area_overlapping_factor.py

from numpy import newaxis as na

import numpy as np


class AreaOverlappingFactor():
    def __init__(self, k=.1):
        self.k = k

    def overlapping_area_factor(self, wake_radius_ijlk, dw_ijlk, cw_ijlk, D_src_il, D_dst_ijl):
        """Calculate overlapping factor

        Parameters
        ----------
        dw_jl : array_like
            down wind distance [m]
        cw_jl : array_like
            cross wind distance [m]
        D_src_l : array_like
            Diameter of source turbines [m]
        D_dst_jl : array_like or None
            Diameter of destination turbines [m]. If None destination is assumed to be a point

        Returns
        -------
        A_ol_factor_jl : array_like
            area overlaping factor
        """

        if np.all(D_dst_ijl == 0) or D_dst_ijl is None:
            return wake_radius_ijlk > cw_ijlk
        else:
            return self._cal_overlapping_area_factor(wake_radius_ijlk,
                                                     (D_dst_ijl[..., na] / 2),
                                                     np.abs(cw_ijlk))

    def _cal_overlapping_area_factor(self, R1, R2, d):
        """ Calculate the overlapping area of two circles with radius R1 and
        R2, centers distanced d.

        The calculation formula can be found in Eq. (A1) of :
        [Ref] Feng J, Shen WZ, Solving the wind farm layout optimization
        problem using Random search algorithm, Reneable Energy 78 (2015)
        182-192
        Note that however there are typos in Equation (A1), '2' before alpha
        and beta should be 1.

        Parameters
        ----------
        R1: array:float
            Radius of the first circle [m]

        R2: array:float
            Radius of the second circle [m]

        d: array:float
            Distance between two centers [m]

        Returns
        -------
        A_ol: array:float
            Overlapping area [m^2]
        """
        # treat all input as array
        R1, R2, d = [np.asarray(a) for a in [R1, R2, d]]
        if R2.shape != R1.shape:
            R2 = np.zeros_like(R1) + R2
        A_ol_f = np.zeros(np.maximum(R1.shape, R2.shape))
        p = (R1 + R2 + d) / 2.0

        # make sure R_big >= R_small
        Rmax = np.where(R1 < R2, R2, R1)
        Rmin = np.where(R1 < R2, R1, R2)

        # full wake cases
        index_fullwake = (d <= (Rmax - Rmin))
        A_ol_f[index_fullwake] = 1

        # partial wake cases
        mask = (d > (Rmax - Rmin)) & (d < (Rmin + Rmax))

        # in somecases cos_alpha or cos_beta can be larger than 1 or less than
        # -1.0, cause problem to arccos(), resulting nan values, here fix this
        # issue.
        def arccos_lim(x):
            return np.arccos(np.maximum(np.minimum(x, 1), -1))

        alpha = arccos_lim((Rmax[mask]**2.0 + d[mask]**2 - Rmin[mask]**2) /
                           (2.0 * Rmax[mask] * d[mask]))

        beta = arccos_lim((Rmin[mask]**2.0 + d[mask]**2 - Rmax[mask]**2) /
                          (2.0 * Rmin[mask] * d[mask]))

        A_triangle = np.sqrt(p[mask] * (p[mask] - Rmin[mask]) *
                             (p[mask] - Rmax[mask]) * (p[mask] - d[mask]))

        A_ol_f[mask] = (alpha * Rmax[mask]**2 + beta * Rmin[mask]**2 -
                        2.0 * A_triangle) / (R2[mask]**2 * np.pi)

        return A_ol_f