Source-linked AI summary
Optimization of vertically mounted agrivoltaic systems
Pietro Elia Campana, Bengt Stridh, Stefano Amaducci, Michele Colauzzi
TL;DR
Agrivoltaic systems must balance food and energy production while addressing linked water, crop, and electricity objectives. This study develops and validates a multi-objective optimization model for vertically mounted bifacial photovoltaic systems. The model finds strong effects of row spacing on crop yield and land equivalent ratios above 1.2 for the investigated crops and location.
Problem
Agrivoltaic design requires evaluating competing electricity, crop, water, and land-use objectives, while prior studies largely lacked optimization of existing systems.
Method
The study develops a multi-objective genetic-algorithm model combining solar radiation and shading, photovoltaic production, and crop-yield submodels.
Results
Land equivalent ratios above 1.2 were obtained for the investigated crops and location, while reducing row distance from 20 m to 5 m could halve crop yield.
Takeaways & Limitations
Agrivoltaic implementation for the investigated crops and location supports using the technology to meet green-economy and sustainability goals.
Takeaways & Limitations
The optimization should consider multiple years, crop rotations, and broader economic and environmental objectives in future work.
Abstract
from arXiv · showhide
Agrivoltaic systems represent a key technology for reaching sustainable development goals reducing the completion of land for food versus land for energy. Moreover, agrivoltaic systems are at the centre of the nexus between electricity production, crop production, and irrigation water saving. In this study, an optimization model for vertically mounted agrivoltaic systems with bifacial photovoltaic models is developed. The model combines three main submodels: solar radiation and shadings, photovoltaic, and crop yield. Validation of the submodels is performed showing good agreement with measured data and commercial software. The optimization model is set as multi objective to explore the trade-offs between competing agrivoltaic key performance indicators. The results shows that the row distance between bifacial photovoltaic modules structure affects significantly the photosyntetically active radiation distribution by reducing the crop yield of potato and oat of about 50% by passing from 20 m to 5 m. The implementation of agrivoltaic system for the investigated crops at the chosen location shows a land equivalent ratio above 1.2 that justify the technology for reaching the country sustainability goals.
1 Introduction
Agrivoltaic systems combine farming and photovoltaic generation to address competition between land for food and energy while linking energy, food, and water benefits. Their relevance is reinforced by expanding photovoltaic deployment and sustainability targets.
- Sweden’s photovoltaic capacity reached 698 MWp in 2019, producing about 540 GWh and supplying 0.41% of total electricity.
- Swedish targets include 100% renewable-based power supply by 2040 and net-zero greenhouse-gas emissions by 2045.
- Agrivoltaic systems combine farm activities and photovoltaic farms, helping overcome competition between land for food and land for energy.
- The technology connects electricity production, crop production, and water-related benefits across energy, food, and water domains.
- Agrivoltaic systems can reduce plant drought stress and increase food yield while also reducing photovoltaic-panel heat stress.
2 Modelling and optimization
The study develops a multi-objective optimization framework for vertically mounted agrivoltaic systems, combining solar radiation and shading, bifacial photovoltaic, and crop-yield models. The framework represents trade-offs among land use, crop production, and electricity generation.
- Modelling framework: The framework calculates photovoltaic production from climatological data using solar-position, radiation-transposition, and shading algorithms, while crop yield uses PAR and climatological and agricultural parameters.The modelling workflow links solar radiation and shading calculations to photovoltaic production and crop-yield estimation.
- Solar radiation and PAR: Diffuse PAR is estimated with a decomposition model, and shading effects are incorporated when calculating total PAR absorbed by crops.The diffuse PAR model is validated separately in the study.
- PV model: The photovoltaic model uses a five-parameter single-diode formulation calibrated by minimizing mean absolute error against measured I-V curves for an 80% bifaciality module.The simulated module is the 380 Wp Jolywood D72N bifacial module.
- Shading losses: Shading is estimated geometrically from the intersection between projected shaded rectangles or parallelograms and the crop area between bifacial-module rows.The shading factor also accounts for beam and diffuse irradiance across a discretized sky dome.
- Crop model: The crop model converts daily PAR into biomass, then applies water, temperature, aeration, nutrient, and harvest-index effects to estimate economic yield.The daily crop growth regulating factor is the lowest of the daily stress values, with soil properties also included.
- Optimization: The genetic-algorithm optimization maximizes land equivalent ratio and annual electricity production while minimizing annual standard deviation of grid-injected power.The agrivoltaic and reference crop and energy terms are defined relative to open-field cultivation and conventional ground-mounted PV.
3 Results and discussion
The validated model supports multi-objective analysis of vertically mounted bifacial agrivoltaics, revealing trade-offs among crop yield, electricity production, power fluctuation, and land-use efficiency. Row distance and azimuth materially shape these outcomes, while validation shows agreement with measurements and PVsyst®.
- Simulation and validation: R^2 greater than 90% indicates good correlation between the developed shading model and PVsyst®.The k-nearest-neighbors extrapolation introduced negligible error relative to direct beam-shading calculations.
- Simulation and validation: Crop yield doubled as mutual row distance increased from 5 m to 20 m, with unshaded maximum yields of 5.1 t/ha for oat and 9.9 t/ha for potato.The sensitivity analysis jointly examined crop yield, specific electricity production, and row distance.
- Simulation and validation: 14% error versus farm measurements and 6% versus county statistics were obtained for crop-yield validation.The validation used Mesan and Strång mesoscale climatological inputs rather than actual weather-station climatological data.
- Optimization: Increasing LER significantly decreased electricity production and power fluctuation, while smaller row distances increased LER despite reducing crop yield and PV production.Specific PV production per unit area contributed more strongly to LER than the crop contribution under smaller row spacing.
- Optimization: 9 m for oat and 8.5 m for potato emerged as crop-specific row-distance trade-offs in the LER contributions.The optimization also found azimuth angles around -40°; production was 19.6 MWh/year at -90° and 20.1 MWh/year at -40°.
- Optimization: Several-year optimization across different crop rotations remains outside the study’s scope.The authors also identify future economic and environmental objectives as extensions beyond the mainly technical objective functions used here.
4 Conclusions
The study develops and applies a bifacial, vertically mounted agrivoltaic optimization model to oat and potato in Sweden. Its conclusions emphasize strong row-distance effects, trade-offs between LER and electricity production, and the need for multi-year, multi-crop design.
- Model and scope: The model integrates shading, PAR decomposition, crop-yield, and PV-production submodels to relate crop productivity and electricity production to system orientation and row distance.The model was applied to two crops at a Swedish location.
- Key findings: Crop yield can be halved when mutual row distance decreases from 20 m to 5 m at the investigated latitude.The conclusion attributes this effect to changes in photosynthetically active radiation distribution.
- Key findings: Maximizing LER tends to drastically reduce electricity production, so LER alone cannot serve as the main optimal-design parameter.The authors recommend including additional objectives to estimate crop–electricity synergies more completely.
- Design implications: 8.5 m for potato and 9.0 m for oat are the reported crop-specific optimal row distances, supporting multi-year and multi-crop optimization.The authors connect these differences to long-term agrivoltaic design under conventional farm activities.
- Design implications: Land equivalent ratios above 1.2 were obtained for the investigated crops and location.The authors relate these results to agrivoltaic implementation and sustainability goals.