Solar Position
This collection of routines computes the solar position for points in time. The topocentric solar parameters are illustrated in Figure 4, which shows a panel tilted at angle β and offset from due southern orientation with an aspect angle γ.
Figure 4. Solar Angles for a Tilted PV Panel
PlantPredict implements the Solar Position Algorithm (SPA) for Solar Radiation Applications by Reda and Andreas,
as described in the NREL report, TP-560-3402.
Inputs
Outputs
Algorithm
The SPA is implemented as-is, with ΔT: TT-UT (difference between the Earth rotation time and the Terrestrial
Time), assumed to be fixed at 67s.
References
Reda, I., Andreas, A. Solar Position Algorithm for the Solar Radiation Applications. NREL Technical Report NREL/TP-560-3402
Site Pressure
This function empirically computes the nominal station pressure given the site elevation.
Inputs
Outputs
Algorithm 1 (Physical)
Algorithm 2 (Empirical)
Where:
References
Wallace, John M., and Peter Victor Hobbs. Atmospheric Science: An Introductory Survey. Pp. 55-60 1977, pp 55-60
Sunrise & Sunset
This routine computes the approximate sunrise and sunset times given the site coordinates and the declination angle, previously computed as part of the solar position equation.
Inputs
Outputs
Algorithm
1.) Find the sunrise and sunset times assuming the standard refraction of the sun at the horizon with the midpoint
of the solar disk about 0.833° below the horizon.
References
http://www.srrb.noaa.gov/highlights/sunrise/solareqns.PDF
Atmospheric Refraction Correction
This function computes the apparent shift in the solar elevation angle caused by atmospheric refraction. Note that the output is a positive number; i.e. near the horizon, the solar disk appears higher in the sky than its true position. The apparent elevation is the true (geometrical) elevation plus the correction factor.
Inputs
Outputs
Algorithm
Where:
References
Reda, I., Andreas, A. Solar Position Algorithm for the Solar Radiation Applications. NREL Technical Report NREL/TP-560-3402
Tilt Angle
Three different types of DC Field tilt technologies are supported by PlantPredict: fixed tilt, seasonal tilt, and horizontal-axis tracking. These three are mutually exclusive and can be configured as part of the DC Field definitions. They impact the available plane-of-array irradiance and row-on-row shading.
DC Field Fixed Tilt
This is the base case. The tilt angle of the DC Field is static and set for all simulation time.
Inputs
Outputs
Algorithm
Seasonal Tilt
This is a variation of the fixed-tilt case, where the effective tilt angle depends on the 12-month lookup table of desired tilt angles as defined in the DC Field definitions.
Inputs
Outputs
Algorithm
Set the instantaneous tilt angle for time t according to the by-month lookup of array tilt angles, where n=1:12:
Tracking
For horizontal north-south axis tracker, this procedure computes the ideal tracker angle φτ, taking into consideration backtracking shade avoidance strategy and the tracker’s mechanical limits of travel. This procedure is generalized for a tracker whose N-S axis is skewed by a tracker yaw angle γτ (azimuth angle).
The coordinate system used in this suite of algorithms is the “North-East-Down” convention (NED), as follows:
- Solar azimuth angle is measured from North (N=0°, E=90°, S=180°, W=270°)
The other angles are positive when rotating counter-clockwise looking towards the origin.
- Tracker roll (tilt) angle is positive East, negative West, 0° is horizontal (facing up)
- Tracker yaw angles are positive east (e.g. 0° is N-S; 10° has a slight NNW-SSE orientation)
This is illustrated in Figure 5.
Figure 5. Modified Tracker Coordinate System
This procedure returns the tracker angle, as well as the effective tilt and azimuth angles, rotated in the reference
frame of a basic fixed-tilt array. In the case of a horizontal north-south tracker with a yaw angle of 10° degrees
east with the tracker set at an evening angle 45° to the east, the effective tilt β and azimuth γ would
be +45° be and +80°, respectively. The derivation of the rotation angle for optimum tracking of a single-axis
trackers is given in the referenced technical report published by NREL.
PlantPredict only supports a horizontal tracker (where the pitch angle is zero). This section summarizes the referenced equations into a form easily implanted in source code.
Note: Unlike in the NREL technical report, the incidence angle is calculated separately in order to have a generalized solution for both fixed-tilt and tracking array configurations.
Inputs
Outputs
Algorithm (True Tracking)
1.) Convert the solar azimuth and yaw angles into the NED reference frame.
Algorithm (Backracking)
If backtracking is activated (as it would typically be for PV technologies using bypass diodes), then compute
the modified tracker angle with shade avoidance:
1.) Find the cutoff tracking angle where the row-to-row shading begins, which depends on the ground coverage
ratio (tracker width / post-to-post spacing)
Algorithm (Tracker Limits)
1.) If the tracker limits are reached, the tracker stops moving.
if the tracker axis is north-south (azimuth is defined relative to the tracking axis, not the collector);
hence in the morning, the tracker has an effective collector azimuth of 90° (facing east), and in the afternoon,
the effective collector azimuth is 270° (facing west).
horizontal trackers).
Reference
Marion, William F. and Dobos, Aron P. “Rotation Angle for the Optimum Tracking of One-Axis Trackers.”NREL. July 2013. NREL/TP-6A20-58891, 2003
Compute Incidence Angle
This function computes the solar angle of incidence on the plane-of-array, i.e. the angle between a line perpendicular (normal) to the module surface and the beam component of the sunlight. The tilt may be constant for fixed-tilt DC Fields, or variable for tracking DC Fields.
Inputs
Outputs
Algorithm
1.) Compute the incidence angle given an array of panel tilts β and aspects γ. The angle is defined
to be zero when the light ray is normal to the surface.
