def mean_hub_height(self):
        r"""
        Calculates the mean hub height of the wind turbine cluster.

        The mean hub height of a wind turbine cluster is necessary for power
        output calculations with an aggregated wind turbine cluster power
        curve. Hub heights of wind farms with higher nominal power weigh more
        than others. Assigns the hub height to the turbine cluster object.

        Returns
        -------
        self

        Notes
        -----
        The following equation is used [1]_:

        .. math:: h_{WTC} = e^{\sum\limits_{k}{ln(h_{WF,k})}
                           \frac{P_{N,k}}{\sum\limits_{k}{P_{N,k}}}}

        with:
            :math:`h_{WTC}`: mean hub height of wind turbine cluster,
            :math:`h_{WF,k}`: hub height of the k-th wind farm of the cluster,
            :math:`P_{N,k}`: installed power of the k-th wind farm

        References
        ----------
        .. [1]  Knorr, K.: "Modellierung von raum-zeitlichen Eigenschaften der
                 Windenergieeinspeisung für wetterdatenbasierte
                 Windleistungssimulationen". Universität Kassel, Diss., 2016,
                 p. 35

        """
        self.hub_height = np.exp(sum(
            np.log(wind_farm.hub_height) * wind_farm.get_installed_power() for
            wind_farm in self.wind_farms) / self.get_installed_power())
        return self