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Impact of torque tube reflection on bifacial photovoltaic single axis tracked system performance

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Abstract

Among the racking elements of bifacial photovoltaic (PV) single-axis tracked systems, the torque tube (TT) introduces the most shading and reflection, increasing irradiance nonuniformity and electrical mismatch loss. We simulate the impact of TT shading and reflection on the irradiance profiles, electrical mismatch, and energy yield for central bifacial PV modules on one-in-portrait (1P) and two-in-portrait (2P) single-axis trackers. TT reflection increases annual irradiance in 1P and 2P systems by 0.17% and 0.30%, respectively. Overall, TT reflection increases the predicted instantaneous energy yield by up to 0.8% and 0.4%, and the annual energy yield by 0.11% and 0.18% in 1P and 2P systems, respectively.

© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Bifacial photovoltaic (PV) modules have greater energy yield than traditional monofacial modules due to their ability to convert both front and rear irradiance to electrical energy. Single-axis tracking systems can further increase yield and reduce the levelized cost of energy [1] by rotating the modules throughout the day to maximize the illuminated cross-sectional area, reducing cosine and angle of incidence (AOI) losses [2]. PV modules are subject to power loss caused by electrical mismatch from varying cell maximum power points due to manufacturing tolerances, temperature gradients, and irradiance nonuniformity stemming from many factors including object shading, passing clouds, soiling, and proximity to the ground [36]. Racking elements in single-axis tracking systems introduce both shade and reflections on the rear face, increasing rear irradiance nonuniformity and causing electrical mismatch that reduces module power [7]. These effects lead to decreased bifacial energy yield gain and can create damaging hot spots in extreme cases [8]. The effects of racking, particularly from the torque tube (TT) as it spans the middle of the rear collector surface, must be accurately quantified in energy yield predictions to further reduce investor risk, increase stakeholder confidence, and hasten the adoption of tracked bifacial PV [9].

Existing field-validated ray tracing bifacial PV modeling software like bifacial_radiance [1012] and others [1317] can capture both shading and reflections from racking elements at a high computational cost by simulating many stochastic rays interacting with multiple textured surfaces. On the other hand, two-dimensional (2D) [1826] and three-dimensional (3D) view factor models [2731] estimate racking shading with user-defined loss factors, known as shading factors, which can be set as annual average values calculated by comparing PV performance with and without racking [2225], or account for racking shading using simulations of instantaneous ray-object intersection [26]. Finally, hybrid modeling approaches employ a view factor method for the front irradiance while capturing the impacts of racking with ray tracing for the rear irradiance only [32]. Comparisons of PV modeling software have been shown previously in Refs. [33,34]. One possible enhancement of 3D view factor models with detailed shading accounted for using ray-object intersection is the inclusion of reflections from racking elements, specifically the TT. However, the isolated impact of racking reflections on PV performance is not well documented.

McIntosh et al. showed that the relative reduction in module power due to nonuniform illumination, including racking shading, is greatest at solar noon in sunny conditions, and greater for one-in-portrait (1P) than two-in-portrait (2P) single-axis tracker frameless modules, decreasing central module yield by 0.23% and 0.09% respectively [7]. However, the racking reflection’s contribution was not isolated. Deline et al. found annual mismatch losses of less than 0.5% for 1P single-axis tracked systems [4]. Guerrero Pérez et al. showed, for a sunny summer day, the rear insolation in a 2P single-axis tracker decreased by 12% with an absorptive TT but only 1.3% with a reflective TT [35]. Our previous work extended this to compare the impact of TT reflection in both 1P and 2P trackers. We showed that including a reflective TT surface rather than a fully absorptive surface increased annual rear insolation by 3% and 5.5% for modules on 1P and 2P single-axis trackers, respectively [36]. However, the impact of racking reflection on energy yield was not reported.

In this work, we quantify the impact of TT reflection on irradiance, electrical mismatch, and total energy yield based on sun position and sky condition using a hybrid modeling approach with a ray tracing model, bifacial_radiance [1012] to extract the TT reflection. We introduce this reflection as an additional irradiance source in DUET [31], a 3D view factor model with detailed shading, to assess the impact of TT reflection in such a model. Using DUET, we can also include and quantify the impact of an incidence angle modifier (IAM) on the TT reflection’s contribution to energy yield. Isolating the TT reflection and accounting for angle of incidence losses was not possible with either simulation method alone, thus bifacial_radiance and DUET are appropriate for this work. First, we will describe the model and the system configuration of the modeled PV arrays. Next, we will discuss the integration of TT-reflected light from bifacial_radiance into DUET. Finally, we will present the impact of TT reflection.

2. Simulation method

2.1 Site description

We modeled a 2P array after the Bifacial Tracker Evaluation Center (BiTEC) site in Livermore, California, USA (37.70° N, 121.82° W, 121 m elevation), and a comparable 1P array [35]. The 1P (and 2P) array included 5 rows of 23 (pairs of) modules in horizontal single-axis tracking configuration with north-south alignment of the TT, and a ground cover ratio of 0.456 (Fig. 1(a) and (b)). The modeled ground albedo is 0.2, emulating the flat terrain at the BiTEC site [35], and is assumed to be spectrally flat. Locations with higher albedo will show increased energy yield [37].

 figure: Fig. 1.

Fig. 1. Center 3 of 5 rows in the (a) 1P and (b) 2P arrays with the collector under test highlighted in dark blue. Frame and purlins modeled on the (c) 1P and (d) 2P rear side of collector under test with the TT spanning the row under test. Portrait configuration means the modules’ long sides are oriented perpendicular to the torque tube.

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Modeling parameters (see Table 2 in Appendix A) emulate a Soltec SF7 2P tracker and a comparable 1P configuration, each with a round TT. The TT diameter is 0.1 m and 0.21 m in the 1P and 2P system, respectively, making the ratio of the TT diameter to the row width identical when including the 0.15 m gap between the east and west modules in the 2P system. The collector tilt angle follows sun position and is calculated by pvlib’s tracking algorithm [38], with a maximum tracking angle of ±60° and backtracking enabled to avoid row-to-row shading.

The module’s geometrical and electrical properties emulate the 460 W Jinko Solar Tiger Bifacial JKM460M-7R13-TV module [39], which includes two parallel strings of 13 × 2 half-cut cells connected to each of its three bypass diodes. The module frame spans the module edges, with side lengths of 1.032 m and 2.205 m, a thickness of 0.03 m perpendicular to the module face, and an overhang of 0.01 m below the rear of the module.

Purlins connect the module frame and the TT, running perpendicular to the TT. The purlins are 0.08 m tall between the TT and the frame, 0.03 m wide, bridging the gap between modules along the row, and 0.44 m and 2.8 m long for the 1P and 2P configurations, respectively. Frames and purlins were included in the model only for the collector under test (Fig. 1(c) and (d)) which is the module in the center of the array in the 1P system, and the east and west module pair in the center of the array in the 2P system. Unless otherwise stated, the collector values reported for the 2P system are taken as an average of the east and west central module values. The TT was modeled on the center row, spanning the length of the entire row. Piles were not included in the array geometry to allow these single-collector results to be interpreted more generally. The reflectivity of all racking components (frame, purlins, TT) was set to 0.745, with a specularity of 0.9 and roughness of 0.2, emulating the racking materials at the BiTEC site [35].

2.2 Software description and implementation

Using hourly typical meteorological year (TMY) data from the United States (US) National Solar Radiation Database (NSRDB) [40], we calculated the irradiance and electrical performance for the central collector of both the 1P and 2P systems. First, the systems were modeled with bifacial_radiance [1012] (version 0.3.4), an open-source software by the US National Renewable Energy Laboratory (NREL), built around the open-source ray tracing software RADIANCE [41]. To isolate the impact of racking reflections, frames and purlins were added to the collector under test in bifacial_radiance and were rotated with the tracker as it tracked the sun throughout the day. In this work, the irradiance of the collector under test was sampled in a 2D array of 52 × 24 sample points, $i$, per module face. This sampling resolution on the 26 × 6 half-cut cell module allows for 2 × 4 equally spaced sample points per cell. This high resolution captures the nonuniform irradiance profile near the module edges and racking elements.

We used bifacial_radiance to isolate the TT-reflected light incident on the collector under test, henceforth referred to as the TT reflection. The PV systems were simulated twice using bifacial_radiance: once with a fully absorptive TT surface (reflectivity of 0); and again with the reflective TT surface. The frame and purlins were reflective for all cases simulated in bifacial_radiance. The TT reflection, ${G_{\textrm{TT}}}$, was calculated for each sample point, $i$, and for each timestamp, $t$, using

$${G_{\textrm{T}{\textrm{T}_{i,t}}}} = {G_{\textrm{TT}{\textrm{A}_{i,t}}}} - {G_{\textrm{TT}{\textrm{R}_{i,t}}}}$$
where ${G_{\textrm{TTA}}}$ is the rear irradiance with the absorptive TT and ${G_{\textrm{TTR}}}$ is the rear irradiance with the reflective TT.

Next, we modeled the PV systems with DUET, our 3D view factor model with detailed shading and an integrated electrical model created by the SUNLAB at the University of Ottawa [31]. In DUET, we simulated the PV array with and without the TT reflection imported from bifacial_radiance to quantify its impact on irradiance, electrical mismatch, and overall energy yield. The sun position and collector tilt angle were set in DUET to be identical to the bifacial_radiance values, as determined by pvlib, at each timestamp. The baseline DUET case includes a fully absorptive TT, absorptive frames, and absorptive purlins. The TT reflection, as calculated in bifacial_radiance, is added to the baseline DUET case for the reflective TT scenario, and nothing is added to the baseline DUET case for the absorptive TT scenario.

Since the TT is not modeled as a reflecting surface in DUET, the TT reflection, as calculated in bifacial_radiance, is added to each sample point on the collector as an additional irradiance source. Due to the TT’s proximity to the collector, the TT reflection typically has a high AOI. Glass, encapsulant, and Si layers of the module were not modeled in bifacial_radiance, so the computed irradiance represents only the total irradiance incident at each sample point on the module surface. To estimate the AOI, we assumed reflections to be uniformly distributed across the TT. An average IAM for each collector sample point was then determined for the array geometry, accounting for frame shading. This 2D effective irradiance profile from the TT reflection was then added to the IAM-corrected rear illumination profiles for sky and ground-reflected light within the electrical calculations in DUET (Appendix B).

3. Results and discussion

Of all racking elements, the TT provides the greatest change in total irradiance and irradiance profile due to reflections [42], with the greatest impact near the TT. In the 2P system, front-incident direct and diffuse light can pass through the TT gap to reflect off the TT and onto the rear face of the collector, increasing rear side irradiance. Conversely, in 1P systems, direct irradiance incident on the TT is relatively low, and the TT shades a larger portion of the collector rear surface, leading to increased electrical mismatch losses. We will show that TT reflection offsets TT shading, increases irradiance, and decreases electrical mismatch in most cases, resulting in increased total energy yield.

3.1 Irradiance

Global horizontal irradiance (GHI) is the sum total of all light incident on a horizontal surface and is comprised of direct normal irradiance (DNI), incident at a single angle on the collector surface, and diffuse horizontal irradiance (DHI), light scattered by the atmosphere coming from all directions incident on a horizontal surface.

The impact of TT reflection on bifacial PV performance varies with sun position and sky condition, resulting in a dependence on the time of day and time of year. The irradiance gain due to TT reflection on the central collector is organized into sun zenith angle bins of 10°, with backtracking timestamps excluded to illustrate the trend of TT reflection decreasing with increasing sun zenith (Fig. 2). During backtracking timestamps, TT reflection makes a larger relative contribution to the irradiance due to the front-side cosine and angle of incidence losses. The irradiance gain is defined as the annual TT reflection in a zenith bin divided by the number of non-zero-GHI timestamps in that zenith bin. It is calculated per sample point, yielding an annual average 2D irradiance profile for each sun zenith bin. We analyze these trends using zenith instead of time of day to better represent a consistent illumination condition across the year. There is no 0-10° bin because this condition did not occur in Livermore. Timestamps with sun zenith greater than 80° were excluded from the analysis due to low incident irradiance.

 figure: Fig. 2.

Fig. 2. Annual average change in irradiance on the rear of central collector due to TT reflection at different sun zenith angles for the (a, b) 1P system, and (c, d) 2P system. Frame widths, purlin widths, and module column gap along row are not to scale. Note the different irradiance scales.

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The TT reflection is localized near the TT and strongest at low zeniths for both the 1P (Fig. 2(b)), and 2P (Fig. 2(d)) central collector. The absolute change in irradiance due to the TT reflection decreases with increasing zenith for both systems because GHI is greatest at solar noon. In a system with higher albedo or TT reflectivity, the impact of TT reflection would increase. Note the difference in color scales between the 1P and 2P configurations, with the 2P system’s TT reflection being larger due to front-side illumination incident on the TT.

The frame shades the collector from the TT reflection along the edges of the module(s). This is most evident on the module edges adjacent and parallel to the TT in the 2P collector (Fig. 2(d)), but is also visible along the north and south collector edges. Purlins also contribute to this effect because, as Livermore is in the northern hemisphere, the southern purlins partially block light incident on the TT, decreasing the TT reflection at the southern edge of the collector.

The irradiance maps in Fig. 2 show that the TT reflection decreases with increasing zenith but do not differentiate between sunny and cloudy sky conditions. In Fig. 3(a) and Fig. 3(b), we report the annual average TT reflection over the central collector, ${\bar{G}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}$ for each combination of zenith, $\theta $, in bins of 10°, and DHI fraction, $d,$ (defined as DHI/GHI), in bins of 0.1. ${\bar{G}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}$ is calculated for each zenith and DHI fraction bin, and defined as the annual TT reflection in a zenith and DHI fraction bin divided by the number of non-zero-GHI timestamps in that bin. Instead of being calculated per sample point, it also condenses the TT reflection profile down to a single per-collector average for each zenith and DHI fraction bin (Fig. 3(a) and Fig. 3(b)). The TT reflection is greater in the 2P system due to the TT gap, and greatest during low DHI fraction and zenith bins due to the high GHI. The white spaces in Fig. 3, and dark grey spaces in Fig. 4, indicate zenith and DHI fraction combinations that did not occur at the test site. Due to the significant difference in irradiation conditions, the data is separated into regular tracking hours (the wide left subplots) and backtracking hours (the narrow right subplots). Regular tracking and backtracking hours include timestamps with zeniths greater than 60°, despite the maximum tracker angle of 60°, because, depending on the time of year, the sun’s azimuth angle can make backtracking to avoid row-to-row shading unnecessary.

 figure: Fig. 3.

Fig. 3. Annual average collector irradiance due to the TT reflection as a function of sun zenith angle and DHI fraction for (a) 1P and (b) 2P systems. Annual average relative change in collector rear irradiance due to TT reflection for (c) 1P and (d) 2P systems as a function of sun zenith angle and DHI fraction

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We also calculate the relative change in rear irradiance due to TT reflection for each zenith and DHI fraction bin,

$${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}} = \frac{{{{\bar{G}}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}}}{{{{\bar{G}}_{\textrm{TT}{\textrm{A}_{\theta ,d}}}}}}$$
where ${\bar{G}_{\textrm{TT}{\textrm{A}_{\theta ,d}}}}$ is the annual average rear irradiance over a central module with an absorptive TT for a given zenith and DHI fraction bin. ${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ increases the 1P system’s central collector rear irradiance by an average of 2.8%, with little variation with respect to zenith and DHI fraction, and the greatest change coming at high DHI and zeniths (Fig. 3(c)). Conversely, in the 2P system (Fig. 3(d)), ${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ increases with decreasing DHI fraction because of the direct beam light’s contribution to the TT reflection. In addition, ${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ in the 2P system is larger for high zenith timestamps because the baseline rear irradiance is smaller. This smaller baseline irradiance is the principal reason for the 2P system’s backtracking timestamps showing the largest relative change in rear irradiance due to TT reflection, up to 10%.

3.2 Electrical mismatch

Cell-to-module electrical mismatch,

$${M_{\textrm{cm}}} = 1 - \frac{{{P_{\textrm{mod}}}}}{{\mathop \sum \nolimits_{c = 1}^N {P_{\textrm{cell},\,c}}}}$$
is the relative difference between the sum of cell maximum power points (${P_{\textrm{cell}}}$) for all N cells in the module, and the maximum power point of the module (${P_{\textrm{mod}}}$). Unlike uniform illumination conditions, where the current and voltage of cells are identical, nonuniform illumination leads to uneven current generation between cells, as seen in Fig. 9 of [7], reducing the current extracted from their series connection. The cell-to-module electrical mismatch quantifies the impact of the irradiance nonuniformity over the module, providing the power loss due to current mismatch in the module. We will refer to cell-to-module electrical mismatch as simply the electrical mismatch.

 figure: Fig. 4.

Fig. 4. Annually averaged absolute difference in cell-to-module electrical mismatch between absorptive and reflective TT as a function of sun zenith angle and DHI fraction in (a) 1P and (b) 2P single-axis tracked systems. Negative values indicate a reduction in electrical mismatch due to TT reflections. Dark grey squares indicate DHI fraction and sun zenith angle combinations that did not occur at the test site.

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TT reflection reduces electrical mismatch for all zenith and DHI fraction combinations in the 1P system (Fig. 4(a)) and most combinations in the 2P system (Fig. 4(b)). The decrease in electrical mismatch is due to the localization of the TT reflection near the TT partially offsetting TT shading. The TT reflection can reduce instantaneous electrical mismatch in the 1P and 2P system by up to 0.55% and 0.24% absolute, respectively, during high DHI fractions and zeniths, particularly at the onset of backtracking when the TT reflection and rear contribution to total irradiance are greatest.

TT reflection can increase electrical mismatch for the 2P module closest to the ground (Lower Module) at high zeniths (see Fig. 6 in Appendix C). While the additional irradiance from TT reflection is similar for both the Lower Module and its counterpart further from the ground (Upper Module), the Upper Module is preferentially shaded by the TT during timestamps with zeniths greater than 50°, see Fig. 1(d) for visual reference. There is therefore little shading on the Lower Module to offset during these timestamps and the additional irradiance from the TT reflection increases the irradiance nonuniformity, increasing the Lower Module’s electrical mismatch for zeniths greater than 50° by ∼0.02% on average. Conversely, TT reflection reduces electrical mismatch during all timestamps for the Upper Module because the TT reflection partially offsets the TT shading. Irradiance nonuniformity can also arise from brightening. This is apparent, for example, where TT reflection increases the Lower Module’s electrical mismatch at high zeniths (see Fig. 6(a) in Appendix C). Despite the increased mismatch, the TT reflection still increases energy yield by increasing incident irradiance.

3.3 Energy yield

Similar to Fig. 3(a) and Fig. 3(b), we calculate the average absolute change in energy yield due to TT reflection over the central collector for a given zenith and DHI fraction bin, ${\bar{E}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}$. We also calculate the relative change in energy yield due to TT reflection given by

$${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}} = \frac{{{{\bar{E}}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}}}{{{{\bar{E}}_{\textrm{TT}{\textrm{A}_{\theta ,d}}}}}}$$
where ${\bar{E}_{\textrm{TT}{\textrm{A}_{\theta ,d}}}}$ is the annual average energy yield over a central module with an absorptive TT for a given zenith and DHI fraction bin. For both 1P and 2P systems, ${\bar{E}_{\textrm{T}{\textrm{T}_{\theta ,d}}}}$ is greatest during low DHI fractions with low zeniths because GHI is greatest under those conditions (Fig. 5(a) and Fig. 5(b), respectively).

 figure: Fig. 5.

Fig. 5. Average difference in total energy yield due to TT-reflected light as a function of sun zenith angle and DHI fraction in (a, c) 1P and (b, d) 2P single-axis tracked systems. Change in total energy yield is absolute (a, b) and relative (c, d).

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For the 1P system, ${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ (Fig. 3(c)) is greatest during high DHI fractions and zeniths, and the TT reflection’s impact is compounded when considering its change to total (front and rear) energy yield, ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$, (Fig. 5(c)). The TT reflection reduces electrical mismatch, and the baseline energy yield without TT reflection is smaller at high DHI fractions and zeniths. During regular tracking, ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ ranges from 0.07% for low DHI fractions and zeniths, and up to 0.8% for high DHI fractions and zeniths. Similarly, during backtracking ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ ranges from 0.03% to 0.6%.

For the 2P system, ${\bar{G}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ (Fig. 3(d)) is greatest during low DHI fractions with high zeniths. However, both the TT reflection contribution to total energy yield$,\; {\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$, (Fig. 5(d)), and the rear contribution are most significant at high DHI fractions with high zeniths due to less optimal conditions for front-incident light. During regular tracking, ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ ranges from 0.17% for low DHI fractions and up to 0.4% for high DHI fractions and zeniths. Similarly, during backtracking ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ ranges from 0.04% to 0.34%.

The maximum ${\bar{E}_{\textrm{TTre}{\textrm{l}_{\theta ,d}}}}$ occurs during high DHI fractions with high zeniths for both the 1P and 2P systems. It is notably higher in the 1P system despite the 2P system’s larger absolute change in irradiance due to TT reflection. Therefore, the TT reflection’s relative contribution to energy yield is greatest during less optimal conditions for front-incident light.

Table 1 reports the average impact of TT reflection on the central collector (per module for the 2P system) across all non-zero-GHI hours in the year. The TT reflection increases insolation, the time-integrated irradiance equivalent, by 0.17% and 0.30% in the 1P and 2P system, respectively. The TT reflection marginally reduces absolute electrical mismatch in both the 1P system and the 2P system. However, the 1P system's large baseline electrical mismatch (see Table 3 Appendix D) results in a smaller relative reduction in electrical mismatch due to TT reflection compared to the 2P system. Overall, TT reflection increases total energy yield by 0.11% and 0.18% for the 1P and 2P system, respectively. While the TT reflection has a smaller impact on the 1P system in most conditions, the TT reflection’s maximum instantaneous relative contribution to total energy yield is greater for the 1P system than the 2P system, at 0.8% and 0.4%, respectively.

Tables Icon

Table 1. Annual Impact of TT reflection for Livermore, California, USA. Difference between the reflective TT and absorptive TT cases.

Despite TT reflection decreasing electrical mismatch, the relative change in energy yield is less than the relative change in insolation. As shown in Fig. 2, the TT-reflected light incident on the collector is localized near the TT, meaning not all the additional irradiance will yield additional energy. The TT reflection may be nonuniform, but it partially offsets TT shading, resulting in a net benefit to electrical mismatch. A point on the module near the TT could go from one of the most shaded regions on the module to one of the most irradiated regions when comparing an absorptive and reflective TT.

4. Conclusions

In this work, we applied TT reflection ray tracing calculations from bifacial_radiance to analyze its performance impact in DUET, a 3D view factor model with detailed shading, over an hourly typical meteorological year for the central 1P and 2P collector of single-axis tracked systems in Livermore, California, USA. We have quantified the effect of IAM on the TT reflection, yielding a larger relative impact than other rear-incident light due to its high average AOI. We identified that TT reflection reduces electrical mismatch by partially offsetting TT shading and, for an albedo of 0.2, TT reflection increases annual irradiance by 0.17% and 0.30% in the 1P and 2P system, respectively, leading to an increase in annual energy yield of 0.11% and 0.18%. The TT reflection is most significant when modelling instantaneous performance, increasing energy yield by up to 0.8% and 0.4% during high DHI fractions and sun zenith angles in the 1P and 2P system, respectively. While the overall impact of TT reflection is greater in the 2P system, the TT reflection’s maximum instantaneous relative contribution to total energy yield is greater in the 1P system, at high DHI fractions and zeniths. The importance of including TT reflection in system simulations, therefore, depends upon the system type (1P vs 2P) and whether total or instantaneous energy yields are required.

Appendix A: Modeling parameters

Table 2 lists the geometric parameters used in the simulations. In bifacial_radiance simulations to isolate TT reflection, the reflectivity of the purlins, frame and TT are all set to 0.745. Then, the TT reflectivity is changed to 0 while the reflectivity of the purlins and frame stays at 0.745. In DUET simulations, the reflectivity of all racking components is 0 and the TT reflection signal isolated from bifacial_radiance is added to the rear irradiance profile as a new irradiance source.

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Table 2. Geometric parameters of the modeled arrays

Appendix B: Incidence angle modifier impact on TT reflection

The incidence angle modifier (IAM), applied here using the ASHRAE model [43], accounts for angle-dependent reflection from the module. The IAM is calculated as

$$\textrm{IAM} = 1 - b({\sec ({{\theta_{\textrm{AOI}}}} )- 1} )$$
where b is a parameter typically on the order of 0.05, and ${\theta _{\textrm{AOI}}}$ is the angle of incidence [38].

In the baseline system with an absorptive TT, applying the collector’s IAM decreases the annual energy yield contributed by rear-incident light by 5.2% and 4.7% in the 1P and 2P systems, respectively. When applying the IAM to light from a reflective TT, the energy contributed by the TT reflection reduces by 7.4% and 8.4% for each system. This higher relative impact compared to other rear incident light is a result of the higher incidence angles between the TT and collector rear face.

Nonetheless, annual energy yield losses due to application of the IAM to the TT reflection remain small at just 0.008% and 0.016% in the 1P and 2P system, respectively, because the TT reflection itself contributes at most 0.8% of the energy yield for timestamps with zenith less than 80°. Considering all illumination sources, the IAM only decreases annual bifacial energy yield by 1.8% for both systems because the tracker minimizes the front-side incidence angle losses throughout the day. For completeness, we include the IAM for all irradiance sources, including TT-reflected light, throughout all our analyses herein.

Appendix C: TT reflection impact on 2P upper and lower module

The TT reflection impact on electrical mismatch differs between the 2P system’s central module closer to the ground (Lower Module), and the module further from the ground (Upper Module) (Fig. 6(a) and (b), respectively). The TT reflection can increase electrical mismatch on the Lower Module (Fig. 6(a)) during high zeniths by up to 0.04% absolute, most of all during backtracking timestamps with high sun zenith angle. In contrast, the TT reflection decreases electrical mismatch on the Upper Module (Fig. 6(b)) for all DHI fraction and zenith combinations.

 figure: Fig. 6.

Fig. 6. Average absolute variation in cell-to-module level electrical mismatch due to TT reflection for the (a) 2P lower module and (b) 2P upper module. Charcoal black squares indicate DHI fraction and sun zenith angle combinations that did not occur at the test site. Large left subplots exclude backtracking timestamps; the narrower right subplots include only backtracking timestamps.

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Appendix D: Annual results for absorptive and reflective TT cases

Table 3 shows annual results for 1P and 2P systems with an absorptive torque tube (TTA) and a reflective torque tube (TTR). The differences between the reflective and absorptive TT values lead to the values in Table 1. They are presented here for convenience.

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Table 3. Annual results for absorptive TT and reflective TT cases.

Funding

Natural Sciences and Engineering Research Council of Canada (CGS-D, CGS-M, CREATE 497981, PGS-D, RGPIN-2015-04782, RGPIN-2022-03877, STPGP 521894-18).

Acknowledgment

The authors would like to thank Javier Guerrero Pérez, Mireia Jiménez Beltran, and Alejandro Conesa from Soltec Innovations for their correspondence regarding the Livermore test site, the Soltec SF7 tracker, and insightful discussions.

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. Center 3 of 5 rows in the (a) 1P and (b) 2P arrays with the collector under test highlighted in dark blue. Frame and purlins modeled on the (c) 1P and (d) 2P rear side of collector under test with the TT spanning the row under test. Portrait configuration means the modules’ long sides are oriented perpendicular to the torque tube.
Fig. 2.
Fig. 2. Annual average change in irradiance on the rear of central collector due to TT reflection at different sun zenith angles for the (a, b) 1P system, and (c, d) 2P system. Frame widths, purlin widths, and module column gap along row are not to scale. Note the different irradiance scales.
Fig. 3.
Fig. 3. Annual average collector irradiance due to the TT reflection as a function of sun zenith angle and DHI fraction for (a) 1P and (b) 2P systems. Annual average relative change in collector rear irradiance due to TT reflection for (c) 1P and (d) 2P systems as a function of sun zenith angle and DHI fraction
Fig. 4.
Fig. 4. Annually averaged absolute difference in cell-to-module electrical mismatch between absorptive and reflective TT as a function of sun zenith angle and DHI fraction in (a) 1P and (b) 2P single-axis tracked systems. Negative values indicate a reduction in electrical mismatch due to TT reflections. Dark grey squares indicate DHI fraction and sun zenith angle combinations that did not occur at the test site.
Fig. 5.
Fig. 5. Average difference in total energy yield due to TT-reflected light as a function of sun zenith angle and DHI fraction in (a, c) 1P and (b, d) 2P single-axis tracked systems. Change in total energy yield is absolute (a, b) and relative (c, d).
Fig. 6.
Fig. 6. Average absolute variation in cell-to-module level electrical mismatch due to TT reflection for the (a) 2P lower module and (b) 2P upper module. Charcoal black squares indicate DHI fraction and sun zenith angle combinations that did not occur at the test site. Large left subplots exclude backtracking timestamps; the narrower right subplots include only backtracking timestamps.

Tables (3)

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Table 1. Annual Impact of TT reflection for Livermore, California, USA. Difference between the reflective TT and absorptive TT cases.

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Table 2. Geometric parameters of the modeled arrays

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Table 3. Annual results for absorptive TT and reflective TT cases.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

G T T i , t = G TT A i , t G TT R i , t
G ¯ TTre l θ , d = G ¯ T T θ , d G ¯ TT A θ , d
M cm = 1 P mod c = 1 N P cell , c
E ¯ TTre l θ , d = E ¯ T T θ , d E ¯ TT A θ , d
IAM = 1 b ( sec ( θ AOI ) 1 )
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