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
Yearlyirrradiation(kWh/m²)
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 The standard sky and ground view factors are no longer valid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 ∗ 𝑉𝐹 𝑚𝑜𝑑𝑢𝑙𝑒→𝑛𝑜𝑛−𝑠ℎ𝑎𝑑𝑜𝑤𝑒𝑑 𝑔𝑟𝑜𝑢𝑛𝑑
+𝛼 ∗ 𝐷𝐻𝐼 ∗ 𝑉𝐹 𝑚𝑜𝑑𝑢𝑙𝑒→𝑠ℎ𝑎𝑑𝑜𝑤𝑒𝑑 𝑔𝑟𝑜𝑢𝑛𝑑
𝐼 𝑑𝑖𝑓𝑓𝑢𝑠𝑒 = 𝐷𝐻𝐼 ∗ 𝑉𝐹 𝑚𝑜𝑑𝑢𝑙𝑒→𝑠𝑘𝑦
𝐼 𝑑𝑖𝑟𝑒𝑐𝑡 = 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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FRONT SIDE
kWh/m²/year
No impact on the front side but…

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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
kWh/m²/year

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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
5
6
Pyranometers in the ray tracing platform
(2 on the Eastern edge, 4 in the center)
Ray tracing simulation of the
irradiances over a sunny day
Experimental 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
5
6
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
 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
Hourly 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

Enhanging bifacial PV modeling with ray-tracing

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