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# Bifacial PV Modeling

### Introduction

Bifacial modules are increasingly being adopted in commercial and utility-scale solar PV systems due to their higher energy yield and economic returns. Unlike monofacial PV modules that collect light from only the front side, bifacial PV modules can collect light from both the front and the rear side. Bifacial PV modules can realize significant energy gains relative to monofacial PV panels. In a validation study conducted by NREL, it was found that energy yield for a bifacial PV system can exceed that of a standard monofacial system by 6-9%. Factors that impact bifacial module production include site-specific surface albedo and PV system row height, ground coverage ratio (GCR), etc.

### Methodology

Bifacial PV simulations are supported in the SolarAnywhere API and can be accessed for historical, real time and forecast time ranges. Additionally, SolarAnywhere supports modeling of purely bifacial PV systems, as well as PV systems with a mix of monofacial and bifacial modules at the energy site, provided a specific inverter in the PV system is connected to either monofacial PV arrays or bifacial PV arrays.

The front side POAI is calculated using the Perez transposition model, similar to how POAI estimates are generated for monofacial PV modules in the SolarAnywhere API. The Infinite Sheds model is used only for the rear-side POAI calculation. Further, the Isotropic model is used as the default irradiance transposition model within Infinite Sheds.

The total POAI for bifacial PV modules is calculated using the following equation:

• Total Plane-of-Array Irradiance (POAI) = Front side POAI + Rear-side POAI * Bifaciality Factor (1+Shade Factor) (1+Transmission Factor)

SolarAnywhere bifacial PV simulations use the pvlib Infinite sheds model to calculate rear-side irradiance. The infinite sheds model is a 2-dimensional model of irradiance on the front and rear surfaces of a PV array. The model assumes the PV system is comprised of parallel, evenly spaced rows on a level, horizontal surface. Rows can be on fixed racking or single-axis trackers. The model calculates irradiance at a location far from the ends of any rows, in effect, assuming the rows (sheds) are infinitely long. The model implicitly assumes that diffuse irradiance from the sky is isotropic, and that module surfaces do not allow irradiance to transmit through the module to the ground through gaps between cells.

The infinite sheds model accounts for the following effects:

• Limited view from the row surfaces to the sky due to blocking by nearby rows.
• Reduction of irradiance reaching the ground due to shadows cast by rows and blocking of the sky by nearby rows.

The model operates using the following steps:

1. Find the fraction of unshaded ground between rows where both direct and diffuse irradiance is received. The model assumes there is no direct irradiance in the shaded fraction.
2. Calculate the view factor from the ground to the sky accounting for the parts of the sky that are blocked from view by the array’s rows. The view factor is multiplied by the sky diffuse irradiance to calculate the diffuse irradiance reaching the ground. Sky diffuse irradiance is thus assumed to be isotropic.
3. Calculate the view factor from the row surface to the ground to determine the fraction of ground-reflected irradiance that reaches the row surface.
4. Find the fraction of the row surface that is shaded from direct irradiance. Only sky and ground-reflected irradiance reach the shaded fraction of the row surface.
5. For the front and rear surfaces, apply the incidence angle modifier to the direct irradiance. Then, compute the plane-of-array (POA) irradiance by summing the diffuse sky, diffuse ground and direct irradiance from each surface.
6. Apply the Bifaciality Factor, Shade Factor and Transmission Factor to the rear surface POA irradiance. Then, add the result to the front surface POA irradiance to calculate the total POA irradiance on the row.
7. Snow and soiling losses are applied to only the front side energy output.

Unless the PV module is mounted vertically, the ground reflected radiation received by the backside is significantly greater than the beam and diffuse sky radiation received. Reflected radiation is difficult to determine because the radiation received by the ground is reduced by shadows from the array and a restricted view of the sky. Additionally, the PV array support structure may prevent ground-reflected radiation from reaching the backside of the PV module.

### Bifacial PV simulation options

When simulating bifacial PV systems in SolarAnywhere, users have the option of accessing front as well as rear-side plane-of-array irradiance (POAI), in addition to total POAI.

The energy output of bifacial systems can vary depending on factors such as ground surface albedo, row-height, bifaciality factor, mounting type, ground coverage ratio (GCR), etc. To make Bifacial PV estimates more site-specific, SolarAnywhere users can specify additional input parameters for bifacial system modeling.

Bifaciality factor is defined as the ratio of the conversion efficiency of the front and back surfaces and is calculated as:

$$\frac{\text{\it{STC Efficiency of Rear side}}}{\text{\it{STC Efficiency of Front side}}}$$

This information may be provided by PV module manufacturers, and common values for this parameter range from 0.6 – 0.9. Bifaciality factor is always less than 1 since the front side is more efficient than the rear side.

The shade factor is the fraction of back surface irradiance that is blocked by array mounting structures such as torque tubes. The transmission factor represents losses due to shading from mechanical structures, and transmission around and through the module.

Array geometry is defined by the following array configuration parameters:

• Relative row spacing, which is the inverse of the ground coverage ratio (GCR). GCR is defined as the ratio of row slant height to the spacing between rows (pitch)
• Row height, which is the height of the center of the row above ground
• Pitch, which is the distance between two rows of PV modules
• Tilt of the row from horizontal
• Azimuth of the row’s normal vector

The following table lists the optional set of input parameters that can be specified to make bifacial PV systems more site specific.

Additionally, bifacial PV output is highly sensitive to the albedo input. To make the performance estimates for bifacial PV systems more site-specific and data-driven, SolarAnywhere uses industry leading time-series albedo data for energy simulations with data model versions v3.5 and higher, and for historical and real-time temporal ranges. Energy site simulations for the forecast time range use the static default of 0.17 for Albedo. The user has the option of overriding the default behavior by specifying a static albedo value in the energy site specification.

The following table lists the default values of albedo for different data versions, power models and simulation time periods.

#### Sensitivity Analysis

To understand how bifacial system energy production is affected by different input parameters, a sensitivity analysis was conducted for an arbitrary fixed-tilt PV system. Figure 1 shows the sensitivity of simulated energy to various input parameters. Bifaciality factor, transmission factor and shade factor are applied directly to POAI, which leads to an effectively linear sensitivity to those parameters. As expected, the effect of surface albedo on energy production is much more pronounced for a bifacial system than for a monofacial system.

###### Figure 1: Sensitivity of Simulated Energy to Bifaciality, Transmission and Shade Factors, and Surface Albedo Similarly, Figure 2 shows that as relative row spacing increases, energy production for a bifacial system increases at a faster rate than that of a monofacial system. Row height and pitch were found to have very little impact on annual energy production (<0.5%).

###### Figure 2: Sensitivity of Simulated Energy to PV Panel Configuration The best methods for bifacial modeling continue to evolve. For example, Sandia National Laboratories facilitates the Bifacial PV Project within the PV Performance Modeling Collaborative. A summary of research relevant to bifacial modeling can be found on the project’s website.

### References

1 Mikofski M, Darawali R, Hamer M, Neuber, A, Newmiller J. 2019. Bifacial Performance Modeling in Large Arrays. 46th IEEE Photovoltaic Specialists Conference (PVSC), June 16 – 21, 2019. DOI: 10.1109/PVSC40753.2019.8980572. Link