `k` is the reduction in actual power at 200 Wm⁻² relative to power
    calculated at 200 Wm-2 as 0.2*`pdc0`. For example, a 500 W module that
    produces 95 W at 200 Wm⁻² (a 5% relative reduction in efficiency) would
    have a value of `k` = 0.01.

    .. math::

        k=\frac{0.2P_{dc0}-P_{200}}{P_{dc0}}

    For positive `k` values, and `k` is typically positive, this adjustment
    increases relative efficiency when irradiance is above 1000 Wm⁻². This may
    not be desired, as modules with nonlinear irradiance response often have
    peak efficiency near 1000 Wm⁻², and it is either flat or declining at
    higher irradiance. An optional parameter, `cap_adjustment`, can address
    this by modifying the adjustment from [2]_ to only apply below 1000 Wm⁻².

    Note that ``pdc0`` is also used as a symbol in
    :py:func:`pvlib.inverter.pvwatts`. ``pdc0`` in this function refers to the DC
    power of the modules at reference conditions. ``pdc0`` in
    :py:func:`pvlib.inverter.pvwatts` refers to the DC power input limit of
    the inverter.

    References
    ----------
    .. [1] A. P. Dobos, "PVWatts Version 5 Manual"
           http://pvwatts.nrel.gov/downloads/pvwattsv5.pdf
           (2014).
    .. [2] B. Marion, "Comparison of Predictive Models for
           Photovoltaic Module Performance,"
           :doi:`10.1109/PVSC.2008.4922586`,
           https://docs.nrel.gov/docs/fy08osti/42511.pdf
           (2008).
    """  # noqa: E501

    pdc = (effective_irradiance * 0.001 * pdc0 *
           (1 + gamma_pdc * (temp_cell - temp_ref)))

    # apply Marion's correction if k is provided
    if k is not None:

        # preserve input types
        index = pdc.index if isinstance(pdc, pd.Series) else None
        is_scalar = np.isscalar(pdc)

        # calculate error adjustments
        err_1 = k * (1 - (1 - effective_irradiance / 200)**4)
        err_2 = k * (1000 - effective_irradiance) / (1000 - 200)
        err = np.where(effective_irradiance <= 200, err_1, err_2)

        # cap adjustment, if needed
        if cap_adjustment:
            err = np.where(effective_irradiance >= 1000, 0, err)

        # make error adjustment
        pdc = pdc - pdc0 * err

        # set negative power to zero
        pdc = np.where(pdc < 0, 0, pdc)

        # preserve input types
        if index is not None:
            pdc = pd.Series(pdc, index=index)
        elif is_scalar:
            pdc = float(pdc)

    return pdc


def pvwatts_losses(soiling=2, shading=3, snow=0, mismatch=2, wiring=2,
                   connections=0.5, lid=1.5, nameplate_rating=1, age=0,
                   availability=3):
    r"""
    Implements NREL's PVWatts system loss model.
    The PVWatts loss model [1]_ is:

    .. math::

        L_{total}(\%) = 100 [ 1 - \Pi_i ( 1 - \frac{L_i}{100} ) ]

    All parameters must be in units of %. Parameters may be
    array-like, though all array sizes must match.

    Parameters
    ----------
    soiling: numeric, default 2
    shading: numeric, default 3
    snow: numeric, default 0
    mismatch: numeric, default 2
    wiring: numeric, default 2
    connections: numeric, default 0.5
    lid: numeric, default 1.5
        Light induced degradation
    nameplate_rating: numeric, default 1
    age: numeric, default 0
    availability: numeric, default 3

    Returns
    -------
    losses: numeric
        System losses in units of %.

    References
    ----------
    .. [1] A. P. Dobos, "PVWatts Version 5 Manual"
           http://pvwatts.nrel.gov/downloads/pvwattsv5.pdf
           (2014).
    """

    params = [soiling, shading, snow, mismatch, wiring, connections, lid,
              nameplate_rating, age, availability]

    # manually looping over params allows for numpy/pandas to handle any
    # array-like broadcasting that might be necessary.
    perf = 1
    for param in params:
        perf *= 1 - param/100

    losses = (1 - perf) * 100.

    return losses


def dc_ohms_from_percent(vmp_ref, imp_ref, dc_ohmic_percent,
                         modules_per_string=1,
                         strings=1):
    r"""
    Calculate the equivalent resistance of the conductors from the percent
    ohmic loss of an array at reference conditions.

    Parameters
    ----------
    vmp_ref: numeric
        Maximum power voltage of one module at reference conditions. [V]
    imp_ref: numeric
        Maximum power current of one module at reference conditions. [A]
    dc_ohmic_percent: numeric
        Array DC power loss as a percent of DC power loss at reference
        conditions. In percent, e.g. 1.5% loss is input as 1.5.
    modules_per_string: int, default 1
        Number of series-connected modules per string in the array.
    strings: int, default 1
        Number of parallel strings in the array.

    Returns
    ----------
    Rw: numeric
        Equivalent resistance. [ohm]

    See Also
    --------
    pvlib.pvsystem.dc_ohmic_losses

    Notes
    -----
    Equivalent resistance is calculated as:

    .. math::

        R_w = \left(\frac{L_{stc}}{100}\right) \times \left(\frac{
        V_{array}}{I_{array}}\right)

    :math:`R_w` is the equivalent resistance in ohms.
    :math:`V_{array}` is the array voltage, equal to ``vmp_ref`` times
    ``modules_per_string``.
    :math:`I_{array}` is the array current, equal to ``imp_ref`` times
    ``strings``.
    :math:`L_{stc}` is the input DC loss percent at reference conditions.

    """
    vmp = modules_per_string * vmp_ref

    imp = strings * imp_ref

    Rw = (dc_ohmic_percent / 100) * (vmp / imp)

    return Rw


def dc_ohmic_losses(resistance, current):
    r"""
    Returns ohmic losses in units of power from the equivalent
    resistance of the wires and the operating current.

    Parameters
    ----------
    resistance: numeric
        Equivalent resistance of wires. [ohm]
    current: numeric, float or array-like
        Operating current. [A]

    Returns
    ----------
    loss: numeric
        Power loss. [W]

    See Also
    --------
    pvlib.pvsystem.dc_ohms_from_percent

    Notes
    -----
    Ohmic (also termed joule or heat) loss is the power lost due to current
    flowing through a conductor. Ohmic loss, :math:`L`, is computed as

    .. math::

        L = I^2 \times R

    where :math:`I` is the current (A) and :math:`R` is the resistance of the
    conductor (ohms).
    """
    return resistance * current * current


def combine_loss_factors(index, *losses, fill_method='ffill'):
    r"""
    Combines Series loss fractions while setting a common index.

    The separate losses are compounded using the following equation:

    .. math::

        L_{total} = 1 - [ 1 - \Pi_i ( 1 - L_i ) ]

    :math:`L_{total}` is the total loss returned
    :math:`L_i` is each individual loss factor input

    Note the losses must each be a series with a DatetimeIndex.
    All losses will be resampled to match the index parameter using
    the fill method specified (defaults to "fill forward").

    Parameters
    ----------
    index : DatetimeIndex
        The index of the returned loss factors

    *losses : Series
        One or more Series of fractions to be compounded

    fill_method : {'ffill', 'bfill', 'nearest'}, default 'ffill'
        Method to use for filling holes in reindexed DataFrame

    Returns
    -------
    Series
        Fractions resulting from the combination of each loss factor
    """
    combined_factor = 1

    for loss in losses:
        loss = loss.reindex(index, method=fill_method)
        combined_factor *= (1 - loss)

    return 1 - combined_factor