Asymmetric Four-Terminal Solar Concentrator Improving Power Collection in Bifacial Solar Cells

Abstract

The exploitation of bifacial solar cells in photovoltaics aims to provide cost-effective solutions to maximize solar power collection on specific surfaces. A prerequisite for this is the effective collection of backscattered diffuse light from albedo, to which self-shading is an obstacle. We discuss the benefits of bifaciality for an asymmetric low-concentrating and spectral-splitting photovoltaic optics system that features a wedged right-prism geometry to address self-shading. The performance of the conceptual design is analyzed, using commercial ray-tracing software, for four different latitudes of installation, by assuming a standard solar AM1.5G spectrum as input. The daily Relative Optical Power Increase (ROPI) is evaluated with respect to standard flat bifacial configurations, reaching ROPI = 293% at a latitude of 25° north at winter solstice. The photocurrent and total Power Conversion Efficiency (PCE) in a four-terminal (4T) configuration are estimated, assuming the operation of a commercial Si HJT bifacial cell and a commercial single-junction GaAs cell. A global increase in PCE of up to 23% is obtained with respect to the best-performing trackless standard bifacial configuration. From this perspective, the use of high-performance, high-bandgap solar cells in 4T configurations might further leverage the advantages of the optics proposed here.

1. Introduction

At the system level, one of the key ingredients for the cost-effectiveness of photovoltaic (PV) energy conversion resides in the optimized usage of the space available for the installation of solar modules. Limitations in the extent of exploitable soil represent a typical constraint in large, utility-scale plants, as well as in domestic systems. When addressing energy demand in a dense urban context, one approach to tackling land occupation issues involves designing and fabricating building-integrated PV (BIPV) systems [1]. The need to cope with restrictions in terms of the surface available is even stronger in the case of “portable PV” solutions for self-powered devices, vehicles, and vessels, which face intrinsic limitations in dimensions. All of these are possible market sectors for integrated PV (IPV) solutions, which are often customized and specifically tailored to a particular application [2,3,4,5,6,7,8,9,10,11,12,13]. For these purposes, IPV solutions may be quite diverse in terms of the shape, size, optical design, and type of solar cell employed. Also, the stringent constraints in terms of cost that heavily affect the utility-scale market can be somewhat relaxed in this context, to the extent that the PV module itself becomes a design element of the final product, and the customer is willing to pay for this. It is worth noting that, when dealing with IPV solutions, in contrast to utility-scale applications, functionality and esthetics typically coexist thanks to innovative designs, e.g., as discussed by Borja Block A. and co-authors in [2]. Especially when dealing with trackless and stationary outer IPV systems, the installation site, its latitude, and the corresponding sun elevation at noon play crucial roles in defining the proper cell orientation, and ultimately in determining the actual efficiency of the PV system.

At the level of PV module technology, one approach to maximizing solar energy conversion per unit of area is to use bifacial solar cells that collect backscattered radiation from the ground at their rear side [14]. Bifacial silicon-based solar cells are presently the most convenient available technology to maximize the Power Conversion Efficiency (PCE) in a given area [15], defined as PCE = P_out,el/P_in,opt, where P_out,el is the electrical power output of the PV system and P_in,opt is the optical power input. These cells generally increase the PCE by 20% in modules [16]. Non-silicon-based solar cell technologies are also increasingly being confronted with the bifacial paradigm [17]. In a recent review by Mahim M.T. and co-authors, a comparative study between mono- and bifacial approaches was reported, concluding that bifaciality is generally the winning choice, providing higher energy collection at lower costs [18,19].

Bifaciality may also be an added feature in multijunction PV systems that aim to overcome the Shockley–Queisser limit in PCE [20], e.g., as is the case of the four-terminal (4T) dual-junction approach. Classically, the 4T configuration is a tandem architecture made of two stacked cells. The top cell, with a higher bandgap, works in the visible (VIS) spectrum, and the bottom cell works in the near-infrared (NIR) one. Stacked cells have a common shape and are optically, but not electrically, “in series”, with no need for monolithic integration [21,22,23].

An alternative solution to cell stacking is spectral splitting, based on the separation of optical paths for light belonging to different spectral ranges [24]. In this case, the need for a common shape is obsolete, and each solar cell technology can be independently optimized [25,26,27,28]. A recent review of spectral splitting for PV modules, mainly devoted to thermal energy recovery, is provided by Hong W. and coworkers [29]. Hence, in principle, the combination of bifaciality, 4T electrical connection, and spectral splitting can be a winning strategy to improve PCE in PV systems, as some authors also suggest in Refs. [25,28]. In particular, Ref. [25] describes the working principle and potentialities of an asymmetric low-gain optical concentrator, designed as a wedged right-angled prism light guide coupled to dichroic mirrors for spectral splitting. The configuration exploits a Si (silicon) bifacial solar cell and a GaAs (gallium arsenide) cell for the NIR and VIS spectra, respectively. By using a right-angled prism, the spectral splitting function is implemented with minimized land occupation, and the result is a PV tile, which can be employed as the primary element of larger PV modules and is also suitable for integration in both indoor and outdoor systems, like BIPV solar venetian blinds and active sunshades [30,31]. Other IPV applications are also possible if one considers similar optical elements in the shape of micro-facets, as proposed by Cook J. M. and co-authors in [32]. In addition, the peculiar geometry of the optical design in [25] entails counter-intuitive angular orientation conditions of PV cells. In particular, the orientation of the bifacial cell with respect to the ground is different from the typical orientation of standard bifacial solutions [33,34]. This specific orientation is claimed to be advantageous for bifacial operation, in that it is expected to lower the self-shading effect of the module, thus improving the collection of diffused radiation from the ground. When a bifacial PV cell is directly exposed to sunlight, the back of the cell receives light from ground that is in the shade of the cell; meanwhile, with the proposed prism configuration, the back of the Si cell receives light from unshaded ground. In this work, we deepen the numerical study of the bifacial performance of a conceptual design of a photovoltaic system, as introduced in Ref. [25], providing an analytical description of the radiation collection on the back face of the bifacial solar cell, in different possible installation conditions. More specifically, a bifacial solar cell inserted in the 4T spectral splitting geometry is compared in terms of performances with equivalent cells in typical standard orientations for flat modules and a daily Relative Optical Power Increase (ROPI) is defined; the goal is to quantify the increase in diffuse optical power collected on the back face of the cell. The ROPI has been numerically evaluated considering the shading effect, the safety height of the PV elements, the diffusive nature of the terrain, and the installation latitudes of the systems. Numerical modelling is based on a commercial ray tracing software environment (ZEMAX OpticStudio, 22.2 Professional) and the standard solar spectrum ASTM G-173-03 AM1.5G [35] is taken as a general reference. We demonstrate that a certain positive degree of ROPI is always present for bifacial cells mounted in 4T prismatic configuration and that the value is higher for installations at lower latitudes and in winter. The total amount of optical power collected is also studied. In particular, the photocurrent and total PCE were estimated as functions of the installation site and the operating parameters of the solar cells. In the following sections, we show and discuss the possible advantages of the 4T bifacial configuration over the standard flat ones.

2. Methods and Analysis

Table 1. List of symbols.

Symbol	Units	Definition
φ	deg (°)	vertex angle of the optical wedge prism
β	deg (°)	inclination angle
ϕs	deg (°)	sun elevation
ϕs,MAX	deg (°)	sun elevation at noon
ΦN	deg (°)	latitude angle (Northern Hemisphere)
α	deg (°)	orientation of the bifacial cell with respect to the ground
θiL	deg (°)	lower limit for the angle of incidence of sunlight
Voc	volt	open circuit voltage
Isc	ampere	short-circuit current
FF	//	Fill Factor
λ	meter	optical wavelength
ROPI	//	Relative Optical Power Increase
TOP	Watt	Total Optical Power
PCE	//	Power Conversion Efficiency
RPI	//	Relative Power Increase (electrical)

lists the symbols used in the text. The conceptual system under consideration is described in Figure 1. The optical core is an orthogonal, dielectric transparent triangular wedge prism with vertex angle φ. Its longer cathetus is the top surface. A bifacial cell (grey in Figure 1) is optically coupled to the bottom side of the prism (hypotenuse) and operates in the NIR spectrum. A high-bandgap solar cell (orange in Figure 1) for the VIS spectrum is coupled to the backside of the prism (shorter cathetus). The prism vertex angle, φ < 45°, defines a geometric concentration gain, G_geom = (A_VIS-cell⁄A_top) > 1, where A_VIS-cell is the area of the VIS cell on the back side of the prism and A_top is the area of the entrance surface at the top. Since G_geom only concerns the VIS spectral region, the concentrator is labeled as “asymmetric”. Light concentration and spectral splitting are performed through total internal reflection (TIR) at the upper glass–air interface and via two complementary dichroic mirrors. A NIR transmitting mirror is placed before the bifacial cell and a VIS transmitting mirror is placed before the high-bandgap cell. The optical performance of the system in direct sunlight has already been analyzed in Ref. [25]. Optical efficiency values reaching 88% and above 80% are demonstrated over an incident angular range of approximately 50°.

The orientation of the prism in the field is quantified by the inclination angle, β. The values of β are set such that the TIR at the upper interface is guaranteed for direct sunlight at all sun elevation values, ϕ_s, up to the noon value at the specific installation site, ϕ_s,MAX. In order to highlight the role played by the site latitude, ϕ, simulations were performed for four different possible locations in the Northern Hemisphere: Dublin, Ireland (ϕ_N = 53°20′ N); Milan, Italy (ϕ_N = 45°28′ N); Catania, Italy (ϕ_N = 37°30′ N); Miami, USA (ϕ_N = 25°46′ N).

In

Table 2. Summary of the sun elevation at the summer solstice of June 21st at four different latitudes (53°20′ N—Dublin, Ireland; 45°28′ N—Milan, Italy; 37°30′ N—Catania, Italy; 25°46′ N—Miami, USA), from a database available online [36]; the corresponding orientation of the bifacial solar cell in the 4T configuration is provided.

Latitude—Town	Sun Elevation (°)	Orientation of 4T Bifacial Solar Cell α (°)
53°20′ N—Dublin	60	−5.47
45°28′ N—Milan	68	−13.47
37°30′ N—Catania	76	−21.47
25°46′ N—Miami	88	−33.47

, the locations are listed in the first column and indexed with i = 1:4. In the second column, the corresponding values of ϕⁱ_s,MAX are shown, referring to the day of the summer solstice. The data come from a database available online: www.sunearthtools.com [36]. The third column reports the corresponding orientation angles of the bifacial solar cell in 4T configuration with respect to the ground αⁱ = 90° − (ϕⁱ_s,MAX + φ + β).

For TIR to occur, the angle of incidence, θ_i, of sunlight on the top surface must exceed a limiting value, θ_iL, that depends on the prism vertex angle, φ, and the refractive index, n, of the dielectric material composing the prism [25]. In turn, φ sets the value for β, where negative β values correspond to north-facing orientations that can occur at ϕ_N < 45° installation sites [25]. Such orientations seem rather strange; however, it is precisely this condition that improves the albedo collection, as is detailed below. Initially, the same wedge geometry as reported in [25] is considered, with vertex angle φ = 14.47° and n = 1.5, leading to θ_iL = 21°. The 4T configuration is considered to work using a bifacial Si HJT (Silicon Heterojunction Technology) cell from 3Sun Enel-GP S.p.A. [37] and a monofacial GaAs (gallium arsenide) reference cell from ReRa Solutions B.V. [38]. The bifacial cell on the bottom side of the prism is a rectangle of 80 mm × 20 mm. The high-bandgap cell measures 20 mm × 20 mm and is optically coupled to the back side of the prism.

The solar cell performance is simulated by a non-sequential numerical model using a commercial 3D ray tracing software (ZEMAX OpticStudio, 22.2 Professional). Data post-processing was performed in the MATLAB (R2019a) environment. Solar irradiation from above is simulated by a direct light source and a uniform diffusion surface represents the ground illuminating the back side of the Si cell. The analysis process is described in detail in Appendix A, Appendix B, Appendix C and Appendix D.

This work starts by comparing the backscattered light collected on the back side of bifacial cells, of equal shape and clearance height, h [39], oriented according to the 4T configuration and according to the standard flat configurations. Specifically, the three standard flat configurations analyzed are horizontal (i.e., parallel to the ground), vertical (i.e., perpendicular to the ground), and normal (i.e., perpendicular to the incoming direct sunlight at midday). The values of the backscattered optical power collected on the back side of the bifacial cell in the 4T and standard configurations are, respectively, denoted by P_4T and P_st, and they depend on the sun elevation and the orientation of the solar cell. The ROPI of the 4T configuration compared to the standard configuration can therefore be defined as follows:

$$\mathrm{R}\mathrm{O}\mathrm{P}\mathrm{I}={\displaystyle \frac{\left({\mathrm{P}}_{4\mathrm{T}}-{\mathrm{P}}_{\mathrm{s}\mathrm{t}}\right)}{{\mathrm{P}}_{\mathrm{s}\mathrm{t}}}}$$

(1)

By integrating P_4T and P_st as functions of ϕ_s throughout the day, it is possible to calculate and study the daily ROPI under different possible operating conditions. The final purpose is to evaluate the benefit that ROPI brings to the overall optical power collected by the PV system and, finally, to perform an overall evaluation of the PCE.

Furthermore, a comparison of the Total Optical Power (TOP) collected by the different bifacial configurations at the four latitudes has been calculated using the ZEMAX software. In the standard flat cases this corresponds to the integration of the optical power collected on both the front and back sides of the bifacial cell over the AM1.5G solar spectrum, summing the direct irradiance and the albedo irradiance. In the 4T configuration, the contribution of the albedo irradiance on the back side of the bifacial cell is added to the contribution of the direct illumination coming from the top surface of the prism, collected separately by the VIS and NIR solar cells. Dichroic mirrors with a cut-off wavelength at λ = 805 nm are considered. Indeed, referring to the External Quantum Efficiency (EQE) curves of the two solar cells considered [29], a wavelength of 805 nm represents the crossover point between the EQE of the Si HJT bifacial cell and the EQE of the GaAs cell, with the EQE for the Si cell being higher than that for the GaAs cell at longer wavelengths.

By orienting the PV system to the midday of the summer solstice, the TOP was evaluated for all latitudes as a function of the solar elevation, ϕ_s. In the Dublin and Miami reference cases, the TOP was also evaluated by orienting the PV system according to the equinox noon, and the role of the vertex angle, φ, was explored. A comparison is made between the TOP values evaluated for a bifacial cell with standard flat normal orientation, for a bifacial cell oriented in 4T configuration with φ = 14.47°, with φ = 30°, and in the absence of wedge optics (φ = 0°). The following considerations are assumed to be valid for an azimuthal angle γ = 0°, i.e., in the presence of an azimuthal tracking system. By varying γ, i.e., under non-sagittal illumination, the only effect is a decrease in the incoming solar flux proportional to cos(γ); meanwhile, it has been shown that the functioning of light-guiding optics on sagittal and non-sagittal/oblique rays is equivalent [25].

The PCE was estimated by assuming the electrical parameters of the cells as per the datasheet, namely V_oc,HJT = 0.73 V, FF_HJT = 0.8, bifaciality factor = 90%, V_oc,GaAs = 1.019 V, FF_GaA = 0.82, and considering the spectral EQE of a Si HJT cell and the EQE of a GaAs cell, respectively. The input photon flux was calculated by sorting the spectrally resolved TOP by photon energy. Then, after multiplying by the EQE values and the electron charge and after spectral integration, the ideal photocurrent output per unit time is obtained, which represents the short-circuit current of the solar cells (I_sc). The electrical output power, P_out,el = I_sc ∙V_oc ∙FF, is estimated independently for the two cells and summed to obtain the total P_out,el (TP_out,el). The reference locations of maximum and minimum latitude, Dublin and Miami, were considered, and TP_out,el at noon was calculated on the days of the equinox and the summer solstice. Moreover, to exemplify the overall advantage of adopting a 4T configuration with φ = 30° compared to the normal one, the values of TP_out,el at midday of the summer and winter solstices were calculated in the case of equinox orientation, only for the Miami site.

3. Results and Discussion

3.1. Albedo Collection of Bifacial Cells

A comparative analysis of the optical performance of bifacial cells oriented according to the 4T configurations, horizontal, vertical, and normal, is presented for the four different installation sites, identified by i, from 1 to 4. Figure 2, panels (a)–(d), show the optical intensity collected on the back side, oriented according to the local value ϕⁱ_s,MAX, as ϕ_s increases up to ϕⁱ_s,MAX at the summer solstice. The 4T configuration is the one with the most northerly orientation.

All simulations were performed at a clearance height of h = 160 mm. More details on the calculation performed to define the clearance height are included in Appendix B and the results are shown in Figure A2. It can be noted that the effective domain of the existence of the curves is limited to the value of ϕⁱ_s,MAX, reached at the summer solstice at each specific latitude. Examining Figure 2, it can also be noted that the 4T configuration performs better than the horizontal and normal configurations at lower latitudes. Furthermore, low values of ϕ_s, i.e., close to sunrise and sunset during the day, represent conditions for a more favorable albedo collection from the back side. In general, a variation in ϕ_s corresponds to a variation in the self-shadowing pattern of the ground-based PV element, which influences the amount of backscattered light collected. Actually, according to the values of β and φ, at lower installation latitudes and at grazing irradiation angles, ϕ_s, the back side of the bifacial cell in the 4T configuration exits the self-shadowing pattern for a whole range of elevation angles, 0 < ϕ_s < (φ−β), with β < φ and φ > 0 (see Figure 1).

The albedo collection improvement obtained from the 4T orientation is quantified by evaluating the ROPI as a function of ϕ_s. Daily ROPI values can be obtained by summing the daily angular excursion, 0 < ϕ_s < ${\mathrm{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i},\mathrm{j}}$, at the four locations and on the dates of the equinoxes and summer/winter solstices (i.e., September 21st, June 21st, and December 21st, indexed by j = 1,2,3). For clarity, the values of ${\mathrm{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i},\mathrm{j}}$ at location i and day j are summarized in

Table 3. Summary of the values of the sun’s elevation at noon on three different days (June 21st, September 21st, and December 21st) at four latitudes (53°20′ N—Dublin, Ireland; 45°28′ N—Milan, Italy; 37°30′ N—Catania, Italy; 25°46′ N—Miami, USA) (from the database available online [36]).

Latitude—Town	Sun Elevation at Noon ${\mathsf{\phi }}_{\mathbf{s},\mathbf{M}\mathbf{A}\mathbf{X}}$ (°)
	Jun 21st	Sep 21st	Dec 21st
53°20′ N—Dublin	60	37	13
45°28′ N—Milan	68	45	21
37°30′ N—Catania	76	53	29
25°46′ N—Miami	88	66	41

.

The results are reported in

Table 4. Summary of the daily percentage Relative Optical Power Increase (ROPI) comparing the 4T configuration with the standard flat horizontal configuration (i.e., parallel to the ground) at four latitudes and for three different dates (summer solstice, equinoxes, and winter solstice). The values reported are integrated over the entire day (June 21st, September 21st, December 21st).

Latitude—Town	ROPIHorizontal (%)
	Jun 21st	Sep 21st	Dec 21st
53°20′ N—Dublin	19	4	29
45°28′ N—Milan	4	11	53
37°30′ N—Catania	8	19	66
25°46′ N—Miami	12	25	75

,

Table 5. Summary of the daily percentage Relative Optical Power Increase (ROPI) comparing the 4T configuration with the standard flat vertical configuration (i.e., perpendicular to the ground) at four latitudes and on three different dates (summer solstice, equinoxes, and winter solstice). The values reported are integrated over the entire day (June 21st, September 21st, December 21st).

Latitude—Town	ROPIVertical (%)
	Jun 21st	Sep 21st	Dec 21st
53°20′ N—Dublin	128	134	186
45°28′ N—Milan	133	150	239
37°30′ N—Catania	141	167	270
25°46′ N—Miami	149	180	293

and

Table 6. Summary of the daily percentage Relative Optical Power Increase (ROPI) comparing the 4T configuration with the standard flat normal configuration (i.e., perpendicular to the incoming solar rays at noon) at four latitudes and on three different dates (summer solstice, equinoxes, and winter solstice). The values reported are integrated over the entire day (June 21st, September 21st, December 21st).

Latitude—Town	ROPI Normal (%)
	Jun 21st	Sep 21st	Dec 21st
53°20′ N—Dublin	13	15	40
45°28′ N—Milan	11	18	61
37°30′ N—Catania	11	22	70
25°46′ N—Miami	12	25	75

, which quantitatively confirm the significant bifacial advantage of the 4T orientation compared to the standard configurations. The daily ROPI is always greater than one, due to the reduced self-shadowing effect in the 4T configurations. Moreover, comparing the values calculated on the same day, an increasing trend is evident as the ϕ_N angles decrease. This is also qualitatively evident by directly observing the curves in Figure 2. Actually, as ϕ_N increases, the upper surface of the PV element is increasingly oriented towards the south, and the 4T configuration increasingly resembles the normal one, the advantage of which becomes less significant. In each selected installation site, the highest daily ROPI values are achieved under typical winter grazing irradiance conditions. Considering the overall results shown in Table 4, Table 5 and Table 6, this trend is evident. The Miami site installation in winter shows the highest daily ROPI values: ROPI_Horizontal = 75%, ROPI_Vertical = 293%, and ROPI_Normal = 75%, with the horizontal and normal orientations almost coinciding. This suggests that the 4T configuration potentially outperforms standard flat configurations, increasing the efficiency of bifacial cells in typical disadvantageous conditions.

3.2. Total Optical Power Collection

The data described in the previous sections refer to improvements in optical power collection on the back side of the bifacial cell. A more general comparison is needed by summing the Total Optical Power (TOP) collected on both the front and back sides of the PV system. In the 4T configuration the TOP collected is equal to the sum of the optical power collected by two different detectors: the front side of the GaAs cell and both the front and the back sides of the bifacial cell. Differently, in the standard configurations, the TOP collected is provided only by the Si bifacial cell.

The TOP values evaluated at different latitudes are shown in Figure 3a–d, calculated over the daily angular excursion of the sun’s elevation $0<{\mathsf{\varphi }}_{\mathrm{s}}<{\mathsf{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i}}$ for PV systems oriented according to ${\mathsf{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i},\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{e}}$. The significant advantage in optical collection on the back side of the bifacial cell of the 4T configuration compared to the standard configuration, as shown in Figure 2 and ROPI Table 4, Table 5 and Table 6, is here compensated by a less efficient collection on the front side. In fact, for the vertical configuration, the TOP is independent of ϕ_N and outperforms the 4T configuration up to ϕ_s = 34.5°. This winning performance is here easily understood in terms of both direct radiation collection and albedo on the front side.

To better understand the dependence of the Total Optical Power (TOP) on the orientation of the PV system, a comparison between the conditions of ${\mathsf{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i},\mathrm{s}\mathrm{u}\mathrm{m}\mathrm{m}\mathrm{e}\mathrm{r}\mathrm{s}\mathrm{o}\mathrm{l}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{c}\mathrm{e}}$ and ${\mathsf{\varphi }}_{\mathrm{s},\mathrm{M}\mathrm{A}\mathrm{X}}^{\mathrm{i},\mathrm{e}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{n}\mathrm{o}\mathrm{x}}$ was performed choosing Dublin and Miami as the two reference sites of maximum and minimum latitude, ϕ_N. The curves are plotted in Figure 4a,b for the Dublin case and in Figure 5a,b for the Miami case. Panels (a.1,b.1) provide sketches of the orientation variations for the 4T and normal configurations resulting from the solstice vs. equinox choice. As a result, TOP variations occur, although there is no clear improvement over the standard vertical configuration for ϕ_s < 34.5°.

Conversely, at higher values of ϕ_s, the TOP collection with normal orientation is always the best.

A further test concerns the role of the vertex angle, φ. To this purpose, once again, the representative sites of Dublin and Miami were selected for a comparison between solstice and equinox. In the present case, the normal configuration is compared with a 4T configuration with φ = 14.47°, with a 4T configuration with φ = 30°, and with a standard flat configuration where the bifacial cell shares the same orientation as the 4T configuration, but in the absence of the wedge prism. The value φ = 30° is chosen because it falls within the range that guarantees the condition for θ_iL = 0. The TOP, as a function of ϕ_s, is reported in Figure 6a,b for the Dublin case and in Figure 7a,b for the Miami case. Examining Figure 6 and Figure 7, it can be observed that, ceteris paribus, the removal of the spectral splitting optics is detrimental to the TOP collection. Conversely, an increase in φ improves the TOP collection and this is even more evident at the summer solstice. In any case, the normal configuration remains the preferred one in terms of optical collection efficiency.

3.3. Electrical Performance and PCE

However, it is necessary to specify that the results shown and discussed so far do not take into account the most qualifying aspect that distinguishes the operation of 4T PV systems, namely the use of solar cells with separate electrical collection in the NIR and VIS spectra. Specifically, the exploitation of high bandgap cells in the VIS band guarantees higher V_oc values for the same photocurrent, so an improvement in optical efficiency is not a necessary condition to obtain a better PCE (Power Conversion Efficiency).

Therefore, it has been verified that there is an actual advantage in choosing the 4T configuration compared to the standard configurations. To increase the total TP_out,el at the same optical input power, P_in,opt, the figure of merit Relative Power Increase (RPI) is defined as follows:

$$\mathrm{R}\mathrm{P}\mathrm{I}={\displaystyle \frac{\left({\mathrm{T}\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{l}-4\mathrm{T}}-{\mathrm{T}\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{l}-\mathrm{s}\mathrm{t}}\right)}{{\mathrm{T}\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{l}-\mathrm{s}\mathrm{t}}}}$$

(2)

In Equation (2), ${\mathrm{T}\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{l}-4\mathrm{T}}$ and ${\mathrm{T}\mathrm{P}}_{\mathrm{o}\mathrm{u}\mathrm{t},\mathrm{e}\mathrm{l}-\mathrm{s}\mathrm{t}}$ are the total electrical power evaluated in the 4T and standard flat configurations, respectively.

Table 7. Summary of ideal photocurrents on each cell and electrical output power in Dublin during the summer solstice at noon for each configuration (4T without prism; 4T with 14.47° vertex angle; 4T with 30° vertex angle; normal; vertical) at a constant area of input illumination.

53°20′ N—Dublin at the Summer Solstice (at Noon–${\mathsf{\varphi }}_{\mathbf{s}}$ = 60°)
Configuration	Photocurrent (A) Collected on the Cell Side			Total Pout,el (W)
	GaAs	Si Front	Si Back
4T without prism	-	0.49	0.42	0.53
4T with 14.47° vertex angle	0.32	0.29	0.49	0.72
4T with 30° vertex angle	0.36	0.30	0.50	0.77
Normal	-	0.72	0.44	0.68
Vertical	-	0.21	0.53	0.43

and

Table 8. Summary of ideal photocurrent on each cell and electrical output power in Miami during the equinox at noon for each configuration (4T without prism; 4T with 14.47° vertex angle; 4T with 30° vertex angle; normal; vertical) at a constant area of input illumination.

25°46′ N—Miami at the Equinox (at Noon–${\mathsf{\varphi }}_{\mathbf{s}}$ = 66°)
Configuration	Photocurrent (A) Collected on the Cell Side			Total Pout,el (W)
	GaAs	Si Front	Si Back
4T without prism	-	0.57	0.49	0.62
4T with 14.47° vertex angle	0.32	0.29	0.51	0.73
4T with 30° vertex angle	0.36	0.31	0.57	0.81
Normal	-	0.72	0.47	0.69
Vertical	-	0.48	0.23	0.41

report the TP_out,el values collected for the different configurations at midday during the summer solstice in Dublin and at the equinox in Miami, respectively. In these two cases, the orientation of the PV systems coincides with the collection conditions (i.e., orientation and collection both based on the equinox/solstice noon). The normal and vertical configurations are compared with the 4T configuration (φ = 0°, φ = 14.47° and φ = 30°) and the ideal photocurrent values for each cell are shown. The normal configuration shows a higher TP_out,el than the vertical configuration. In turn, the 4T configuration (φ > 0°) shows better performance than the normal configuration. The highest values are obtained at the Miami site, with an RPI = 6% for φ = 14.47° and RPI = 16% for φ = 30°. The worst-performing cases of equinox at the Dublin site and solstice at the Miami site are reported in Appendix E (

Table A1. Summary of photocurrent at each detector and output electrical power in Dublin during the equinox at noon for each configuration (4T without prism; 4T with 14.47° vertex angle; 4T with 30° vertex angle; normal; vertical) at constant area of input illumination.

53°20′ N—Dublin at the Equinox (at Noon–ϕs = 37°)
Configuration	Photocurrent (A) Collected on the Cell Side			Total Pout,el (W)
	GaAs	Si Front	Si Back
4T without prism	-	0.57	0.31	0.52
4T with 14.47° vertex angle	0.25	0.23	0.34	0.54
4T with 30° vertex angle	0.36	0.31	0.37	0.39
Normal	-	0.75	0.25	0.58
Vertical	-	0.70	0.15	0.49

and

Table A2. Summary of photocurrent at each detector and output electrical power in Miami during the summer solstice at noon for each configuration (4T without prism; 4T with 14.47° vertex angle; 4T with 30° vertex angle; normal; vertical) at constant area of input illumination.

25°46′ N—Miami at the Summer Solstice (at Noon–ϕs = 88°)
Configuration	Photocurrent (A) Collected on the Cell Side			Total Pout,el (W)
	GaAs	Si Front	Si Back
4T without prism	-	0.60	0.49	0.63
4T with 14.47° vertex angle	0.33	0.29	0.51	0.74
4T with 30° vertex angle	0.36	0.30	0.58	0.82
Normal	-	0.71	0.55	0.74
Vertical	-	0.72	0.47	0.69

).

RPI variations at the Miami site were further investigated for the cases of 4T (φ = 30°) and normal configurations, since the PV systems are oriented to the equinox and the optical power is harvested at noon during the winter and summer solstices.

Table 9. Summary of the output power for the 4T configuration with 30° vertex angle and fixed-orientation normal configurations at equinox in Miami. Output power at constant input illumination area is collected during equinox and summer and winter solstices, respectively. The Relative Power Increase (RPI) is reported in the last row.

25°46′ N—Miami (Equinox Orientation)
Configuration	TPout,el Collection (W)
	Equinox	Summer Solstice	Winter Solstice
4T with 30° vertex angle	0.81	0.83	0.66
Normal	0.69	0.69	0.57
Relative Power Increase	16%	20%	16%

reports the values of TP_out,el and RPI, which exceed 16% throughout the year. These results suggest that a stationary equinox orientation can be considered at the Miami site. Different orientations may be more profitable at different installation sites. For completeness, a comparison of the PCE at noon for the normal and 4T configurations with a vertex angle of φ = 30° in Miami maintaining the equinox orientation has been calculated for the illumination conditions at the equinox and at the summer and winter solstices.

Table 10. Summary of noon PCE values for 4T configuration with 30° vertex angle and fixed-orientation normal configurations at equinox in Miami. PCE values are calculated at a constant input illumination area for data collection during equinox and summer and winter solstice, respectively. The relative increase in PCE at noon is reported in the bottom row.

25°46′ N—Miami (Equinox Orientation)
PCE (%) at Noon	Equinox	Summer Solstice	Winter Solstice
4T φ = 30°	30	32	27
Normal	26	27	22
Relative Increase in PCE	15%	18%	23%

reports the power conversion values for the same input illumination area. The last row shows the relative increase values of the PCE, which reaches a maximum of 23% at the winter solstice, thus confirming the advantage of the 4T configuration even in the case of fixed installation.

4. Conclusions

The performances of a conceptual design of a four-terminal bifacial photovoltaic system (4T PV system) were evaluated using numerical analysis and compared with typical standard flat configurations. The comparison was performed at different possible installation sites and allowing azimuthal sun tracking. The 4T system uses low-concentration, spectrally splitting optics in the shape of a right-wedge prism, which promotes albedo collection while reducing self-shadowing, and it couples a Si HJT bifacial cell to a single-junction GaAs cell. Silicon HJT bifacial cells were also considered for standard flat configurations. A perfect optical coupling between the spectral splitting concentrator and the solar cells is assumed. The datasheet values for V_oc and FF of the solar cells are considered as input parameters. A standard AM1.5G solar spectrum, with an albedo coefficient of 0.8, is considered as the input.

The 4T and standard configurations have been evaluated against each other by defining the Relative Optical Power Increase (ROPI) for albedo collection and the Relative Power Increase (RPI) for the total electrical output power. The 4T configuration offers better performance than the standard flat configuration for lower-latitude installations. ROPI values up to 293% and RPI values up to 20% can be obtained at a latitude of ϕ_N = 25°46′ N (Miami, FL, USA). Considering the estimated Power Conversion Efficiency (PCE), a relative increase of 23% is calculated for the Miami site at the winter solstice for the 4T configuration compared to the normal flat configuration. The results presented here suggest that, although azimuthal sun tracking remains advantageous, it is possible to maintain a stationary orientation of the 4T system throughout the year. This choice is economically attractive and could offset the expected cost increases due to the increased manufacturing complexity. Looking ahead, a thorough estimation of the Levelized Cost of Energy for the 4T PV system at specific installation sites is recommended. Overall, the proposed design could be profitably exploited as a small-sized and versatile “tile” in bifacial integrated photovoltaic systems, provided that the 4T approach is a resource to exploit reliable, cost-effective, and high-efficiency solar cells for the visible spectrum. This study is preliminary to the implementation of a prototype to be tested in an outdoor environment.