Enhanging bifacial PV modeling with ray-tracing

ENHANCING BIFACIAL PV

MODELLING WITH RAY-TRACING

Amy Lindsay, Matthieu Chiodetti, Didier Binesti, Sophie Mousel,

Eric Lutun, Khalid Radouane, Sébastien Bermes, Régis Lecussan

6th PV PMC Workshop

25th of October 2016

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TABLE OF CONTENTS

Enhancing bifacial PV modelling with ray-tracing | 10/2016

1. INTRODUCTION TO BIFACIAL PV

2. HOW TO MODEL REAR SIDE IRRADIANCES

3. ADVANTAGES OF RAY-TRACING

4. EXPERIMENTAL MEASUREMENTS

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INTRODUCTION

The ground-reflected irradiance is of prime

importance for the rear irradiance of bifacial PV


29.8% 17.7% 12.6%

68.1%

81.0%

86.5%

0

50

100

150

200

250

300

350

albedo = 0.2 albedo = 0.4 albedo = 0.6

Year

ly ir

rrad

iati

on

(kW

h/m

²)

Beam irradiation Diffuse irradiation Ground-reflected

Relative contribution of the different components of light to the

rear side irradiance (Illustrative case: large-scale bifacial

plant, Mediterranean climate)

Need for precise modelling of

ground-reflected irradiance

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INTRODUCTION

Challenges of bifacial PV modelling:

The standard sky and ground view factors are no longer valid


1 − cos(𝑡𝑖𝑙𝑡)

2

1 + cos(𝑡𝑖𝑙𝑡)

2X

Comparison level Module* String* Plant*

Gain compared to monofacial

equivalent (kWh/kWp)25% 18.5% 9%

* Measured, on clear concrete ground

The shadow cast on the ground is highly impacting

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HOW TO MODEL REAR SIDE IRRADIANCES

1st approach : the view factor methodology

View factors quantify the proportion of radiation which leaves surface m and strikes

surface S

Requires a meshing of the ground, the shadow, the PV installation…


Pros:

- Easy to implement for simple geometries

Cons:

- Accuracy depends on the meshing

- Calculation time explodes with the size of the system

- Difficult to take into account irregular geometries

- Difficult to take into account structures

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REAR IRRADIANCE MODEL

Calculates the rear irradiances

based upon:

(1): the position of the module within

the stand

(2): the shadow cast on the ground

(3): the ground albedo

(4): the stand behind

𝐼𝑔𝑟𝑜𝑢𝑛𝑑−𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑑 = 𝛼 ∗ 𝐺𝐻𝐼 ∗ 𝑉𝐹𝑚𝑜𝑑𝑢𝑙𝑒→𝑛𝑜𝑛−𝑠ℎ𝑎𝑑𝑜𝑤𝑒𝑑 𝑔𝑟𝑜𝑢𝑛𝑑

+𝛼 ∗ 𝐷𝐻𝐼 ∗ 𝑉𝐹𝑚𝑜𝑑𝑢𝑙𝑒→𝑠ℎ𝑎𝑑𝑜𝑤𝑒𝑑 𝑔𝑟𝑜𝑢𝑛𝑑

𝐼𝑑𝑖𝑓𝑓𝑢𝑠𝑒 = 𝐷𝐻𝐼 ∗ 𝑉𝐹𝑚𝑜𝑑𝑢𝑙𝑒→𝑠𝑘𝑦

𝐼𝑑𝑖𝑟𝑒𝑐𝑡 = max(𝐵𝑁𝐼 ∗ cos 𝑖 , 0)


α: ground albedo

VF: view factor

GHI, DHI, BNI: Global Horizontal, Diffuse Horizontal

and Beam Normal Irradiances

i: incidence angle of beam

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HOW TO MODEL REAR SIDE IRRADIANCES

2nd approach : ray tracing

Tracing back the path of light:

from the PV cell to the light source (= sun and diffuse) by

taking into account its encounters with obstacles

Rays of light = straight lines

Diffuse and/or specular reflection

Example : eye = one PV cell 1 million of rays are sent by

Monte Carlo, equiprobably distributed on the hemisphere

by successive reflections, they reach the light sources : sun

and diffuse from the sky


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Ray tracing platform developed in partnership with EnerBIM

RAY TRACING PLATFORM


Pros:

- Gives irradiance inhomogeneity

- Shading

- Impact of structures

- Flexible (different configurations…)

- User friendly

Cons:

- Relatively hard to implement

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COMPARISON OF THE TWO METHODS

Case 1 : array of 60 frameless bifacial modules, 1.3m above the ground, no

structures, albedo 30%


FRONT SIDE

1206.0 1206.2 1204.3 1203.6 1203.0 1202.5 1202.0 1201.7 1201.5 1201.4 1201.4 1201.6 1201.8 1202.1 1202.5 1203.0 1203.7 1204.4 1205.2 1206.1

1207.0 1206.2 1205.5 1204.8 1204.3 1203.9 1203.5 1203.2 1203.1 1203.0 1203.0 1203.1 1203.3 1203.5 1203.9 1204.4 1204.9 1205.6 1206.3 1207.1

1208.1 1207.4 1206.8 1206.3 1205.8 1205.4 1205.1 1204.9 1204.8 1204.7 1204.7 1204.8 1204.9 1205.2 1205.5 1205.9 1206.3 1206.9 1207.5 1208.2

kWh/m²/year

kWh/m²/yearAverage: 1204 kWh/m²/y

Average: 1198 kWh/m²/y

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Case 1 : array of 60 frameless bifacial modules, 1.3m above the ground, no

structures


REAR SIDE

kWh/m²/year

kWh/m²/year

313.1 250.9 251.8 241.5 236.5 234.1 233.0 233.0 233.0 233.0 233.0 233.0 233.0 233.0 234.0 236.4 241.4 251.7 273.2 313.1

288.6 250.9 231.7 222.8 218.6 216.6 215.8 215.8 215.8 215.8 215.8 215.8 215.8 215.8 216.6 218.5 222.7 231.7 251.3 288.6

280.4 249.5 234.5 227.7 224.6 223.2 222.6 222.6 222.6 222.6 222.6 222.6 222.6 222.6 223.2 224.7 227.9 234.7 250.1 280.4

Min: 215.8 kWh/m²/y

Average: 236.5 kWh/m²/y

Min: 216.3 kWh/m²/y

Average: 233.3kWh/m²/y

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Good agreement of the two methodologies for a simple case

Ray tracing platform allows to go quite easily to the cell-level

Reduced computation time with ray tracing


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RAY TRACING ENHANCEMENTS

Case 2: an isolated bifacial module, with and without a frame, without structure,

albedo 30%


Frameless bifacial module Framed bifacial module

(difficult to model with view factor method)

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Frameless bifacial module Framed bifacial moduleFRONT SIDE

kW

h/m

²/ye

ar

No impact on the front side but…

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Frameless bifacial module Framed bifacial module

REAR SIDE

Min = 141.3 kWh/m²/y

Average = 197.2 kWh/m²/y



-13% on the least illuminated cell

-9% on the total irradiance

kW

h/m

²/ye

ar

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The frame can have a strong impact on the irradiance received on the

rear side

Currently, the frame, or the junction boxes are not optimized for bifacial

PV


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Case 3: one 60 bifacial module array, with frames, with/without structures, albedo

30%


Bifacial array without structure Bifacial array with structure

(difficult to model with view factor method)

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FRONT SIDE

kWh/m²/year

No impact on the front side but…

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REAR SIDE

kWh/m²/year





-58% on the least illuminated cell

-22% on the total irradiance

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Structures have an impact on the rear side irradiance

Ray tracing allows to quantify the losses associated to complex

shading


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EXPERIMENTAL MEASUREMENTS

15 kWp bifacial array near Paris

Plant configuration for the rear side (GCR = 50%)

Albedo 30%

6 pyranometers on the rear side to validate the irradiances


60 bifacial modules at EDF R&D 6 pyranometers on the rear side

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RAY TRACING MODEL VALIDATION


3D model of the test zone

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Rear irradiances


1

2

3

4

56

Pyranometers in the ray tracing platform

(2 on the Eastern edge, 4 in the center)

Ray tracing simulation of the

irradiances over a sunny dayExperimental measurements of the

irradiances over a sunny day

Pyranometers in the center (5 and 6) are the most

impacted by the shadow and the structures

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Rear irradiances


1

2

3

4

56

Example of hourly correlation of the

simulated and measured rear side

irradiances of pyranometer n°1 over 3

months

Over 3 months of data, on all

pyranometers :

RMSE: 15.7 W/m²

Close to the pyranometers’ uncertainties

Good agreement measures / simulation

Mean Bias Error: + 10 W/m²

Slight overestimation of the rear irradiances

Under investigation

| 24Enhancing bifacial PV modelling with ray-tracing | 10/2016


Overview of the irradiance inhomogeneity over 3 months

kWh/m²kWh/m²

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Irradiances considered at a bypass diode level

ELECTRIC MODEL


Bifaciality factor depending on the irradiance

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ELECTRIC MODEL

I-V curve simulation taking into account irradiance inhomogeneity


1000 W/m2

300 W/m2

Developed under a Dymola/Modelica environment

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ELECTRIC MODEL VALIDATION

DC voltage


DC current

Example of voltage measurements and

simulation over 3 days

Example of current measurements and

simulation over 3 days

MBE = +1.4% MBE = -2.5%

Over 3 months of data:

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ELECTRIC MODEL VALIDATION

DC power and yield


Example of power measurements and

simulation over 3 daysHourly correlation of simulated and

measured yield over 3 months

MBE = -0.9%

RMSE = 4.1%Over 3 months of data:

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SUMMARY

Ray tracing is a powerful tool for modelling bifacial PV:

Quantifies the losses due to rear side shading (frames, structures, junction boxes,…),

which can be significant

Quantifies the impact of casted shadow on the ground and on the other rows

Modelling of large scale bifacial PV installations is feasible:

Ray tracing + Dymola model shows a good accuracy

Error on the yield < 1%

Model validation to be pursued:

On a longer period

On different locations


Thank you for your attention!

Technology

Enhanging bifacial PV modeling with ray-tracing