2.1. The solar developer’s choice problem

We represent the annualized profits per acre, $ {\pi}_S^{PV} $ , for a solar developer from a PV-only system by

(1) $$ {\pi}_S^{PV}={S}^{PV}\left({P}_S^{PV}-{LCOE}^{PV}\right)-L-M $$

where $ {S}^{PV} $ is the annual solar energy output from the PV-only system (MWh/year/acre); $ {P}_S^{PV} $ is the price of solar electricity under a PV-only system ($/MWh);Footnote ⁴ $ {LCOE}^{PV} $ is the levelized cost of solar energy under PV-only ($/MWh) and is defined in more detail in Section 3.2; M is the annual vegetation management cost ($/acre), and L is the annual cost of leasing the land ($/acre).Footnote ⁵ Profits and costs of solar energy vary over the life time of the installation, resulting in a time-varying stream of costs and revenues over the 25-year project life. For ease of algebraic representation, all profit and cost expressions in this framework are annualized values derived from the net present value of costs and revenues over the 25-year project life, using a constant discount rate.

Suppose that the developer is considering adopting an IAV system in which a share x of the 1-acre field will be under PV and (1−x) will be under crop production. In this setup, the solar developer pays the landowner both an annual lease payment for the use of the land under PV and a vegetation management fee to maintain ground cover around the solar panels – a practice commonly reported in focus group discussions with farmers. These arrangements shift vegetation maintenance responsibilities to the farmer while compensating them for this service. The returns per acre for the solar developer on the portion of land that is under PV in an IAV system are thus represented by

(2) $$ {\pi}_S^{IAV}={S}^{IAV}\left({P}_S^{IAV}-{LCOE}^{IAV}\right)-x\left(L+M\right), $$

where $ {\pi}_S^{IAV}/x $ is the annual profit per acre from the land under PV in the IAV system for the solar developer; $ {S}^{IAV} $ is the annual solar energy output from the IAV portion of the field (MWh/year), $ {P}_S^{IAV} $ is the price of electricity under the IAV system ($/MWh) (that may or may not be the same as $ {P}_S^{PV} $ and $ {LCOE}^{IAV} $ is the levelized cost of solar energy generation under the IAV system ($/MWh). We expect $ {LCOE}^{IAV} $ ≥ $ {LCOE}^{PV} $ . We denote $ {S}^{IAV}=x{\delta}_S{S}^{PV} $ where $ {\delta}_S\gtreqless $ 1. Thus: $ {\pi}_S^{IAV}=x{\delta}_S{S}^{PV}\left({P}_S^{IAV}-{LCOE}^{IAV}\right)-x\left(L+M\right) $ . Specifically, we define $ {\delta}_S $ as the energy output per unit of land area under solar panels in an IAV system relative to PV-only, which depends on IAV design and environmental factors. Recent studies suggest that IAV systems can achieve similar or modestly higher energy yields compared to PV-only systems, largely due to elevated panel heights and cooling effects from underlying vegetation, which can lower panel temperatures (Barron-Gafford et al., Reference Barron-Gafford, Pavao-Zuckerman, Minor, Sutter, Barnett-Moreno, Blackett, Thompson, Dimond, Gerlak, Nabhan and Macknick2019; Miljkovic et al., Reference Miljkovic, Du, Solecki, Hoque, Garimella, Jia, Peng, Mwebaze, McCall, Majeed, Time, Kim, Sturchio, Guan, Khanna, Bernacchi, Lee, Knapp, Barron-Gafford and Branham2024; Williams et al., Reference Williams, Hashad, Wang and Max Zhang2023). However, these gains are not uniform and can vary depending on site-specific factors such as climate, crop type and system design – some studies even report slight reductions in yield under certain conditions (Macknick et al., Reference Macknick, Hartmann, Barron-Gafford, Beatty, Burton, Choi, Davis, Davis, Figueroa, Garrett, Hain, Herbert, Janski, Kinzer, Knapp, Lehan, Losey, Marley, MacDonald, McCall, Nebert, Ravi, Schmidt, Staie and Walston2022).

We assume that the solar developer will have an economic incentive to adopt IAV if the profit per unit of land from the share of land under PV in the IAV system is larger than or equal to the profit per unit of land from a stand-alone PV system. That is, the solar developer will choose the IAV system if $ {\pi}_S^{IAV}/x\ge {\pi}_S^{PV} $ , which implies that IAV will be chosen if:

(3) $$ {\delta}_S{S}^{PV}\left({P}_S^{IAV}-{LCOE}^{IAV}\right)\ge {S}^{PV}\left({P}_S^{PV}-{LCOE}^{PV}\right). $$

Note that the term (L + M) – representing lease and vegetation management payments to the farmer – cancels out on both sides of the inequality. This leads to a simplified profitability condition that can be solved to determine the breakeven price of electricity, $ {P}_S^{\ast IAV} $ at which an IAV system becomes as profitable as a PV-only system for the solar developer:

(4) $$ \left({\delta}_S{P}_S^{\ast IAV}-{P}_S^{PV}\right)=\left({\delta}_S{LCOE}^{IAV}-{LCOE}^{PV}\right) $$

(5) $$ \iff {P}_S^{\ast IAV}={LCOE}^{IAV}+\frac{P_S^{PV}-{LCOE}^{PV}}{\delta_S} $$

Since $ {LCOE}^{IAV} $ is greater than $ {LCOE}^{PV} $ , it implies that the breakeven price $ {P}_S^{\ast IAV} $ is greater than $ {P}_S^{PV} $ if $ {\delta}_S $ is equal to 1. Additionally, $ {P}_S^{\ast IAV} $ increases as $ {LCOE}^{IAV} $ increases and as $ {\delta}_S $ decreases, since we expect that $ {P}_S^{PV}-{LCOE}^{PV}\ge 0 $ . On the other hand, as $ {\delta}_S $ increases above 1 and the IAV system produces more electricity than the PV-only system – perhaps due to cooler microclimates from crops, or other synergies, then the required breakeven price for electricity under IAV ( $ {P}_S^{\ast IAV} $ ) decreases. The difference between the breakeven price of electricity under IAV and the prevailing electricity price under PV-only ( $ {P}_S^{\ast IAV}-{P}_S^{PV} $ ) represents the feed-in tariff or price premium required to make IAV systems economically competitive.

Alternatively, if the price of electricity is the same under the IAV system and the PV-only system ( $ {P}_S^{IAV}={P}_S^{PV} $ ), then we can solve for the breakeven value of the levelized cost of electricity (LCOE) in the IAV system ( $ {LCOE}^{\ast IAV} $ ) as follows:

(6) $$ {LCOE}^{\ast IAV}=\frac{1}{\delta_S}\left({LCOE}^{PV}+\left({\delta}_S-1\right){P}_S^{PV}\right) $$

If $ {\delta}_S $ =1, then the breakeven $ {LCOE}^{\ast IAV} $ must be equal to $ {LCOE}^{PV}. $ If solar developers are just breaking even with PV-only, then (6) indicates that $ {LCOE}^{\ast IAV} $ must be equal to $ {P}_S^{PV} $ . For other cases, $ {LCOE}^{\ast IAV} $ could be higher or lower than $ {LCOE}^{PV} $ . The difference between the breakeven LCOE for IAV and the actual or prevailing LCOE of IAV ( $ {LCOE}^{\ast IAV}-{LCOE}^{IAV} $ ) represents the production tax credit required to make IAV economically viable relative to PV-only. By expressing the breakeven conditions in terms of both electricity price and LCOE, this framework shows that IAV systems can be incentivized through either a feed-in tariff (which raises the price received for IAV-generated electricity) or a production tax credit (which reduces the cost of electricity generation under an IAV system). These two instruments – price support and production cost-related support – offer two alternative policy levers to incentivize IAV deployment.

2.2. The farmer’s choice problem

A farmer can choose to produce crops only or lease the land to a solar or an IAV system. We suppose that the farmer adopts the IAV if the annual profit per acre from IAV exceeds the annual profit per acre from leasing land for PV alone and the annual profit per acre from crop production alone. A farmer’s annual per-acre profit from crop production alone (C) is represented by:

(7) $$ {\pi}_Y^C={Y}^C\left({P}^C-{V}^C\right)-{F}^C $$

We represent the farmer’s annualized profits per acre under an IAV system by $ {\pi}_Y^{IAV} $ , which combines crop production with elevated solar panels:

(8) $$ {\pi}_Y^{IAV}=\left(1-x\right)\left[\left({Y}^C{\delta}_Y\left({P}^C-{V}^C\right)-{F}^C\right)\right]+x\left(L+M\right), $$

where $ {P}^C $ denotes the crop price ($/bushel); $ {Y}^C $ is annual crop yield in full sun (bushels/acre); $ {\delta}_Y $ (could be greater than, less than or equal to 1) is the crop yield per unit crop area under an IAV system relative to a Crop-only system; thus, $ {Y}^{IAV}=\left(1-x\right){\delta}_Y{Y}^C $ ; $ {V}^C $ and $ {F}^C $ are annual variable costs ($/bushel) and fixed costs ($/acre) of crop production, respectively. The share of land under crop production in an IAV system is (1−x); some of this land may be unused to provide a buffer zone between panels and crops to allow safe operation of farm equipment. The term $ {\delta}_Y $ could be greater than 1 for shade-tolerant crops and less than or equal to 1 for crops that require full sun. The first term in (8) represents profits from the cropped portion of the field, and the second term shows income from the solar panel-covered portion of the land. In addition to receiving lease payments (L) for the solar panel-covered area, the farmer may also be contracted to perform vegetation maintenance under the panels. Therefore, M is included in the farmer’s profit function as additional net income from vegetation maintenance services provided under the IAV system.

The farmer will choose an IAV system if it is more profitable than a crop-only system $ {\pi}_Y^C $ and leasing the entire land for PV-only and earning income from the lease and a maintenance fee (L + M) ($/per acre/per year):

(9) $$ \frac{\pi_Y^{IAV}}{\left(1-x\right)}\ge \max \left\{{\pi}_Y^C,L+M\right\} $$

We represent the difference in profits between IAV and crop-only systems for the farmer below and denote $ {Y}^{IAV}=\left(1-x\right){\delta}_Y{Y}^C $ . Simplifying and collecting the relevant terms together, we can solve for the break-even crop price in an IAV system by solving the following condition, where $ {P}^C $ denotes the price of the crop under the crop-only and $ {P}_Y^{IAV} $ denotes the price of the crop produced under the IAV system:

(10) $$ \frac{\pi_Y^{IAV}}{\left(1-x\right)}-{\pi}_Y^C=\frac{\left(1-x\right)\left[{Y}^C{\delta}_Y\left({P}_Y^{IAV}-{V}^C\right)-{F}^C\right]+x\left(L+M\right)}{\left(1-x\right)}-\left({Y}^C\left({P}^C-{V}^C\right)-{F}^C\right)\gtreqless 0 $$

Solving this condition, we obtain the $ {P}_Y^{\ast IAV} $ as the breakeven price of the crop under the IAV system as follows:

(11) $$ {P}_Y^{\ast IAV}=\frac{P^C-{V}^C\left(1-{\delta}_Y\right)-\frac{x\left(L+M\right)}{\left(1-x\right){Y}^C}}{\delta_Y} $$

When δ_Y = 1, $ {P}_Y^{\ast IAV}<{P}^C $ because the farmer is receiving income from the land lease and maintenance, for other values of δ_Y, the gap between the two prices needs to be empirically determined. The breakeven crop price under IAV, $ {P}_Y^{\ast IAV} $ , increases when crop yields Y^C are lower, or when a smaller share of land is allocated to solar (lower x). In contrast, higher lease and vegetation maintenance payments (L + M) reduce the breakeven crop price, making IAV more attractive to the farmer. Depending on the balance of these factors, $ {P}_Y^{\ast IAV} $ can be either greater or less than the prevailing crop price $ {P}^C $ . If $ {P}_Y^{\ast IAV}>{P}^C $ , IAV would not be competitive without additional support, such as a production subsidy. Conversely, if $ {P}_Y^{\ast IAV}<{P}^C $ , the IAV system is profitable on its own without a subsidy.

For the farmer to choose IAV, it must be profitable not only compared to crop production but also leasing land for PV-only and earning L + M ($/per acre/per year). Thus,

(12) $$ \frac{\pi_Y^{IAV}}{\left(1-x\right)}-\left(L+M\right)=\frac{\left(1-x\right)\left[{Y}^C{\delta}_Y\left({P}_Y^{IAV}-{V}^C\right)-{F}^C\right]+x\left(L+M\right)}{\left(1-x\right)}-\left(L+M\right)\gtreqless 0 $$

To determine the breakeven price of the crop at which a farmer would prefer adopting an IAV system over leasing the land entirely for PV, we derive the breakeven condition for $ {P}_Y^{\ast \ast IAV} $ . Solving the farmer’s profitability condition yields the following expression:

(13) $$ \iff {P}_Y^{\ast \ast IAV}={V}^C+\frac{1}{Y^C{\delta}_Y}\left[\frac{\left(1-2x\right)\left(L+M\right)}{1-x}+{F}^C\right] $$

$ {P}_Y^{\ast \ast IAV} $ represents the breakeven price of the crop under an IAV system that makes it as profitable for the farmer as leasing the entire land to a PV-only solar developer. This breakeven price increases with higher fixed production costs (F^C) and decreases with larger lease payments or vegetation management compensation (L + M). Additionally, higher crop yields (Y^C) and improved crop productivity under IAV conditions (δ_Y) reduce the required crop price, making the IAV system more economically attractive. This result highlights the importance of IAV system design, particularly features that enhance δ_Y (such as panel height, spacing, or light management strategies), as well as the magnitude of supplemental income from solar developers (L + M). When $ {P}_Y^{\ast \ast IAV} $ is below the prevailing market price of the crop, it indicates that the IAV is not only more profitable than the PV-only lease option but – given that PV-only leases typically outperform returns from crop-only – also more profitable than Crop-only production.

2.3. The combined profitability of solar and crop production at the field scale

We now compare the combined profitability of the whole field under two alternative systems. The first is an IAV system and includes returns from both solar energy and crop production. The second is a configuration where PV and crops are produced adjacent to each other (AAPV system) on the same field. In both cases, we assume that the same share of land (x) is allocated to solar energy production, with the remaining share (1-x) allocated to crop production. For the AAPV system, where crops and panels are spatially separated and managed independently, the total profit ( $ {\pi}^{AAPV} $ ) for the whole field is calculated as a land-share weighted sum of solar and crop profits:

(14) $$ {\pi}^{AAPV}={x\pi}_S^{PV}+\left(1-x\right){\pi}_Y^C $$

Similarly, for the IAV design, the total profit ( $ {\pi}^{IAV} $ ) of the field is given by:

(15) $$ {\pi}^{IAV}={x\pi}_S^{IAV}+\left(1-x\right){\pi}_Y^{IAV} $$

In both cases, the solar developer pays the landowner an annual lease payment and a vegetation management fee (L + M) for the use and maintenance of the land under solar panels. We assume the IAV system is adopted if it leads to profits in the field that exceed those with the AAPV system. This condition is expressed as:

(16) $$ {\pi}^{IAV}\ge {\pi}^{AAPV}\iff {x\pi}_S^{IAV}+\left(1-x\right){\pi}_Y^{IAV}\ge {x\pi}_S^{PV}+\left(1-x\right){\pi}_Y^C. $$

Substituting in the full expressions for each profit term yields:

(17) $$ {\displaystyle \begin{array}{c}x{\delta}_S{S}^{PV}\left({P}_S^{IAV}-{LCOE}^{IAV}\right)-x\left(L+M\right)+\left(1-x\right)\left[{Y}^C{\delta}_Y\left({P}_Y^{IAV}-{V}^C\right)-{F}^C\right]+x\left(L+M\right)\\ {}\ge x\left({S}^{PV}\left({P}_S^{PV}-{LCOE}^{PV}\right)\right)-x\left(L+M\right)+\left(1-x\right)\left({Y}^C\left({P}^C-{V}^C\right)-{F}^C\right)+x\left(L+M\right)\end{array}}\hskip0.84em $$

Since the lease and vegetation management payments (L + M) cancel out on both sides, the inequality simplifies to:

(18) $$ {\displaystyle \begin{array}{c}x{\delta}_S{S}^{PV}\left({P}_S^{IAV}-{LCOE}^{IAV}\right)+\left(1-x\right)\left[{Y}^C{\delta}_Y\left({P}_Y^{IAV}-{V}^C\right)-{F}^C\right]\\ {}\ge x\left({S}^{PV}\left({P}_S^{PV}-{LCOE}^{PV}\right)\right)+\left(1-x\right)\left({Y}^C\left({P}^C-{V}^C\right)-{F}^C\right)\end{array}} $$

Assuming the price of crops is the same with IAV and AAPV ( $ {P}_Y^{IAV}={P}^C $ ), we solve this expression for the breakeven price of electricity $ {P}_S^{\ast \ast IAV} $ at which the IAV system becomes as profitable as the AAPV system, which yields:

(19) $$ \iff {P}_S^{\ast \ast IAV}=\frac{P_S^{PV}-{LCOE}^{PV}}{\delta_S}+{LCOE}^{IAV}+\frac{\left(1-x\right){Y}^C\left(1-{\delta}_Y\right)\left({P}^C-{V}^C\right)}{x{\delta}_S{S}^{PV}} $$

This expression defines the breakeven price of electricity $ {P}_S^{\ast \ast IAV} $ that makes the IAV system as profitable as the AAPV alternative, where land is partially leased for PV-only and the rest is farmed conventionally. The expression contains nonlinear interactions involving solar efficiency (δ_S) and crop productivity (δ_Y), making the directional effects of these parameters sensitive to their relative magnitudes and to other terms in the equation. In general, when both δ_S ≤ 1 and δ_Y ≤ 1, the breakeven price $ {P}_S^{\ast \ast IAV} $ will exceed the PV-only electricity price $ {P}_S^{PV} $ , reflecting the performance penalties under IAV. Improved solar generation (δ_S > 1) or crop yields (δ_Y > 1) under IAV can reduce the required price, but the extent of this reduction depends on the weight of each component in the expression. Because of the complexity of these interactions, we rely on numerical simulations to compare the profitability of AAPV and IAV and determine $ {P}_S^{IAV} $ . This result underscores the value of targeted incentives such as feed-in tariffs or crop price-support payments to bridge the profitability gap between IAV and alternative land uses in locations where agronomic or generation trade-offs exist.

Equation (19) presents the breakeven condition in terms of the electricity price, but it can also be rearranged to express the breakeven condition in terms of the required LCOE for the IAV system:

(20) $$ {LCOE}^{\ast \ast IAV}={P}_S^{PV}-\frac{P_S^{PV}-{LCOE}^{PV}}{\delta_S}-\frac{\left(1-x\right){Y}^C\left(1-{\delta}_Y\right)\left({P}^C-{V}^C\right)}{x{\delta}_S{S}^{PV}} $$

Equation (20) defines the breakeven LCOE for an IAV system to match the profitability of the AAPV alternative. The expression above shows that there are various determinants of the $ {LCOE}^{IAV} $ , including the market price of electricity ( $ {P}_S^{PV} $ ), the level of solar productivity (δ_S) and crop productivity (δ_Y) in an IAV setting. Because these interactions are nonlinear, we rely on numerical simulations to evaluate the viability of the IAV system. By presenting breakeven conditions for both electricity prices and levelized costs, this analysis shows how IAV systems can compete with AAPV configurations under the right conditions. It underscores the role of targeted policy instruments: feed-in tariffs can raise the effective price of AV-generated electricity, while production cost credits lower system costs, both helping to make IAV economically viable. Together, these policies can provide complementary levers to support AV deployment in areas where yield or generation trade-offs would otherwise limit profitability.

We also evaluate the crop price needed to make the IAV system as profitable as the AAPV system, assuming the price of solar electricity with IAV is the same as the price with PV-only. The IAV system is preferred when the net profit from solar and crop production, adjusted for any changes in crop yield under IAV and compensation received for vegetation management, exceeds the profit achievable under the AAPV system. After canceling the (L + M) identical terms on both sides and simplifying, we obtain the following breakeven condition:

(21) $$ {\displaystyle \begin{array}{c}x{\delta}_S{S}^{PV}\left({P}_S^{PV}-{LCOE}^{IAV}\right)+\left(1-x\right)\left[{Y}^C{\delta}_Y\left({P}_C^{IAV}-{V}^C\right)-{F}^C\right]\\ {}\ge x\left({S}^{PV}\left({P}_S^{PV}-{LCOE}^{PV}\right)\right)+\left(1-x\right)\left({Y}^C\left({P}^C-{V}^C\right)-{F}^C\right)\end{array}}\hskip0.84em $$

(22) $$ \iff {P}_Y^{\ast \ast \ast IAV}={V}^C+\frac{1}{\delta_Y}\left[\left({P}^C-{V}^C\right)+\frac{x{S}^{PV}}{\left(1-x\right){Y}^C}\left(\left({P}_S^{PV}-{LCOE}^{PV}\right)-{\delta}_S\left({P}_S^{PV}-{LCOE}^{IAV}\right)\right)\right] $$

Equation (22) defines the breakeven crop price under IAV needed to match the profitability of the AAPV system. The expression shows that $ {P}_Y^{\ast \ast \ast IAV} $ increases as crop yield efficiency (δ_Y) and solar generation efficiency (δ_S) decline, since more crop revenue is required to offset reduced solar profits. The adjustment term capturing the foregone solar revenue becomes more influential when the crop share of the land is large (1 − x) or when solar inefficiencies are pronounced. If PV-only is more profitable than IAV, the second term in the square bracket is positive, which raises the required crop price. Thus, $ {P}_Y^{\ast \ast \ast IAV} $ must compensate both for reduced crop productivity (δ_Y < 1) and for the opportunity cost of not operating PV-only. This double burden explains why the breakeven price under IAV can be substantially above the prevailing crop price $ {P}^C $ . Because the relationship among these parameters is nonlinear, we rely on numerical simulations to explore how biophysical trade-offs affect breakeven price outcomes. This highlights how improving IAV system design and reducing LCOE^IAV – for example, through production tax credits – can improve profitability and make IAV systems competitive with current land uses.

2.4. LER and profitability

We now analyze the relationship between IAV’s land use efficiency (LER) and profitability. The LER is formally defined as below:

(23) $$ LER=\frac{S^{IAV}}{S^{PV}}+\frac{Y^{IAV}}{Y^C}=\frac{x{\delta}_S{S}^{PV}}{S^{PV}}+\frac{\left(1-x\right){\delta}_Y{Y}^C}{Y^C}=x{\delta}_S+\left(1-x\right){\delta}_Y $$

However, even if LER > 1, this does not imply that IAV is more profitable than PV-only and Crop-only unless the prices of solar energy and crops are high, as Equations (5) and (11) indicate. Similarly, even if LER is less than 1, IAV may still be profitable compared to PV-only and Crop-only if the LCOE of IAV is low and the land rental rate for PV and the vegetation management cost are high, as shown in Equations (6) and (13).

Furthermore, we can substitute for $ {\delta}_Y $ in terms of LER into the expression for the profit difference between the IAV and AAPV to examine the conditions for AV profitability for the whole field. We define the profit difference $ \Delta \pi ={\pi}^{IAV}-{\pi}^{AAPV} $ . Assuming the same electricity and crop prices in both systems ( $ {P}_S^{PV} $ and $ {P}_C $ for IAV and AAPV) and simplifying yields:

(24) $$ \Delta \pi =x{S}^{PV}\left({P}_S^{PV}\left({\delta}_S-1\right)+{LCOE}^{PV}-{\delta}_S{LCOE}^{IAV}\right)+\left(1-x\right){Y}^C\left({\delta}_Y-1\right)\left({P}^C-{V}^C\right) $$

From Equation (23), $ {\delta}_Y=\frac{LER-x{\delta}_S}{1-x} $ , hence

$$ \left(1-x\right)\left({\delta}_Y-1\right)= LER-1+x\left(1-{\delta}_S\right) $$

We substitute this expression into (24) to get the profit-difference condition:

(25) $$ \Delta \pi =x{S}^{PV}\left({P}_S^{PV}\left({\delta}_S-1\right)+{LCOE}^{PV}-{\delta}_S{LCOE}^{IAV}\right)+{Y}^C\left({P}^C-{V}^C\right)\left( LER-1+x\left(1-{\delta}_S\right)\right) $$

Equation (25) shows that even when LER > 1, Δπ can still be negative if the first term is sufficiently negative (e.g. high $ {LCOE}^{IAV} $ or low $ {P}_S^{PV} $ ) or if the profit margin from crop production is small, so the crop profits do not offset losses from solar energy in an IAV system.

3.1. Impacts of agrivoltaics on energy and crop yields

We applied the APSIM model (Archontoulis et al., Reference Archontoulis, Miguez and Moore2014; Brown et al., Reference Brown, Huth, Holzworth, Teixeira, Zyskowski, Hargreaves and Moot2014) to simulate soybean yields and solar energy generation under AV conditions (Miljkovic et al., Reference Miljkovic, Du, Solecki, Hoque, Garimella, Jia, Peng, Mwebaze, McCall, Majeed, Time, Kim, Sturchio, Guan, Khanna, Bernacchi, Lee, Knapp, Barron-Gafford and Branham2024). The model simulates the interception of solar irradiance by PV panels for energy generation and the photosynthetically active radiation (PAR) available to crops under PV panels. The model dynamically captures the nuanced patterns of PV energy generation and shade distribution under the panels over time and accounts for various geographical factors, including latitude, longitude, PV array density, panel height and orientation (Miljkovic et al., Reference Miljkovic, Du, Solecki, Hoque, Garimella, Jia, Peng, Mwebaze, McCall, Majeed, Time, Kim, Sturchio, Guan, Khanna, Bernacchi, Lee, Knapp, Barron-Gafford and Branham2024). The model was further adapted to consider solar generation and its impacts to model the shading effects of PV panels and how that varies with the distance between the panels and their height, among other variables. Soybean yield under AV conditions was determined as a function of critical variables, including the intercepted solar radiation, radiation use efficiency, and harvest index (see Supplementary Information Section 1 for more details of the crop model). The model simulates different levels of light between the panels and different zones and shows how the amount of light varies as one moves further away from the panels. Using the model, we illustrate the potential correlation between the solar irradiance distribution and the crop output and the PV design matrix (crop buffer, height and density of PV panels). We validate the model using data from measurements at Solar Farm 2.0, a 54-acre, 12.3 megawatt (MWdc) solar farm located in Champaign County, Illinois (40.0692 degrees N, 88.2481 degrees W) at the University of Illinois Urbana-Champaign. The installation features bi-facial PV panels with an east–west tracking system, moving daily to follow the sun’s trajectory.

We apply the System Advisor Model (SAM), a widely used techno-economic model for estimating location-specific solar electricity generation and the LCOE in both a PV-only and AV system with varying configurations (SAM, 2023). The prediction of the PV generation from the solar model in APSIM was in close agreement with the measured output from Solar Farm 2.0, with most discrepancies being less than 6% (Miljkovic et al., Reference Miljkovic, Du, Solecki, Hoque, Garimella, Jia, Peng, Mwebaze, McCall, Majeed, Time, Kim, Sturchio, Guan, Khanna, Bernacchi, Lee, Knapp, Barron-Gafford and Branham2024). We also observed a high level of agreement between the simulation results from the solar model and the SAM model, with a slight difference of less than 2% in energy output (see Supplementary Information, Section 2). We validated the soybean model utilizing historical soybean yields from 2016 to 2022 for Champaign County in Illinois. The results showed a high level of agreement between the predictions of the soybean model and the actual historical field data from the USDA statistics (USDA NASS, 2024), as shown in Supplementary Figures 1f-h.

3.2. Levelized cost of electricity estimation

We estimate the LCOE by dividing the discounted sum of the capital and operating costs by the discounted total electricity production over the lifetime of the system, as given below:

(26) $$ {LCOE}_i=\frac{{\sum \limits}_{t=1}^T\frac{I_{it}+{A}_{it}+{L}_t+{R}_t}{{\left(1+r\right)}^t}}{{\sum \limits}_{t=1}^T\frac{S_{it}\ast {\left(1-D\right)}^t}{{\left(1+r\right)}^t}} $$

where i denotes various AV configurations and PV-only, and t is the year; $ {I}_{it} $ denotes the capital/investment cost for each scenario i, $ {A}_{it} $ represents annual operating and maintenance costs in year t; $ {L}_t $ is the fixed rental rate per acre per year; $ {R}_t $ is the fixed transmission cost; $ {S}_{it} $ is the solar energy generation in year t; D is the annual reduction/degradation in PV module efficiency over time and is the same for PV and AV; r is the real discount rate, and T is the economic life of the system. It is important to note that Equation (26) accounts only for the capital costs of solar energy, which are assumed to be borne entirely by the developer and not the farmer. While AV systems have higher capital costs than PV due to increased design complexity, they can potentially reduce the vegetation management cost on a field for solar developers and also increase solar energy yield (McCall et al., Reference McCall, Macdonald, Burton and Macknick2023). The implications for LCOE^IAV relative to LCOE^PV will depend, among other factors, on the extent to which the upfront capital cost increases and on the annual increase in energy yield and decrease in vegetation management cost with AV and on the discount rate.

3.3. Description of Agrivoltaic configurations

We considered several designs of AV systems to explore the trade-offs between electricity production and crops and the implications for the profitability of AV systems. We compare their performance to the case of stand-alone PV (PV-only) and stand-alone crop production (Crop-only) cases. In a PV-only system, the distance between panels is about 15–18 feet to prevent the panels from shading each other, and the height of the panels is 4 feet (Dupraz et al., Reference Dupraz, Marrou, Talbot, Dufour, Nogier and Ferard2011). Given a fixed amount of land (e.g. an 80-hectare farm, the average farm size in Illinois), this configuration leads to 70-panel rows. In a Crop-only system, the entire 80 acres is cropped under full sun. The most common and profitable cropping system in Illinois is to grow corn and soybeans in rotation.

The design configuration of an AV system, including panel height and row spacing, will affect the type of crops produced, available solar radiation, compatibility with farm equipment, AV costs and returns (Macknick et al., Reference Macknick, Hartmann, Barron-Gafford, Beatty, Burton, Choi, Davis, Davis, Figueroa, Garrett, Hain, Herbert, Janski, Kinzer, Knapp, Lehan, Losey, Marley, MacDonald, McCall, Nebert, Ravi, Schmidt, Staie and Walston2022). The height of corn would require extremely tall panels that would be cost-prohibitive. We, therefore, consider growing soybeans in an AV system and compare its profitability to that of a corn–soybean rotation in full sun. There are many different ways to configure an AV field. To integrate PV with crops and continue farming using conventional farm equipment, there is a need to increase the spacing between panels to 43.5 feet and to raise the height of panels to 8 feet to avoid shading of the solar panels by the crops. This scenario assumes that a tractor needs 10 feet of space based on current AV design guidelines and publicly available manufacturer specifications (Macknick et al., Reference Macknick, Hartmann, Barron-Gafford, Beatty, Burton, Choi, Davis, Davis, Figueroa, Garrett, Hain, Herbert, Janski, Kinzer, Knapp, Lehan, Losey, Marley, MacDonald, McCall, Nebert, Ravi, Schmidt, Staie and Walston2022; U.S. Department of Energy, 2023). We justify the 10-ft inter-row spacing as an equipment-access corridor sized for conventional utility/row-crop tractors (Macknick et al., Reference Macknick, Hartmann, Barron-Gafford, Beatty, Burton, Choi, Davis, Davis, Figueroa, Garrett, Hain, Herbert, Janski, Kinzer, Knapp, Lehan, Losey, Marley, MacDonald, McCall, Nebert, Ravi, Schmidt, Staie and Walston2022). Manufacturer specifications show overall widths typically ~66–90 inches (5.5–7.5 ft) for common mid-size models (e.g. John Deere 6120R: 66.1 inches; Kubota M6–111: 82.7 inches; New Holland T6.165: 89.8 inches) (John Deere, 2021; New Holland Agriculture, 2023; Kubota Tractor Corporation, 2015). There is also a need to have an 11.8-inch buffer between the panel edge and crop planting to avoid damage to the PV panels (Figure 1). We refer to this as the IAV configuration. This configuration affects the amount of cultivable area, resulting in unused land in buffer areas and leading to areas with full sun, partial sun and full shade, affecting crop yield. The need to elevate solar panels raises the capital cost of the PV installation and can add 200–300% to the total installation cost of solar, depending on design and market conditions (Ramasamy et al., Reference Ramasamy, Zuboy, O’Shaughnessy, Feldman, Desai, Woodhouse, Basore and Margolis2022).

Figure 1.

Integrated AV (IAV) configuration. This reference scenario shows ground-mounted/elevated PV modules with the area between the panels used for farming. The spacing between the PV modules has been increased to allow standard-sized farming equipment to pass between the rows.

We compare the yield and profitability of the IAV configuration to a configuration where crop production and solar energy generation are placed adjacent to each other (AAPV). In this configuration, we keep the same PV capacity (10.36 MW), but the panels are 18 feet apart and 4 feet high. The AAPV system uses standard utility-scale PV spacing because modifications are not needed to accommodate space to grow crops. In contrast, an IAV configuration requires wider spacing to enable agricultural equipment to operate; we hold PV capacity constant to ensure comparability with the AAPV scenario. The layouts considered here represent reasonable, representative configurations and ensure a consistent basis for comparison across different configurations. The AAPV scenario results in 16% more land available for crop production than in the IAV configuration. Additionally, since the crops are grown in full sun, their yield is the same as that in the Crop-only case.

Another approach to reducing the need for a large buffer area between panels and crops is to raise panels even higher, to 12 feet, so that farming could be conducted underneath the panels with only a small buffer area to avoid damaging the PV posts. This TAV configuration results in the PV panels covering the entire 80 acres and the same solar capacity as in the PV-only case, as well as 93% of the land covered with crops, compared to 57% in the IAV configuration. Lastly, we consider the case of the Reduced Buffer Integrated AV (RAV), which allocates a smaller buffer area between solar panels and crops. While such a configuration could benefit from autonomous farm equipment to enhance precision and reduce operational risks near solar infrastructure, our analysis, consistent with the IAV design, assumes that farming remains feasible using conventional equipment. As a result, we do not account for the cost of specialized machinery in this configuration. The reduced buffer increases the cropped area from 57% (in IAV) to 76%, while maintaining the same level of solar generation. Table 1 provides a detailed summary of each configuration, including panel spacing and height, crop and PV area, installed PV capacity, acres per MW and associated capital expenditures (CAPEX). Figure 2 shows the various arrangements of crops and panels considered in this analysis.

Figure 2.

Alternative configurations of crops and solar panels.

Figure 2. Long description

A four-panel diagram showing site layouts for P V (photovoltaic) and A V (agrivoltaic) systems. All panels share a common outer boundary of 1260 feet by 2580 feet.

* Panel a, Utility-scale P V: Features two blocks of blue P V panels separated by a 10-foot Row Access. Each block has five columns of panels. Dimensions include an 18-foot column width, 7.75-foot panel length, and 396-foot tracker length. A 30-foot P V Buffer surrounds the array. P V Height is 4 feet.

* Panel b, Integrated A V: Similar to panel a but replaces the second and fourth columns of P V panels with green Crop strips. The spacing between P V columns increases to 43.5 feet to accommodate a Farm Buffer. P V Height is 8 feet.

* Panel c, Adjacent Ag-P V: The left half of the site contains two blocks of P V panels (two columns each) with a 30-foot buffer. The entire right half of the site is a solid green block labeled Crops. P V Height is 4 feet.

* Panel d, Tall Panels A V: P V panels are arranged in five columns across the entire site, but the background is entirely green, indicating Crops are planted underneath and between all panels. P V Height is 12 feet.

Figure 3 illustrates the trade-off between solar energy capacity and cropped acreage across the configurations analyzed. The IAV configuration achieves 43% of the solar capacity of the PV-only system while maintaining 57% of the cropped acreage of the Crop-only case. This configuration requires 3.3 acres per MW, slightly more than the 3.1 acres per MW in the PV-only case (Table 1). In contrast, the AAV and RAV configurations make more efficient use of land: the former matches the PV-only system at 3.1 acres per MW, while the latter requires only 1.8 acres per MW by converting previously unused buffer space into cropped area. These trade-offs reflect the representative design parameters adopted for this study, and while keeping PV capacity constant maintains comparability across both IAV and AAPV systems, alternative design choices in other contexts may lead to different quantitative outcomes.

Figure 3.

PV capacity and cropped acres trade-off. Notes: The Tall Panels AV (TAV) configuration has an increased crop area with high solar energy capacity as PV-only. The Reduced Buffer AV (RAV) configuration has higher crop acres but reduced PV capacity. Both the Integrated AV (IAV) and Adjacent Ag-PV (AAPV) configurations have the same PV capacity (10.36 MW) and are hence shown as overlapping points in the figure above.

Figure 3. Long description

The scatter plot uses an X-axis representing Crop area in acres, ranging from 0 to 80, and a Y-axis representing P V capacity in M W, ranging from 0 to 25. A dashed diagonal line connects the two extremes of the trade-off.

* At the top-left corner, a point labeled P V-only is located at 0 acres and approximately 26 M W.

* At the bottom-right corner, a point labeled Crop-only is located at 80 acres and 0 M W.

* Along the dashed line in the center, two overlapping points labeled I A V and A A P V are positioned at approximately 46 acres and 10.36 M W.

* To the right of the dashed line, a point labeled R A V is located at approximately 61 acres and 10.36 M W.

* At the top-right, significantly above the dashed line, a point labeled T A V is located at approximately 74 acres and 26 M W, indicating high performance in both metrics.

3.4. Data

We analyzed the effects of AV on crop and energy output per acre of land on an 80-acre field in Champaign County, Illinois (Latitude/Longitude: 40.13, −88.22). The Supplementary Information provides an overview of the model parameters and sources of data. The data on technology parameters were obtained from National Renewable Energy Laboratory (NREL) reports (Horowitz et al., Reference Horowitz, Ramasamy, Macknick and Margolis2020; Ramasamy et al., Reference Ramasamy, Zuboy, O’Shaughnessy, Feldman, Desai, Woodhouse, Basore and Margolis2022). We assume the PV system has a lifetime of 25 years with a degradation rate of 0.5% per year and annual operating expenses (OPEX) of $15 kW⁻¹ (Supplementary Information). Since AV systems require elevated PV panels to accommodate crop production, capital costs (CAPEX) for AV increase significantly compared to ground-mounted PV (Shindele et al., Reference Shindele, Trommsdorff, Schlaak, Obergfell, Bopp, Reise, Braun, Weselek, Bauerle, Högy, Goetzberger and Weber2020); this translates to a CAPEX of $2.66 W⁻¹ for 8-foot tall panels and $3.06 W⁻¹ for 12-foot tall panels compared to $1.15 W⁻¹ for conventional PV systems (Ramasamy et al., Reference Ramasamy, Zuboy, O’Shaughnessy, Feldman, Desai, Woodhouse, Basore and Margolis2022). Further, we applied a discount rate of 6.5% per year to calculate the LCOE consistent with recommended guidelines that vary between 6% and 8% year⁻¹ (Burgess & Zerbe, Reference Burgess and Zerbe2011), with alternative values used to test for sensitivity analysis (Boardman et al., Reference Boardman, Greenberg, Vining and Weimer2018). To address variability in the price of electricity, we conducted a sensitivity analysis using three electricity price scenarios: a baseline price of $75.7 MWh⁻¹ – based on recent average utility-scale solar Power Purchase Agreement (PPA) prices in the US. (Heeter et al. Reference Heeter, O’Shaughnessy and Burd2021) and two alternative values, $66.3 MWh⁻¹ and $85.6 MWh⁻¹. These scenarios represent a plausible range of market conditions over time and allow us to test the robustness of our results to changes in electricity pricing. We assume the utility will obtain renewable energy credits (REC)Footnote ⁶ valued at $6. MWh⁻¹ (Heeter et al. Reference Heeter, O’Shaughnessy and Burd2021) and that the solar developer benefits from the 30% federal Investment Tax Credit for both PV and AV, which is already embedded in the LCOE estimates used in our analysis. No additional state or federal subsidies are considered, and we list this as a caveat in the discussion of model limitations.

For the Crop-only case, we model a corn–soybean rotation using yield data from USDA NASS (2024) and cost estimates from the Illinois crop budget (Schnitkey et al., Reference Schnitkey, Paulson, Zulauf and Baltz2024), which include variable costs (fertilizer, seed) and fixed costs (equipment). Baseline values are $2.50/bushel (variable) and $136/acre (fixed) for soybeans, and $1.73/bushel (variable) and $247/acre (fixed) for corn. To account for potential changes in commodity prices and input costs over the 25-year modeling period, we conduct sensitivity analyses using a range of values around these estimates (see Supplementary Tables 3–4). For the AV case, we assume continuous soybean production, applying the same Illinois crop budget data to ensure consistency with the Crop-only scenario in both baseline and sensitivity analyses.