Add function for logarithmic interpolation/extrapolation

Author: SabineHaas

windpowerlib/tools.py

@@ -13,7 +13,7 @@
 
 def linear_interpolation_extrapolation(df, target_height):
     r"""
-    Inter- or extrapolates between the values of a data frame.
+    Linear inter- or extrapolates between the values of a data frame.
 
     This function can be used for the inter-/extrapolation of a parameter
     (e.g wind speed) available at two or more different heights, to approximate
@@ -73,6 +73,60 @@ def linear_interpolation_extrapolation(df, target_height):
             (target_height - heights_sorted[0]) + df[heights_sorted[0]])
 
 
+def logarithmic_interpolation_extrapolation(df, target_height):
+    r"""
+    Logarithmic inter- or extrapolates between the values of a data frame.
+
+    This function can be used for the inter-/extrapolation of the wind speed if
+    it is available at two or more different heights, to approximate
+    the value at hub height. The function is carried out when the parameter
+    `wind_speed_model` :class:`~.modelchain.ModelChain` class is
+    'log_interpolation_extrapolation'.
+
+    Parameters
+    ----------
+    df : pandas.DataFrame
+        DataFrame with time series for parameter that is to be interpolated or
+        extrapolated. The columns of the DataFrame are the different heights
+        for which the parameter is available. If more than two heights are
+        given, the two closest heights are used. See example in
+        :py:func:`~.linear_interpolation_extrapolation` on how the
+        DataFrame should look like and how the function can be used.
+    target_height : float
+        Height for which the parameter is approximated (e.g. hub height).
+
+    Returns
+    -------
+    pandas.Series
+        Result of the inter-/extrapolation (e.g. wind speed at hub height).
+
+    Notes
+    -----
+
+    For the logarithmic inter- and extrapolation the following equation is
+    used [1]_:
+
+    .. math:: f(x) = \frac{\ln(x) \cdot (f(x_2) - f(x_1)) - f(x_2) \cdot \ln(x_1) + f(x_1) \cdot \ln(x_2)}{\ln(x_2) - \ln(x_1)}
+
+    References
+    ----------
+    .. [1] Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der
+             Windenergieeinspeisung für wetterdatenbasierte
+             Windleistungssimulationen". Universität Kassel, Diss., 2016,
+             p. 83
+
+    """
+    # find closest heights
+    heights_sorted = df.columns[
+        sorted(range(len(df.columns)),
+               key=lambda i: abs(df.columns[i] - target_height))]
+    return ((np.log(target_height) *
+             (df[heights_sorted[1]] - df[heights_sorted[0]]) -
+             df[heights_sorted[1]] * np.log(heights_sorted[0]) +
+             df[heights_sorted[0]] * np.log(heights_sorted[1])) /
+            (np.log(heights_sorted[1]) - np.log(heights_sorted[0])))
+
+
 def gaussian_distribution(function_variable, standard_deviation, mean=0):
     r"""
     Normal distribution or gaussian distribution.