Ray-trace Modelling of Bifacial Single Axis Tracker Client

Innovation in photovoltaics since 1979

Ray-trace Modelling of Bifacial Single Axis Tracker

Client: MecaSolar

Steve Askins, Madrid, Fall 2020

2MecaSolar Bifacial Modelling - CONFIDENTIAL

Overview

• Literature Review / Background

– Modelling of bifacial (BiFi) PV

– Anisotropic sky models for BiFi PV

– Selection of experimental data from literature to validate IES Modeling

• BiFiRot Test Bed @ ZHAW in Winterhur, Switzerland

• Nussbaumer et. al., 2020 (Solar Energy)

• Reference Model

– Sky Modeling in LightTools

– Modeling of BiFiRot Installations

– Results & Comparison

• MecaSolar Skyline Tracker Model

– Modeling Skyline tracker in LightTools

– Parametric study of tracker design constants

– Results of SECOND bifacial modelling with Skyline tracker

• Madrid Spain (using selected days for PVGIS TMY for Madrid)

• Implemented automated tracker modelling.

• Updated all tracker parameters to final Skyline values

• Improved module model to include frame, solar cells with gaps, recessed rear plane, etc.


Bifacial Modeling: VF vs. RT

• Key question: determine back side irradiance

• Two main methods: View Factor analysis & Ray Tracing.

• View Factors: Analytical method to determine all

components to back side irradiance.

• Ray Tracing: Plant is modelled geometrically (scene) and

monte carlo ray tracing is performed to calculate irradiance

on all required surfaces


Bifacial Modeling: VF vs. RT

• View factor

– Analytical, fast

– Used by PVSyst, SAM, and othere well known modelling software

– Geometry must be simple.

• Not easy to include detailed geometries, obstructions, etc.

• NOT sufficient for analyzing BiFi tracker geometries

• Ray tracing

– Complex geometries can be included.

– Simulation is time consuming (backward ray tracing may help.)

– Software does not have built in sky modelling

In this work we will

use RT approach

using commercial

software: ORA Light

Tools 8.7


Sky Modeling: Where does diffuse light come from?

• Diffuse light is anisotropic, sky brightness varies over dome dependent on conditions

• Even for non-bifacial modeling, irradiance on any tilted plane is dependent on the

distribution of light over the whole sky, depending on conditions.

– Typically, GHI is known but determining irradiance on arbitrarily tilted plane (GTilt) is not trivial

– Sky modeling has been a critical part of improving PV modelling over the last 30 years


Discrete Sky modelling: the “Perez” model.

• Most well-known model(s) published by R. Perez, (SUNY-Albany) from the 80s onward.

– “Discrete” models (1986,1987,1990)

– Continuous models (1990, 1993)

• Discrete model (1986): divide diffuse irradiance into three

components

– Isotropic region (most of the sky): Radiance = L

– Circumsolar Radiation (CSR): Radiance = F1 × L

• Brighter than isotropic due to forward scattering (aerosols), possible

cloud reflection

– Horizon region: Radiance = F2 × L

• Brighter than isotropic due to multiple Rayleigh scattering and

backscattering, distance clouds, etc.


Sky modelling: the “Perez” model

• Updated discreet model (1987 / 1990)

• New definition for F1 and F2

• Usually used to find ED (tilted diffuse)

…used by PVSyst, NREL-SAM etc.

Clearness →

Brightness →

( )( )

( )1 1 2

1 cos1́ sin

2

Tilt

d T

aE DHI F F F

b

+ = − + +

( )

1 2 1 2

1 1 2

11 23

3

3

1

where

... emprical in bins of

(DHI+DNI)

=1

Iso CS Horiz

x x x Z x

Z

Z

a

a

DHI DHI DHI DHI

DHI F F DHI F DHI F DHI

F f f f

f f

DNI

DHI AM

E

= + +

= − − + +

= + +

=

+

+

=


Sky Modelling in Light Tools

• For this first effort we will use Perez 1990 model.

• Model four light sources

– All sources emitting / calibrated to a square reception area

• 10m x10m for reference simulation

– Direct beam: moving disk, ⌀100m @ 25km.

– Diffuse

• CSR: Rotating Spherical source, limited to

– Since DHICSR provided as component of DHI,

• Isometric: Fixed Hemispherical source

• Horizon: Fixed spherical source limited to ξ = [°0 – 6°]

• Parameterized for loading/simulating hourly irradiance &

sun position

– LightTools Solar Movement generator used to validate own

calculations


Reference Model: Modelling ZHAW Installation

• Best available data found in literature for initial validation model were those published on

BiFiRot experiment near Zurich.

– Presentations at BiFi-PV workshope and especially Nussbaumer (2020) in Progress in Photovoltaics.

– Important: Irradiance time series and corresponding Front side Irradiance and Bifacial gain was published.

– Modules are rotated daily to simulation simulations with many tilt angles.

• Good for model validation (tendencies)


BiFiRot Modelled in LightTools

• Very basic geometry from BiFiRot installation modelled

– No structure or obstructions.

– Modules are rectangles with 100% Absorbance

– Ground is white with variable % reflection (abedo).

• Simple Lambertian scattering applied.

• Modules could be rotated

• As in experimental data, we measured irradiance at

– M1-Back, M2-Front, M2-Back, and M3-Front

M1

M2

M3


Reference Simulation Process

1. Extract irradiance data (GHI & DNI) for 3 days (Zurich, Fall, 2017)

– Interpolate to 20 pts/day (~25min interval)

2. Calculate sun positions & Air Mass (solpos.c / NREL)

3. Calculate DNI → ε, Δ → F1, F2 →DHIIso, DHICSR, DHIHoriz

4. Create input file for LT (3 days, 20 times, 12 Tilt angles, 4 Albedo values)

5. Run ray tracing simulation: 250k rays per simulation for each configuration

6. Integrate daily irradiance on front and rear surfaces and compare to published data.


Reference Simulation Results: Front & Rear Irradiance

• Front side irradiance:

– Good agreement except for overcast day (8/11)

– Sky modeling validated.

– Overestimation on cloudiest day (also on other

days to a smaller extent) probably due to

unmodelled obstructions (see image slide 10)

• Back side irradiance*:

– Correct magnitude.

– Similar trends though “skewed”.

– Best agreement for Albedo = 35%

• Reported measured value of 51%.

• Assume “Albedo tuning factor” of 35/51 =

70%.

– Our simulation underestimates for low-tilt and

overestimates for high-tilt:

• Could indicate a need for using “guassian” or

directional scattering rather than Lambertian.

• Also, we applied “white paint” over a 10m

x10m area whereas in actual system painted

area

IES; Albedo=25%

IES; Albedo=30%

IES; Albedo=35%

Measurement*

* From Nussbaumer 2020 Figs 8 & 13. Nussbaumer reports front

side irradiance and bifacial gain, measured values for rear side

irradiance are calculated from GRear = GFront/BG


Reference Simulation Results: Bifacial Gain

• IES agreement to measurement is similar to view factor model provided by PVSyst.

– PVSyst also underestimates low-tilt & overestimates high-tilt, probably uses Lambertian assumption.

– Since we used only a simple geometry, the advantages of RT over VF are not apparent.

• Conclusion: Sufficient for relative analysis of MecaSolar Tracker.

* PVSyst model results included in

Nussbaumer, 2020, Figure 13.

-2

-2

(kw h m )

(kw h m )

Back

Front

EBG

E

=

Integrated

over all 3

days


Modelling the Skyline Tracker in LightTools

• 1V and 2V tracker designs modelled

• Geometry taken from drawings and emailed information

– “2006_BIOPDE_2V_ASSEMBLY_SR_SUNRIDER_2Vx4_V0.pdf”

– “2006_BIOPDE_2V_ASSEMBLY_SR_SUNRIDER_1Vx4_V0.pdf”

• Used three tracker rows and assumed 1/GCR = 3 (~6m spacing).

• Two “sections” (piers) on either side of center are modelled


• Notes:

1. E-W Spacing of Trackers (LEW) varies number

of modules with E-W Gap

2. In the simulations, it is the Aspect Ratio (AR)

that is fixed or varied, not Axis Height (H). For

2V trackers AR, HAxis and GEW are related as:

This means that in simulation results for

increasing GEW are not representative of

simply separating the modules but represent

separating the modules while increasing axis

height.

Modelling the Skyline Tracker in LightTools

• Summary of parameter defaults and other dimensions

Real Tracker

1V 2V

Tra

cker

1/GCR 3 3

E-W Spacing1 6.3 m 13.2m

Aspect Ratio2 53.5% 45.9%

Axis Height 1120 2020

Center Space 39.8 cm

Pie

r

Height 80 mm

Width 46 mm

Thick 5 mm

N-S Spacing 7.5 m

Torque

Tube

Shape Square

Size 120 cm

Purl

in

Height 100 mm

Width 40 mm

Flange Width 90 mm

Length 43 cm 362 cm

Module

Height 2094 mm

Width 1038 mm

N-S Spacing 25 mm

E-W Gap 0 210

Other From datasheet

• Parameters varied as requested by MecaSolar

– 1V vs 2V

– Aspect Ratio (AR) → Axis Height (HAxis)

– Purlin Height (h)

– E-W Spacing (GEW, for 2V Only)𝑳𝑬𝑾 = 𝟏 𝒐𝒓 𝟐 ∙ 𝑯𝑴𝒐𝒅𝒖𝒍𝒆 + 𝑮𝑬𝑾

𝑨𝑹 =𝑯𝑨𝒙𝒊𝒔

𝟏 𝒐𝒓 𝟐 ∙ 𝑯𝑴𝒐𝒅𝒖𝒍𝒆 + 𝑮𝑬𝑾

• Detailed structural elements

– Purlins are modelled as omegas, etc.

• Tracker reflections

– Tracker assumed to be metallic

• 50% reflectivity

– Black tracker also modelled for comparison


Module Simulation setup

• Simulation extent

– 10% Greater than space of 3 trackers

– Due to higher LEW, 2V tracker simulation is ~2x larger

• Dummy & Monitored modules

– Monitored modules

• Inner 12 modules of inner row

• 3 Recievers per module (see next slide)

• Results presented are average values from all 12

– Dummy Modules

• Simplified modules used at corners where less important to reduce

complexity for simulation at corner positions

• Outer modules of outer rows

Dummy

Detailed


Module model

• Longi LR4-72HBD

• Dimensions taken from data sheet:

– “4. LR4-72HBD 425-455M（35x30Frame+2.0mm Glass+IEC-UL）-DraftV02（NEW Hi-MO4.pdf”

• Modeled as Frame and solar cells

– Solar cells are “connected” in vertical direction, where gap is very small.

– Gap is modeled in horizontal direction such that overall transparent fraction is correct

– Central area is left free from cells.

– Ability to model glass as well, but suppressed for these runs

• 3 Receivers per module

– One on front surface active area (including center)

– Two on back surface covering only cells


Tracker Simulation Input

• Daylight modelling unchanged from previous results

• Tracking equations, including back-tracking, from

Lorenzo, 2011 [1]

– Assumed tracking range = ±60°

– When necessary, tracking range further limited to avoid ground

(low AR simulations)

• Simulated in Madrid, Spain

– TMY from PVGIS

– 6 reference days used over the course of the year with a variety

of diffuse fractions.

DayDiffuse

Fraction

21-Jan 34%

22-Mar 80%

29-Mar 16%

23-Jun 20%

14-Sep 52%

29-Nov 66%

[1] E. Lorenzo, L. Narvarte, and J. Muñoz, “Tracking and back-tracking,” Prog.

Photovolt: Res. Appl., vol. 19, no. 6, pp. 747–753, Sep. 2011, doi: 10.1002/pip.1085.

https://doi.org/10.1002/pip.1085


Results: Aspect Ratio & E-W Gap

-2

-2

(kw h m )

(kw h m )

Back

Front

EBG

E

=

Integrated

over all 6

days

• Bifacial gain (BG) vs. Aspect Ratio

– BG calculated for irradiance only (not electric)

– Approx. 12% irradiance BG expected in

Madrid.

– Aspect Ratio is a significant factor for BG

• Very similar Bifacial Gain for 1V vs. 2V

– Slight advantage for 1V tracker

• BG vs E-Gap

– Fixed AR: relatively small effect on BG

– For fixed Haxis advantage of increasing E-W

gap reduced ~50%.


Results: Shadow Factor

• Shadow factor is a required input for PV-Syst

– Defined as the amount of rear surface irradiance lost as compared to

a “no structure” case (where the trackers are floating in air)

– Simulated by simply removing structure in light tools

• SF significantly lower for 1V trackers

– Shadowing from long purlins for 2V plays a role

– For no structure case, 2V tracker is more transparent (EW-Gap)

increasing irradiated ground area

• SF vs AR trend is opposite for 1V vs 2V

– Most likely related to purlin dominated vs. torque tube dominated

shadowing

, ,

,

Back NoStructure Back Structure

Back NoStructure

E ESF

E

−=


Results: Purlin Height and Length (2V Only)

• Purlin geometry varied

– Purlin Height (for 1V and 2V)

– Purlin Length (2V only)

• Metallic tracker has effect on BG

– Approx. 1% absolute BG increase due to reflections.

• Increasing Purlin height offers no advantage or

causes BG decrease

– While higher purlin provides separation from torque tube,

tall purlins also create shadow from certain directions

(see images)

– Worse for no reflections (black tracker)

• Purlin Length in 2V is shown to be important

– Supports hypothesis that long purlins in 2V tracker design

causes BG disadvantage

200 mm Purlin60 mm Purlin

0 50 100 150 200

Purlin eight(mm)

10

10.5

11

11.5

12

12.5

13

13.5

14

ifacia

l

ain

(

)

1 1.5 2 2.5 3 3.5 4

Tracker nly2) mm(Purlin Length

10.8

11

11.2

11.4

11.6

11.8

12

12.2

12.4

12.6

ifacia

l

ain

(

)

M eta l l i c Trac k er (R = 50 ) lac k Trac k er (R=0 )

1 2


Conclusion / Next Steps

• Complete:

– Developed a modelling environment for examining performance of bifacial modules on SATs, using well-known sky models

and the Light Tools Ray Tracing Software.

• Using a ray tracing technique and LT allows us to model arbitrarily complex geometry in the future (e.g. step file import.

– Validated our implemented daylight models against published bifacial performance data and shown sufficient agreement to

move forward with initial tracker study.

– Implemented programmatic tracker modelling in Light tools

– Performed final bifacial ray tracing study with detailed Tracker and Module model

• Main conclusions:

– From the studies so far realized, we show that 2V trackers offer no advantage in terms of bifacial collection of

overall irradiance

• Possible next steps for future work:

– Use NREL Bifacial SAT dataset as a better reference

– Simulation improvements

• Cumulative skies, mirrored tracker movement.

– Study irradiance profile on rear surface of modules – PV-Syst “Mismatch” factor

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Ray-trace Modelling of Bifacial Single Axis Tracker Client