2.1 Experimental design and management
The OKwind solar tracker system is a high solar system developed by OKwind (Torcé, France). It consists of a plateau of 117m² of solar panel, mounted at 7m heigh, that can follow the sun during the day. It is implanted in soil with a concrete square block of 2.5x2.5m and 2m depth (figure 2).
The experimental sites were located in western France (Bretagne, Normandie and Pays-de-Loire). All sites are under a Cfb climate (name of the classification). Information for each site is available in complementary data (table 4). One to two solar trackers per site were studied. The field crop types considered for the two field years in 2022 and 2023 are those most frequently farmed in the study area, i.e. wheat and maize. In total, 24 trackers were studied, 6 in 2022 (2 for wheat and 4 for maize), and 18 in 2023 (9 for wheat and 9 for maize).
2.2 Sampling design
To assess solar tracker’s impact on crop yield, a sampling plan was built based on the study of tracker thrown shade and total radiation received (RR) by crop (figure 3) (Noirot-Cosson et al., 2022).(Noirot-Cosson et al., 2022). To grasp the shade gradient effect, the eight cardinal axes were considered, as well several distance from the solar tracker centre (5 meters, 10 meters, 15 meters, 20 meters, 25 meters (only in 2023) and 35 meters), leading to 48 studied points (40 in 2022). Maximum studied distance from the tracker was fixed at 35 meters, where received radiation is reduced by only 1% on crop cultural period.
2.3 Collected data
a. Field and crop data
Crop development and growth were monitored every two weeks from sowing to harvest. At crop maturity, aboveground biomass was sampled on 1m² for each sampling point and weighted. Grains and straw were separated, and crop grain were weighted.
Tractors wheel’s impact was noted if sampling point were less than a meter close to it. Wiring underground was noted for each site using field cartography of tracker implantation. These two parameters were each noted with a presence/absence notation, with 1 when a sampling point was impacted by wiring and tractor’s wheel, and 0 when not.
To explore tracker influence on crop yield, field related parameters were considered (table 1). For each wheat and maize sites, data about tracker age and field management were gathered. Sowing date, harvest date, and cultivated varieties were collected. Studied varieties consisted in 3 varieties for wheat (Chevignon, LG Absalon, and a mixt of different varieties) and 4 varieties in maize (Caroleen, Havelio KWS, LG31270, Amandeen).
b. Microclimatic and soil data
Microclimatic data and soil density were measured on 4 of the 9 wheat trackers studied. The latter measurements were focused on a limited number of sites. On these trackers, microclimatic data and soil density were collected at every sampling point, excepted those at 25 meters from the tracker. Soil temperature (°C) and humidity (%H) were measured using TMS4 (TOMST, Czech Republic) and air temperature (°C) and humidity (raw TMS soil moisture) were measured using EM300-TH (Milesight, Fujian, China). Once field mechanical treatment were over, microclimatic sensors were placed. Sensors were placed in early March for the TMS4 and in early April for the EM300-TH. All sensors were removed in July at harvest. Data was measured every 10 minutes by the TMS4 and every 15min for the EM300-TH. To ensure that air temperature was measured at canopy level, sensors were moved regularly to stay at canopy height. Soil compaction (kPa) was measured after harvest using a compaction meters Soil compaction tool (Spectrum Technologies, Inc., Aurora, Illinois, U.S.A) at the same sampling points than microclimatic data. Soil samples for soil texture and chemical properties analysis were taken at a 30cm depth for each studied point. Analyses were performed by an outside laboratory (Laboratoire d’analyses des sols (LAS), Arras, France). Quantities of peebles (<5mm) (g/kg), gravel (2-5mm) (g/kg), dirt (<2mm) (g/kg), total nitrogen (g/kg), total carbon (g/kg), total organic carbon (COT) (g/kg), C/N ratio, organic matter (g/kg), clay (0 to 0.002mm) (g/kg), silt (0.002 to 0.063mm) (g/kg) and sand (0.063 to 2mm) (g/kg) were analysed.
c. RR calculations
Shade cast by tracker was considered using simulation of total received radiation (RR) under each solar tracker. Sowing and harvest date were considered for each site, as well as shadow cast by nearby trackers. This allows us to integrate potential overlapping shade in the RR. RR was then calculated using the equation bellow (equation 1), based on Noirot-Cosson et al. (2022) .
Equation 1: Calculation of % RR
RR were considered: (i) equal to diffuse radiations when under a tracker shadow, and to the sum of direct and diffuse radiations otherwise, (ii) on plants implementation periods. Then, the total received radiations ratio (%RR) was calculated as in the equation below. Rdh stands for radiation received by plants (Wh.m-2) at a certain hour (h) and certain day (d), Rrefdh stands for Rdh in a location with no tracker shadow (Noirot-Cosson et al., 2022).
2.4 Statistical analysis
We first calculated yield relative ratio for each crop and site. Reference yield was calculated using sampling point for which RR was between 0.99 and 1 for each site, representing 18 plots over the 48, leading to 1 reference yield per site. Then, relative yield was calculated for each sampling point. Relative aboveground biomass ratio was calculated using the same method.
All statistical analysis was performed using the R software. Statistical analysis was done using Generalised Linear Mixted Model (GLMM). For crop yield, three GLMM were realised, two for wheat: one with microclimate and soil data (equation 2: pedoclimatic model), two without pedo-climatic data (equation 3: all sites model) for wheat and maize . The same models were used to study crop biomass (equation 4 and 5). Variables used for each model are available in complementary data (table 5).
Equation 2: lmer model used to for wheat yield study using microclimate data (pedoclimatic model)
lmer (Relative grain yield ~ Air humidity + Soil humidity + Air temperature + Soil temperature + Soil_ compaction (8cm depth) + Soil_ compaction (16cm depth) + Soil_ compaction (24cm depth) + Tractor wheel impact + RR + cultivated variety + wiring : tracker’s_age + cardinal axis : distance + reference yield + Peeble + Gravel + Dirt + N_total + C_total + COT + C/N + MO + Clay + Silt + Sand + (1|site))
Equation 3: lmer model used for wheat and maize yield study using all data (all sites model)
lmer (Relative grain yield ~ Tractor wheel impact + RR + cultivated variety + wiring : tracker’s_age + cardinal axis : distance + reference yield + (1|site))
Equation 4: lmer model used to for wheat biomass study using microclimate data (pedoclimatic model)
lmer (Relative aboveground biomass ~ Air humidity + Soil humidity + Air temperature + Soil temperature + Soil_ compaction (8cm depth) + Soil_ compaction (16cm depth) + Soil_ compaction (24cm depth) + Tractor wheel impact + RR + cultivated variety + wiring : tracker’s_age + cardinal axis : distance + reference yield + Peeble + Gravel + Dirt + N_total + C_total + COT + C/N + MO + Clay + Silt + Sand + (1|site))
Equation 5: lmer model used for wheat and maize yield study using all data (all sites model)
lmer (Relative aboveground Biomass ~ Tractor wheel impact + RR + cultivated variety + wiring : tracker’s_age + cardinal axis : distance + reference yield + (1|site))
The GLMM examines the effect of field management, cultivated variety and tracker age (independent variables) on crop yield or crop biomass (dependent variables), while considering the site as a random effect. This gave GLMM result for every site (all sites model). For the 4 wheat sites studied with microclimatic conditions and soil density, two separate GLMM were done including this data (pedoclimatic model) for yield and biomass. The GLMM allowed to determine the most impacting variable on crop yield and aboveground biomass for each culture. Once the most impacting variable were identified, linear regressions were traced, one per culture and per year.
2.5 Simulation of yield on different solar power plant design
To explore the effect of different agrivoltaic plant designs on crop grain and biomass yields , 3 theorical agrivoltaic fields were built. Fields with 20 trackers were considered as it represents a targeted dimension for such plants, and as, a rectangle form allows easier simulations and results interpretations. Different distances between PV trackers were tested (table 1). In the north-south axis, distance of 25 meters, 30 meters and 35 meters were tested, commonly set to avoid shadow from one tracker to the northern one. In the east-west axis, 40 meters, 50 meters and 58 meters were tested based on one or two passages of agricultural sprayer and with popular sprayer widths. The three tested designs are illustrated figure 4. For these three designs, RR was calculated for each m² based on 2022-2023 weather data from Torcé (35870), the Okwind headquarters location around which most of trackers were installed, 40km east from Rennes, and for both wheat and maize classical implementation period: from the 1st of October to the 1st of July for wheat and from the 15th of April to the 15th of September for Maize. Then, using the built regression between crop yields and RR, crop yields were spatially simulated, and the average field yields were calculated, using the linear regression previously traced. All linear regression were used, except the one for “maize 2022” for both yield and aboveground biomass simulation. An outer field area was considered and dimensioned on half of the inter PV tracker distance, in order to avoid as much as possible a border effect and to make results scalable to design with a different number of PV trackers.
Table 1: Experimental designs characteristics, with North-South distance and East-West distance between each tracker, as well as tracker density for a theorical field for each design.
|
North-South distance
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East-West distance
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Tracker density
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Design 1
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25 m
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40 m
|
10
|
Design 2
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30 m
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50 m
|
6.66
|
Design 3
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35 m
|
58 m
|
4.93
|
2.6 Method summary (figure 5)