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Photosynthetically active radiation separation model for high-latitude regions in agrivoltaic systems modeling
Mälardalen University, School of Business, Society and Engineering, Future Energy Center.ORCID iD: 0000-0003-4075-8855
School of Electrical Engineering and Automation, Harbin Institute of Technology 2, Harbin, Heilongjiang, China.ORCID iD: 0000-0003-2162-6873
USDA ARS, Hydrology and Remote Sensing Laboratory 3, Beltsville, Maryland 20705, USA.ORCID iD: 0000-0003-0748-5525
Mälardalen University, School of Business, Society and Engineering, Future Energy Center.ORCID iD: 0000-0003-2225-029X
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2024 (English)In: Journal of Renewable and Sustainable Energy, E-ISSN 1941-7012, Vol. 16, no 1, article id 013503Article in journal (Refereed) Published
Abstract [en]

Photosynthetically active radiation is a key parameter for determining crop yield. Separating photosynthetically active radiation into direct and diffuse components is significant to agrivoltaic systems. The varying shading conditions caused by the solar panels produce a higher contribution of diffuse irradiance reaching the crops. This study introduces a new separation model capable of accurately estimating the diffuse component from the global photosynthetically active radiation and conveniently retrievable meteorological parameters. The model modifies one of the highest-performing separation models for broadband irradiance, namely, the Yang2 model. Four new predictors are added: atmospheric optical thickness, vapor pressure deficit, aerosol optical depth, and surface albedo. The proposed model has been calibrated, tested, and validated at three sites in Sweden with latitudes above 58 °N, outperforming four other models in all examined locations, with R2 values greater than 0.90. The applicability of the developed model is demonstrated using data retrieved from Sweden's first agrivoltaic system. A variety of data availability cases representative of current and future agrivoltaic systems is tested. If on-site measurements of diffuse photosynthetically active radiation are not available, the model calibrated based on nearby stations can be a suitable first approximation, obtaining an R2 of 0.89. Utilizing predictor values derived from satellite data is an alternative method, but the spatial resolution must be considered cautiously as the R2 dropped to 0.73.

Place, publisher, year, edition, pages
AIP Publishing , 2024. Vol. 16, no 1, article id 013503
National Category
Energy Engineering
Identifiers
URN: urn:nbn:se:mdh:diva-66129DOI: 10.1063/5.0181311ISI: 001163102700001Scopus ID: 2-s2.0-85185347410OAI: oai:DiVA.org:mdh-66129DiVA, id: diva2:1840657
Funder
Swedish Energy Agency, 52693-1Swedish Research Council Formas, FR-2021/0005Swedish Energy Agency, 51000-1Swedish Energy Agency, P2022-00809Available from: 2024-02-26 Created: 2024-02-26 Last updated: 2026-01-20Bibliographically approved
In thesis
1. Solar Irradiance Assessment in Agrivoltaic Systems: Understanding Photosynthetically Active Radiation Separation Models and Dynamic Crop Albedo Effect in Agrivoltaic Systems Modelling
Open this publication in new window or tab >>Solar Irradiance Assessment in Agrivoltaic Systems: Understanding Photosynthetically Active Radiation Separation Models and Dynamic Crop Albedo Effect in Agrivoltaic Systems Modelling
2024 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Agrivoltaics, also referred as agrivoltaic systems, present an appealing solution, owing to its dual land use and integrated food-energy system, for the shift to renewable energy. However, it raises concerns about the complex synergies and trade-offs between crop growth and solar photovoltaic panels. Crops grown under open-field traditional agriculture receive uniformly distributed Sun irradiance, whereas agrivoltaics introduces variable shadowing, which interferes with the homogeneity of light collected by crops. 

Agrivoltaics emphasises the significance of the diffuse irradiance component during shading conditions when direct irradiance is blocked by solar panels. Decomposition models are essential for estimating the diffuse light component from the global one. This thesis conducts a benchmarking investigation of state-of-the-art solar irradiance decomposition models to identify the most suitable ones for decomposing photosynthetically active radiation in specific Swedish sites. The results lead to a novel separation model that outperforms the top models revealed in the benchmarking analysis. Various scenarios common in agrivoltaic sites are used to test the applicability of the model and guide model selection based on available data. 

In agrivoltaic systems, where solar panels disrupt incoming sunlight to crops, the crop reflectivity or albedo influences solar panels, particularly those with bifacial solar cells. This thesis further investigates how ground-reflected irradiance components affect the front and rear sides of bifacial system designs under varied ground albedo circumstances. Using Agri-OptiCE®, this research examines how albedo data quality affects bifacial systems. The findings contribute to improve the precision of plane-of-array irradiance and power output estimations, hence aiding the practical implementation of agrivoltaic systems across the globe. 

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2024
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 359
Keywords
Agrivoltaics, Albedo, Photosynthetically Active Radiation, Decomposition Model, Solar Energy
National Category
Energy Engineering
Research subject
Energy- and Environmental Engineering
Identifiers
urn:nbn:se:mdh:diva-66407 (URN)978-91-7485-645-3 (ISBN)
Presentation
2024-05-15, Paros, Mälardalens universitet, Västerås, 09:00 (English)
Opponent
Supervisors
Funder
Swedish Energy Agency, 52693-1
Available from: 2024-04-17 Created: 2024-04-10 Last updated: 2025-10-10Bibliographically approved
2. A Solar Irradiance Journey into Agrivoltaics: From Light Quantity to Quality
Open this publication in new window or tab >>A Solar Irradiance Journey into Agrivoltaics: From Light Quantity to Quality
2026 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Agrivoltaics integrate agricultural activities with solar photovoltaic (PV) energy conversion on the same land, offering a promising solution to competing demands for food and renewable energy. However, agrivoltaic systems introduce complex interactions between PV installations and crops, primarily by altering both the quantity and quality of solar irradiance reaching the canopy. This thesis investigated solar irradiance in agrivoltaic systems from both broadband and spectral perspectives, combining modelling developments with experimental validation to improve system assessment and design. From a light-quantity perspective, the work advances methods for estimating photosynthetically active radiation (PAR), with a particular focus on its diffuse component, which is highly relevant for plant growth but rarely measured. Existing broadband irradiance decomposition models were adapted and evaluated for high-latitude conditions, demonstrating that performance depends strongly on local calibration and solar geometry. A new PAR decomposition model was developed and shown to outperform commonly used approaches under Nordic conditions. The results also highlighted a trade-off between model complexity and data availability, indicating that simpler models may be preferable when high-quality input data are limited. In parallel, the influence of ground albedo on irradiance and power output in bifacial PV systems was examined, revealing that ground-reflected irradiance can contribute substantially to plane-of-array irradiance, particularly under high-albedo conditions such as snow. Incorporating time-varying albedo significantly improves modelling accuracy compared to static assumptions. Beyond broadband irradiance, the thesis addressed spectral light management through novel wavelength-selective PV (WSPV) technologies. A classification framework for WSPVs in agricultural applications was developed to enable systematic comparison of spectral selectivity approaches and implementation pathways. To support implementation, spectral-aware modelling frameworks were developed to simulate light transmission through WSPVs and estimate leaf-level photosynthetic responses. These models were validated against experimental data and applied to assess crop suitability and optimise spectral transmittance across different climates to aid future designs. Based on current constraints, a higher transmission of blue and red wavelengths favoured crop productivity and full transparency within the PAR range was not required to sustain growth. Finally, the feasibility of WSPV-based agrivoltaics was demonstrated through a full-season, open-field experiment using semi-transparent magenta cadmium telluride thin-film PV modules, where crop yields were comparable to open-field conditions while radiation use efficiency and land-use productivity increased. Overall, this work advances the modelling and experimental foundations of agrivoltaics by improving irradiance assessment, integrating spectral effects, and validating emerging PV technologies under field conditions providing insights for researchers, industry, and policymakers.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2026
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 460
Keywords
Agrivoltaics, Albedo, Photosynthetically Active Radiation, Decomposition Model, Wavelength-Selective PV, Semi-Transparent PV, Solar Irradiance
National Category
Energy Engineering
Research subject
Energy- and Environmental Engineering
Identifiers
urn:nbn:se:mdh:diva-75386 (URN)978-91-7485-747-4 (ISBN)
Public defence
2026-03-06, Delta, Mälardalens universitet, Västerås, 14:00 (English)
Opponent
Supervisors
Available from: 2026-01-21 Created: 2026-01-20 Last updated: 2026-02-13Bibliographically approved

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Ma Lu, SilviaZainali, SebastianStridh, BengtAvelin, AndersCampana, Pietro Elia

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