Bifacial Irradiance

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Summary

The Bifacial Irradiance model calculates rear-side irradiance for bifacial PV modules using view factor geometry, ground-reflected irradiance, and ray-tracing for structural shading. PlantPredict calculates rear-side irradiance by dividing row spacing into 100 intervals and computing sky configuration factors and ground shading factors for each interval. The model accounts for row type (interior, first, last, single), module geometry (tilt, clearance height, row spacing), surface properties (glass or AR glass), and tracking. Rear-side irradiance is combined with front-side irradiance weighted by the bifaciality factor to calculate effective POA irradiance.

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Inputs

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Outputs

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Detailed Description

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Calculation Sequence

1. Calculate sky configuration factors for front and rear surfaces (100 ground intervals)
2. Calculate ground shading factors for front and rear surfaces
3. Apply Perez transposition to calculate ground GHI at each interval
4. Calculate front surface irradiances (6 cell row positions)
5. Calculate rear surface irradiances (6 cell row positions)
6. Apply structure shading and backside mismatch losses
7. Calculate average rear irradiance
8. Weight rear irradiance by bifaciality factor

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Tracking Geometry

For single-axis tracking, module tilt $\beta$ and clearance $C$ are updated at each timestep: $$h = \sin(\beta)$$ $$x_1 = \cos(\beta)$$ $$D = \text{row spacing} - x_1$$ $$C = \text{hub height} - h \cdot \frac{\text{collector bandwidth}}{2}$$ where hub height is ground clearance at tilt = 0, and collector bandwidth is module width.

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Sky Configuration Factors

The model divides row-to-row spacing into 100 intervals ($\Delta = \frac{D + x_1}{100}$) and calculates sky view factors at the midpoint of each interval. For each interval $i$, horizontal position: $x = -\frac{\Delta}{2} + i \cdot \Delta$ Angles to adjacent row edges: $$\beta_1 = \max\left(\arctan\frac{h+C}{2(D+x_1) - x}, \arctan\frac{C}{2(D+x_1) - x_1 - x}\right)$$ $$\beta_2 = \min\left(\arctan\frac{h+C}{D+x_1-x}, \arctan\frac{C}{D+x_1-x_1-x}\right)$$ $$\beta_3 = \max\left(\arctan\frac{h+C}{D+x_1-x}, \arctan\frac{C}{D+x_1-x_1-x}\right)$$ $$\beta_4 = \arctan\frac{h+C}{x_1-x}$$ $$\beta_5 = \arctan\frac{C}{-x}$$ $$\beta_6 = \arctan\frac{h+C}{-D-x}$$ Sky view factor components: $$\text{sky}_1 = \begin{cases} 0.5(\cos\beta_1 - \cos\beta_2), & \beta_2 > \beta_1 \\ 0, & \text{otherwise} \end{cases}$$ $$\text{sky}_2 = \begin{cases} 0.5(\cos\beta_3 - \cos\beta_4), & \beta_4 > \beta_3 \\ 0, & \text{otherwise} \end{cases}$$ $$\text{sky}_3 = \begin{cases} 0.5(\cos\beta_5 - \cos\beta_6), & \beta_6 > \beta_5 \\ 0, & \text{otherwise} \end{cases}$$ $$\text{Sky Config Factor}[i] = \text{sky}_1 + \text{sky}_2 + \text{sky}_3$$ Row type modifications:

• First row rear: $\beta_6 = \pi$ (no row in front)
• Last row rear: $\beta_3 = 0$ (no row behind)
• Single row rear: $\beta_3 = 0, \beta_6 = \pi$
• Similar adjustments for front surface

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Ground Irradiance at Intervals

Perez transposition applied to horizontal plane ($\beta = 0$): $$I_{Perez} = I_{iso} + I_{cs} + I_{beam}$$ For each of 100 ground intervals: $$\text{Ground GHI}[i] = I_{iso} \cdot \text{Sky Config}[i] + \begin{cases} (I_{beam} + I_{cs}), & \text{unshaded} \\ (I_{beam} + I_{cs}) \cdot \tau_{trans}, & \text{shaded} \end{cases}$$ where shading status determined by ground shading factors (ray-tracing calculation).

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Rear Surface Irradiance

Calculate at 6 cell row positions (evenly spaced across module height). For each cell row position $j$: IAM for rear surface: Rear tilt = $180° - \beta$, rear azimuth = module azimuth $-180°$ Calculate rear incidence angle and apply Physical IAM (glass or AR glass). Rear sky diffuse: $$I_{rear,sky}[j] = I_{DH} \cdot \text{Marion Diffuse}(\text{rear orientation}) \cdot f_{IAM,rear}$$ Rear ground-reflected: Sample ground GHI from 100-element array based on cell row position, apply albedo and view geometry. Rear beam: If sun is behind module ($\theta_{rear} < 90°$): $$I_{rear,beam}[j] = I_{DN} \cdot \cos(\theta_{rear}) \cdot f_{IAM,rear}$$ Otherwise: $I_{rear,beam}[j] = 0$ Total rear GTI: $$\text{Rear GTI}[j] = I_{rear,sky}[j] + I_{rear,ground}[j] + I_{rear,beam}[j]$$

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Structure Shading and Mismatch

Version 09 and Earlier: $$E_{rear,avg} = \overline{\text{Rear GTI}} \cdot (1 - f_{structure})$$ Version 10 and Later: $$E_{rear,avg} = \overline{\text{Rear GTI}} \cdot (1 - f_{structure}) \cdot (1 - f_{mismatch})$$ where:

• $\overline{\text{Rear GTI}}$ = mean of 6 cell row irradiances
• $f_{structure}$ = structure shading fraction (user-defined)
• $f_{mismatch}$ = backside mismatch fraction (user-defined)

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Effective POA Irradiance

$$E_{POA,eff} = E_{POA,front} + \phi \cdot E_{rear,avg}$$ where $\phi$ is bifaciality factor (rear-to-front efficiency ratio).

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Alternate Mode: User-Specified Backside POAI

If UseBacksidePOAI = true, user provides rear irradiance directly: $$E_{rear,avg} = \text{Backside POAI (user)} \cdot (1 - f_{structure}) \cdot (1 - f_{mismatch})$$

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References

• Marion, B., MacAlpine, S., Deline, C., et al. (2017). A practical irradiance model for bifacial PV modules. 2017 IEEE 44th Photovoltaic Specialist Conference (PVSC), 1537-1542.
• Deline, C., Ayala Pelaez, S., MacAlpine, S., & Olalla, C. (2020). Bifacial PV system mismatch loss estimation and parameterization. 2020 47th IEEE Photovoltaic Specialists Conference (PVSC), 2281-2286.