Comparing the methods for calculating solar heating in CIGRE601 and IEEE738

In this example, we see how the solar heating varies with different variables. This calculation is done using with the CIGRE-601 standard and the IEEE-738 standard.

Imports and utilities

import matplotlib.pyplot as plt
import numpy as np

from linerate.equations import cigre601, ieee738, solar_angles, solar_heating
from linerate.equations.math import switch_cos_sin

Simulation parameters

time = np.datetime64("2022-06-01T13:00")

omega = solar_angles.compute_hour_angle_relative_to_noon(time, 0)
delta = solar_angles.compute_solar_declination(time)

vals_with_range = {
    "D": np.linspace(0.011, 0.038)[:, np.newaxis],
    "sin_H_s": np.linspace(-0.05, 1)[:, np.newaxis],
}

for k, v in vals_with_range.items():
    alpha_s = 0.8  # alpha in IEEE
    phi = 60  # Lat in IEEE
    gamma_c = 0  # Z_l i IEEE
    y = 0  # H_e in IEEE
    D = 0.025  # D_0 in IEEE
    F = 0.1
    N_s = 1
    sin_H_s = solar_angles.compute_sin_solar_altitude(phi, delta, omega)

    dict_in_loop = {k: v}
    locals().update(dict_in_loop)

    ###############################################################################
    # CIGRE601 calculations
    # ^^^^^^^^^^^^^^^^^^^^^^^^^

    chi = solar_angles.compute_solar_azimuth_variable(phi, delta, omega)
    C = solar_angles.compute_solar_azimuth_constant(chi, omega)
    Z_c = solar_angles.compute_solar_azimuth(C, chi)
    cos_eta = solar_angles.compute_cos_solar_effective_incidence_angle(sin_H_s, Z_c, gamma_c)
    sin_eta = switch_cos_sin(cos_eta)

    I_B = cigre601.solar_heating.compute_direct_solar_radiation(sin_H_s, N_s, y)
    I_d = cigre601.solar_heating.compute_diffuse_sky_radiation(I_B, sin_H_s)
    I_T = cigre601.solar_heating.compute_global_radiation_intensity(I_B, I_d, F, sin_eta, sin_H_s)

    ###############################################################################
    # IEEE738 calculations
    # ^^^^^^^^^^^^^^^^^^^^

    Q_s = ieee738.solar_heating.compute_total_heat_flux_density(sin_H_s, True)
    K_solar = ieee738.solar_heating.compute_solar_altitude_correction_factor(y)
    Q_se = ieee738.solar_heating.compute_elevation_correction_factor(K_solar, Q_s)
    chi = solar_angles.compute_solar_azimuth_variable(phi, delta, omega)
    C = solar_angles.compute_solar_azimuth_constant(chi, omega)
    Z_c = solar_angles.compute_solar_azimuth(C, chi)
    cos_theta = solar_angles.compute_cos_solar_effective_incidence_angle(sin_H_s, Z_c, gamma_c)

    ###############################################################################
    # Calculate P_c with different varying parameters
    # ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

    P_s_cigre = solar_heating.compute_solar_heating(alpha_s, I_T, D)
    P_s_ieee = ieee738.solar_heating.compute_solar_heating(alpha_s, Q_se, cos_theta, D)

    ###############################################################################
    # Create visualisation
    # ^^^^^^^^^^^^^^^^^^^^

    fig = plt.figure()
    plt.plot(globals()[k][:, 0], P_s_cigre[:, 0], color="g", label="CIGRE")
    plt.plot(globals()[k][:, 0], P_s_ieee[:, 0], color="orange", label="IEEE")
    if k == "D":
        plt.xlabel("Conductor outer diameter [m]")
        plt.title(
            r"Solar heating calculated using the CIGRE-601 and the IEEE-736 standards."
            "\n"
            r"The only varying parameter in the calculations was conductor diameter.",
            fontsize=11,
        )
    elif k == "sin_H_s":
        plt.xlabel("Solar altitude [$^\\circ$]")
        plt.xticks(ticks=[0, 1 / 3, 2 / 3, 1], labels=[0, 30, 60, 90])
        plt.title(
            r"Solar heating calculated using the CIGRE-601 and the IEEE-736 standards."
            "\n"
            r"The only varying parameter in the calculations was solar altitude.",
            fontsize=11,
        )

    plt.legend()
    plt.xlim(np.min(globals()[k][:, 0]), np.max(globals()[k][:, 0]))
    plt.ylabel("Solar heating [W/m]")
    plt.ylim(-2, 32)
    plt.show()

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