# 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 φ_{τ}, 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 γ_{τ} (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.