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«Contents 1. Requirements 2. Introduction 3. Assumptions and Limitations 4. Determination of Glare Occurrence 4.1 Sun Position 4.2 Reflected Sun ...»

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Solar Glare Hazard Analysis Tool (SGHAT)

Technical Reference Manual

Clifford K. Ho, Cianan A. Sims, Julius Yellowhair, and Evan Bush

Sandia National Laboratories

(505) 844-2384, ckho@sandia.gov

SAND2014-18360 O

September 2014


1. Requirements

2. Introduction

3. Assumptions and Limitations

4. Determination of Glare Occurrence

4.1 Sun Position

4.2 Reflected Sun Vector

4.3 Scattering and Subtended Beam Angle

4.4 Beam Projection onto PV Array Plane

4.5 PV Single-Axis Tracking

4.6 PV Dual-Axis Tracking

5. Determination of Ocular Impact

5.1 Ocular Hazard Plot

5.2 Direct Normal Irradiance (DNI)

5.3 Reflectance

5.4 Subtended Beam Angle

6. Annual Energy Production

7. Other Formulations

7.1 Flight Path Calculations

8. Acknowledgments

9. References

–  –  –

2. Introduction With growing numbers of solar energy installations throughout the United States, glare from photovoltaic (PV) arrays and concentrating solar systems has received increased attention as a real hazard for pilots, air-traffic control personnel, motorists, and others. Sandia has developed a web-based interactive tool that provides a quantified assessment of (1) when and where glare will occur throughout the year for a prescribed solar installation, (2) potential effects on the human eye at locations where glare occurs, and (3) an estimate of the maximum annual energy production.

The Solar Glare Hazard Analysis Tool (SGHAT) employs an interactive Google map where the user can quickly locate a site, draw an outline of the proposed PV array, and specify observer locations or paths. Latitude, longitude, and elevation are automatically recorded through the Google interface, providing necessary information for sun position and vector calculations.

Additional information regarding the orientation and tilt of the PV panels, reflectance, environment, and ocular factors are entered by the user.

If glare is found, the tool calculates the retinal irradiance and subtended angle (size/distance) of the glare source to predict potential ocular hazards ranging from temporary after-image to retinal burn. The results are presented in a simple, easy-to-interpret plot that specifies when glare will occur throughout the year, with color codes indicating the potential ocular hazard. The tool can also predict relative energy production while evaluating alternative designs, layouts, and locations to identify configurations that maximize energy production while mitigating the impacts of glare.

This Technical Reference Manual describes the theory and models used in SGHAT.

3. Assumptions and Limitations

Below is a list of assumptions and limitations of the models and methods used in SGHAT:

 The software currently only applies to flat reflective surfaces. For curved surfaces (e.g., focused mirrors such as parabolic troughs or dishes used in concentrating solar power systems), methods and models derived by Ho et al. (2011) [1] can be used and are currently being evaluated for implementation into future versions SGHAT.

 When enabled, PV array single- or dual-axis tracking does not account for backtracking or the effects of panel shading and blocking.

2|Page  SGHAT does not rigorously represent the detailed geometry of a system; detailed features such as gaps between modules, variable height of the PV array, and support structures may impact actual glare results. However, we have validated our models against several systems, including a PV array causing glare to the air-traffic control tower at Manchester-Boston Regional Airport and several sites in Albuquerque, and the tool accurately predicted the occurrence and intensity of glare at different times and days of the year.

 SGHAT assumes that the PV array is aligned with a plane defined by the total heights of the coordinates outlined in the Google map. For more accuracy, the user should perform runs using minimum and maximum values for the vertex heights to bound the height of the plane containing the solar array. Doing so will expand the range of observed solar glare when compared to results using a single height value.

 SGHAT does not consider obstacles (either man-made or natural) between the observation points and the prescribed solar installation that may obstruct observed glare, such as trees, hills, buildings, etc.

 The variable direct normal irradiance (DNI) feature (if selected) scales the userprescribed peak DNI using a typical clear-day irradiance profile. This profile has a lower DNI in the mornings and evenings and a maximum at solar noon. The scaling uses a clear-day irradiance profile based on a normalized time relative to sunrise, solar noon, and sunset, which are prescribed by a sun-position algorithm [2] and the latitude and longitude obtained from Google maps. The actual DNI on any given day can be affected by cloud cover, atmospheric attenuation, and other environmental factors.

 The ocular hazard predicted by the tool depends on a number of environmental, optical, and human factors, which can be uncertain. We provide input fields and typical ranges of values for these factors so that the user can vary these parameters to see if they have an impact on the results. The speed of SGHAT allows expedited sensitivity and parametric analyses.

4. Determination of Glare Occurrence Determination of glare occurrence requires knowledge of the following: sun position, observer location, and the tilt, orientation, location, extent, and optical properties of the modules in the solar array. Vector algebra is then used to determine if glare is visible from the prescribed observation points.

4.1 Sun Position The sun position algorithm[2] calculates the sun position in two forms: first as a unit vector extending from the Cartesian origin toward the sun, and second as azimuthal and altitudinal angles. The algorithm relies on the latitude, longitude and time zone offset from UTC in order to determine the position of the sun at every time step throughout the year.

First, we calculate the solar time:

–  –  –


( ) Lst is the local standard meridian, Lloc is the given longitude and E is the equation of time, in minutes.

The solar time can then be used to calculate the Hour angle, :

Where is the difference between solar time and solar noon.

Once the declination, is known, the solar zenith and azimuthal angle of the sun can be found:

( ) ( ) ( )| ( )|


–  –  –

The sun altitude and azimuth can be converted to unit vector components as follows:

⃗⃗ ⃗⃗ ⃗⃗⃗

–  –  –

4.3 Scattering and Subtended Beam Angle The reflected sun vector defines the axis of a conical beam representing the actual beam of sunlight. This sunbeam is translated to extend from the OP toward the PV array. The aperture of this conical sun beam is equivalent to β, the subtended beam angle, which is the sum of the sun

shape and the scattering caused by slope error:

( )

–  –  –

These 30 points are calculated by randomly generating two coordinates and solving for the third

using the following equation:

This equation states that the cone axis is orthogonal to the radius vectors of the conical section upon which the 30 conical points lie.

Next, conical edge vectors are defined by subtracting the cone apex (the OP) from the cone points. This collection of vectors extends from the OP toward the PV array plane. These vectors define the conical sun beam. At their center, or the axis of the cone, is the reflected sun vector calculated in 4.2.

These conical vectors are then intersected with the PV array plane. This cone-plane intersection will be an elliptical conical section defined by 30 co-planar points.

These intersection points are calculated using line-plane intersection equations [5]:

( )⃗ ⃗⃗ ( )


 ⃗⃗ is the PV array panel normal vector

–  –  –

 d is the distance from the OP to the intersection point, and  (x, y, z) define the intersection point for this vector.

The n intersection points found using the above equations define the elliptical conical section of the sun beam cone as it intersects the PV array plane.

–  –  –

4.5 PV Single-Axis Tracking Single-axis tracking allows for the PV panels to rotate over one dimension in order to track the apparent movement of the sun over time. This rotation is modeled using the normal vector of the

PV array panels, ⃗⃗. The components of ⃗ are calculated using the following:

 – Tracking axis tilt where 0º is parallel with flat ground and 90º is perpendicular to the ground, facing the horizon.

 – Panel offset from the tracking axis.

 – Tracking, or rotation, angle designating the rotation of the panel at a given time.

Clockwise and counter-clockwise over the tracking axis (see below).

 – Orientation of the tracking axis. Clockwise from due south (0º).

Figure 2 - PV panel with single-axis tracking. The panel normal is displayed as N. Source:


–  –  –

⃗⃗ ⃗ ⃗⃗

These components are converted back to the standard Cartesian system:

⃗⃗ ⃗ ⃗ () () () () () ⃗⃗ ⃗ ⃗ ⃗ () () () () () ⃗ ⃗ ⃗ ⃗⃗ Vector components are calculated for the panels at each time step.

4.6 PV Dual-Axis Tracking Dual-axis tracking implies the PV panels face “toward” the sun at every time step. Again, the panel normal varies every minute. Because the variance occurs in two dimensions, the sun vector (extending from the origin toward the sun) can be used as the panel normal:

⃗ ⃗

–  –  –

5.1 Ocular Hazard Plot The ocular impact of viewed glare can be classified into three levels based on the retinal irradiance and subtended source angle: low potential for after-image, potential for after-image, and potential for permanent eye damage [1, 3]. The following log-log plot illustrates these three

areas of glare intensity:

Figure 3 - Glare hazard plot illustrating the ocular impact as a function of retinal irradiance and subtended source angle [1, 3].

The subtended source angle represents the size of the glare viewed by an observer, while the retinal irradiance determines the amount of energy impacting the retina of the observer. Larger source angles can result in glare of high intensity, even if the retinal irradiance is low.

The boundary between the “yellow” and “red” regions, signifying glare that transitions from causing an after-image to causing permanent eye damage, can be quantified with the following


–  –  –

The second boundary, between the low potential for after-image (green) and potential for afterimage (yellow) areas, adheres to the following equation:

5.2 Direct Normal Irradiance (DNI) The variable direct normal irradiance (DNI) feature (if selected) scales the user-prescribed peak DNI using a typical clear-day irradiance profile. This profile has a lower DNI in the mornings and evenings and a maximum at solar noon. The scaling uses a clear-day irradiance profile based on a normalized time relative to sunrise, solar noon, and sunset, which are prescribed by a sunposition algorithm [2] and the latitude and longitude obtained from Google maps.

( ) Here represents the normalized time relative to solar noon. Normalization is based on the amount of time between sunrise or sunset and solar noon.

The DNI scaling profile was determined by fitting empirical DNI data to the cosine function, as illustrated in Figure 4. Note that DNI on any given day can be affected by cloud cover, atmospheric attenuation, and other environmental factors.

–  –  –

5.3 Reflectance Panel reflectivity can be varied for each time step to account for the position of the sun relative to the array. Smooth glass and light textured glass with and without Anti-Reflection coating, along with deeply textured glass were analyzed to derive accurate functions for computing reflectivity based on sun incidence angle [7].

Table 1 contains the fit functions for panel reflectivity.

–  –  –

5.4 Subtended Beam Angle The glare analysis must account for the actual visible area of the PV array when viewed from the observation point. For example, less viewable area will be apparent when viewing an array with panel tilt of 0 degrees on a flat surface from the side than when viewing it from above in an aircraft.

To account for this, the analysis replaces the solar beam angle computed in Section Error!

Reference source not found. with an array-limiting beam angle if the latter is a smaller value.

This represents the physical situation where the sun beam “overflows” the PV array from the viewer’s perspective, and thus less glare is possible.

| | √


–  –  –

Next, this power is multiplied by the scaled time increment to get the energy produced in that time interval (kWh).

Finally, the energy produced over the year is summed to get the maximum annual energy produced by the array, assuming clear sunny skies each day.

7. Other Formulations

7.1 Flight Path Calculations The flight path OP coordinates are computed based on the latitude and longitude of the selected threshold, and the specified direction of the flight path.

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