Design of an Agrivoltaic System with Building Integrated Photovoltaics

Building integrated photovoltaics (BIPVs) are becoming popular as building elements such as windows, roofs, and outer walls. Because BIPVs have both a construction material function and an electricity generation function, they are a promising alternative to sustainable buildings. This study aims to propose a novel agrivoltaic system design that produces crops underneath photovoltaic (PV) modules. Regarding the fact that crop growth is significantly influenced by shading from PV modules, roof BIPVs with different shading ratios can lead to increased crop productivity. Thus, BIPV design should be investigated based on the performance estimation and feasibility evaluation of different shading ratios in an agrivoltaic system. To this end, electricity generation and crop production models are devised by polynomial regression (PR) based on field experiment data collected from the agrivoltaic system at the Agricultural Research Service Center in Naju-si, South Korea. The experiment shows that a shading ratio of 30% allows for the maximization of the profitability of electricity and soybean production in an agrivoltaic system equipped with BIPVs. As a result, this research will contribute to implementing an agrivoltaic system with various BIPVs.


Introduction
For decades, photovoltaics (PVs) have been used as a popular material for generating electricity from renewable energy source (i.e., solar energy) [1]. The global movement to reduce greenhouse gas (GHG) emission [2] has become a more popular material in renewable energy production. Because PVs can be attached to a wall and a roof, they have the potential to be used as building element, in a system which is also known as building integrated photovoltaics (BIPV) [3]. Considering that buildings consume 30% of global energy, using PVs as building elements can mitigate GHG emissions [4]. Accordingly, the levelized cost of electricity (LCOE) of a roof top BIPV system is only 72% of the LCOE of a green roof system in Texas, USA [5]. Hence, it is a profitable alternative to implement the concept of green buildings. Notice that a green roof (or a vegetation roof) is another well-known option for thermal and energy efficient buildings [6].
The most significant advantage of BIPVs is renewable energy production, but BIPVs also have other benefits [7]. For example, BIPVs reduce air conditioner use in a building in summer because the PV cells in BIPVs can block the excessive solar radiation from windows [8]. In addition, the warranty duration of PV modules is between 20 and 25 years. Therefore, BIPVs are highly reliable in the long term [9]. The thickness and strength of BIPV involving PV cells made of c-Si, a-Si, or CdTe PV cells provide better thermal insulation and acoustic insulation functions than windows [10]. Due to the multiple benefits of BIPVs, their global market value was 19.82 billion U.S. dollars in 2022, and the compound annual growth rate from 2023 to 2030 is expected to be 21% [11]. to 30-53% at a shading ratio of 32%. Nevertheless, due to the revenue from electricity production through PV modules, the agrivoltaic system eventually contributes to increase the income of farmers. Agrivoltaic systems have been studied in multiple countries such as Germany, Jap China, United States, France, Chile, and South Korea [14,[17][18][19]. In particular, it is ben cial for countries with land shortage problems, as it simultaneously utilizes the lim land resources to produce electricity and crops [2]. Accordingly, the agrivoltaic sys preserves moisture and organic matter in the soil, which results in water use reduct [20].
However, because PV modules in an agrivoltaic system create shade, crop harv yields may differ from those produced from regular farms in open fields. In fact, accord to the field study conducted to understand the shading impact on the yield of crops (e sesame, mung bean, red bean, corn, and soybean) [2], the yield of five crops were creased to 30-53% at a shading ratio of 32%. Nevertheless, due to the revenue from e tricity production through PV modules, the agrivoltaic system eventually contribute increase the income of farmers.
The roof BIPV has three different classifications: (1) PV modules on a rooftop [21] PV modules attached to a roof [22]; and (3) PV modules integrated in a roof (or a gre house roof) [23]. Figure 2 illustrates three different types of roof BIPVs. PV modules on a rooftop (i.e., rooftop PVs) are traditional rooftop PVs taking 80% the BIPV market [3]. The PV modules attached to a roof (i.e., roof attached PVs) are a p ular design for the individual household because they do not change any existing r design and require additional cost to construct pillars to support PV modules. The modules integrated into a roof (i.e., roof integrated PVs) are novel alternatives to sub tute building elements. Although the strength and durability of roof integrated PVs The roof BIPV has three different classifications: (1) PV modules on a rooftop [21]; (2) PV modules attached to a roof [22]; and (3) PV modules integrated in a roof (or a greenhouse roof) [23]. Figure 2 illustrates three different types of roof BIPVs. Agrivoltaic systems have been studied in multiple countries such as Germany, Japan, China, United States, France, Chile, and South Korea [14,[17][18][19]. In particular, it is beneficial for countries with land shortage problems, as it simultaneously utilizes the limited land resources to produce electricity and crops [2]. Accordingly, the agrivoltaic system preserves moisture and organic matter in the soil, which results in water use reduction [20].
However, because PV modules in an agrivoltaic system create shade, crop harvest yields may differ from those produced from regular farms in open fields. In fact, according to the field study conducted to understand the shading impact on the yield of crops (e.g., sesame, mung bean, red bean, corn, and soybean) [2], the yield of five crops were decreased to 30-53% at a shading ratio of 32%. Nevertheless, due to the revenue from electricity production through PV modules, the agrivoltaic system eventually contributes to increase the income of farmers.
The roof BIPV has three different classifications: (1) PV modules on a rooftop [21]; (2) PV modules attached to a roof [22]; and (3) PV modules integrated in a roof (or a greenhouse roof) [23]. Figure 2 illustrates three different types of roof BIPVs. PV modules on a rooftop (i.e., rooftop PVs) are traditional rooftop PVs taking 80% of the BIPV market [3]. The PV modules attached to a roof (i.e., roof attached PVs) are a popular design for the individual household because they do not change any existing roof design and require additional cost to construct pillars to support PV modules. The PV modules integrated into a roof (i.e., roof integrated PVs) are novel alternatives to substitute building elements. Although the strength and durability of roof integrated PVs are relatively weaker than those of a roof made of cement and brick, they are appropriate alternatives for a thin roof made of glasses [8]. For example, they can be used as a roof for a nursery in agriculture because they do not block all solar radiation needed for crop production. Figure 3 illustrates the structure of a semi-transparent BIPV [24]. Unlike traditional PV modules, solar radiation can penetrate the semi-transparent BIPV. PV modules on a rooftop (i.e., rooftop PVs) are traditional rooftop PVs taking 80% of the BIPV market [3]. The PV modules attached to a roof (i.e., roof attached PVs) are a popular design for the individual household because they do not change any existing roof design and require additional cost to construct pillars to support PV modules. The PV modules integrated into a roof (i.e., roof integrated PVs) are novel alternatives to substitute building elements. Although the strength and durability of roof integrated PVs are relatively weaker than those of a roof made of cement and brick, they are appropriate alternatives for a thin roof made of glasses [8]. For example, they can be used as a roof for a nursery in agriculture because they do not block all solar radiation needed for crop production. Figure 3 illustrates the structure of a semi-transparent BIPV [24]. Unlike traditional PV modules, solar radiation can penetrate the semi-transparent BIPV.
Suppose the semi-transparent BIPV is used as a roof integrated PV for an agrivoltaic system. In that case, the shading ratios of the system can be reduced, which improves crop production. In an agrivoltaic system, the distance between the pillars supporting the PV modules primarily affects the shading ratio. However, using roof integrated PVs provides another opportunity to easily control shading ratios by changing the design of semi-transparent BIPVs.  Suppose the semi-transparent BIPV is used as a roof integrated PV for an agrivo system. In that case, the shading ratios of the system can be reduced, which improves production. In an agrivoltaic system, the distance between the pillars supporting th modules primarily affects the shading ratio. However, using roof integrated PVs pro another opportunity to easily control shading ratios by changing the design of semi-t parent BIPVs.

Design of an Agrivoltaic System with Building Integrated Photovoltaics
This study proposes a design framework for an agrivoltaic system integrated BIPVs. Figure 4 illustrates the proposed framework with seven stages. Once a structu the agrivoltaic system is determined, the BIPV design must be selected. However, th a significant correlation between a shading ratio and BIPV design, and an approp shading ratio should be determined. To this end, the performance of an agrivoltaic sy in terms of electricity generation quantity and crop production yield is estimated estimated performance is transformed to economic value in the feasibility analysis s This process continues until the optimum shading ratio is found. After that, the fr work designs a BIPV under the selected shaded ratio. The following sections provid primary stage in detail.

Design of an Agrivoltaic System with Building Integrated Photovoltaics
This study proposes a design framework for an agrivoltaic system integrated with BIPVs. Figure 4 illustrates the proposed framework with seven stages. Once a structure of the agrivoltaic system is determined, the BIPV design must be selected. However, there is a significant correlation between a shading ratio and BIPV design, and an appropriate shading ratio should be determined. To this end, the performance of an agrivoltaic system in terms of electricity generation quantity and crop production yield is estimated. The estimated performance is transformed to economic value in the feasibility analysis stage. This process continues until the optimum shading ratio is found. After that, the framework designs a BIPV under the selected shaded ratio. The following sections provide the primary stage in detail. Suppose the semi-transparent BIPV is used as a roof integrated PV for an agrivoltaic system. In that case, the shading ratios of the system can be reduced, which improves crop production. In an agrivoltaic system, the distance between the pillars supporting the PV modules primarily affects the shading ratio. However, using roof integrated PVs provides another opportunity to easily control shading ratios by changing the design of semi-transparent BIPVs.

Design of an Agrivoltaic System with Building Integrated Photovoltaics
This study proposes a design framework for an agrivoltaic system integrated with BIPVs. Figure 4 illustrates the proposed framework with seven stages. Once a structure of the agrivoltaic system is determined, the BIPV design must be selected. However, there is a significant correlation between a shading ratio and BIPV design, and an appropriate shading ratio should be determined. To this end, the performance of an agrivoltaic system in terms of electricity generation quantity and crop production yield is estimated. The estimated performance is transformed to economic value in the feasibility analysis stage This process continues until the optimum shading ratio is found. After that, the framework designs a BIPV under the selected shaded ratio. The following sections provide the primary stage in detail.  Figure 4 shows the electricity generation quantity by BIPV estimated through polynomial regression (PR). This popular machine-learning technique captures the correlation between independent and dependent variables through their coefficients [16]. The PR model is described in Equations (1) and (2) [5].  Figure 4 shows the electricity generation quantity by BIPV estimated through polynomial regression (PR). This popular machine-learning technique captures the correlation between independent and dependent variables through their coefficients [16]. The PR model is described in Equations (1) and (2) [5].
Notice that Equation (3) estimates an electricity generation quantity regarding climate variables having a non-linear relationship with E BIPV (S). Regarding the coefficient of shading ratio S, there is a positive correlation between a shading ratio and electricity generation quantity. Table 1 describes the yield estimation model of Soybean production devised under different shading ratios based on the field study data. In 2020, soybean (Glycine max) was planted and harvested from June to October at the Jeollanam-do Agricultural Research and Extension Services (35.0161 • N, 126.7108 • E), located in Naju-si, South Korea [2]. The average temperature and total rainfall were 23.55 • C and 1477.9 mm, respectively. Accordingly, in the experiment, the reduction ratios from the yield of the open field (0% shading ratio) were −13%, −21%, and −30%, respectively.  (4) represents the yield estimation model of soybean.
where S is a shading ratio (0 ≤ S ≤ 0.32). The coefficient of determination (R 2 ) of Equation (4) is 99.72% so that the developed model can accurately estimate soybean yields under different shading ratios. In Figure 5, the harvest yields nonlinearly decrease as the shading ratio increases. Regrading the fact that the quantity of electricity generation increases as the shading ratio increases, this nonlinear relationship conflicts with the quantity of electricity generation. It implies that a farmer must determine the optimal shading ratio which produces electricity without causing harmful impact on the production yield of a crop.

Feasibility Analysis and Shading Ratio Determination
The estimation models of electricity generation and soybean production can be us to identify the best shade ratio of BIPV with maximum profit of in Equation (5).
where is the shading ratio generated by BIPV; is the unit price of electricity sal is the unit production cost of electricity; is the selling price of soybea is the unit production cost of soybean; is the profit function su tracting the production cost of electricity from the total revenue of electricity generatio is the profit function subtracting the production cost of soybean from the to revenue of soybean; and , is the minimum required yield of soybean. Not that an agrivoltaic system aims to generate electricity without affecting food security sues. Therefore, the minimum required yield of a crop should be considered in its desig

Scenario
The proposed performance estimation framework was used to design an agrivolt system consisting of roof integrated BIPVs. Figure 3 shows the semi-transparent BIPV us on the roof of an agrivoltaic system. Figure 6 reveals the structure of the agrivoltaic syste considered in this study.

Feasibility Analysis and Shading Ratio Determination
The estimation models of electricity generation and soybean production can be used to identify the best shade ratio of BIPV with maximum profit of Z in Equation (5).
0 ≤ S ≤ 0.32 (9) where S is the shading ratio generated by BIPV; β BIPV is the unit price of electricity sales; γ BIPV is the unit production cost of electricity; β soybean is the selling price of soybean; γ soybean is the unit production cost of soybean; f electricity (S) is the profit function subtracting the production cost of electricity from the total revenue of electricity generation; f soybean (S) is the profit function subtracting the production cost of soybean from the total revenue of soybean; and Y soybean,min is the minimum required yield of soybean. Notice that an agrivoltaic system aims to generate electricity without affecting food security issues. Therefore, the minimum required yield of a crop should be considered in its design.

Scenario
The proposed performance estimation framework was used to design an agrivoltaic system consisting of roof integrated BIPVs. Figure 3 shows the semi-transparent BIPV used on the roof of an agrivoltaic system. Figure 6 reveals the structure of the agrivoltaic system considered in this study.
In Figure 6, e 1 is the horizontal distance of an area shaded by a BIPV; e 2 is the horizontal distance of the open area between BIPVs; q is the length of a BIPV; ω is the solar altitude angle ( • ); τ is a tilt angle of a BIPV( • ). The value of e 1 is calculated by Equation (10).  Figure 6. Design of the subject agrivoltaic system.
In Figure 6, is the horizontal distance of an area shaded by a BIPV; is the h izontal distance of the open area between BIPVs; q is the length of a BIPV; ω is the so altitude angle (°); τ is a tilt angle of a BIPV(°). The value of is calculated by Equat (10).

= cos τ
According to theory [25], ω should be the solar altitude angle at noon to maxim the productivity of BIPVs, and it should be 45°≤ ω ≤ 90°. In South Korea, most PV m ules have a tilt angle (τ) of 30° to maximize the productivity of PVs [26]. Regarding b conditions, 1 should be between and 2 √3 ⁄ . In other words, when = 0, the sh ing ratio (S) can be between 86.6% and 100% according to Equation (11).

= + ⁄
However, in this condition, crops underneath BIPVs cannot grow due to the h shading ratio, so an additional distance between the BIPVs ( ) must be considered. cording to [2], the maximum shading ratio of 32% is required for the agrivoltaic crop p duction system. Thus, this study assumes the maximum shading ratio of 32% to meet soybean's minimum production quantity (0.25 kg/m 2 ). In other words, should greater than 1.9 when = 2 √3 ⁄ . Table 2 describes the climate data of the subject area (i.e., the Agricultural Resea Service Center in Naju-si, South Korea) from 2012 to 2022 [27]. Note that the crop grow season from June to October generally has higher solar radiation values than ot months. This results in higher productivity in terms of electricity generation. The d average solar radiation, surface temperature high, surface temperature low, precipitat humidity, and wind speed are 2.14 MJ/m 2 , 18.22 °C, 10.91 °C, 97.29 mm, 77.68%, and 3 m/s, respectively. The data are used to estimate the electricity generation quantities roof integrated BIPV.  According to theory [25], ω should be the solar altitude angle at noon to maximize the productivity of BIPVs, and it should be 45 • ≤ ω ≤ 90 • . In South Korea, most PV modules have a tilt angle (τ) of 30 • to maximize the productivity of PVs [26]. Regarding both conditions, e 1 should be between q and 2q/ √ 3. In other words, when e 2 = 0, the shading ratio (S) can be between 86.6% and 100% according to Equation (11).
However, in this condition, crops underneath BIPVs cannot grow due to the high shading ratio, so an additional distance between the BIPVs (e 2 ) must be considered. According to [2], the maximum shading ratio of 32% is required for the agrivoltaic crop production system. Thus, this study assumes the maximum shading ratio of 32% to meet the soybean's minimum production quantity (0.25 kg/m 2 ). In other words, e 2 should be greater than 1.9 q when e 1 = 2q/ √ 3. Table 2 describes the climate data of the subject area (i.e., the Agricultural Research Service Center in Naju-si, South Korea) from 2012 to 2022 [27]. Note that the crop growing season from June to October generally has higher solar radiation values than other months. This results in higher productivity in terms of electricity generation. The daily average solar radiation, surface temperature high, surface temperature low, precipitation, humidity, and wind speed are 2.14 MJ/m 2 , 18.22 • C, 10.91 • C, 97.29 mm, 77.68%, and 3.32 m/s, respectively. The data are used to estimate the electricity generation quantities of a roof integrated BIPV.
The system marginal price (SMP) and renewable energy certificate (REC) are considered to calculate the electricity revenue produced. The SMP and REC are USD 0.12/kWh and USD 0.05/kWh in south Korea in 2023, respectively [28]. The electricity production costs are estimated based on the data in Table 3. According to [29], BIPVs are 1.46 times more expensive than regular PV modules due to their customized design. The lifetime of PV is assumed to be 25 years regarding the warranty duration of PVs [30].  The total construction costs (the present values) are transformed into annual values via Equation (12) under the given discount rate of r. It is known as the equal-payment-series capital-recovery factor [32].
where A is the annual worth (USD); P is the present worth (USD); and n is the lifetime of a BIPV (year). As a result, the annual cost of electricity generation computes to include investment (i.e., construction), operating, and maintenance costs. Table 4 describes soybean production cost involving material, labor, and overhead costs. The total production cost is USD 0.56/m 2 /year. According to [33], the selling price of soybean in 2022 is USD 5.68/kg. The profitability of electricity under given costs and sales data and crop production under different shading ratios are used in Section 3.2.

Identification of the Best Shading Ratio for an Agrivoltaic System
The best shading ratio of a roof integrated BIPV at the subject agrivoltaic system is identified through Equation (5), shown in Section 2.2.3. From the given climate data in Table 2, the daily electricity generation quantities (E PV (S), kWh/m 2 /day) of PV modules are initially estimated. Figure 7 illustrates the estimated results. As the shading ratio increases, more PV modules can be installed within a unit area (m 2 ) to increase electricity generation quantities. In Figure 7, the crop growing period from June to October has the highest productivity due to climate characteristics described in Table 2.

Identification of the Best Shading Ratio for an Agrivoltaic System
The best shading ratio of a roof integrated BIPV at the subject agrivoltaic s identified through Equation (5), shown in Section 2.2.3. From the given climate Table 2, the daily electricity generation quantities ( , kWh/m 2 /day) of PV mod initially estimated. Figure 7 illustrates the estimated results. As the shading ratio in more PV modules can be installed within a unit area (m 2 ) to increase electricity ge quantities. In Figure 7, the crop growing period from June to October has the productivity due to climate characteristics described in Table 2.  Figure 8 represents the annual revenue, cost, and profit of electricity genera der two cases, such as the REC and SMP case and the SMP case. As mentioned in 3.1, the electricity sales price in the REC and SMP case is USD 0.17/kWh, and price in the SMP case is USD 0.12/kWh. Notice that a discount rate of 0.05 is consi both cases. In the case of REC and SMP, there is a positive profit when the shad is more significant than and equal to 0.23. In other words, if the shading ratio is lo 0.23, there is no profit due to high production costs involving the construction, op and maintenance costs. Under the SMP case, there is no positive profit under all t ing ratios. This implies the significance of REC in making a positive profit from e sales generated by BIPVs.  Figure 8 represents the annual revenue, cost, and profit of electricity generation under two cases, such as the REC and SMP case and the SMP case. As mentioned in Section 3.1, the electricity sales price in the REC and SMP case is USD 0.17/kWh, and the sales price in the SMP case is USD 0.12/kWh. Notice that a discount rate of 0.05 is considered in both cases. In the case of REC and SMP, there is a positive profit when the shading ratio is more significant than and equal to 0.23. In other words, if the shading ratio is lower than 0.23, there is no profit due to high production costs involving the construction, operating, and maintenance costs. Under the SMP case, there is no positive profit under all the shading ratios. This implies the significance of REC in making a positive profit from electricity sales generated by BIPVs.

Identification of the Best Shading Ratio for an Agrivoltaic System
The best shading ratio of a roof integrated BIPV at the subject agrivoltaic system is identified through Equation (5), shown in Section 2.2.3. From the given climate data in Table 2, the daily electricity generation quantities ( , kWh/m 2 /day) of PV modules are initially estimated. Figure 7 illustrates the estimated results. As the shading ratio increases, more PV modules can be installed within a unit area (m 2 ) to increase electricity generation quantities. In Figure 7, the crop growing period from June to October has the highest productivity due to climate characteristics described in Table 2.  Figure 8 represents the annual revenue, cost, and profit of electricity generation under two cases, such as the REC and SMP case and the SMP case. As mentioned in Section 3.1, the electricity sales price in the REC and SMP case is USD 0.17/kWh, and the sales price in the SMP case is USD 0.12/kWh. Notice that a discount rate of 0.05 is considered in both cases. In the case of REC and SMP, there is a positive profit when the shading ratio is more significant than and equal to 0.23. In other words, if the shading ratio is lower than 0.23, there is no profit due to high production costs involving the construction, operating, and maintenance costs. Under the SMP case, there is no positive profit under all the shading ratios. This implies the significance of REC in making a positive profit from electricity sales generated by BIPVs. On the other hand, in Figure 9, profit from crop production nonlinearly decreases as the shading ratio increases. The profit becomes the minimum value of USD 0.49/m 2 at the shading ratio of 32%. Notice that the required minimum production quantity of soybean is 0.25 kg/m 2 , so that the shading cannot be more excellent than 32% in this study. On the other hand, in Figure 9, profit from crop production nonlinearly decreases as the shading ratio increases. The profit becomes the minimum value of USD 0.49/m 2 at the shading ratio of 32%. Notice that the required minimum production quantity of soybean is 0.25 kg/m 2 , so that the shading cannot be more excellent than 32% in this study.
The values are a summation between electricity production and crop production (see Fig  ures 8 and 9). In the REC and SMP case, the shading ratio of 0.3 is the best solution, with a profit of USD 1.76/m 2 /year. Because of soybean production, the shading ratios between 0.16 and 0.32 have positive profits. In the SMP case, the shading ratio of 0.26 is the bes solution, with a USD 1.00/m 2 /year profit. Due to the value of SMP, profits are more influ enced by soybean sales than those of the REC and SMP cases. In both cases, producing electricity does not increase farmer's profit. Similarly, regarding the fact of a profit of soy bean sales only being USD 1.5/m 2 /year, the agrivoltaic system was able increase farmers income to USD 1.76/m 2 /year under the REC and SMP case. Once the shading ratio of 0.30 is selected, a BIPV can be designed under the agri voltaic structure shown in Figure 6. Since a semi-transparent BIPV consists of glass and resin, some of solar radiation penetrates BIPVs. It means that the horizontal distance be tween BIPVs ( + ) and the area of glass and resin in a semi-transparent BIPV can affec the shading ratio. Figure 11 shows the design of LG405N2W-V5 with 72 PV cells modifying the semi transparent BIPV. The devised semi-transparent BIPV consists of 36 PV cells with 202. W. Let be a penetration rate of the BIPV, so Equation (11) can be modified as Equation (13).
Since = 0.5, the horizontal distance between BIPVs can be computed as Equation (14).  Figure 10 reveals the total annual revenue, cost, and profit of the agrivoltaic system. The values are a summation between electricity production and crop production (see Figures 8 and 9). In the REC and SMP case, the shading ratio of 0.3 is the best solution, with a profit of USD 1.76/m 2 /year. Because of soybean production, the shading ratios between 0.16 and 0.32 have positive profits. In the SMP case, the shading ratio of 0.26 is the best solution, with a USD 1.00/m 2 /year profit. Due to the value of SMP, profits are more influenced by soybean sales than those of the REC and SMP cases. In both cases, producing electricity does not increase farmer's profit. Similarly, regarding the fact of a profit of soybean sales only being USD 1.5/m 2 /year, the agrivoltaic system was able increase farmers' income to USD 1.76/m 2 /year under the REC and SMP case.
Agronomy 2023, 13, x FOR PEER REVIEW 10 of 13 Figure 10 reveals the total annual revenue, cost, and profit of the agrivoltaic system. The values are a summation between electricity production and crop production (see Figures 8 and 9). In the REC and SMP case, the shading ratio of 0.3 is the best solution, with a profit of USD 1.76/m 2 /year. Because of soybean production, the shading ratios between 0.16 and 0.32 have positive profits. In the SMP case, the shading ratio of 0.26 is the best solution, with a USD 1.00/m 2 /year profit. Due to the value of SMP, profits are more influenced by soybean sales than those of the REC and SMP cases. In both cases, producing electricity does not increase farmer's profit. Similarly, regarding the fact of a profit of soybean sales only being USD 1.5/m 2 /year, the agrivoltaic system was able increase farmers' income to USD 1.76/m 2 /year under the REC and SMP case. Once the shading ratio of 0.30 is selected, a BIPV can be designed under the agrivoltaic structure shown in Figure 6. Since a semi-transparent BIPV consists of glass and resin, some of solar radiation penetrates BIPVs. It means that the horizontal distance between BIPVs ( + ) and the area of glass and resin in a semi-transparent BIPV can affect the shading ratio. Figure 11 shows the design of LG405N2W-V5 with 72 PV cells modifying the semitransparent BIPV. The devised semi-transparent BIPV consists of 36 PV cells with 202.5 W. Let be a penetration rate of the BIPV, so Equation (11) can be modified as Equation (13).
Since = 0.5, the horizontal distance between BIPVs can be computed as Equation (14). Once the shading ratio of 0.30 is selected, a BIPV can be designed under the agrivoltaic structure shown in Figure 6. Since a semi-transparent BIPV consists of glass and resin, some of solar radiation penetrates BIPVs. It means that the horizontal distance between BIPVs (e 1 + e 2 ) and the area of glass and resin in a semi-transparent BIPV can affect the shading ratio. Figure 11 shows the design of LG405N2W-V5 with 72 PV cells modifying the semitransparent BIPV. The devised semi-transparent BIPV consists of 36 PV cells with 202.5 W. Let K T be a penetration rate of the BIPV, so Equation (11) can be modified as Equation (13).
As a result, the subject agrivoltaic system can be designed to maximize its profit from both electricity generation and soybean production.
Since soybean showed the average yield reduction trend among the crops, it was selected to demonstrate the proposed design framework of an agrivoltaic system with BIPVs. Notice that most of crops' yields underneath PV modules were reduced. Nevertheless, the agrivoltaic system enabled an increase in the income of farmers because of the revenue from electricity sales. The experiment in Section 3.2 showed that the agrivoltaic system increased farmers' income to USD 1.76/m 2 /year under the REC and SMP case when the profit of soybean sales was only USD 1.5/m 2 /year. In addition, the shading ratio of 0.3 is the best solution in the REC and SMP case with a profit of USD 1.76/m 2 /year. In addition, BIPV is designed to meet a shading ratio of 0.3. As a result, regarding that the profit of an agrivoltaic system is heavily dependent on both REC and SMP prices, sustainable renewable energy policy should be devised to increase farmers' income.

Conclusions
This study proposed a framework identifying the optimal design of an agrivoltaic system integrated with a semi-transparent BIPV regarding its economic value. The economic value was estimated based on the performance of an agrivoltaic system in terms of electricity generation and soybean production under different shading ratios. To this end, two estimation models were developed through PR using the data collected from an Agrivoltaic system located at the Jeollanam-do Agricultural Research and Extension Services in Naju-si (35.0161° N, 126.7108° E), Jeollanam-do, South Korea. Under the different shading ratios between 0.16 and 0.32, the optimization model identified the best shading ratio of the agrivoltaic system and devised an appropriate semi-transparent BIPV. In the REC and SMP case, a shading ratio of 0.3 was the best solution, yielding a profit of USD 1.76/m 2 /year. A shading ratio of 0.26 was the best solution in the SMP case, yielding a USD 1.00/m 2 /profit per year. Consequently, this study shows that the selected shading ratio can Since K T = 0.5, the horizontal distance between BIPVs can be computed as Equation (14).
Since soybean showed the average yield reduction trend among the crops, it was selected to demonstrate the proposed design framework of an agrivoltaic system with BIPVs. Notice that most of crops' yields underneath PV modules were reduced. Nevertheless, the agrivoltaic system enabled an increase in the income of farmers because of the revenue from electricity sales. The experiment in Section 3.2 showed that the agrivoltaic system increased farmers' income to USD 1.76/m 2 /year under the REC and SMP case when the profit of soybean sales was only USD 1.5/m 2 /year. In addition, the shading ratio of 0.3 is the best solution in the REC and SMP case with a profit of USD 1.76/m 2 /year. In addition, BIPV is designed to meet a shading ratio of 0.3. As a result, regarding that the profit of an agrivoltaic system is heavily dependent on both REC and SMP prices, sustainable renewable energy policy should be devised to increase farmers' income.

Conclusions
This study proposed a framework identifying the optimal design of an agrivoltaic system integrated with a semi-transparent BIPV regarding its economic value. The economic value was estimated based on the performance of an agrivoltaic system in terms of electricity generation and soybean production under different shading ratios. To this end, two estimation models were developed through PR using the data collected from an Agrivoltaic system located at the Jeollanam-do Agricultural Research and Extension Services in Naju-si (35.0161 • N, 126.7108 • E), Jeollanam-do, South Korea. Under the different shading ratios between 0.16 and 0.32, the optimization model identified the best shading ratio of the agrivoltaic system and devised an appropriate semi-transparent BIPV. In the REC and SMP case, a shading ratio of 0.3 was the best solution, yielding a profit of USD 1.76/m 2 /year. A shading ratio of 0.26 was the best solution in the SMP case, yielding a USD 1.00/m 2 /profit per year. Consequently, this study shows that the selected shading ratio can be used to design a semi-transparent BIPV with maximum profit. These results will contribute to the implementation of BIPVs in agrivoltaic systems.