In the context of agrivoltaics, the integration of solar panels with agricultural land offers a dual land-use strategy that can enhance both renewable energy generation and crop production. However, the shading effect created by solar panels significantly influences the microclimate beneath them, directly impacting crop growth and yield. Understanding the spatial and temporal distribution of shading is essential for optimizing panel configurations to balance energy output and agricultural productivity. This study employs Ladybug, a three-dimensional simulation tool, to systematically investigate how variations in panel spacing, installation height, and tilt angle affect shading patterns and cumulative solar radiation under solar panels. Using meteorological data from two distinct locations in Yunnan Province, China—one with higher solar irradiance (Kunming) and one with more moderate irradiance (Pu’er)—we simulate shading scenarios during the peak solar radiation period (9:00–16:00) on the summer solstice (June 21). Our results reveal that shading rates are highly sensitive to geometric parameters and geographic location, with differences up to 0.9 percentage points between the two sites in December. Increasing the inter-panel spacing and tilt angle significantly reduces shading, thereby improving light availability for crops, whereas increasing installation height can paradoxically elevate shading in certain zones. These findings provide actionable insights for designing agrivoltaic systems that optimize both photovoltaic output and agricultural yield.
Introduction
The rapid expansion of photovoltaic power generation has created a land-use conflict between energy production and agriculture. Agrivoltaics, which combines solar panels with crop cultivation, offers a promising solution by allowing the same land to serve both purposes. However, the shading cast by solar panels alters the light environment underneath, affecting photosynthesis, transpiration, and ultimately crop yield. Previous studies have investigated the impact of solar panels on microclimate and crop growth, but few have systematically quantified the shading effect as a function of panel arrangement using simulation tools. Ladybug, a parametric environmental simulation engine, is particularly well-suited for this task as it can compute solar radiation on complex geometries using site-specific weather data.
Our study focuses on three key variables: the spacing between solar panels along the x-axis (20, 50, 100 cm), the installation height of the panels (150, 200, 250 cm), and the tilt angle of the panels (0°, 15°, 30°). All simulations are performed for two representative cities in Yunnan Province: Kunming (latitude 25.07°N, longitude 102.44°E, elevation 1770 m) and Pu’er (latitude 23.04°N, longitude 101.02°E, elevation 1302 m). The meteorological data used for the simulations come from the Chinese Standard Weather Database (CSWD) available via EnergyPlus. We extract annual cumulative direct normal irradiation for both locations and focus the analysis on the summer solstice, when solar altitude is highest and the shading effect is most pronounced.
By simulating the cumulative solar radiation at each grid point beneath the solar panels, we compute the shading rate—defined as the percentage of incoming solar radiation blocked by the panels relative to the unobstructed open field. Shading rate is calculated as:
$$
\text{Shading Rate (\%)} = \left(1 – \frac{E_{\text{under}}}{E_{\text{open}}}\right) \times 100
$$
where \(E_{\text{under}}\) is the cumulative solar radiation received at a point under the solar panels during the analysis period, and \(E_{\text{open}}\) is the cumulative solar radiation received at the same location without any obstruction. This metric allows us to compare the effectiveness of different panel configurations in modulating light availability for crops.
Methodology
Simulation Setup
We constructed a three-dimensional model of a photovoltaic array in Rhinoceros 3D and used the Ladybug plugin to perform radiation analysis. The array consists of multiple solar panels arranged in rows, with a fixed y-axis spacing of 50 cm between rows. The panels are standard rectangular modules with dimensions typical of commercial solar panels. The simulation domain covers an area of 20 m × 13 m, divided into a grid of 1 m × 1 m cells. For each cell, Ladybug computes the cumulative solar radiation over the period 9:00–16:00 on June 21, using the Perez all-weather solar radiation model applied to the site-specific weather data.
The experimental variables are summarized in Table 1.
| Variable | Values |
|---|---|
| x-axis spacing (cm) | 20, 50, 100 |
| Installation height (cm) | 150, 200, 250 |
| Tilt angle (°) | 0, 15, 30 |
In each simulation, two variables are held constant while the third is varied. For the height and tilt experiments, the x-axis spacing is fixed at 20 cm; for the spacing experiments, height is fixed at 150 cm and tilt at 0°.
Data Analysis
For each configuration, we extract the cumulative solar radiation at every grid cell and compute the shading rate. We then analyze the shading rate distribution across the length of the array (along the x-direction), focusing on the maximum and minimum values. Additionally, we compare monthly average shading rates for a reference configuration (20 cm spacing, 150 cm height, 0° tilt) to examine seasonal variations between the two sites.
Results and Discussion
Geographic Variation in Shading Rate
First, we present the monthly shading rate for the reference configuration (20 cm, 150 cm, 0°) at both locations. Table 2 lists the monthly cumulative solar radiation under natural light and under the solar panels, along with the derived shading rate.
| Month | Kunming open (kWh/m²) | Pu’er open (kWh/m²) | Kunming shaded (kWh/m²) | Pu’er shaded (kWh/m²) | Kunming shading (%) | Pu’er shading (%) |
|---|---|---|---|---|---|---|
| Jan | 103.76 | 104.93 | 38.97 | 39.26 | 62.4 | 62.6 |
| Feb | 108.08 | 115.42 | 40.55 | 43.92 | 62.5 | 61.9 |
| Mar | 153.38 | 148.76 | 60.50 | 58.92 | 60.6 | 60.4 |
| Apr | 159.56 | 149.45 | 62.84 | 58.77 | 60.6 | 60.7 |
| May | 135.69 | 135.61 | 52.26 | 52.68 | 61.5 | 61.2 |
| Jun | 121.13 | 126.96 | 46.57 | 49.14 | 61.6 | 61.3 |
| Jul | 125.12 | 126.88 | 48.32 | 49.29 | 61.4 | 61.2 |
| Aug | 122.64 | 124.73 | 47.77 | 48.67 | 61.1 | 61.0 |
| Sep | 107.13 | 121.69 | 42.49 | 48.36 | 60.3 | 60.3 |
| Oct | 100.39 | 112.66 | 38.68 | 44.18 | 61.5 | 60.8 |
| Nov | 82.83 | 93.32 | 31.11 | 35.74 | 62.4 | 61.7 |
| Dec | 85.60 | 101.41 | 33.02 | 38.22 | 61.4 | 62.3 |
As shown, the shading rate varies monthly, with the greatest difference between the two cities occurring in December: 61.4% for Kunming vs. 62.3% for Pu’er, a difference of 0.9 percentage points. This discrepancy is attributed to differences in solar altitude angles and cloud cover patterns. Overall, the shading rate ranges between 60.3% and 62.6%, indicating that this particular panel configuration provides substantial but relatively uniform year-round shading.
Influence of Panel Spacing
To evaluate the effect of x-axis spacing, we fixed the installation height at 150 cm and tilt angle at 0°, varying the spacing among 20, 50, and 100 cm. The unobstructed cumulative solar radiation on the summer solstice (9:00–16:00) at Kunming was 1.63 kWh/m², while at Pu’er it was 3.60 kWh/m². Tables 3a and 3b summarize the shading rate in different zones along the array for Pu’er and Kunming.
| Zone (distance from first row) | 20 cm spacing | 50 cm spacing | 100 cm spacing |
|---|---|---|---|
| 0–1 m (edge) | 50.5 | 45.8 | 41.0 |
| 1–6 m (mid) | 63.4 | 56.1 | 44.8 |
| 6–10 m (deep) | 64.4 | 58.5 | 44.8 |
| 10–13 m (far edge) | 59.1 | 47.1 | 43.8 |
| 13–20 m (recovery) | – | 47.1 | 40.9 |
| Zone | 20 cm spacing | 50 cm spacing | 100 cm spacing |
|---|---|---|---|
| 0–1 m | 41.7 | 36.0 | 36.6 |
| 1–3 m | 60.1 | 54.1 | 44.0 |
| 3–9 m | 65.1 | 56.3 | 44.0 |
| 9–13 m | 59.5 | 51.2 | 42.7 |
| 13–20 m | – | 51.2 | 40.9 |
The results clearly demonstrate that increasing the spacing between solar panels reduces the shading rate. For example, at Pu’er, the maximum shading rate drops from 64.4% at 20 cm spacing to 44.8% at 100 cm spacing. A similar trend is observed at Kunming, where the maximum shading decreases from 65.1% to 44.0%. Wider spacing allows more sunlight to penetrate gaps between panels, improving light availability for crops underneath. This is particularly beneficial for shade-tolerant crops; however, it also reduces the total number of solar panels installed per unit area, thereby lowering energy generation density. An optimal balance must be struck.
Influence of Installation Height
Next, we examine the effect of installation height (150, 200, 250 cm) with fixed spacing (20 cm) and tilt (0°). Tables 4a and 4b present the shading rate zones for both locations.
| Zone | 150 cm | 200 cm | 250 cm |
|---|---|---|---|
| 0–1 m | 50.5 | 55.7 | 45.0 |
| 1–3 m | 63.4 | 67.6 | 64.5 |
| 3–10 m | 64.4 | 70.0 | 71.8 |
| 10–13 m | 59.1 | 62.2 | 55.1 |
| Zone | 150 cm | 200 cm | 250 cm |
|---|---|---|---|
| 0–1 m | 41.7 | 40.8 | 31.5 |
| 1–3 m | 60.1 | 59.7 | 52.3 |
| 3–10 m | 65.1 | 69.3 | 66.8 |
| 10–13 m | 59.5 | 58.4 | 53.9 |
Counterintuitively, increasing the installation height does not uniformly reduce shading. At Pu’er, the maximum shading rate increases from 64.4% at 150 cm to 70.0% at 200 cm and further to 71.8% at 250 cm in the central zone (3–10 m). However, at the edge zone (0–1 m), the shading rate decreases from 50.5% to 45.0% when height is increased from 150 cm to 250 cm. At Kunming, the maximum shading also rises from 65.1% to 69.3% when height increases from 150 cm to 200 cm, but then decreases slightly to 66.8% at 250 cm. This non-monotonic behavior arises because higher panels cast longer shadows but also allow more diffuse light to reach the edges. The central region, far from the array edges, experiences deeper shading as the angle of incidence changes. Therefore, simply raising solar panels does not guarantee improved light penetration; the effect depends on the specific location within the array.
Influence of Tilt Angle
Finally, we assess the impact of tilt angle (0°, 15°, 30°) with fixed spacing (20 cm) and height (150 cm). Tables 5a and 5b summarize the results.
| Zone | 0° | 15° | 30° |
|---|---|---|---|
| 0–1 m | 50.5 | 48.1 | 46.5 |
| 1–3 m | 63.4 | 60.4 | 56.2 |
| 3–10 m | 64.4 | 61.0 | 57.3 |
| 10–13 m | 59.1 | 55.0 | 51.7 |
| Zone | 0° | 15° | 30° |
|---|---|---|---|
| 0–1 m | 41.7 | 38.6 | 36.3 |
| 1–3 m | 60.1 | 56.2 | 52.0 |
| 3–10 m | 65.1 | 61.7 | 56.9 |
| 10–13 m | 59.5 | 55.2 | 50.9 |
Increasing the tilt angle from 0° to 30° consistently reduces shading rates across all zones in both cities. At Pu’er, the maximum shading drops from 64.4% to 57.3%; at Kunming, from 65.1% to 56.9%. This is because a tilted panel intercepts sunlight at a more oblique angle, reducing the area of the shadow cast directly beneath it. Additionally, tilting allows more light to reach the ground near the panel edge. From an agricultural perspective, tilting solar panels can be an effective strategy to enhance light availability, especially for crops that require moderate sunlight. However, tilting also reduces the energy yield per panel if not optimally oriented toward the sun. For a fixed latitude, a tilt angle equal to the latitude maximizes annual energy harvest, but that may not be optimal for agrivoltaics. Our results suggest that a moderate tilt (e.g., 15°–30°) can significantly improve under-panel lighting while maintaining reasonable efficiency.
Practical Implications for Agrivoltaic Design
The findings from our simulation provide quantitative guidance for designing solar panel arrays that balance power generation with agricultural needs. For example, if the goal is to achieve a shading rate below 50% in the growing zone to support crops like tomatoes or peppers, the spacing should be at least 100 cm (at 150 cm height, 0° tilt). Conversely, for shade-loving crops such as mushrooms or certain leafy greens, a 20 cm spacing that yields 60–65% shading may be preferable. The installation height should be chosen carefully: lower heights (150 cm) cause less central shading than higher heights (200–250 cm) due to the geometry of shadow casting, though higher heights may improve access for machinery. Tilt adjustment can further fine-tune the light distribution. Ultimately, an integrated optimization considering local solar resource, crop light requirements, and economic factors is needed.
The figure below illustrates a typical solar panel array used in agrivoltaic systems, highlighting the spatial arrangement that our simulation modeled.
Conclusion
This study systematically analyzed the shading effect of solar panels using Ladybug simulation, focusing on the influence of panel spacing, installation height, and tilt angle on the shading rate beneath arrays. Key conclusions are as follows:
- Geographic variation: For the same panel configuration, the shading rate differed by up to 0.9 percentage points between Kunming and Pu’er in December, demonstrating the importance of local solar geometry.
- Spacing effect: Increasing the x-axis spacing from 20 cm to 100 cm reduced the maximum shading rate from approximately 65% to 44%, significantly improving light availability for crops.
- Height effect: Raising the installation height from 150 cm to 250 cm increased the shading rate in central zones (from ~65% to ~72% at Pu’er), but decreased it near the array edges. The relationship is non-linear and zone-dependent.
- Tilt effect: Increasing the tilt angle from 0° to 30° consistently reduced the shading rate, with maximum shading dropping from ~65% to ~57% in both cities.
These results provide a quantitative basis for optimizing solar panel layout in agrivoltaic systems. By adjusting spacing, height, and tilt, it is possible to tailor the shading environment to match the specific light requirements of different crops, thereby enhancing agricultural productivity while maintaining viable solar energy generation. Future work should incorporate long-term crop growth models and economic analyses to develop comprehensive design guidelines.