Solar angles

linerate.equations.solar_angles.compute_hour_angle_relative_to_noon(when, longitude)

Compute the hour angle.

Described in the text on p. 18 of [2]. The hour angle is the number of hours from noon times 15^circ. This means that the hour angle for 11:00 is -15^circ, and the hour angle for 14:00 is 30^circ.

This function converts the hour angle to radians by multiplying it by frac{pi}{12}, which is the same as 15^circ.

The hour angle is used when calculating the solar altitude. This function does not take into account the difference between apparent/actual and mean solar time, which means that the result may be up to 15 minutes from the correct hour angle.

Parameters:

when (datetime64 | ndarray[tuple[int, ...], dtype[datetime64]]) – The time and date.

Returns:

:math:’omega~left[text{radian}right]`. The hour angle relative to noon.

Return type:

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

linerate.equations.solar_angles.compute_solar_declination(when)

Compute the solar declination

Equation (16b) on page 18 of [2].

The function takes in a numpy.datetime64 object, and uses the _get_day_of_year function to find the day number of the year to be used to compute the solar declination.

Parameters:

when (datetime64 | ndarray[tuple[int, ...], dtype[datetime64]]) – The time and date.

Returns:

\(\delta~\left[\text{radian}\right]\). The declination of the earth.

Return type:

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

linerate.equations.solar_angles.compute_solar_azimuth_variable(latitude, solar_declination, hour_angle_relative_to_noon)

Compute the solar azimuth variable.

Equation (17b) on page 18 of [2].

Parameters:

• latitude (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], '°']) – \(Lat~\left[\text{degrees}\right]\). The latitude of the span (center).

• solar_declination (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(\delta~\left[\text{radian}\right]\). Solar declination (-23.45 to +23.45).

• hour_angle_relative_to_noon (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – :math:’omega~left[text{radian}right]`. The hour angle relative to noon.

Returns:

\(\chi~\left[\text{radian}\right]\). The solar azimuth variable.

Return type:

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

linerate.equations.solar_angles.compute_solar_azimuth_constant(solar_azimuth_variable, hour_angle_relative_to_noon)

Compute the solar azimuth constant.

Table 2 on page 18 of:cite:p:ieee738.

Parameters:

• solar_azimuth_variable (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(\chi~\left[\text{radian}\right]\). The solar azimuth variable.

• hour_angle_relative_to_noon (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – :math:’omega~left[text{radian}right]`. The hour angle relative to noon.

Returns:

\(C~\left[\text{radian}\right]\). The solar azimuth constant.

Return type:

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

linerate.equations.solar_angles.compute_solar_azimuth(solar_azimuth_constant, solar_azimuth_variable)

Compute the solar azimuth.

Equation (17a) on page 18 of [2].

Parameters:

• solar_azimuth_constant (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(C~\left[\text{radian}\right]\). The solar azimuth constant.

• solar_azimuth_variable (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(\chi~\left[\text{radian}\right]\). The solar azimuth variable.

Returns:

\(Z_c~\left[\text{radian}\right]\). The solar azimuth.

Return type:

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

linerate.equations.solar_angles.compute_sin_solar_altitude(latitude, solar_declination, hour_angle_relative_to_noon)

Compute the sine of the solar altitude

This is an alteration of equation (16a) on page 18 of [2]. \(sin(H_c)\) is calculated instead of \(H_c\).

Parameters:

• latitude (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], '°']) – \(Lat~\left[^\circ\right]\). The latitude of the span (center).

• ssolar_declination – \(\delta~\left[\text{radian}\right]\). Solar declination (-23.45 to +23.45).

• hour_angle_relative_to_noon (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – :math:’omega~left[text{radian}right]`. The hour angle relative to noon.

Returns:

\(\sin\left(H_c\right)\). The sine of the solar altitude.

Return type:

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

linerate.equations.solar_angles.compute_cos_solar_effective_incidence_angle(sin_solar_altitude, solar_azimuth, conductor_azimuth)

Compute the cosine of the effective angle of incidence of the sun rays.

This is an alteration of equation (9) on page 13 of [2]. \(cos(\theta)\) is calculated instead of \(\theta\).

Parameters:

• sin_solar_altitude (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(sin(H_c)~\left[\text{radian}~\right]\). The sin of the solar altitude.

• solar_azimuth (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(Z_c~\left[\text{radian}~\right]\). The azimuth of the sun.

• conductor_azimuth (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], 'rad']) – \(Z_l~\left[\text{radian}~\right]\). The azimuth of the conductor/line.

Returns:

\(cos(\theta)\). The cosine of the effective angle of incidence of the sun rays.

Return type:

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

linerate.equations.solar_angles.compute_sin_solar_altitude_for_span(span, time)

Compute the sine of the solar altitude for a given span and time.

This function computes the sine of the solar altitude at the midpoint of the span. It uses the latitude, longitude of the span to compute the hour angle and solar declination.

Parameters:

• span (Span) – The span for which to compute the sine of the solar altitude.

• time (datetime64 | ndarray[tuple[int, ...], dtype[datetime64]]) – The time at which to compute the sine of the solar altitude.

Returns:

The sine of the solar altitude at the midpoint of the span. (sin H_s)

Return type:

Unitless

linerate.equations.solar_angles.compute_sin_solar_effective_incidence_angle_for_span(span, time, sin_H_s)

Compute the sine of the solar effective incidence angle for a given span and time.

This function computes the sine of the solar effective incidence angle at the midpoint of the span. It uses the latitude, longitude, conductor azimuth, and solar altitude to compute the sine of the effective incidence angle.

Parameters:

• span (Span) – The span for which to compute the sine of the solar effective incidence angle.

• time (datetime64 | ndarray[tuple[int, ...], dtype[datetime64]]) – The time at which to compute the sine of the solar effective incidence angle.

• sin_H_s (Annotated[float | float64 | ndarray[tuple[int, ...], dtype[float64]], '']) – The sine of the solar altitude at the midpoint of the span (computed with compute_sin_solar_altitude_for_span).

Returns:

The sine of the solar effective incidence angle at the midpoint of the span. (sin eta)

Return type:

Unitless