Solar heating in CIGRE207

linerate.equations.cigre207.solar_heating.compute_direct_solar_radiation(sin_solar_altitude, height_above_sea_level)

Compute the direct solar radiation.

On page 19 of [1]. Equation (10) states that the direct solar radiation on a surface normal to the solar beam at sea level, \(I_{B(0)}\), is given by

\[N_s \frac{1280 \sin(H_s)}{\sin(H_s) + 0.314},\]

where \(H_s\) is the solar altitude. To correct for height above sea level, we use the Eq. 19 from Cigre 601, since no equation is provided in Cigre 207.

Parameters:

• sin_solar_altitude (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(\sin\left(H_s\right)\). The sine of the solar altitude.

• height_above_sea_level (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'm']) – \(y~\left[\text{m}\right]\). The conductor’s altitude.

Returns:

\(I_D~\left[\text{W}~\text{m}^{-2}\right]\). The direct solar radiation.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

linerate.equations.cigre207.solar_heating.compute_diffuse_sky_radiation(direct_solar_radiation, sin_solar_altitude)

Compute the diffuse radiation (light scattered in the atmosphere).

On page 38 of [4].

This equation differ from [1], however the difference is small, and the diffuse radiation is a small contributor to the overall solar radiation, so the total discrepancy between the models is small.

Parameters:

• direct_solar_radiation (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'W/m²']) – \(I_D~\left[\text{W}~\text{m}^{-2}\right]\). The direct solar radiation.

• sin_solar_altitude (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(\sin\left(H_s\right)\). The sine of the solar altitude.

Returns:

\(I_d~\left[\text{W}~\text{m}^{-2}\right]\).The diffuse solar radiation.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

linerate.equations.cigre207.solar_heating.compute_global_radiation_intensity(direct_solar_radiation, diffuse_sky_radiation, albedo, sin_angle_of_sun_on_line, sin_solar_altitude)

Compute the global radiation intensity experienced by the conductor.

Equation (47) on page 38 of [4] state that the global radiation intensity, \(I_T\), is given by

\[I_T = I_D \left(\sin(\eta) + 0.5 F \pi \sin(H_s)\right) + 0.5 I_d \pi \left(1 + F \right),\]

where \(\eta\) is the incidence angle of the sun on the line, \(H_s\) is the solar altitude and \(F\) is the ground albedo (amount of radiation diffusely reflected from the ground). The factor \(0.5 \pi\) is due the assumption that the ground reflects light diffusely and uniformly in all directions, so the reflected energy is always directed normally to the line. In CIGRE207, it is also assumed that the diffuse radiation is uniformly directed, which leads to \(I_d \pi/2 (1 + F)\) instead of \(I_d (1 + 0.5 F \pi)\)

Parameters:

• direct_solar_radiation (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'W/m²']) – \(I_D~\left[\text{W}~\text{m}^{-2}\right]\). The direct solar radiation.

• diffuse_sky_radiation (Annotated[float | float64 | ndarray[Any, dtype[float64]], 'W/m²']) – \(I_d~\left[\text{W}~\text{m}^{-2}\right]\).The diffuse solar radiation.

• albedo (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(F\). The ground albedo.

• sin_angle_of_sun_on_line (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(\sin\left(\eta\right)\). The sine of the angle of the sun on the line.

• sin_solar_altitude (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(\sin\left(H_s\right)\). The sine of the solar altitude.

Returns:

\(I_T~\left[\text{W}~\text{m}^{-2}\right]\). The global radiation intensity.

Return type:

Union[float, float64, ndarray[Any, dtype[float64]]]

Note

The following values are given for the albedo in [1]:

Ground	Albedo
Water (\(H_s > 30^\circ\))	0.05
Forest	0.1
Urban areas	0.15
Soil, grass and crops	0.2
Sand	0.3
Ice	0.4-0.6
Snow	0.6-0.8