POA Irradiance Components

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Summary

Plane-of-Array (POA) irradiance is the total irradiance incident on the tilted module surface after transposition, shading, soiling, and optical adjustments. PlantPredict calculates POA irradiance by integrating transposition models (Hay-Davies or Perez), geometric shading factors, diffuse shading, horizon shading, soiling losses, incidence angle modifiers (IAM), and spectral corrections. The final POA irradiance consists of beam, sky diffuse, and ground-reflected components, each subject to appropriate loss factors. For bifacial modules, rear-side irradiance is calculated separately and added to front-side irradiance weighted by the bifaciality factor.

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Inputs

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Outputs

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Detailed Description

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Calculation Sequence

POA irradiance is calculated through a series of transformations applied to horizontal irradiance components:

1. Transposition: Convert horizontal irradiance ($GHI, DNI, DHI$) to tilted plane components ($I_{beam}, I_{sky}, I_{ground}$) using Hay-Davies or Perez model
2. Horizon Shading: Apply far-field shading to beam component only
3. Geometric Shading: Apply near-field shading factors to beam, sky, and ground components
4. Soiling: Apply uniform soiling transmission factor to all components
5. Incidence Angle Modifier (IAM): Apply angle-dependent optical losses
6. Spectral Correction: Apply spectral mismatch adjustment
7. Bifacial (if applicable): Calculate rear-side irradiance and combine with front-side

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Front-Side Beam Component

The beam POA irradiance after all adjustments: $$E_{POA,beam} = I_{beam} \times U_{horizon} \times U_{shd,B} \times u_{dirt} \times f_b \times M$$ where:

• $I_{beam} = DNI \times \cos(\theta)$ is the transposed beam irradiance
• $U_{horizon}$ is the horizon (far-field) shading factor (applied first)
• $U_{shd,B}$ is the geometric (near-field) beam shading factor
• $u_{dirt}$ is the soiling transmission factor
• $f_b$ is the beam incidence angle modifier
• $M$ is the spectral shift factor

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Front-Side Sky Diffuse Component

The sky diffuse POA irradiance (horizon shading not applied to diffuse components): $$E_{POA,sky} = I_{sky} \times U_{shd,D} \times u_{dirt} \times f_d \times M$$ where:

• $I_{sky}$ is the transposed sky diffuse irradiance (isotropic + circumsolar + horizon terms)
• $U_{shd,D}$ is the diffuse shading factor (sky-view factor reduction)
• $f_d$ is the sky diffuse incidence angle modifier

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Front-Side Ground Component

The ground-reflected POA irradiance (horizon shading not applied to diffuse components): $$E_{POA,ground} = I_{ground} \times U_{shd,G} \times u_{dirt} \times f_g \times M$$ where:

• $I_{ground} = GHI \times \rho_g \times \frac{1 - \cos(\beta)}{2}$ is the transposed ground-reflected irradiance
• $U_{shd,G}$ is the ground shading factor (may be split into direct/diffuse components)
• $f_g$ is the ground diffuse incidence angle modifier

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Total Front-Side POA Irradiance

The total front-side POA irradiance is the sum of all components: $$E_{POA,front} = E_{POA,beam} + E_{POA,sky} + E_{POA,ground}$$

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Bifacial Rear-Side Irradiance

For bifacial modules, rear-side irradiance is calculated based on ground-reflected light and sky diffuse reaching the rear surface: $$E_{POA,rear} = E_{rear,ground} + E_{rear,sky}$$ Rear-side irradiance calculations account for:

• Ground view factor from rear surface
• Row-to-row shading of ground-reflected light
• Module height and tilt geometry
• Rear-side IAM and soiling (typically same as front-side)

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Effective POA Irradiance

For bifacial modules, the effective POA irradiance combines front and rear contributions weighted by the bifaciality factor: $$E_{POA,eff} = E_{POA,front} + \phi \times E_{POA,rear}$$ where $\phi$ is the bifaciality factor (ratio of rear-to-front efficiency). For monofacial modules: $$E_{POA,eff} = E_{POA,front}$$

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Loss Factor Aggregation

The cumulative effect of all loss factors can be expressed as: Beam component: $$\text{Transmission}_{beam} = U_{horizon} \times U_{shd,B} \times u_{dirt} \times f_b \times M$$ Diffuse components (no horizon shading): $$\text{Transmission}_{diffuse} = U_{shd,D/G} \times u_{dirt} \times f_{d/g} \times M$$

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Quality Control

Physical constraints applied throughout the calculation:

• All shading factors: $0 \leq U_{shd} \leq 1$
• Soiling factor: $0 \leq u_{dirt} \leq 1$
• IAM factors: $0 \leq f \leq 1$
• Spectral factor: typically $0.85 \leq M \leq 1.15$ (wider range possible in extreme conditions)
• Final POA irradiance: $E_{POA} \geq 0$
• If angle of incidence $\theta \geq 90°$, beam component set to zero

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References

• Perez, R., Ineichen, P., Seals, R., Michalsky, J., & Stewart, R. (1990). Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy, 44(5), 271–289.
• Hay, J. E., & Davies, J. A. (1980). Calculation of the solar radiation incident on an inclined surface. Proceedings of First Canadian Solar Radiation Data Workshop.
• Marion, B. (2017). Numerical method for angle-of-incidence correction factors for diffuse radiation incident photovoltaic modules. Solar Energy, 147, 344–348.
• King, D. L., Boyson, W. E., & Kratochvil, J. A. (2004). Photovoltaic array performance model. SAND2004-3535, Sandia National Laboratories.