Solar heating in CIGRE601#

linerate.equations.cigre601.solar_heating.compute_direct_solar_radiation(sin_solar_altitude, clearness_ratio, height_above_sea_level)[source]#

Compute the direct solar radiation.

Equation (10-11) 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 \(N_s\) is the clearness ratio which is used to adjust the amount of radiation compared to what goes through a standard Indian atmosphere, and \(H_s\) is the solar altitude.

While the solar radiation model is based on [3] and therefore have parameters estimated for an Indian atmosphere, it gives comparable results to the solar radiation model in the IEEE standard [2]. It is therefore reasonable to assume that the parameters work in other climates as well.

Parameters:

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

  • clearness_ratio (Annotated[float | float64 | ndarray[Any, dtype[float64]], '']) – \(N_s\). The clearness ratio (or clearness number in [3, 4]).

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

Returns:

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

Return type:

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

Note

The 1280 originates and 0.314 in the above equation originates from [3], which is cited in [8] (which is listed as the reference in [1]). In [3] the empirical relationship

\[I_{B(0)} = \frac{1.842 \sin(H_s)}{\sin(H_s) + 0.3135}~\text{Ly}~\text{min}^{-1}\]

is introduced, and by converting from Langley per minute to \(\text{W}~\text{m}^{-2}\), we obtain

\[I_{B(0)} = N_s \frac{1284.488 \sin(H_s)}{\sin(H_s) + 0.3135}~\text{W}~\text{m}^{-2},\]

which is equal to the equation we use (with three significant digits).

linerate.equations.cigre601.solar_heating.compute_diffuse_sky_radiation(direct_solar_radiation, sin_solar_altitude)[source]#

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

Equation (13) on page 20 of [1].

This equation differs from [4], 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']) – \(I_B~\left[\text{W}~\text{m}^{-2}\right]\). 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.cigre601.solar_heating.compute_global_radiation_intensity(direct_solar_radiation, diffuse_sky_radiation, albedo, sin_angle_of_sun_on_line, sin_solar_altitude)[source]#

Compute the global radiation intensity experienced by the conductor.

Equation (9) on page 18 of [1] state that the global radiation intensity, \(I_T\), is given by

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

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 \(I_d (0.5 \pi + 0.5 F \pi)\) instead of \(I_d (1 + 0.5 F \pi)\)

Parameters:

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