Integration of bifacial photovoltaics in agrivoltaic systems: A synergistic design approach

To safeguard future renewable energy and food supply the use of agrophotovoltaic (APV) systems was investigated


Introduction
The continuous development of solar photovoltaic (PV) technologies coupled with rapid cost reductions and advances in conversion efficiency have resulted in a remarkable reduction of the levelized cost of electricity (LCOE) of ground mounted PV (GMPV) [1]. Therefore, their economic competitiveness is promoted, which is essential as the global energy consumption is projected to rise by 50% from 2018 to 2050 [2]. To mitigate any further intensification of global climate change, this energy should be supplied by renewable sources, such as PV; however, due to the relatively low PV module efficiency substantial land coverage would be required to meet this demand. This could be partially alleviated through aggressive installation of building integrated PV (BIPV); nonetheless, the rising demand for GMPV will inevitably lead to the establishment of these systems on agricultural land [3]. One promising solution is the application of agrophotovoltaic (APV) [4] or agrivoltaic [5] systems that permit the simultaneous cultivation of crops and production of renewable electricity; consequently, diminishing the land-use conflict. In this work both terms were used interchangeably as they refer to stilt mounted PV systems elevated above cropland.
To satisfy crop specific needs, some innovative technologies have emerged such as concentrator PV (CPV) [6], and semi-transparent PV achieved either spectrally [7], or regionally [8]. The main drawback of micro CPV is mass production [9] and subsequently cost, while organic PV (OPV) are still premature for large-scale installations due to their reduced efficiency [10] and degradation [11]. For the latter additional performance testing should be achieved to ensure compatibility with infield conditions and various crop [12][13][14]. Contrary, by adopting c-Si bifacial cells, whose market share is expected to be at least 35% by 2030 [15], APV could also benefit from the evolving learning curve. In addition, as the maximization of specific electrical yield is of increasing importance for solar installations, the integration of bifacial PV and their potential synergistic behavior with crop cultivation becomes intriguing.
While the concept of APV was conceived in 1981 [4], only a limited amount of modelling frameworks is available, and up to the authors' knowledge these are restricted to the use of conventional PV module and cell arrangements. Such topologies can lead to intense and nonhomogeneous shading, which can be detrimental to crop productivity, especially in regions with limited solar insolation. By examining several PV topologies and performing customizations in the design of modules, the needs of crops can be met more appropriately.
The aim of this study is to present a multi-scale modelling framework for deriving the optimal topology for a medium-to-large-scale and static bifacial agrivoltaic array. For all the simulations performed, we used Boston, USA (42.37 N, 71.01 W) as the study's location. Although in southern climates the potential of such systems would be higher, an agricultural solar tariff unit has been in effect in MA, USA since April 2018 [16]; thus, promoting their deployment.
At first, an extensive literature review on the various environmental and genetic factors that influence the growth rate of plants was achieved. In addition, the impact of diffuse light and shade casted by the PV array on crop productivity were also explored. This review was concluded with studies relevant to bifacial PV optimization and selection of the most appropriate optical modelling technique when integrated in APV systems. The development of the Radiance model followed, along with the AC electrical and crop yield models. A multiscale sensitivity analysis was carried out, which included modifications ranging from module-to-string-to-array, to identify parameters that have a dominant impact on APV performance. In specific, three main PV topologies were investigated, and their performance was evaluated. Lastly, the potential of a customised bifacial PV module for APV applications was examined.

Plant productivity and growth
The rate of photosynthesis is influenced by a plethora of environmental factorslight intensity and homogeneity, available carbon dioxide, ground and ambient temperature as well as humiditythat are interrelated. To successfully photosynthesize, plants require CO 2 which they obtain through their pores. These stomata are hydraulically operated valves that control the size of the opening according to external climatic conditions and the plant's water availability [17]. When there is enough water, they become swollen and allow the uptake of CO 2 . However, under conditions of water stress, either due to high irradiance and temperature, or low humidity, they become flaccid and obstruct the process of photosynthesis (hydropassive closure) [18].
Similar to PV cells, leaf absorptance depends on the spectral distribution of the incident light. The portion that is useful for photosynthesis corresponds to the visible spectrum and it is termed as photosynthetically active radiation (PAR) (μmol m − 2 s − 1 ). The minimum light intensity required to balance the opposing processes of respiration and photosynthesis is known as the light compensation point (LCP), while at a sufficiently high photon flux the rate of growth saturates, denoted by the light saturation point (LSP) (Fig. 1). Essentially, incident irradiance that exceeds saturation cannot be utilized, rather it is converted into heat, thus reducing productivity. This is directly relevant to hydropassive closure which occurs during midday, leading to a transient reduction in the plant's photosynthetic capability [19]. Subsequent opening of the stomata occurs when the water shortage has been fulfilled.
In addition to environmental conditions, there are also crop specific genetic factors such as plant architecture, and carbon assimilation pathway that greatly impact the process of photosynthesis [20]. Based on the latter, crops can be divided into C3 and C4 species. Naturally, as C3 crops tend to saturate at a significantly lower PAR [21], they are preferable for cultivation under an agrivoltaic array. Furthermore, although shade tolerance is a trait that can be inherited [22][23][24][25][26][27][28], C3 species outperform C4 when grown under low light conditions [29][30]. In general, shade-grown leaves experienced a reduction in number and thickness, while their surface area increased [23,[31][32][33][34][35][36][37][38]. By occupying a larger area leaves can intercept light more efficiently. Furthermore, under shade, a large vascular network is unnecessary, thus such tissue is substituted by photosynthetic cells. This acclimation to low light conditions was found to be more intrinsic for C3 species [39]; consequently, enhancing their compatibility with APV.

Diffuse light
Depending on crop architecture, a more uniform horizontal and vertical distribution of light could improve light interception throughout the canopy and subsequently enhance growth. Crop canopies that are short and compact result in substantial self-shading [40]; which could be compensated through an increase in diffuse light. Contrary, canopies with a low leaf area index (LAI), are associated with minimal selfshading and thus do not necessitate a diffuse cover [41]. For instance, the photosynthetic behaviour of cucumbers was enhanced when light penetration throughout the canopy was increased [42]. A similar boost in productivity was observed during cloudy skies, or under forests [43][44][45][46]. Therefore, diffuse light can penetrate deeper into the lower leaves of the canopy [47][48].
To amplify the fraction of diffuse light, covering materials like those in greenhouses [49][50] could be examined. The integration of a light diffusion film increased plant production by 5%, thus ensuring profitability [51]. This was verified for various plants; cucumbers with 8% increase, roses with 10%, and tomatoes with 8-11% [52][53][54]. Light interception amplified on clear days, especially in the middle layers of the canopy [55], thus complementing photosynthetic performance [47,52,55]. This could also be explained by the decreased crop temperature (around half a degree) at the top of the canopy [52,54].
Overall, a diffuse cover enhances the spatial distribution of light, and depending on the plant's architecture, species, and local climatic conditions the increase in photosynthetic rate and thus productivity can be substantial. Therefore, such a cover could be greatly beneficial in APV systems.

Influence of the PV array
With the integration of the PV array various microclimatic alterations are anticipateddepending on topologythat can directly influence the photosynthetic rate of the canopy and ultimately its biomass production. Researchers in [56] concluded that only a few adaptations are required to switch from open cropping to APV, instead one should emphasize on mitigating light reduction and selecting crops that could adapt under such conditions. Experimental results indicated that mean daily air temperature did not vary significantly relative to full sun (FS) conditions [56]. On the other hand, soil temperature reduced under shade casted by the PV array. This reduction in temperature can lead to a decrease in soil evaporation; ultimately, increasing crop yield as was observed for maize in [57] for non-irrigated conditions. In addition, crops were cooler throughout the day, especially around solar noon, while at night the opposite occurred [56,58]. This, in combination with the reduced evapotranspiration rate promoted improved conditions for photosynthesis and growth for some species [56,59].
Naturally, these microclimatic changes will depend on local climatic conditions and PV topology, while the associated influence on crop yield will differ across the various crop species [60]. It is beyond the scope of this paper to exhaust all the potential factors. Nonetheless, based on the aforementioned findings a reasonable estimate of crop yield reduction can be formulated, which will be further discussed under Section 3.4 Performance indicators.

Bifacial PV optimization
Through the utilization of bifacial solar cells significant reductions in Table 1 Literature review of various studies related to optimization of bifacial PV [61,.
PV system LCOE are expected in comparison to their monofacial counterpart [61]. To address bifacial specific benefits a literature review of the main parameters influencing their performance was achieved (Table 1).
Rear side power generation and thus overall energy yield are dependent on the bifaciality factor (BF) defined as the ratio of rear side efficiency to front side efficiency under standard test conditions (STC): To measure the relative energy yield gain the bifacial gain (BG) was used which is defined as the ratio of rear side annual energy yield (kWh/ yr) to front side: For experimental or small demonstration systems BG is expected to vary 15-25%, while for PV farms 5-15% [62]. Besides design criteria, albedo has a significant influence on bifacial gain as well.
The integration of bifacial PV in agrivoltaic applications offers various synergistic effects. As stilt mounted APV systems are significantly elevated from ground level, rear irradiance homogeneity is enhanced, thus omitting one of the main limiting factors in bifacial performance [63]. Coupled with the increase in view factor (VF) from PV to unshaded ground, the magnitude of rear irradiance and subsequently BG also benefit. To allow sufficient light for crop cultivation, APV arrays are deployed at lower densities; consequently, BG is further boosted. As a result, other PV topologies become compelling such as vertically installed and E-W facing (E-W vertical), which could expand the diversity of crops cultivated. Finally, the combination of convective cooling due to high elevation and the microclimate below could reduce the array's operating temperature, enhance its efficiency, and energy yield [59,86]. Moreover, PV integrated in agrivoltaics could benefit from the reduced operating temperature extremes [59], potentially increasing the module's lifetime and solidifying the overall synergistic behaviour.

Ground albedo
The albedo can vary according to optical and morphological properties of surroundings and based on PV configuration among others [87]. However, for APV systems, ground albedo will also be cropspecific and thus change seasonally as well [88]. Crop architecture is particularly important [89], especially canopy height and LAI, as additional ground shading can occur leading to a reduction of the overall albedo. This would also depend on planting density and the crop's phenological stage.
The fraction of light transmitted through the crop I could be estimated through Beer-Lambert's law [90]: where I 0 is the irradiation incident on a horizontal plane on the top of the canopy. The light extinction coefficient k accounts for the influence of leaf arrangement and tilt [91], which was estimated to be between 0.7-1.0 and 0.3-0.5 for horizontal and vertical leaves respectively [90].
The variable x describes the cumulative LAI of the canopy along the vertical direction. For most agricultural systems to be productive LAI values usually lie between 3 and 5 [20]. Additional complications arise when considering that in natural stands the lower leaves are oriented closer to horizontal, while in the upper layers they are more erect. To represent a more realistic case of the irradiation incident on the canopy plane I ' , additional modifications can be performed on Eq. (3) [91]: where τ leaf is the leaf's transmittance. Although omitted in this paper, if parameters k, and x are known then Eq. (4) can be used to estimate the amount of light intercepted by the leaves. Other surfaces that heavily impact light intensity and distribution throughout the farm are reflective mulches [92][93]. When coupled with decreased PV densities, light demanding crops could be cultivated. Such an alternative is compelling as specific electrical yield (kWh/kWp) of bifacial PV arrays would be enhanced.

Ray tracing validity
To achieve the objective of this study, the modelling approach utilized should be robust, yet flexible in manipulating the PV topology, while addressing detailed features of the design such as cell spacing [98][99][100]. Bifacial arrays that are close to ground mounted can be accurately modelled with either approach; VF, or ray tracing (RT) [94]; however, after a certain elevation the VF model heavily underestimates rear-side irradiance [96][97]. Consequently, in this study RT was adopted for the optical modelling of bifacial stilt mounted APV.
An increasing number of studies have explored the use of RT and more specifically Radiance for the derivation of rear-side irradiance, thus justifying its reliability for various system sizes, topologies, and climates ( Table 2). Note that both bifacial_radiance (developed by NREL) [103] and Franhofer ISE RT [98] software are based on Radiance [104]. Radiance is a physically based illuminance mapping software, which recursively solves Kajiya's rendering equation [105] using backward RT [104]. The propagation of electromagnetic waves is simulated as rays travelling in straight lines, while interactions are described through refraction and reflection at each boundary (ray optics).
RT is associated with an increased computational burden. To speed up the computation, Radiance based daylighting simulation tool Daysim [106] could be adopted without a significant loss of accuracy [107]. Its performance was compared to measured data and the relative error was found to be less than 2% [108], which was attributed almost equally to both Perez model [109] and Radiance's algorithm. For overcast conditions modelled and measured values coincided [108,110], while for clear skies the error was between 5 and 10%, and for intermittent 10-15% [110]. Overall, considering the disparate collection of PV topologies and the time limitation the combination of Daysim and Radiance was deemed as a more practical alternative.

Methodology
The modelling framework and tools utilized are summarized in Fig. 2, which is divided into three stages: geometric, irradiance, and yield modelling. In the first phase, a CAD model of the APV system was generated. Due to the plethora of parameters necessary to define such topologies, Grasshopper [111] -a plug-in of Rhinoceroswas incorporated as it offers precise parametric control. After assigning material properties to each geometry and selecting Radiance parameters, RT was initiated for the surfaces of interest, front and rear PV side, as well as ground. Irradiance modelling was performed with Radiance's RT algorithm in combination with the daylight coefficient approach of Daysim and the Perez All Weather sky model [109]. The intensity and distribution of irradiance could then be visualized. To couple geometric with irradiance modelling, an environmental analysis tool was used, DIVA [112]. The third stage involved the utilization of the simulated irradiance/irradiation values along with the underlying climatic conditions to model crop and AC electrical yield. The latter depends on PV module operating temperature and conversion efficiency along with various DC to AC losses, which will be further elaborated. This procedure was iterated for various PV topologies and based on the land's productivity the most optimal was identified.

Geometric modelling
The aim of the geometric model was to interrelate all the parameters that establish the APV topology. This was accomplished by conducting a multi-scale (array-string-module) parametrization in 3D (Fig. 3). Starting from the "micro" scale, cell dimensions, number, and spacing, were all parametrically defined. Front, and rear cover as well as aluminium frame were included to define a single module. By varying the intercolumn-spacing (ICS) and inter-row-spacing (IRS), or through additional rows per row, numerous arrangements were examined. Finally, the string of modules was converted into an array based on the specified row spacing (RS) and column spacing (CS).
The support structure and its associated shading effect on crops are omitted throughout the analysis, as conventional mounting structures could lead to an underestimation of the actual light intensity on ground. Though the impact cannot be assumed negligible, there is a great deal of an on-going effort to meticulously design such elements to further optimize APV system performance.

Irradiance modelling
The optical properties of each geometry were either obtained from literature or estimated as listed in Table 3. Note that the seasonal variation of ground albedo is disregarded, as 3D modelling of interactions between light and crops is quite complex.
After the APV topologies were parametrically defined and material properties were assigned to each geometry, the sizing of each sample followed. As it is computationally infeasible to simulate large-scale systems, only a portion was modelled. Nonetheless, to faithfully represent the underlying shading conditions the sample size of the APV array was significantly larger than the farm's as shown in Fig. 4 (a). In fact, as agrivoltaic arrays are highly elevated shadow length is extended; consequently, the adopted sample size was bigger than then one suggested in [96] for modelling of bifacial PV systems. Furthermore, by positioning the farm sample right at the centre of the array the influence of border effects was mitigated, as would be the case for the central region of a large-scale system.
Irradiance incident on the solar array was simulated for only a fraction of it, which was defined as the PV modelling sample (Fig. 4 (b)). Since bifacial PV heavily rely on reflected irradiancedepending on topologythe ground was extended and the gain in VF from ground to PV was recorded (Fig. 4 (c, d, e)). The size of ground adopted agreed with [113]; however, it was undersized in comparison to that of [64] to reduce computational burden. Note that for crop yield modelling the surface area covered by the farm sample was used instead. Table 4 presents a list of Radiance parameters adopted.

Electrical AC yield
In this section, the procedure of converting the plane of array (POA) irradiation to annual AC electrical yield is elaborated. Most of the associated losses in this conversion are estimated through literature findings, a summary of which is listed in Table 5. Although an in-depth electrical performance model was not formulated, the distinct differences between topologies remained intact and insightful.
A recent experimental study concluded that significant soiling rates of up to 0.35%/day were present on an agrivoltaic array located in Chile [114]. Naturally, this is expected to vary based on region, agricultural activities during certain periods (tillage, harvesting), as well as PV array   Diffuse reflectance is the fraction of light that is scattered off a surface at various angles, while specular refers to a single outgoing direction. Normal transmittance signifies the amount of light transmitted for a ray that is perpendicular to the surface of interest, while hemispherical quantifies the overall transmission for various incident angles throughout the hemisphere. The haze factor is defined as the ratio of diffuse to overall transmittance.
tilt angle and elevation. The power losses due to soiling could be mitigated by integrating PV cleaning with an irrigation system [115]. Nonetheless, to estimate the annual soiling losses the value obtained from [116] for an industrial area in Boston, USA was modified based on module tilt angle according to the trends provided in [117][118].
To relate the plane of array irradiance G POA with the module's electrical performanceshort circuit current I sc , open circuit voltage V oc , maximum power point P mpp -and efficiency the following equations were used: η(25 where N s is the number of cells in series, n is the ideality factor (assumed as one), and A m,act is the active surface area. These constants along with the module's STC characteristics were derived from the data sheet in [133]. The effect of temperature was accounted for through the SNL model [134], which was claimed to be more accurate than the NOCT [135][136][137], and others that consider wind-induced convection (e.g. Faiman [138]) under certain conditions. The following equation was used to estimate the module's operating temperature T m [134]: where the coefficients (a, b) were estimated to be − 3.47 and − 0.0594 respectively.Then, the influence of operating temperature was coupled to determine the actual P mpp [139], and module efficiency: where κ P is the temperature coefficient of the P mpp (%/K) obtained from [133].

Performance indicators
The use of the land equivalent ratio (LER) for assessing the performance of agrivoltaic systems was proposed in [5] and was defined as a sum of two ratios; AC electrical and crop yield of APV divided by the reference case: For crop yield the reference is an open field (FS conditions), while for    [132] electrical yield it is a conventional GMPV array. To obtain a realistic LER the design of the latter should be optimized. As monofacial arrays can be employed in high PV densities, the design was tailored to maximize electricity production and land utilization ( Table 6). The formulation of a comprehensive crop yield model, which depends on various microclimatic parameters and crop genetic characteristics, is complex. Nonetheless, a reasonable estimate of crop yield reduction can be obtained based on the net CO 2 assimilation rate A [140]. For the study case of blueberries, this was achieved by simulating PAR incident on a horizontal plane at canopy height and relating that to A, through the trend provided in Fig. 1. The magnitude of light intercepted by each leaf will differ, depending on its orientation and location in the canopy. However, for this analysis, it was assumed that the crop is uniformly illuminated or shaded, which is partially justified by the diffuse cover and the frequently intermittent to overcast climate of Boston.
To estimate the seasonal variability of light, PAR at solar noon was obtained for two days per month: one with clear, and one with overcast sky conditions. Then, the corresponding net CO 2 uptake rates were determined for both open field conditions A FS , and under shade A APV : The parameter c signifies the loss of cultivatable land that is occupied by pillars, which lies between 2 and 10% depending on support structure and APV design [5,141]. For the case of blueberries, it was assumed that this loss is negligible (c = 1). In clear days, particularly during summer, the amount of PAR incident on crops largely surpasses the LSP. This is usually accompanied by high evapotranspiration rates that lead to stomata hydropassive closure; ultimately, reducing growth as shown in Fig. 1. Nonetheless, the positive effect of shading on crop productivity was neglected, since in open field conditions shading nets are usually applied. Thus, in FS conditions, when incident PAR was above the LSP, A FS was set equal to the saturated growth rate (12 μmols/m 2 /s). This might lead to an underestimation of crop yield. On the other hand, a significant portion of leaves within the canopy do not attain light saturation, due to partial shading.
Note that depending on the crop's phenological stage, the sensitivity of yield and quality to shading can vary. To simplify the analysis, it was assumed that each month contributed equally, irrespective of sky conditions, to the crop yield ratio. The latter is partially true, as blueberries can photosynthesize effectively even under overcast sky conditions. A weighted average could be used to account for important developmental stages of the crop. Finally, by considering PAR at solar noon only, diurnal changes that occur from the introduction of the APV array are omitted.
Because of the presence of the array, irradiance on ground is nonuniform, which can jeopardize the overall marketable yield of crops (depending on species and climatic conditions). The statistical measure used to assess light inhomogeneity was the coefficient of variation (CV), defined as the ratio of sample standard deviation σ to mean μ [142]:

Array sensitivity -Macro scale
By omitting border effects, the influence of module elevation on ground irradiation diminished. The annual and average ground irradiation of the farm sample increased linearly by 3.4% when the array was raised from 2 to 7 m. Essentially, with higher elevation the sky view factor (SVF) of the ground increases, thus allowing additional diffuse horizontal irradiance (DHI) to penetrate. Nonetheless, BG was not affected considerably (data not shown). Therefore, the main incentive for elevating modules is to ensure that there is sufficient ground clearance (~4-5 m) for the operation of agricultural machinery [3]. Nonetheless, elevated modules benefit from free convection and the reduced dust deposition rate. Ultimately, to minimize capital costs and facilitate the operation of most machinery an elevation of 5 m was selected for the following simulations, apart from the study case of blueberries discussed in 4.3 Module sensitivitymicro scale.
To conceptualize how the deployment configuration of the array influences ground and POA irradiationtwo main parameters used to assess the performance of APVa multi-dimensional sensitivity analysis was performed. Generally, light availability on ground was significantly higher for E-W facing topologies; however, the gain with wider RS was lesser (Fig. 5 a and b). In specific, when the RS was doubled, ground irradiation increased from 58.1% to 79.6% for a south facing array with a 35tilt, while for E-W facing and vertical it enhanced from 75.9% to 88.6%. In addition, for a wider RS, sensitivity to module orientationtilt and azimuthgreatly diminished. This is reasonable as with decreasing PV density, the influence of orientation on ground irradiation decays.
The analysis is continued for the POA irradiation on both sides of the bifacial PV module (Fig. 5 c and d). Overall, S-N topologies received a higher amount of POA irradiation, which is mainly attributed to the low ground albedo. A wider RS amplified ground reflected irradiation subsequently increasing POA. This gain was depended on PV module orientation with the tilt angle being dominant. For example, when the RS of a south facing array was doubled it received a boost in POA by 3.1% (10tilt), and 5.6% (50tilt), while for E-W vertical the gain was 9%. Higher tilts become beneficial with increasing RS; consequently, promoting E-W vertical as a viable alternative. Ultimately, this will depend on ground albedo [66,76] and module bifaciality. Tilted modules further benefit since partial shading and masking between rows is mitigated. For topologies facing due south, the tilt that maximized POA was between 30 and 35 , depending on the RS. Nonetheless, optimum tilt was mainly dictated by absorption of the front side, similar to monofacial PV. For both topologies, POA irradiation sensitivity to orientation enhanced as the RS was widened. Nonetheless, the influence of the azimuth angle was not significant, and specifically for vertically installed it was negligible (less than 1% reduction in POA). Therefore, it is intriguing to orient arrays south-west, subsequently allowing increased light penetration for crops in the morning, while providing additional shading in the afternoon. In this way crop productivity is prioritized, without significantly affecting PV performance.
To conceptualize the underlying trade-offs of each APV topology, the RS was extended and its influence on agrivoltaic performance was investigated (Fig. 6). Both topologies followed a similar behaviour; as the RS was widened ground irradiation increased, while electrical yield decreased. Initially, the gain in ground irradiation was abrupt as overlapping ground shadows were resolved. Eventually, it saturated following a logarithmic trend. Likewise, BG also saturated with increasing RS (data not shown). In reverse, energy yield portrayed a negative exponential trend. Essentially, a lower PV density decreases the overall energy yield of the APV farm, yet it maximizes light availability for both PV and crops. Hence, another trade-off arises; a sustainable or synergistic design, and one that exploits the land most effectively in terms of produced energy. However, the latter does not necessarily maximize LER since crop yield is greatly impinged depending on crop shade tolerance.

String sensitivity -Meso scale
Other string arrangements were investigated and compared to the conventional ones discussed previously. From those simulated four were selected (Fig. 7); S-N facing labelled as S1 and S2, and E-W vertical as E1 and E2 for conventional and checkerboard module arrangements, respectively. For S2 and E2 a wider RS was adopted to mitigate partial shading on modules and overlapping shadows on ground. Specifically, for topology E2, module elevation was decreased to 1.5 m, mainly due to the extended RS. Although machinery operating will not be allowed to pass under the array, farming activities can still proceed.
The agrivoltaic performance of each topology was assessed and compared to the conventional and separate production of food and energy (Fig. 8). Overall, annual AC yield was significantly impinged, due to the reduced PV density. Topologies S1 and S2 permitted a relatively higher electricity conversion mainly due to their orientation. In contrast, to facilitate crop growth in winter, E1 and E2 are non-optimal for direct light. This is also reflected on their specific yield (kWh/kWp), which is much lower than that of south facing; nonetheless, E-W vertical bifacial enabled a considerable gain (~13%) in comparison to optimally inclined monofacial PV. Furthermore, such PV configurations led to the lowest ground irradiation reduction. Overall, owing to the decreased PV density a reduction of the initial PV system cost is expected, which is proportionate to the total peak power installed [143].
To further investigate the unique features of each design the underlying shading pattern and schedule, ranging from hourly to monthly timescales, were examined. At first, daily ground irradiation and CV were simulated for one day per month, with May and December being displayed in Fig. 9. For clear days shading intensity and inhomogeneity increased significantly, unlike days with overcast or intermittent sky conditions. This was more apparent in winter, where solar elevation is lower, thus extending the length of shadows and the area of insufficient crop growth as depicted in purple. Nonetheless, due to the frequently intermittent climate of Boston, these inconsistencies averaged out on a larger timescale. This is verified by the cumulative ground irradiation and CV in Fig. 9 (c, f, i, l) for seasonal (mid-March to mid-Oct), and annual cultivation periods. E-W vertical topologies amplified light penetration, especially during the winter months; consequently, they are preferable for the cultivation of permanent crops that are grown throughout the year, while S-N facing are more suitable for summer. The conventional arrangements casted striped patterns; therefore, promoting intercropping and subsequently sustainable agriculture [144]. On  the other hand, the checkerboard layout of topologies S2 and E2 resulted in a patchy shading layout with sharp irradiation gradients; thus, other arrangements should be investigated.
The evaluation of the shading schedule is continued for an hourly timescale (Fig. 10) for three distinct topologies. In south facing arrays the distribution of shade was non-homogeneous, it rather accumulated at a certain region. This effect was intensified during winter solstice. Contrary, E-W vertical topologies resulted in a more uniform distribution of shade. However, as they do not shade at noon, plant productivity is reduced due to the combination of high irradiance and temperature. To alleviate stomata mid-day hydropassive closure, the E-W wings topology is introduced, which offers semi-microclimatic control. Because of its orientation, crops are effectively shaded at noon, while light is distributed homogeneously throughout the day.
Based on these findings, when conventional modules are employed, S-N facing topologies should be used for shade tolerant crops and E-W wings those that necessitate shading at mid-day.

Module sensitivity -Micro scale
Through the previous analysis the limitations of conventional modules, due to their large size and opaqueness, were identified. These include non-homogeneous irradiance distribution (short timescales) and intense shading, thus necessitating reduced PV densities to maintain sufficient crop yields. By designing a customized module, tailored for the cultivation of a certain crop under a specific climate, it is possible to overcome these limitations. In particular, the micro-scale sensitivity was performed to investigate the cultivation of the 'bluecrop' highbush blueberry (Vaccinium corymbosum) under an E-W wings topology ( Fig. 11 (a)). As it is a high value crop, the PV array was installed right above to offer protection against harmful weather conditions and irradiance during noon.

Glass extension
Various cell spacings and arrangements were examined; however, although light uniformity on ground was enhanced the gain in magnitude was not significant.
Therefore, other cover materials were examined such as the prismatic glass SG80 [50] with the given optical properties listed in Table 3. Through its integration, the overall fraction of diffuse light increased significantly, thus softening irradiation gradients, while amplifying ground albedo. As a result, soil evaporation is expected to be reduced. With increasing front cover length, PAR right belowon a horizontal plane and at canopy heightincreased linearly (Fig. 11 (c)). At first glance, this effect might seem counter intuitive. However, since the translucent material was treated by Radiance as a Lambertian scatterer,  the cover's scatter angle was not modelled appropriately. Hence, omitting saturation of transmitted irradiance on crops after a certain front cover extension. Through a trial-and-error process, the necessary extension of the top cover was determined to be 35 cm for each side.

Cell spacing & arrangement
By widening the spacing between cells, additional light is transmitted and converted into diffuse; ultimately, enhancing light interception by the crop. Yet another trade-off arises between energy yield and PAR at canopy height ( Fig. 11 (d)). Analogous to the RS, the relationship between module transparency and irradiance was found to be logarithmic. A similar behaviour was observed for the BG, where an increase in transparency from 7% to 55% led to a boost in BG by 3.8%. Comparable results were found in [65]. In contrast, annual AC yield decreased with a linear slope. Note that the positive influence of decreased cell density on heat dissipation and module efficiency was not Fig. 9. Shading intensity and distribution on ground for the selected topologies. The average ground irradiation for each corresponding period and coefficient of variation (CV) are displayed. The daily irradiation is included for two days; one in May with intermittent to overcast sky conditions, and one in December with clear skies. Note that irradiation was calculated for a horizontal plane close to ground, which is applicable to low-height field crops.
considered. To minimize yield reduction (~17%) of blueberries a module transparency of 38% was used. This value is unique for the E-W wings PV topology, and it refers to the fraction of inactive area within the module, while neglecting the area occupied by the extended front cover. Any additional increase of module transparency would lead to insufficient shading in summer, as well as heavily reduced AC yield.

Agrivoltaic performance
In general, crops are effectively shaded from harmful irradiance without impinging their growth. Simulation results of PAR (at canopy height) during solar noon can be observed in Fig. 12. Irradiance under shade is shown in blue, while the gain under FS conditions is displayed in orange. Irradiance reduction (shading rate) can vary from 20% in overcast up to 65% in clear sky conditions. This is desirable, since during clear days light saturation can occur, thus the shading rate is high. Even under an overcast sky the array permits sufficient light apart from some days in winter. Nevertheless, under such conditions, crops would not be able to attain saturation even in an open field.
Additional performance indicators were calculated (Table 7) for the E-W wings topology. Electrical yield was significantly enhanced (57% higher yield than topology S1). Furthermore, by utilizing a shade tolerant crop and a customised module, denser arrays can be installed. Although in relation to the reference GMPV array AC yield decreased, specific yield amplified owing to the integration of bifacial modules. The PV array's average BG was 15.4% (5-15% for conventional large-scale bifacial systems [62]). The simplified LER was found to be in the  upper range of stationary APV systems [5,57,145] partly due to the moderate reductions in crop yield ratio. Note that the ground cover ratio (GCR) was determined to be 68%; however, by considering the increased cell spacing and glass transparency it was estimated to be 34.1%.

Conclusions
In this study, a series of insights were provided to promote the deployment of bifacial agrivoltaic arrays as they offer various synergistic effects with crop cultivation.
Irradiance homogeneity of PV module rear-side and bifacial gain (BG) were enhanced owing to the increased elevation, row spacing (RS), and customised module transparency. Specifically, as the row or cell spacing were widened, ground and subsequently PV rear-side irradiation amplified in a logarithmic fashion. Contrary, electrical yield reduced; however, this effect was partly mitigated by the augmented specific yield. In addition, deviation in module orientationtilt and azimuthfrom conventional topologies did not significantly diminish the potential of bifacial APV.
The performance and unique features of three main APV topologies were investigated. In comparison to a ground mounted monofacial PV array, specific yield increased by 39%, 18%, and 13% for S-N facing, E-W wings, and E-W vertical bifacial systems, respectively. South facing topologies are preferable for cultivation during summer and necessitate the use of shade tolerant species as they prioritize electricity generation. Contrary, E-W vertical enhanced the distribution and intensity of light, especially during winter; consequently, they are compatible with permanent crops. Finally, the E-W wings topology resulted in the most superior shading schedule and a partially controlled microclimate. Crop and APV topology selection are directly linked, therefore, it is crucial to know the appropriate shading rate and sequence before proceeding with the APV design.
To enhance the rate of photosynthesis under shade, modules were modified to have a wider cell spacing and a diffuse cover. For the cultivation of blueberries, through an E-W wings APV topology, land productivity increased by 50%, whereas energy yield reduced by 33% relative to the conventional and separate production of food and energy.
By conducting an individual assessment per selected bifacial APV array topology, their unique characteristics can be identified. When addressed properly, APV can provide supplementary functions; act as a shading element and offer protection against harmful weather conditions. These, along with the simultaneous and synergistic production of food and renewable energy establish this emerging PV sector as one of the main pillars of the energy transition.