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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def smooth_power_curve(power_curve_wind_speeds, power_curve_values, block_width=0.5, wind_speed_range=15.0, standard_deviation_method='turbulence_intensity', mean_gauss=0, **kwargs):
 r""" Smooths the input power curve values by using a Gauss distribution. The smoothing serves for taking the distribution of wind speeds over space into account. Parameters power_curve_wind_speeds : pandas.Series or numpy.array Wind speeds in m/s for which the power curve values are provided in `power_curve_values`. power_curve_values : pandas.Series or numpy.array Power curve values corresponding to wind speeds in `power_curve_wind_speeds`. block_width : float Width between the wind speeds in the sum of equation :eq:`power`. Default: 0.5. wind_speed_range : float The sum in the equation below is taken for this wind speed range below and above the power curve wind speed. Default: 15.0. standard_deviation_method : string Method for calculating the standard deviation for the Gauss distribution. Options: 'turbulence_intensity', 'Staffell_Pfenninger'. Default: 'turbulence_intensity'. mean_gauss : float Mean of the Gauss distribution in :py:func:`~.tools.gauss_distribution`. Default: 0. Other Parameters turbulence intensity : float, optional Turbulence intensity at hub height of the wind turbine, wind farm or wind turbine cluster the power curve is smoothed for. Returns ------- smoothed_power_curve_df : pd.DataFrame Smoothed power curve. DataFrame has 'wind_speed' and 'value' columns with wind speeds in m/s and the corresponding power curve value in W. Notes ----- The following equation is used to calculated the power curves values of the smoothed power curve [1]_: .. math:: P_{smoothed}(v_{std}) = \sum\limits_{v_i} \Delta v_i \cdot P(v_i) \cdot \frac{1}{\sigma \sqrt{2 \pi}} \exp \left[-\frac{(v_{std} - v_i -\mu)^2}{2 \sigma^2} \right] :label: power with: P: power [W], v: wind speed [m/s], :math:`\sigma`: standard deviation (Gauss), :math:`\mu`: mean (Gauss) :math:`P_{smoothed}` is the smoothed power curve value, :math:`v_{std}` is the standard wind speed in the power curve, :math:`\Delta v_i` is the interval length between :math:`v_\text{i}` and :math:`v_\text{i+1}` Power curve smoothing is applied to take account for the spatial distribution of wind speed. This way of smoothing power curves is also used in [2]_ and [3]_. The standard deviation :math:`\sigma` of the above equation can be calculated by the following methods. 'turbulence_intensity' [2]_: .. math:: \sigma = v_\text{std} \cdot \sigma_\text{n} = v_\text{std} \cdot TI with: TI: turbulence intensity 'Staffell_Pfenninger' [4]_: .. math:: \sigma = 0.6 \cdot 0.2 \cdot v_\text{std} References .. [1] Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der Windenergieeinspeisung für wetterdatenbasierte Windleistungssimulationen". Universität Kassel, Diss., 2016, p. 106 .. [2] Nørgaard, P. and Holttinen, H.: "A Multi-Turbine and Power Curve Approach". Nordic Wind Power Conference, 1.–2.3.2004, 2000, p. 5 .. [3] Kohler, S. and Agricola, A.-Cl. and Seidl, H.: "dena-Netzstudie II. Integration erneuerbarer Energien in die deutsche Stromversorgung im Zeitraum 2015 – 2020 mit Ausblick 2025". Technical report, 2010. .. [4] Staffell, I. and Pfenninger, S.: "Using Bias-Corrected Reanalysis to Simulate Current and Future Wind Power Output". 2005, p. 11 """

    # Specify normalized standard deviation
    if standard_deviation_method == 'turbulence_intensity':
        if ('turbulence_intensity' in kwargs and
                kwargs['turbulence_intensity'] is not np.nan):
            normalized_standard_deviation = kwargs['turbulence_intensity']
        else:
            raise ValueError("Turbulence intensity must be defined for " +
                             "using 'turbulence_intensity' as " +
                             "`standard_deviation_method`")
    elif standard_deviation_method == 'Staffell_Pfenninger':
        normalized_standard_deviation = 0.2
    else:
        raise ValueError("{} is no valid `standard_deviation_method`. Valid "
                         + "options are 'turbulence_intensity', or "
                         + "'Staffell_Pfenninger'".format(
                                 standard_deviation_method))
    # Initialize list for power curve values
    smoothed_power_curve_values = []
    # Append wind speeds to `power_curve_wind_speeds`
    maximum_value = power_curve_wind_speeds.values[-1] + wind_speed_range
    while power_curve_wind_speeds.values[-1] < maximum_value:
        power_curve_wind_speeds = power_curve_wind_speeds.append(
            pd.Series(power_curve_wind_speeds.iloc[-1] + 0.5,
                      index=[power_curve_wind_speeds.index[-1] + 1]))
        power_curve_values = power_curve_values.append(
            pd.Series(0.0, index=[power_curve_values.index[-1] + 1]))
    for power_curve_wind_speed in power_curve_wind_speeds:
        # Create array of wind speeds for the sum
        wind_speeds_block = (np.arange(
            -wind_speed_range, wind_speed_range + block_width, block_width) +
            power_curve_wind_speed)
        # Get standard deviation for Gauss function
        standard_deviation = (
            (power_curve_wind_speed * normalized_standard_deviation + 0.6)
            if standard_deviation_method is 'Staffell_Pfenninger'
            else power_curve_wind_speed * normalized_standard_deviation)
        # Get the smoothed value of the power output
        if standard_deviation == 0.0:
            # The gaussian distribution is not defined for a standard deviation
            # of zero. Smoothed power curve value is set to zero.
            smoothed_value = 0.0
        else:
            smoothed_value = sum(
                block_width * np.interp(wind_speed, power_curve_wind_speeds,
                                        power_curve_values, left=0, right=0) *
                tools.gauss_distribution(
                    power_curve_wind_speed - wind_speed,
                    standard_deviation, mean_gauss)
                for wind_speed in wind_speeds_block)
        # Add value to list - add zero if `smoothed_value` is nan as Gauss
        # distribution for a standard deviation of zero.
        smoothed_power_curve_values.append(smoothed_value)
    # Create smoothed power curve data frame
    smoothed_power_curve_df = pd.DataFrame(
        data=[list(power_curve_wind_speeds.values),
              smoothed_power_curve_values]).transpose()
    # Rename columns of the data frame
    smoothed_power_curve_df.columns = ['wind_speed', 'value']
    return smoothed_power_curve_df